travelling through time definition

Is Time Travel Possible?

We all travel in time! We travel one year in time between birthdays, for example. And we are all traveling in time at approximately the same speed: 1 second per second.

We typically experience time at one second per second. Credit: NASA/JPL-Caltech

NASA's space telescopes also give us a way to look back in time. Telescopes help us see stars and galaxies that are very far away . It takes a long time for the light from faraway galaxies to reach us. So, when we look into the sky with a telescope, we are seeing what those stars and galaxies looked like a very long time ago.

However, when we think of the phrase "time travel," we are usually thinking of traveling faster than 1 second per second. That kind of time travel sounds like something you'd only see in movies or science fiction books. Could it be real? Science says yes!

This image from the Hubble Space Telescope shows galaxies that are very far away as they existed a very long time ago. Credit: NASA, ESA and R. Thompson (Univ. Arizona)

How do we know that time travel is possible?

More than 100 years ago, a famous scientist named Albert Einstein came up with an idea about how time works. He called it relativity. This theory says that time and space are linked together. Einstein also said our universe has a speed limit: nothing can travel faster than the speed of light (186,000 miles per second).

Einstein's theory of relativity says that space and time are linked together. Credit: NASA/JPL-Caltech

What does this mean for time travel? Well, according to this theory, the faster you travel, the slower you experience time. Scientists have done some experiments to show that this is true.

For example, there was an experiment that used two clocks set to the exact same time. One clock stayed on Earth, while the other flew in an airplane (going in the same direction Earth rotates).

After the airplane flew around the world, scientists compared the two clocks. The clock on the fast-moving airplane was slightly behind the clock on the ground. So, the clock on the airplane was traveling slightly slower in time than 1 second per second.

Credit: NASA/JPL-Caltech

Can we use time travel in everyday life?

We can't use a time machine to travel hundreds of years into the past or future. That kind of time travel only happens in books and movies. But the math of time travel does affect the things we use every day.

For example, we use GPS satellites to help us figure out how to get to new places. (Check out our video about how GPS satellites work .) NASA scientists also use a high-accuracy version of GPS to keep track of where satellites are in space. But did you know that GPS relies on time-travel calculations to help you get around town?

GPS satellites orbit around Earth very quickly at about 8,700 miles (14,000 kilometers) per hour. This slows down GPS satellite clocks by a small fraction of a second (similar to the airplane example above).

GPS satellites orbit around Earth at about 8,700 miles (14,000 kilometers) per hour. Credit: GPS.gov

However, the satellites are also orbiting Earth about 12,550 miles (20,200 km) above the surface. This actually speeds up GPS satellite clocks by a slighter larger fraction of a second.

Here's how: Einstein's theory also says that gravity curves space and time, causing the passage of time to slow down. High up where the satellites orbit, Earth's gravity is much weaker. This causes the clocks on GPS satellites to run faster than clocks on the ground.

The combined result is that the clocks on GPS satellites experience time at a rate slightly faster than 1 second per second. Luckily, scientists can use math to correct these differences in time.

If scientists didn't correct the GPS clocks, there would be big problems. GPS satellites wouldn't be able to correctly calculate their position or yours. The errors would add up to a few miles each day, which is a big deal. GPS maps might think your home is nowhere near where it actually is!

In Summary:

Yes, time travel is indeed a real thing. But it's not quite what you've probably seen in the movies. Under certain conditions, it is possible to experience time passing at a different rate than 1 second per second. And there are important reasons why we need to understand this real-world form of time travel.

If you liked this, you may like:

Time travel: Is it possible?

Science says time travel is possible, but probably not in the way you're thinking.

Albert Einstein's theory

• General relativity and GPS
• Wormhole travel
• Alternate theories

Science fiction

Is time travel possible? Short answer: Yes, and you're doing it right now — hurtling into the future at the impressive rate of one second per second. 

You're pretty much always moving through time at the same speed, whether you're watching paint dry or wishing you had more hours to visit with a friend from out of town. 

But this isn't the kind of time travel that's captivated countless science fiction writers, or spurred a genre so extensive that Wikipedia lists over 400 titles in the category "Movies about Time Travel." In franchises like " Doctor Who ," " Star Trek ," and "Back to the Future" characters climb into some wild vehicle to blast into the past or spin into the future. Once the characters have traveled through time, they grapple with what happens if you change the past or present based on information from the future (which is where time travel stories intersect with the idea of parallel universes or alternate timelines). 

Related: The best sci-fi time machines ever

Although many people are fascinated by the idea of changing the past or seeing the future before it's due, no person has ever demonstrated the kind of back-and-forth time travel seen in science fiction or proposed a method of sending a person through significant periods of time that wouldn't destroy them on the way. And, as physicist Stephen Hawking pointed out in his book " Black Holes and Baby Universes" (Bantam, 1994), "The best evidence we have that time travel is not possible, and never will be, is that we have not been invaded by hordes of tourists from the future."

Science does support some amount of time-bending, though. For example, physicist Albert Einstein 's theory of special relativity proposes that time is an illusion that moves relative to an observer. An observer traveling near the speed of light will experience time, with all its aftereffects (boredom, aging, etc.) much more slowly than an observer at rest. That's why astronaut Scott Kelly aged ever so slightly less over the course of a year in orbit than his twin brother who stayed here on Earth. 

Related: Controversially, physicist argues that time is real

There are other scientific theories about time travel, including some weird physics that arise around wormholes , black holes and string theory . For the most part, though, time travel remains the domain of an ever-growing array of science fiction books, movies, television shows, comics, video games and more. 

Einstein developed his theory of special relativity in 1905. Along with his later expansion, the theory of general relativity , it has become one of the foundational tenets of modern physics. Special relativity describes the relationship between space and time for objects moving at constant speeds in a straight line. 

The short version of the theory is deceptively simple. First, all things are measured in relation to something else — that is to say, there is no "absolute" frame of reference. Second, the speed of light is constant. It stays the same no matter what, and no matter where it's measured from. And third, nothing can go faster than the speed of light.

From those simple tenets unfolds actual, real-life time travel. An observer traveling at high velocity will experience time at a slower rate than an observer who isn't speeding through space. 

While we don't accelerate humans to near-light-speed, we do send them swinging around the planet at 17,500 mph (28,160 km/h) aboard the International Space Station . Astronaut Scott Kelly was born after his twin brother, and fellow astronaut, Mark Kelly . Scott Kelly spent 520 days in orbit, while Mark logged 54 days in space. The difference in the speed at which they experienced time over the course of their lifetimes has actually widened the age gap between the two men.

"So, where[as] I used to be just 6 minutes older, now I am 6 minutes and 5 milliseconds older," Mark Kelly said in a panel discussion on July 12, 2020, Space.com previously reported . "Now I've got that over his head."

General relativity and GPS time travel

The difference that low earth orbit makes in an astronaut's life span may be negligible — better suited for jokes among siblings than actual life extension or visiting the distant future — but the dilation in time between people on Earth and GPS satellites flying through space does make a difference. 

Read more: Can we stop time?

The Global Positioning System , or GPS, helps us know exactly where we are by communicating with a network of a few dozen satellites positioned in a high Earth orbit. The satellites circle the planet from 12,500 miles (20,100 kilometers) away, moving at 8,700 mph (14,000 km/h). 

According to special relativity, the faster an object moves relative to another object, the slower that first object experiences time. For GPS satellites with atomic clocks, this effect cuts 7 microseconds, or 7 millionths of a second, off each day, according to the American Physical Society publication Physics Central .  

Read more: Could Star Trek's faster-than-light warp drive actually work?

Then, according to general relativity, clocks closer to the center of a large gravitational mass like Earth tick more slowly than those farther away. So, because the GPS satellites are much farther from the center of Earth compared to clocks on the surface, Physics Central added, that adds another 45 microseconds onto the GPS satellite clocks each day. Combined with the negative 7 microseconds from the special relativity calculation, the net result is an added 38 microseconds. 

This means that in order to maintain the accuracy needed to pinpoint your car or phone — or, since the system is run by the U.S. Department of Defense, a military drone — engineers must account for an extra 38 microseconds in each satellite's day. The atomic clocks onboard don’t tick over to the next day until they have run 38 microseconds longer than comparable clocks on Earth.

Given those numbers, it would take more than seven years for the atomic clock in a GPS satellite to un-sync itself from an Earth clock by more than a blink of an eye. (We did the math: If you estimate a blink to last at least 100,000 microseconds, as the Harvard Database of Useful Biological Numbers does, it would take thousands of days for those 38 microsecond shifts to add up.) 

This kind of time travel may seem as negligible as the Kelly brothers' age gap, but given the hyper-accuracy of modern GPS technology, it actually does matter. If it can communicate with the satellites whizzing overhead, your phone can nail down your location in space and time with incredible accuracy. 

Can wormholes take us back in time?

General relativity might also provide scenarios that could allow travelers to go back in time, according to NASA . But the physical reality of those time-travel methods is no piece of cake. 

Wormholes are theoretical "tunnels" through the fabric of space-time that could connect different moments or locations in reality to others. Also known as Einstein-Rosen bridges or white holes, as opposed to black holes, speculation about wormholes abounds. But despite taking up a lot of space (or space-time) in science fiction, no wormholes of any kind have been identified in real life. 

Related: Best time travel movies

"The whole thing is very hypothetical at this point," Stephen Hsu, a professor of theoretical physics at the University of Oregon, told Space.com sister site Live Science . "No one thinks we're going to find a wormhole anytime soon."

Primordial wormholes are predicted to be just 10^-34 inches (10^-33 centimeters) at the tunnel's "mouth". Previously, they were expected to be too unstable for anything to be able to travel through them. However, a study claims that this is not the case, Live Science reported . 

The theory, which suggests that wormholes could work as viable space-time shortcuts, was described by physicist Pascal Koiran. As part of the study, Koiran used the Eddington-Finkelstein metric, as opposed to the Schwarzschild metric which has been used in the majority of previous analyses.

In the past, the path of a particle could not be traced through a hypothetical wormhole. However, using the Eddington-Finkelstein metric, the physicist was able to achieve just that.

Koiran's paper was described in October 2021, in the preprint database arXiv , before being published in the Journal of Modern Physics D.

Alternate time travel theories

While Einstein's theories appear to make time travel difficult, some researchers have proposed other solutions that could allow jumps back and forth in time. These alternate theories share one major flaw: As far as scientists can tell, there's no way a person could survive the kind of gravitational pulling and pushing that each solution requires.

Infinite cylinder theory

Astronomer Frank Tipler proposed a mechanism (sometimes known as a Tipler Cylinder ) where one could take matter that is 10 times the sun's mass, then roll it into a very long, but very dense cylinder. The Anderson Institute , a time travel research organization, described the cylinder as "a black hole that has passed through a spaghetti factory."

After spinning this black hole spaghetti a few billion revolutions per minute, a spaceship nearby — following a very precise spiral around the cylinder — could travel backward in time on a "closed, time-like curve," according to the Anderson Institute. 

The major problem is that in order for the Tipler Cylinder to become reality, the cylinder would need to be infinitely long or be made of some unknown kind of matter. At least for the foreseeable future, endless interstellar pasta is beyond our reach.

Time donuts

Theoretical physicist Amos Ori at the Technion-Israel Institute of Technology in Haifa, Israel, proposed a model for a time machine made out of curved space-time — a donut-shaped vacuum surrounded by a sphere of normal matter.

"The machine is space-time itself," Ori told Live Science . "If we were to create an area with a warp like this in space that would enable time lines to close on themselves, it might enable future generations to return to visit our time."

Amos Ori is a theoretical physicist at the Technion-Israel Institute of Technology in Haifa, Israel. His research interests and publications span the fields of general relativity, black holes, gravitational waves and closed time lines.

There are a few caveats to Ori's time machine. First, visitors to the past wouldn't be able to travel to times earlier than the invention and construction of the time donut. Second, and more importantly, the invention and construction of this machine would depend on our ability to manipulate gravitational fields at will — a feat that may be theoretically possible but is certainly beyond our immediate reach.

Time travel has long occupied a significant place in fiction. Since as early as the "Mahabharata," an ancient Sanskrit epic poem compiled around 400 B.C., humans have dreamed of warping time, Lisa Yaszek, a professor of science fiction studies at the Georgia Institute of Technology in Atlanta, told Live Science .  

Every work of time-travel fiction creates its own version of space-time, glossing over one or more scientific hurdles and paradoxes to achieve its plot requirements. 

Some make a nod to research and physics, like " Interstellar ," a 2014 film directed by Christopher Nolan. In the movie, a character played by Matthew McConaughey spends a few hours on a planet orbiting a supermassive black hole, but because of time dilation, observers on Earth experience those hours as a matter of decades. 

Others take a more whimsical approach, like the "Doctor Who" television series. The series features the Doctor, an extraterrestrial "Time Lord" who travels in a spaceship resembling a blue British police box. "People assume," the Doctor explained in the show, "that time is a strict progression from cause to effect, but actually from a non-linear, non-subjective viewpoint, it's more like a big ball of wibbly-wobbly, timey-wimey stuff." 

Long-standing franchises like the "Star Trek" movies and television series, as well as comic universes like DC and Marvel Comics, revisit the idea of time travel over and over. 

Related: Marvel movies in order: chronological & release order

Here is an incomplete (and deeply subjective) list of some influential or notable works of time travel fiction:

Books about time travel:

• Rip Van Winkle (Cornelius S. Van Winkle, 1819) by Washington Irving
• A Christmas Carol (Chapman & Hall, 1843) by Charles Dickens
• The Time Machine (William Heinemann, 1895) by H. G. Wells
• A Connecticut Yankee in King Arthur's Court (Charles L. Webster and Co., 1889) by Mark Twain
• The Restaurant at the End of the Universe (Pan Books, 1980) by Douglas Adams
• A Tale of Time City (Methuen, 1987) by Diana Wynn Jones
• The Outlander series (Delacorte Press, 1991-present) by Diana Gabaldon
• Harry Potter and the Prisoner of Azkaban (Bloomsbury/Scholastic, 1999) by J. K. Rowling
• Thief of Time (Doubleday, 2001) by Terry Pratchett
• The Time Traveler's Wife (MacAdam/Cage, 2003) by Audrey Niffenegger
• All You Need is Kill (Shueisha, 2004) by Hiroshi Sakurazaka

Movies about time travel:

• Planet of the Apes (1968)
• Superman (1978)
• Time Bandits (1981)
• The Terminator (1984)
• Back to the Future series (1985, 1989, 1990)
• Star Trek IV: The Voyage Home (1986)
• Bill & Ted's Excellent Adventure (1989)
• Groundhog Day (1993)
• Galaxy Quest (1999)
• The Butterfly Effect (2004)
• 13 Going on 30 (2004)
• The Lake House (2006)
• Meet the Robinsons (2007)
• Hot Tub Time Machine (2010)
• Midnight in Paris (2011)
• Looper (2012)
• X-Men: Days of Future Past (2014)
• Edge of Tomorrow (2014)
• Interstellar (2014)
• Doctor Strange (2016)
• A Wrinkle in Time (2018)
• The Last Sharknado: It's About Time (2018)
• Avengers: Endgame (2019)
• Tenet (2020)
• Palm Springs (2020)
• Zach Snyder's Justice League (2021)
• The Tomorrow War (2021)

Television about time travel:

• Doctor Who (1963-present)
• The Twilight Zone (1959-1964) (multiple episodes)
• Star Trek (multiple series, multiple episodes)
• Samurai Jack (2001-2004)
• Lost (2004-2010)
• Phil of the Future (2004-2006)
• Steins;Gate (2011)
• Outlander (2014-2023)
• Loki (2021-present)

Games about time travel:

• Chrono Trigger (1995)
• TimeSplitters (2000-2005)
• Kingdom Hearts (2002-2019)
• Prince of Persia: Sands of Time (2003)
• God of War II (2007)
• Ratchet and Clank Future: A Crack In Time (2009)
• Sly Cooper: Thieves in Time (2013)
• Dishonored 2 (2016)
• Titanfall 2 (2016)
• Outer Wilds (2019)

Additional resources

Explore physicist Peter Millington's thoughts about Stephen Hawking's time travel theories at The Conversation . Check out a kid-friendly explanation of real-world time travel from NASA's Space Place . For an overview of time travel in fiction and the collective consciousness, read " Time Travel: A History " (Pantheon, 2016) by James Gleik. 

Join our Space Forums to keep talking space on the latest missions, night sky and more! And if you have a news tip, correction or comment, let us know at: [email protected].

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Vicky Stein is a science writer based in California. She has a bachelor's degree in ecology and evolutionary biology from Dartmouth College and a graduate certificate in science writing from the University of California, Santa Cruz (2018). Afterwards, she worked as a news assistant for PBS NewsHour, and now works as a freelancer covering anything from asteroids to zebras. Follow her most recent work (and most recent pictures of nudibranchs) on Twitter. 

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Where Does the Concept of Time Travel Come From?

Time; he's waiting in the wings.

The dream of traveling through time is both ancient and universal. But where did humanity's fascination with time travel begin, and why is the idea so appealing?

The concept of time travel — moving through time the way we move through three-dimensional space — may in fact be hardwired into our perception of time . Linguists have recognized that we are essentially incapable of talking about temporal matters without referencing spatial ones. "In language — any language — no two domains are more intimately linked than space and time," wrote Israeli linguist Guy Deutscher in his 2005 book "The Unfolding of Language." "Even if we are not always aware of it, we invariably speak of time in terms of space, and this reflects the fact that we think of time in terms of space."

Deutscher reminds us that when we plan to meet a friend "around" lunchtime, we are using a metaphor, since lunchtime doesn't have any physical sides. He similarly points out that time can not literally be "long" or "short" like a stick, nor "pass" like a train, or even go "forward" or "backward" any more than it goes sideways, diagonal or down.

Related: Why Does Time Fly When You're Having Fun?

Perhaps because of this connection between space and time, the possibility that time can be experienced in different ways and traveled through has surprisingly early roots. One of the first known examples of time travel appears in the Mahabharata, an ancient Sanskrit epic poem compiled around 400 B.C., Lisa Yaszek, a professor of science fiction studies at the Georgia Institute of Technology in Atlanta, told Live Science 

In the Mahabharata is a story about King Kakudmi, who lived millions of years ago and sought a suitable husband for his beautiful and accomplished daughter, Revati. The two travel to the home of the creator god Brahma to ask for advice. But while in Brahma's plane of existence, they must wait as the god listens to a 20-minute song, after which Brahma explains that time moves differently in the heavens than on Earth. It turned out that "27 chatur-yugas" had passed, or more than 116 million years, according to an online summary , and so everyone Kakudmi and Revati had ever known, including family members and potential suitors, was dead. After this shock, the story closes on a somewhat happy ending in that Revati is betrothed to Balarama, twin brother of the deity Krishna. 

Time is fleeting

To Yaszek, the tale provides an example of what we now call time dilation , in which different observers measure different lengths of time based on their relative frames of reference, a part of Einstein's theory of relativity.

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Such time-slip stories are widespread throughout the world, Yaszek said, citing a Middle Eastern tale from the first century BCE about a Jewish miracle worker who sleeps beneath a newly-planted carob tree and wakes up 70 years later to find it has now matured and borne fruit (carob trees are notorious for how long they take to produce their first harvest). Another instance can be found in an eighth-century Japanese fable about a fisherman named Urashima Tarō who travels to an undersea palace and falls in love with a princess. Tarō finds that, when he returns home, 100 years have passed, according to a translation of the tale published online by the University of South Florida . 

In the early-modern era of the 1700 and 1800s, the sleep-story version of time travel grew more popular, Yaszek said. Examples include the classic tale of Rip Van Winkle, as well as books like Edward Belamy's utopian 1888 novel "Looking Backwards," in which a man wakes up in the year 2000, and the H.G. Wells 1899 novel "The Sleeper Awakes," about a man who slumbers for centuries and wakes to a completely transformed London. 

Related: Science Fiction or Fact: Is Time Travel Possible ?

In other stories from this period, people also start to be able to move backward in time. In Mark Twain’s 1889 satire "A Connecticut Yankee in King Arthur's Court," a blow to the head propels an engineer back to the reign of the legendary British monarch. Objects that can send someone through time begin to appear as well, mainly clocks, such as in Edward Page Mitchell's 1881 story "The Clock that Went Backwards" or Lewis Carrol's 1889 children's fantasy "Sylvie and Bruno," where the characters possess a watch that is a type of time machine . 

The explosion of such stories during this era might come from the fact that people were "beginning to standardize time, and orient themselves to clocks more frequently," Yaszek said. 

Time after time

Wells provided one of the most enduring time-travel plots in his 1895 novella "The Time Machine," which included the innovation of a craft that can move forward and backward through long spans of time. "This is when we’re getting steam engines and trains and the first automobiles," Yaszek said. "I think it’s no surprise that Wells suddenly thinks: 'Hey, maybe we can use a vehicle to travel through time.'"

Because it is such a rich visual icon, many beloved time-travel stories written after this have included a striking time machine, Yaszek said, referencing The Doctor's blue police box — the TARDIS — in the long-running BBC series "Doctor Who," and "Back to the Future"'s silver luxury speedster, the DeLorean . 

More recently, time travel has been used to examine our relationship with the past, Yaszek said, in particular in pieces written by women and people of color. Octavia Butler's 1979 novel "Kindred" about a modern woman who visits her pre-Civil-War ancestors is "a marvelous story that really asks us to rethink black and white relations through history," she said. And a contemporary web series called " Send Me " involves an African-American psychic who can guide people back to antebellum times and witness slavery. 

"I'm really excited about stories like that," Yaszek said. "They help us re-see history from new perspectives."

Time travel has found a home in a wide variety of genres and media, including comedies such as "Groundhog Day" and "Bill and Ted's Excellent Adventure" as well as video games like Nintendo's "The Legend of Zelda: Majora's Mask" and the indie game "Braid." 

Yaszek suggested that this malleability and ubiquity speaks to time travel tales' ability to offer an escape from our normal reality. "They let us imagine that we can break free from the grip of linear time," she said. "And somehow get a new perspective on the human experience, either our own or humanity as a whole, and I think that feels so exciting to us." 

That modern people are often drawn to time-machine stories in particular might reflect the fact that we live in a technological world, she added. Yet time travel's appeal certainly has deeper roots, interwoven into the very fabric of our language and appearing in some of our earliest imaginings. 

"I think it's a way to make sense of the otherwise intangible and inexplicable, because it's hard to grasp time," Yaszek said. "But this is one of the final frontiers, the frontier of time, of life and death. And we're all moving forward, we're all traveling through time."

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Originally published on Live Science .

Adam Mann is a freelance journalist with over a decade of experience, specializing in astronomy and physics stories. He has a bachelor's degree in astrophysics from UC Berkeley. His work has appeared in the New Yorker, New York Times, National Geographic, Wall Street Journal, Wired, Nature, Science, and many other places. He lives in Oakland, California, where he enjoys riding his bike. 

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Is Time Travel Even Possible? An Astrophysicist Explains The Science Behind The Science Fiction

If traveling into the past is possible, one way to do it might be sending people through tunnels in space..

Have you ever dreamed of traveling through time, like characters do in science fiction movies? For centuries, the concept of time travel has captivated people’s imaginations. Time travel is the concept of moving between different points in time, just like you move between different places. In movies, you might have seen characters using special machines, magical devices or even hopping into a futuristic car to travel backward or forward in time.

But is this just a fun idea for movies, or could it really happen?

The question of whether time is reversible remains one of the biggest unresolved questions in science. If the universe follows the  laws of thermodynamics , it may not be possible. The second law of thermodynamics states that things in the universe can either remain the same or become more disordered over time.

It’s a bit like saying you can’t unscramble eggs once they’ve been cooked. According to this law, the universe can never go back exactly to how it was before. Time can only go forward, like a one-way street.

Time is relative

However, physicist Albert Einstein’s  theory of special relativity  suggests that time passes at different rates for different people. Someone speeding along on a spaceship moving close to the  speed of light  – 671 million miles per hour! – will experience time slower than a person on Earth.

People have yet to build spaceships that can move at speeds anywhere near as fast as light, but astronauts who visit the International Space Station orbit around the Earth at speeds close to 17,500 mph. Astronaut Scott Kelly has spent 520 days at the International Space Station, and as a result has aged a little more slowly than his twin brother – and fellow astronaut – Mark Kelly. Scott used to be 6 minutes younger than his twin brother. Now, because Scott was traveling so much faster than Mark and for so many days, he is  6 minutes and 5 milliseconds younger .

Time isn’t the same everywhere.

Some scientists are exploring other ideas that could theoretically allow time travel. One concept involves  wormholes , or hypothetical tunnels in space that could create shortcuts for journeys across the universe. If someone could build a wormhole and then figure out a way to move one end at close to the speed of light – like the hypothetical spaceship mentioned above – the moving end would age more slowly than the stationary end. Someone who entered the moving end and exited the wormhole through the stationary end would come out in their past.

However, wormholes remain theoretical: Scientists have yet to spot one. It also looks like it would be  incredibly challenging  to send humans through a wormhole space tunnel.

Paradoxes and failed dinner parties

There are also paradoxes associated with time travel. The famous “ grandfather paradox ” is a hypothetical problem that could arise if someone traveled back in time and accidentally prevented their grandparents from meeting. This would create a paradox where you were never born, which raises the question: How could you have traveled back in time in the first place? It’s a mind-boggling puzzle that adds to the mystery of time travel.

Famously, physicist Stephen Hawking tested the possibility of time travel by  throwing a dinner party  where invitations noting the date, time and coordinates were not sent out until after it had happened. His hope was that his invitation would be read by someone living in the future, who had capabilities to travel back in time. But no one showed up.

As he  pointed out : “The best evidence we have that time travel is not possible, and never will be, is that we have not been invaded by hordes of tourists from the future.”

Telescopes are time machines

Interestingly, astrophysicists armed with powerful telescopes possess a unique form of time travel. As they peer into the vast expanse of the cosmos, they gaze into the past universe. Light from all galaxies and stars takes time to travel, and these beams of light carry information from the distant past. When astrophysicists observe a star or a galaxy through a telescope, they are not seeing it as it is in the present, but as it existed when the light began its journey to Earth millions to billions of years ago.

NASA’s newest space telescope, the  James Webb Space Telescope , is peering at galaxies that were formed at the very beginning of the Big Bang, about 13.7 billion years ago.

While we aren’t likely to have time machines like the ones in movies anytime soon, scientists are actively researching and exploring new ideas. But for now, we’ll have to enjoy the idea of time travel in our favorite books, movies and dreams.

Adi Foord is an Assistant Professor of Astronomy and Astrophysics at the University of Maryland, Baltimore County. This article is republished from  The Conversation  under a  Creative Commons license . Read the  original article .

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Time Travel and Modern Physics

Time travel has been a staple of science fiction. With the advent of general relativity it has been entertained by serious physicists. But, especially in the philosophy literature, there have been arguments that time travel is inherently paradoxical. The most famous paradox is the grandfather paradox: you travel back in time and kill your grandfather, thereby preventing your own existence. To avoid inconsistency some circumstance will have to occur which makes you fail in this attempt to kill your grandfather. Doesn’t this require some implausible constraint on otherwise unrelated circumstances? We examine such worries in the context of modern physics.

1. Paradoxes Lost?

2. topology and constraints, 3. the general possibility of time travel in general relativity, 4. two toy models, 5. slightly more realistic models of time travel, 6. the possibility of time travel redux, 7. even if there are constraints, so what, 8. computational models, 9. quantum mechanics to the rescue, 10. conclusions, other internet resources, related entries.

• Supplement: Remarks and Limitations on the Toy Models

Modern physics strips away many aspects of the manifest image of time. Time as it appears in the equations of classical mechanics has no need for a distinguished present moment, for example. Relativity theory leads to even sharper contrasts. It replaces absolute simultaneity, according to which it is possible to unambiguously determine the time order of distant events, with relative simultaneity: extending an “instant of time” throughout space is not unique, but depends on the state of motion of an observer. More dramatically, in general relativity the mathematical properties of time (or better, of spacetime)—its topology and geometry—depend upon how matter is arranged rather than being fixed once and for all. So physics can be, and indeed has to be, formulated without treating time as a universal, fixed background structure. Since general relativity represents gravity through spacetime geometry, the allowed geometries must be as varied as the ways in which matter can be arranged. Alongside geometrical models used to describe the solar system, black holes, and much else, the scope of variation extends to include some exotic structures unlike anything astrophysicists have observed. In particular, there are spacetime geometries with curves that loop back on themselves: closed timelike curves (CTCs), which describe the possible trajectory of an observer who returns exactly back to their earlier state—without any funny business, such as going faster than the speed of light. These geometries satisfy the relevant physical laws, the equations of general relativity, and in that sense time travel is physically possible.

Yet circular time generates paradoxes, familiar from science fiction stories featuring time travel: [ 1 ]

• Consistency: Kurt plans to murder his own grandfather Adolph, by traveling along a CTC to an appropriate moment in the past. He is an able marksman, and waits until he has a clear shot at grandpa. Normally he would not miss. Yet if he succeeds, there is no way that he will then exist to plan and carry out the mission. Kurt pulls the trigger: what can happen?
• Underdetermination: Suppose that Kurt first travels back in order to give his earlier self a copy of How to Build a Time Machine. This is the same book that allows him to build a time machine, which he then carries with him on his journey to the past. Who wrote the book?
• Easy Knowledge: A fan of classical music enhances their computer with a circuit that exploits a CTC. This machine efficiently solves problems at a higher level of computational complexity than conventional computers, leading (among other things) to finding the smallest circuits that can generate Bach’s oeuvre—and to compose new pieces in the same style. Such easy knowledge is at odds with our understanding of our epistemic predicament. (This third paradox has not drawn as much attention.)

The first two paradoxes were once routinely taken to show that solutions with CTCs should be rejected—with charges varying from violating logic, to being “physically unreasonable”, to undermining the notion of free will. Closer analysis of the paradoxes has largely reversed this consensus. Physicists have discovered many solutions with CTCs and have explored their properties in pursuing foundational questions, such as whether physics is compatible with the idea of objective temporal passage (starting with Gödel 1949). Philosophers have also used time travel scenarios to probe questions about, among other things, causation, modality, free will, and identity (see, e.g., Earman 1972 and Lewis’s seminal 1976 paper).

We begin below with Consistency , turning to the other paradoxes in later sections. A standard, stone-walling response is to insist that the past cannot be changed, as a matter of logic, even by a time traveler (e.g., Gödel 1949, Clarke 1977, Horwich 1987). Adolph cannot both die and survive, as a matter of logic, so any scheme to alter the past must fail. In many of the best time travel fictions, the actions of a time traveler are constrained in novel and unexpected ways. Attempts to change the past fail, and they fail, often tragically, in just such a way that they set the stage for the time traveler’s self-defeating journey. The first question is whether there is an analog of the consistent story when it comes to physics in the presence of CTCs. As we will see, there is a remarkable general argument establishing the existence of consistent solutions. Yet a second question persists: why can’t time-traveling Kurt kill his own grandfather? Doesn’t the necessity of failures to change the past put unusual and unexpected constraints on time travelers, or objects that move along CTCs? The same argument shows that there are in fact no constraints imposed by the existence of CTCs, in some cases. After discussing this line of argument, we will turn to the palatability and further implications of such constraints if they are required, and then turn to the implications of quantum mechanics.

Wheeler and Feynman (1949) were the first to claim that the fact that nature is continuous could be used to argue that causal influences from later events to earlier events, as are made possible by time travel, will not lead to paradox without the need for any constraints. Maudlin (1990) showed how to make their argument precise and more general, and argued that nonetheless it was not completely general.

Imagine the following set-up. We start off having a camera with a black and white film ready to take a picture of whatever comes out of the time machine. An object, in fact a developed film, comes out of the time machine. We photograph it, and develop the film. The developed film is subsequently put in the time machine, and set to come out of the time machine at the time the picture is taken. This surely will create a paradox: the developed film will have the opposite distribution of black, white, and shades of gray, from the object that comes out of the time machine. For developed black and white films (i.e., negatives) have the opposite shades of gray from the objects they are pictures of. But since the object that comes out of the time machine is the developed film itself it we surely have a paradox.

However, it does not take much thought to realize that there is no paradox here. What will happen is that a uniformly gray picture will emerge, which produces a developed film that has exactly the same uniform shade of gray. No matter what the sensitivity of the film is, as long as the dependence of the brightness of the developed film depends in a continuous manner on the brightness of the object being photographed, there will be a shade of gray that, when photographed, will produce exactly the same shade of gray on the developed film. This is the essence of Wheeler and Feynman’s idea. Let us first be a bit more precise and then a bit more general.

For simplicity let us suppose that the film is always a uniform shade of gray (i.e., at any time the shade of gray does not vary by location on the film). The possible shades of gray of the film can then be represented by the (real) numbers from 0, representing pure black, to 1, representing pure white.

Let us now distinguish various stages in the chronological order of the life of the film. In stage \(S_1\) the film is young; it has just been placed in the camera and is ready to be exposed. It is then exposed to the object that comes out of the time machine. (That object in fact is a later stage of the film itself). By the time we come to stage \(S_2\) of the life of the film, it has been developed and is about to enter the time machine. Stage \(S_3\) occurs just after it exits the time machine and just before it is photographed. Stage \(S_4\) occurs after it has been photographed and before it starts fading away. Let us assume that the film starts out in stage \(S_1\) in some uniform shade of gray, and that the only significant change in the shade of gray of the film occurs between stages \(S_1\) and \(S_2\). During that period it acquires a shade of gray that depends on the shade of gray of the object that was photographed. In other words, the shade of gray that the film acquires at stage \(S_2\) depends on the shade of gray it has at stage \(S_3\). The influence of the shade of gray of the film at stage \(S_3\), on the shade of gray of the film at stage \(S_2\), can be represented as a mapping, or function, from the real numbers between 0 and 1 (inclusive), to the real numbers between 0 and 1 (inclusive). Let us suppose that the process of photography is such that if one imagines varying the shade of gray of an object in a smooth, continuous manner then the shade of gray of the developed picture of that object will also vary in a smooth, continuous manner. This implies that the function in question will be a continuous function. Now any continuous function from the real numbers between 0 and 1 (inclusive) to the real numbers between 0 and 1 (inclusive) must map at least one number to itself. One can quickly convince oneself of this by graphing such functions. For one will quickly see that any continuous function \(f\) from \([0,1]\) to \([0,1]\) must intersect the line \(x=y\) somewhere, and thus there must be at least one point \(x\) such that \(f(x)=x\). Such points are called fixed points of the function. Now let us think about what such a fixed point represents. It represents a shade of gray such that, when photographed, it will produce a developed film with exactly that same shade of gray. The existence of such a fixed point implies a solution to the apparent paradox.

Let us now be more general and allow color photography. One can represent each possible color of an object (of uniform color) by the proportions of blue, green and red that make up that color. (This is why television screens can produce all possible colors.) Thus one can represent all possible colors of an object by three points on three orthogonal lines \(x, y\) and \(z\), that is to say, by a point in a three-dimensional cube. This cube is also known as the “Cartesian product” of the three line segments. Now, one can also show that any continuous map from such a cube to itself must have at least one fixed point. So color photography can not be used to create time travel paradoxes either!

Even more generally, consider some system \(P\) which, as in the above example, has the following life. It starts in some state \(S_1\), it interacts with an object that comes out of a time machine (which happens to be its older self), it travels back in time, it interacts with some object (which happens to be its younger self), and finally it grows old and dies. Let us assume that the set of possible states of \(P\) can be represented by a Cartesian product of \(n\) closed intervals of the reals, i.e., let us assume that the topology of the state-space of \(P\) is isomorphic to a finite Cartesian product of closed intervals of the reals. Let us further assume that the development of \(P\) in time, and the dependence of that development on the state of objects that it interacts with, is continuous. Then, by a well-known fixed point theorem in topology (see, e.g., Hocking & Young 1961: 273), no matter what the nature of the interaction is, and no matter what the initial state of the object is, there will be at least one state \(S_3\) of the older system (as it emerges from the time travel machine) that will influence the initial state \(S_1\) of the younger system (when it encounters the older system) so that, as the younger system becomes older, it develops exactly into state \(S_3\). Thus without imposing any constraints on the initial state \(S_1\) of the system \(P\), we have shown that there will always be perfectly ordinary, non-paradoxical, solutions, in which everything that happens, happens according to the usual laws of development. Of course, there is looped causation, hence presumably also looped explanation, but what do you expect if there is looped time?

Unfortunately, for the fan of time travel, a little reflection suggests that there are systems for which the needed fixed point theorem does not hold. Imagine, for instance, that we have a dial that can only rotate in a plane. We are going to put the dial in the time machine. Indeed we have decided that if we see the later stage of the dial come out of the time machine set at angle \(x\), then we will set the dial to \(x+90\), and throw it into the time machine. Now it seems we have a paradox, since the mapping that consists of a rotation of all points in a circular state-space by 90 degrees does not have a fixed point. And why wouldn’t some state-spaces have the topology of a circle?

However, we have so far not used another continuity assumption which is also a reasonable assumption. So far we have only made the following demand: the state the dial is in at stage \(S_2\) must be a continuous function of the state of the dial at stage \(S_3\). But, the state of the dial at stage \(S_2\) is arrived at by taking the state of the dial at stage \(S_1\), and rotating it over some angle. It is not merely the case that the effect of the interaction, namely the state of the dial at stage \(S_2\), should be a continuous function of the cause, namely the state of the dial at stage \(S_3\). It is additionally the case that path taken to get there, the way the dial is rotated between stages \(S_1\) and \(S_2\) must be a continuous function of the state at stage \(S_3\). And, rather surprisingly, it turns out that this can not be done. Let us illustrate what the problem is before going to a more general demonstration that there must be a fixed point solution in the dial case.

Forget time travel for the moment. Suppose that you and I each have a watch with a single dial neither of which is running. My watch is set at 12. You are going to announce what your watch is set at. My task is going to be to adjust my watch to yours no matter what announcement you make. And my actions should have a continuous (single valued) dependence on the time that you announce. Surprisingly, this is not possible! For instance, suppose that if you announce “12”, then I achieve that setting on my watch by doing nothing. Now imagine slowly and continuously increasing the announced times, starting at 12. By continuity, I must achieve each of those settings by rotating my dial to the right. If at some point I switch and achieve the announced goal by a rotation of my dial to the left, I will have introduced a discontinuity in my actions, a discontinuity in the actions that I take as a function of the announced angle. So I will be forced, by continuity, to achieve every announcement by rotating the dial to the right. But, this rotation to the right will have to be abruptly discontinued as the announcements grow larger and I eventually approach 12 again, since I achieved 12 by not rotating the dial at all. So, there will be a discontinuity at 12 at the latest. In general, continuity of my actions as a function of announced times can not be maintained throughout if I am to be able to replicate all possible settings. Another way to see the problem is that one can similarly reason that, as one starts with 12, and imagines continuously making the announced times earlier, one will be forced, by continuity, to achieve the announced times by rotating the dial to the left. But the conclusions drawn from the assumption of continuous increases and the assumption of continuous decreases are inconsistent. So we have an inconsistency following from the assumption of continuity and the assumption that I always manage to set my watch to your watch. So, a dial developing according to a continuous dynamics from a given initial state, can not be set up so as to react to a second dial, with which it interacts, in such a way that it is guaranteed to always end up set at the same angle as the second dial. Similarly, it can not be set up so that it is guaranteed to always end up set at 90 degrees to the setting of the second dial. All of this has nothing to do with time travel. However, the impossibility of such set ups is what prevents us from enacting the rotation by 90 degrees that would create paradox in the time travel setting.

Let us now give the positive result that with such dials there will always be fixed point solutions, as long as the dynamics is continuous. Let us call the state of the dial before it interacts with its older self the initial state of the dial. And let us call the state of the dial after it emerges from the time machine the final state of the dial. There is also an intermediate state of the dial, after it interacts with its older self and before it is put into the time machine. We can represent the initial or intermediate states of the dial, before it goes into the time machine, as an angle \(x\) in the horizontal plane and the final state of the dial, after it comes out of the time machine, as an angle \(y\) in the vertical plane. All possible \(\langle x,y\rangle\) pairs can thus be visualized as a torus with each \(x\) value picking out a vertical circular cross-section and each \(y\) picking out a point on that cross-section. See figure 1 .

Figure 1 [An extended description of figure 1 is in the supplement.]

Suppose that the dial starts at angle \(i\) which picks out vertical circle \(I\) on the torus. The initial angle \(i\) that the dial is at before it encounters its older self, and the set of all possible final angles that the dial can have when it emerges from the time machine is represented by the circle \(I\) on the torus (see figure 1 ). Given any possible angle of the emerging dial, the dial initially at angle \(i\) will develop to some other angle. One can picture this development by rotating each point on \(I\) in the horizontal direction by the relevant amount. Since the rotation has to depend continuously on the angle of the emerging dial, circle \(I\) during this development will deform into some loop \(L\) on the torus. Loop \(L\) thus represents all possible intermediate angles \(x\) that the dial is at when it is thrown into the time machine, given that it started at angle \(i\) and then encountered a dial (its older self) which was at angle \(y\) when it emerged from the time machine. We therefore have consistency if \(x=y\) for some \(x\) and \(y\) on loop \(L\). Now, let loop \(C\) be the loop which consists of all the points on the torus for which \(x=y\). Ring \(I\) intersects \(C\) at point \(\langle i,i\rangle\). Obviously any continuous deformation of \(I\) must still intersect \(C\) somewhere. So \(L\) must intersect \(C\) somewhere, say at \(\langle j,j\rangle\). But that means that no matter how the development of the dial starting at \(I\) depends on the angle of the emerging dial, there will be some angle for the emerging dial such that the dial will develop exactly into that angle (by the time it enters the time machine) under the influence of that emerging dial. This is so no matter what angle one starts with, and no matter how the development depends on the angle of the emerging dial. Thus even for a circular state-space there are no constraints needed other than continuity.

Unfortunately there are state-spaces that escape even this argument. Consider for instance a pointer that can be set to all values between 0 and 1, where 0 and 1 are not possible values. That is, suppose that we have a state-space that is isomorphic to an open set of real numbers. Now suppose that we have a machine that sets the pointer to half the value that the pointer is set at when it emerges from the time machine.

Figure 2 [An extended description of figure 2 is in the supplement.]

Suppose the pointer starts at value \(I\). As before we can represent the combination of this initial position and all possible final positions by the line \(I\). Under the influence of the pointer coming out of the time machine the pointer value will develop to a value that equals half the value of the final value that it encountered. We can represent this development as the continuous deformation of line \(I\) into line \(L\), which is indicated by the arrows in figure 2 . This development is fully continuous. Points \(\langle x,y\rangle\) on line \(I\) represent the initial position \(x=I\) of the (young) pointer, and the position \(y\) of the older pointer as it emerges from the time machine. Points \(\langle x,y\rangle\) on line \(L\) represent the position \(x\) that the younger pointer should develop into, given that it encountered the older pointer emerging from the time machine set at position \(y\). Since the pointer is designed to develop to half the value of the pointer that it encounters, the line \(L\) corresponds to \(x=1/2 y\). We have consistency if there is some point such that it develops into that point, if it encounters that point. Thus, we have consistency if there is some point \(\langle x,y\rangle\) on line \(L\) such that \(x=y\). However, there is no such point: lines \(L\) and \(C\) do not intersect. Thus there is no consistent solution, despite the fact that the dynamics is fully continuous.

Of course if 0 were a possible value, \(L\) and \(C\) would intersect at 0. This is surprising and strange: adding one point to the set of possible values of a quantity here makes the difference between paradox and peace. One might be tempted to just add the extra point to the state-space in order to avoid problems. After all, one might say, surely no measurements could ever tell us whether the set of possible values includes that exact point or not. Unfortunately there can be good theoretical reasons for supposing that some quantity has a state-space that is open: the set of all possible speeds of massive objects in special relativity surely is an open set, since it includes all speeds up to, but not including, the speed of light. Quantities that have possible values that are not bounded also lead to counter examples to the presented fixed point argument. And it is not obvious to us why one should exclude such possibilities. So the argument that no constraints are needed is not fully general.

An interesting question of course is: exactly for which state-spaces must there be such fixed points? The arguments above depend on a well-known fixed point theorem (due to Schauder) that guarantees the existence of a fixed point for compact, convex state spaces. We do not know what subsequent extensions of this result imply regarding fixed points for a wider variety of systems, or whether there are other general results along these lines. (See Kutach 2003 for more on this issue.)

A further interesting question is whether this line of argument is sufficient to resolve Consistency (see also Dowe 2007). When they apply, these results establish the existence of a solution, such as the shade of uniform gray in the first example. But physicists routinely demand more than merely the existence of a solution, namely that solutions to the equations are stable—such that “small” changes of the initial state lead to “small” changes of the resulting trajectory. (Clarifying the two senses of “small” in this statement requires further work, specifying the relevant topology.) Stability in this sense underwrites the possibility of applying equations to real systems given our inability to fix initial states with indefinite precision. (See Fletcher 2020 for further discussion.) The fixed point theorems guarantee that for an initial state \(S_1\) there is a solution, but this solution may not be “close” to the solution for a nearby initial state, \(S'\). We are not aware of any proofs that the solutions guaranteed to exist by the fixed point theorems are also stable in this sense.

Time travel has recently been discussed quite extensively in the context of general relativity. General relativity places few constraints on the global structure of space and time. This flexibility leads to a possibility first described in print by Hermann Weyl:

Every world-point is the origin of the double-cone of the active future and the passive past [i.e., the two lobes of the light cone]. Whereas in the special theory of relativity these two portions are separated by an intervening region, it is certainly possible in the present case [i.e., general relativity] for the cone of the active future to overlap with that of the passive past; so that, in principle, it is possible to experience events now that will in part be an effect of my future resolves and actions. Moreover, it is not impossible for a world-line (in particular, that of my body), although it has a timelike direction at every point, to return to the neighborhood of a point which it has already once passed through. (Weyl 1918/1920 [1952: 274])

A time-like curve is simply a space-time trajectory such that the speed of light is never equaled or exceeded along this trajectory. Time-like curves represent possible trajectories of ordinary objects. In general relativity a curve that is everywhere timelike locally can nonetheless loop back on itself, forming a CTC. Weyl makes the point vividly in terms of the light cones: along such a curve, the future lobe of the light cone (the “active future”) intersects the past lobe of the light cone (the “passive past”). Traveling along such a curve one would never exceed the speed of light, and yet after a certain amount of (proper) time one would return to a point in space-time that one previously visited. Or, by staying close to such a CTC, one could come arbitrarily close to a point in space-time that one previously visited. General relativity, in a straightforward sense, allows time travel: there appear to be many space-times compatible with the fundamental equations of general relativity in which there are CTC’s. Space-time, for instance, could have a Minkowski metric everywhere, and yet have CTC’s everywhere by having the temporal dimension (topologically) rolled up as a circle. Or, one can have wormhole connections between different parts of space-time which allow one to enter “mouth \(A\)” of such a wormhole connection, travel through the wormhole, exit the wormhole at “mouth \(B\)” and re-enter “mouth \(A\)” again. CTCs can even arise when the spacetime is topologically \(\mathbb{R}^4\), due to the “tilting” of light cones produced by rotating matter (as in Gödel 1949’s spacetime).

General relativity thus appears to provide ample opportunity for time travel. Note that just because there are CTC’s in a space-time, this does not mean that one can get from any point in the space-time to any other point by following some future directed timelike curve—there may be insurmountable practical obstacles. In Gödel’s spacetime, it is the case that there are CTCs passing through every point in the spacetime. Yet these CTCs are not geodesics, so traversing them requires acceleration. Calculations of the minimal fuel required to travel along the appropriate curve should discourage any would-be time travelers (Malament 1984, 1985; Manchak 2011). But more generally CTCs may be confined to smaller regions; some parts of space-time can have CTC’s while other parts do not. Let us call the part of a space-time that has CTC’s the “time travel region” of that space-time, while calling the rest of that space-time the “normal region”. More precisely, the “time travel region” consists of all the space-time points \(p\) such that there exists a (non-zero length) timelike curve that starts at \(p\) and returns to \(p\). Now let us turn to examining space-times with CTC’s a bit more closely for potential problems.

In order to get a feeling for the sorts of implications that closed timelike curves can have, it may be useful to consider two simple models. In space-times with closed timelike curves the traditional initial value problem cannot be framed in the usual way. For it presupposes the existence of Cauchy surfaces, and if there are CTCs then no Cauchy surface exists. (A Cauchy surface is a spacelike surface such that every inextendable timelike curve crosses it exactly once. One normally specifies initial conditions by giving the conditions on such a surface.) Nonetheless, if the topological complexities of the manifold are appropriately localized, we can come quite close. Let us call an edgeless spacelike surface \(S\) a quasi-Cauchy surface if it divides the rest of the manifold into two parts such that

• every point in the manifold can be connected by a timelike curve to \(S\), and
• any timelike curve which connects a point in one region to a point in the other region intersects \(S\) exactly once.

It is obvious that a quasi-Cauchy surface must entirely inhabit the normal region of the space-time; if any point \(p\) of \(S\) is in the time travel region, then any timelike curve which intersects \(p\) can be extended to a timelike curve which intersects \(S\) near \(p\) again. In extreme cases of time travel, a model may have no normal region at all (e.g., Minkowski space-time rolled up like a cylinder in a time-like direction), in which case our usual notions of temporal precedence will not apply. But temporal anomalies like wormholes (and time machines) can be sufficiently localized to permit the existence of quasi-Cauchy surfaces.

Given a timelike orientation, a quasi-Cauchy surface unproblematically divides the manifold into its past (i.e., all points that can be reached by past-directed timelike curves from \(S)\) and its future (ditto mutatis mutandis ). If the whole past of \(S\) is in the normal region of the manifold, then \(S\) is a partial Cauchy surface : every inextendable timelike curve which exists to the past of \(S\) intersects \(S\) exactly once, but (if there is time travel in the future) not every inextendable timelike curve which exists to the future of \(S\) intersects \(S\). Now we can ask a particularly clear question: consider a manifold which contains a time travel region, but also has a partial Cauchy surface \(S\), such that all of the temporal funny business is to the future of \(S\). If all you could see were \(S\) and its past, you would not know that the space-time had any time travel at all. The question is: are there any constraints on the sort of data which can be put on \(S\) and continued to a global solution of the dynamics which are different from the constraints (if any) on the data which can be put on a Cauchy surface in a simply connected manifold and continued to a global solution? If there is time travel to our future, might we we able to tell this now, because of some implied oddity in the arrangement of present things?

It is not at all surprising that there might be constraints on the data which can be put on a locally space-like surface which passes through the time travel region: after all, we never think we can freely specify what happens on a space-like surface and on another such surface to its future, but in this case the surface at issue lies to its own future. But if there were particular constraints for data on a partial Cauchy surface then we would apparently need to have to rule out some sorts of otherwise acceptable states on \(S\) if there is to be time travel to the future of \(S\). We then might be able to establish that there will be no time travel in the future by simple inspection of the present state of the universe. As we will see, there is reason to suspect that such constraints on the partial Cauchy surface are non-generic. But we are getting ahead of ourselves: first let’s consider the effect of time travel on a very simple dynamics.

The simplest possible example is the Newtonian theory of perfectly elastic collisions among equally massive particles in one spatial dimension. The space-time is two-dimensional, so we can represent it initially as the Euclidean plane, and the dynamics is completely specified by two conditions. When particles are traveling freely, their world lines are straight lines in the space-time, and when two particles collide, they exchange momenta, so the collision looks like an “\(X\)” in space-time, with each particle changing its momentum at the impact. [ 2 ] The dynamics is purely local, in that one can check that a set of world-lines constitutes a model of the dynamics by checking that the dynamics is obeyed in every arbitrarily small region. It is also trivial to generate solutions from arbitrary initial data if there are no CTCs: given the initial positions and momenta of a set of particles, one simply draws a straight line from each particle in the appropriate direction and continues it indefinitely. Once all the lines are drawn, the worldline of each particle can be traced from collision to collision. The boundary value problem for this dynamics is obviously well-posed: any set of data at an instant yields a unique global solution, constructed by the method sketched above.

What happens if we change the topology of the space-time by hand to produce CTCs? The simplest way to do this is depicted in figure 3 : we cut and paste the space-time so it is no longer simply connected by identifying the line \(L-\) with the line \(L+\). Particles “going in” to \(L+\) from below “emerge” from \(L-\) , and particles “going in” to \(L-\) from below “emerge” from \(L+\).

Figure 3: Inserting CTCs by Cut and Paste. [An extended description of figure 3 is in the supplement.]

How is the boundary-value problem changed by this alteration in the space-time? Before the cut and paste, we can put arbitrary data on the simultaneity slice \(S\) and continue it to a unique solution. After the change in topology, \(S\) is no longer a Cauchy surface, since a CTC will never intersect it, but it is a partial Cauchy surface. So we can ask two questions. First, can arbitrary data on \(S\) always be continued to a global solution? Second, is that solution unique? If the answer to the first question is \(no\), then we have a backward-temporal constraint: the existence of the region with CTCs places constraints on what can happen on \(S\) even though that region lies completely to the future of \(S\). If the answer to the second question is \(no\), then we have an odd sort of indeterminism, analogous to the unwritten book: the complete physical state on \(S\) does not determine the physical state in the future, even though the local dynamics is perfectly deterministic and even though there is no other past edge to the space-time region in \(S\)’s future (i.e., there is nowhere else for boundary values to come from which could influence the state of the region).

In this case the answer to the first question is yes and to the second is no : there are no constraints on the data which can be put on \(S\), but those data are always consistent with an infinitude of different global solutions. The easy way to see that there always is a solution is to construct the minimal solution in the following way. Start drawing straight lines from \(S\) as required by the initial data. If a line hits \(L-\) from the bottom, just continue it coming out of the top of \(L+\) in the appropriate place, and if a line hits \(L+\) from the bottom, continue it emerging from \(L-\) at the appropriate place. Figure 4 represents the minimal solution for a single particle which enters the time-travel region from the left:

Figure 4: The Minimal Solution. [An extended description of figure 4 is in the supplement.]

The particle “travels back in time” three times. It is obvious that this minimal solution is a global solution, since the particle always travels inertially.

But the same initial state on \(S\) is also consistent with other global solutions. The new requirement imposed by the topology is just that the data going into \(L+\) from the bottom match the data coming out of \(L-\) from the top, and the data going into \(L-\) from the bottom match the data coming out of \(L+\) from the top. So we can add any number of vertical lines connecting \(L-\) and \(L+\) to a solution and still have a solution. For example, adding a few such lines to the minimal solution yields:

Figure 5: A Non-Minimal Solution. [An extended description of figure 5 is in the supplement.]

The particle now collides with itself twice: first before it reaches \(L+\) for the first time, and again shortly before it exits the CTC region. From the particle’s point of view, it is traveling to the right at a constant speed until it hits an older version of itself and comes to rest. It remains at rest until it is hit from the right by a younger version of itself, and then continues moving off, and the same process repeats later. It is clear that this is a global model of the dynamics, and that any number of distinct models could be generating by varying the number and placement of vertical lines.

Knowing the data on \(S\), then, gives us only incomplete information about how things will go for the particle. We know that the particle will enter the CTC region, and will reach \(L+\), we know that it will be the only particle in the universe, we know exactly where and with what speed it will exit the CTC region. But we cannot determine how many collisions the particle will undergo (if any), nor how long (in proper time) it will stay in the CTC region. If the particle were a clock, we could not predict what time it would indicate when exiting the region. Furthermore, the dynamics gives us no handle on what to think of the various possibilities: there are no probabilities assigned to the various distinct possible outcomes.

Changing the topology has changed the mathematics of the situation in two ways, which tend to pull in opposite directions. On the one hand, \(S\) is no longer a Cauchy surface, so it is perhaps not surprising that data on \(S\) do not suffice to fix a unique global solution. But on the other hand, there is an added constraint: data “coming out” of \(L-\) must exactly match data “going in” to \(L+\), even though what comes out of \(L-\) helps to determine what goes into \(L+\). This added consistency constraint tends to cut down on solutions, although in this case the additional constraint is more than outweighed by the freedom to consider various sorts of data on \({L+}/{L-}\).

The fact that the extra freedom outweighs the extra constraint also points up one unexpected way that the supposed paradoxes of time travel may be overcome. Let’s try to set up a paradoxical situation using the little closed time loop above. If we send a single particle into the loop from the left and do nothing else, we know exactly where it will exit the right side of the time travel region. Now suppose we station someone at the other side of the region with the following charge: if the particle should come out on the right side, the person is to do something to prevent the particle from going in on the left in the first place. In fact, this is quite easy to do: if we send a particle in from the right, it seems that it can exit on the left and deflect the incoming left-hand particle.

Carrying on our reflection in this way, we further realize that if the particle comes out on the right, we might as well send it back in order to deflect itself from entering in the first place. So all we really need to do is the following: set up a perfectly reflecting particle mirror on the right-hand side of the time travel region, and launch the particle from the left so that— if nothing interferes with it —it will just barely hit \(L+\). Our paradox is now apparently complete. If, on the one hand, nothing interferes with the particle it will enter the time-travel region on the left, exit on the right, be reflected from the mirror, re-enter from the right, and come out on the left to prevent itself from ever entering. So if it enters, it gets deflected and never enters. On the other hand, if it never enters then nothing goes in on the left, so nothing comes out on the right, so nothing is reflected back, and there is nothing to deflect it from entering. So if it doesn’t enter, then there is nothing to deflect it and it enters. If it enters, then it is deflected and doesn’t enter; if it doesn’t enter then there is nothing to deflect it and it enters: paradox complete.

But at least one solution to the supposed paradox is easy to construct: just follow the recipe for constructing the minimal solution, continuing the initial trajectory of the particle (reflecting it the mirror in the obvious way) and then read of the number and trajectories of the particles from the resulting diagram. We get the result of figure 6 :

Figure 6: Resolving the “Paradox”. [An extended description of figure 6 is in the supplement.]

As we can see, the particle approaching from the left never reaches \(L+\): it is deflected first by a particle which emerges from \(L-\). But it is not deflected by itself , as the paradox suggests, it is deflected by another particle. Indeed, there are now four particles in the diagram: the original particle and three particles which are confined to closed time-like curves. It is not the leftmost particle which is reflected by the mirror, nor even the particle which deflects the leftmost particle; it is another particle altogether.

The paradox gets it traction from an incorrect presupposition. If there is only one particle in the world at \(S\) then there is only one particle which could participate in an interaction in the time travel region: the single particle would have to interact with its earlier (or later) self. But there is no telling what might come out of \(L-\): the only requirement is that whatever comes out must match what goes in at \(L+\). So if you go to the trouble of constructing a working time machine, you should be prepared for a different kind of disappointment when you attempt to go back and kill yourself: you may be prevented from entering the machine in the first place by some completely unpredictable entity which emerges from it. And once again a peculiar sort of indeterminism appears: if there are many self-consistent things which could prevent you from entering, there is no telling which is even likely to materialize. This is just like the case of the unwritten book: the book is never written, so nothing determines what fills its pages.

So when the freedom to put data on \(L-\) outweighs the constraint that the same data go into \(L+\), instead of paradox we get an embarrassment of riches: many solution consistent with the data on \(S\), or many possible books. To see a case where the constraint “outweighs” the freedom, we need to construct a very particular, and frankly artificial, dynamics and topology. Consider the space of all linear dynamics for a scalar field on a lattice. (The lattice can be though of as a simple discrete space-time.) We will depict the space-time lattice as a directed graph. There is to be a scalar field defined at every node of the graph, whose value at a given node depends linearly on the values of the field at nodes which have arrows which lead to it. Each edge of the graph can be assigned a weighting factor which determines how much the field at the input node contributes to the field at the output node. If we name the nodes by the letters a , b , c , etc., and the edges by their endpoints in the obvious way, then we can label the weighting factors by the edges they are associated with in an equally obvious way.

Suppose that the graph of the space-time lattice is acyclic , as in figure 7 . (A graph is Acyclic if one can not travel in the direction of the arrows and go in a loop.)

Figure 7: An Acyclic Lattice. [An extended description of figure 7 is in the supplement.]

It is easy to regard a set of nodes as the analog of a Cauchy surface, e.g., the set \(\{a, b, c\}\), and it is obvious if arbitrary data are put on those nodes the data will generate a unique solution in the future. [ 3 ] If the value of the field at node \(a\) is 3 and at node \(b\) is 7, then its value at node \(d\) will be \(3W_{ad}\) and its value at node \(e\) will be \(3W_{ae} + 7W_{be}\). By varying the weighting factors we can adjust the dynamics, but in an acyclic graph the future evolution of the field will always be unique.

Let us now again artificially alter the topology of the lattice to admit CTCs, so that the graph now is cyclic. One of the simplest such graphs is depicted in figure 8 : there are now paths which lead from \(z\) back to itself, e.g., \(z\) to \(y\) to \(z\).

Figure 8: Time Travel on a Lattice. [An extended description of figure 8 is in the supplement.]

Can we now put arbitrary data on \(v\) and \(w\), and continue that data to a global solution? Will the solution be unique?

In the generic case, there will be a solution and the solution will be unique. The equations for the value of the field at \(x, y\), and \(z\) are:

Solving these equations for \(z\) yields

which gives a unique value for \(z\) in the generic case. But looking at the space of all possible dynamics for this lattice (i.e., the space of all possible weighting factors), we find a singularity in the case where \(1-W_{zx}W_{xz} - W_{zy}W_{yz} = 0\). If we choose weighting factors in just this way, then arbitrary data at \(v\) and \(w\) cannot be continued to a global solution. Indeed, if the scalar field is everywhere non-negative, then this particular choice of dynamics puts ironclad constraints on the value of the field at \(v\) and \(w\): the field there must be zero (assuming \(W_{vx}\) and \(W_{wy}\) to be non-zero), and similarly all nodes in their past must have field value zero. If the field can take negative values, then the values at \(v\) and \(w\) must be so chosen that \(vW_{vx}W_{xz} = -wW_{wy}W_{yz}\). In either case, the field values at \(v\) and \(w\) are severely constrained by the existence of the CTC region even though these nodes lie completely to the past of that region. It is this sort of constraint which we find to be unlike anything which appears in standard physics.

Our toy models suggest three things. The first is that it may be impossible to prove in complete generality that arbitrary data on a partial Cauchy surface can always be continued to a global solution: our artificial case provides an example where it cannot. The second is that such odd constraints are not likely to be generic: we had to delicately fine-tune the dynamics to get a problem. The third is that the opposite problem, namely data on a partial Cauchy surface being consistent with many different global solutions, is likely to be generic: we did not have to do any fine-tuning to get this result.

This third point leads to a peculiar sort of indeterminism, illustrated by the case of the unwritten book: the entire state on \(S\) does not determine what will happen in the future even though the local dynamics is deterministic and there are no other “edges” to space-time from which data could influence the result. What happens in the time travel region is constrained but not determined by what happens on \(S\), and the dynamics does not even supply any probabilities for the various possibilities. The example of the photographic negative discussed in section 2, then, seems likely to be unusual, for in that case there is a unique fixed point for the dynamics, and the set-up plus the dynamical laws determine the outcome. In the generic case one would rather expect multiple fixed points, with no room for anything to influence, even probabilistically, which would be realized. (See the supplement on

Remarks and Limitations on the Toy Models .

It is ironic that time travel should lead generically not to contradictions or to constraints (in the normal region) but to underdetermination of what happens in the time travel region by what happens everywhere else (an underdetermination tied neither to a probabilistic dynamics nor to a free edge to space-time). The traditional objection to time travel is that it leads to contradictions: there is no consistent way to complete an arbitrarily constructed story about how the time traveler intends to act. Instead, though, it appears that the more significant problem is underdetermination: the story can be consistently completed in many different ways.

Echeverria, Klinkhammer, and Thorne (1991) considered the case of 3-dimensional single hard spherical ball that can go through a single time travel wormhole so as to collide with its younger self.

Figure 9 [An extended description of figure 9 is in the supplement.]

The threat of paradox in this case arises in the following form. Consider the initial trajectory of a ball as it approaches the time travel region. For some initial trajectories, the ball does not undergo a collision before reaching mouth 1, but upon exiting mouth 2 it will collide with its earlier self. This leads to a contradiction if the collision is strong enough to knock the ball off its trajectory and deflect it from entering mouth 1. Of course, the Wheeler-Feynman strategy is to look for a “glancing blow” solution: a collision which will produce exactly the (small) deviation in trajectory of the earlier ball that produces exactly that collision. Are there always such solutions? [ 4 ]

Echeverria, Klinkhammer & Thorne found a large class of initial trajectories that have consistent “glancing blow” continuations, and found none that do not (but their search was not completely general). They did not produce a rigorous proof that every initial trajectory has a consistent continuation, but suggested that it is very plausible that every initial trajectory has a consistent continuation. That is to say, they have made it very plausible that, in the billiard ball wormhole case, the time travel structure of such a wormhole space-time does not result in constraints on states on spacelike surfaces in the non-time travel region.

In fact, as one might expect from our discussion in the previous section, they found the opposite problem from that of inconsistency: they found underdetermination. For a large class of initial trajectories there are multiple different consistent “glancing blow” continuations of that trajectory (many of which involve multiple wormhole traversals). For example, if one initially has a ball that is traveling on a trajectory aimed straight between the two mouths, then one obvious solution is that the ball passes between the two mouths and never time travels. But another solution is that the younger ball gets knocked into mouth 1 exactly so as to come out of mouth 2 and produce that collision. Echeverria et al. do not note the possibility (which we pointed out in the previous section) of the existence of additional balls in the time travel region. We conjecture (but have no proof) that for every initial trajectory of \(A\) there are some, and generically many, multiple-ball continuations.

Friedman, Morris, et al. (1990) examined the case of source-free non-self-interacting scalar fields traveling through such a time travel wormhole and found that no constraints on initial conditions in the non-time travel region are imposed by the existence of such time travel wormholes. In general there appear to be no known counter examples to the claim that in “somewhat realistic” time-travel space-times with a partial Cauchy surface there are no constraints imposed on the state on such a partial Cauchy surface by the existence of CTC’s. (See, e.g., Friedman & Morris 1991; Thorne 1994; Earman 1995; Earman, Smeenk, & Wüthrich 2009; and Dowe 2007.)

How about the issue of constraints in the time travel region \(T\)? Prima facie , constraints in such a region would not appear to be surprising. But one might still expect that there should be no constraints on states on a spacelike surface, provided one keeps the surface “small enough”. In the physics literature the following question has been asked: for any point \(p\) in \(T\), and any space-like surface \(S\) that includes \(p\) is there a neighborhood \(E\) of \(p\) in \(S\) such that any solution on \(E\) can be extended to a solution on the whole space-time? With respect to this question, there are some simple models in which one has this kind of extendability of local solutions to global ones, and some simple models in which one does not have such extendability, with no clear general pattern. The technical mathematical problems are amplified by the more conceptual problem of what it might mean to say that one could create a situation which forces the creation of closed timelike curves. (See, e.g., Yurtsever 1990; Friedman, Morris, et al. 1990; Novikov 1992; Earman 1995; and Earman, Smeenk, & Wüthrich 2009). What are we to think of all of this?

The toy models above all treat billiard balls, fields, and other objects propagating through a background spacetime with CTCs. Even if we can show that a consistent solution exists, there is a further question: what kind of matter and dynamics could generate CTCs to begin with? There are various solutions of Einstein’s equations with CTCs, but how do these exotic spacetimes relate to the models actually used in describing the world? In other words, what positive reasons might we have to take CTCs seriously as a feature of the actual universe, rather than an exotic possibility of primarily mathematical interest?

We should distinguish two different kinds of “possibility” that we might have in mind in posing such questions (following Stein 1970). First, we can consider a solution as a candidate cosmological model, describing the (large-scale gravitational degrees of freedom of the) entire universe. The case for ruling out spacetimes with CTCs as potential cosmological models strikes us as, surprisingly, fairly weak. Physicists used to simply rule out solutions with CTCs as unreasonable by fiat, due to the threat of paradoxes, which we have dismantled above. But it is also challenging to make an observational case. Observations tell us very little about global features, such as the existence of CTCs, because signals can only reach an observer from a limited region of spacetime, called the past light cone. Our past light cone—and indeed the collection of all the past light cones for possible observers in a given spacetime—can be embedded in spacetimes with quite different global features (Malament 1977, Manchak 2009). This undercuts the possibility of using observations to constrain global topology, including (among other things) ruling out the existence of CTCs.

Yet the case in favor of taking cosmological models with CTCs seriously is also not particularly strong. Some solutions used to describe black holes, which are clearly relevant in a variety of astrophysical contexts, include CTCs. But the question of whether the CTCs themselves play an essential representational role is subtle: the CTCs arise in the maximal extensions of these solutions, and can plausibly be regarded as extraneous to successful applications. Furthermore, many of the known solutions with CTCs have symmetries, raising the possibility that CTCs are not a stable or robust feature. Slight departures from symmetry may lead to a solution without CTCs, suggesting that the CTCs may be an artifact of an idealized model.

The second sense of possibility regards whether “reasonable” initial conditions can be shown to lead to, or not to lead to, the formation of CTCs. As with the toy models above, suppose that we have a partial Cauchy surface \(S\), such that all the temporal funny business lies to the future. Rather than simply assuming that there is a region with CTCs to the future, we can ask instead whether it is possible to create CTCs by manipulating matter in the initial, well-behaved region—that is, whether it is possible to build a time machine. Several physicists have pursued “chronology protection theorems” aiming to show that the dynamics of general relativity (or some other aspects of physics) rules this out, and to clarify why this is the case. The proof of such a theorem would justify neglecting solutions with CTCs as a source of insight into the nature of time in the actual world. But as of yet there are several partial results that do not fully settle the question. One further intriguing possibility is that even if general relativity by itself does protect chronology, it may not be possible to formulate a sensible theory describing matter and fields in solutions with CTCs. (See SEP entry on Time Machines; Smeenk and Wüthrich 2011 for more.)

There is a different question regarding the limitations of these toy models. The toy models and related examples show that there are consistent solutions for simple systems in the presence of CTCs. As usual we have made the analysis tractable by building toy models, selecting only a few dynamical degrees of freedom and tracking their evolution. But there is a large gap between the systems we have described and the time travel stories they evoke, with Kurt traveling along a CTC with murderous intentions. In particular, many features of the manifest image of time are tied to the thermodynamical properties of macroscopic systems. Rovelli (unpublished) considers a extremely simple system to illustrate the problem: can a clock move along a CTC? A clock consists of something in periodic motion, such as a pendulum bob, and something that counts the oscillations, such as an escapement mechanism. The escapement mechanism cannot work without friction; this requires dissipation and increasing entropy. For a clock that counts oscillations as it moves along a time-like trajectory, the entropy must be a monotonically increasing function. But that is obviously incompatible with the clock returning to precisely the same state at some future time as it completes a loop. The point generalizes, obviously, to imply that anything like a human, with memory and agency, cannot move along a CTC.

Since it is not obvious that one can rid oneself of all constraints in realistic models, let us examine the argument that time travel is implausible, and we should think it unlikely to exist in our world, in so far as it implies such constraints. The argument goes something like the following. In order to satisfy such constraints one needs some pre-established divine harmony between the global (time travel) structure of space-time and the distribution of particles and fields on space-like surfaces in it. But it is not plausible that the actual world, or any world even remotely like ours, is constructed with divine harmony as part of the plan. In fact, one might argue, we have empirical evidence that conditions in any spatial region can vary quite arbitrarily. So we have evidence that such constraints, whatever they are, do not in fact exist in our world. So we have evidence that there are no closed time-like lines in our world or one remotely like it. We will now examine this argument in more detail by presenting four possible responses, with counterresponses, to this argument.

Response 1. There is nothing implausible or new about such constraints. For instance, if the universe is spatially closed, there has to be enough matter to produce the needed curvature, and this puts constraints on the matter distribution on a space-like hypersurface. Thus global space-time structure can quite unproblematically constrain matter distributions on space-like hypersurfaces in it. Moreover we have no realistic idea what these constraints look like, so we hardly can be said to have evidence that they do not obtain.

Counterresponse 1. Of course there are constraining relations between the global structure of space-time and the matter in it. The Einstein equations relate curvature of the manifold to the matter distribution in it. But what is so strange and implausible about the constraints imposed by the existence of closed time-like curves is that these constraints in essence have nothing to do with the Einstein equations. When investigating such constraints one typically treats the particles and/or field in question as test particles and/or fields in a given space-time, i.e., they are assumed not to affect the metric of space-time in any way. In typical space-times without closed time-like curves this means that one has, in essence, complete freedom of matter distribution on a space-like hypersurface. (See response 2 for some more discussion of this issue). The constraints imposed by the possibility of time travel have a quite different origin and are implausible. In the ordinary case there is a causal interaction between matter and space-time that results in relations between global structure of space-time and the matter distribution in it. In the time travel case there is no such causal story to be told: there simply has to be some pre-established harmony between the global space-time structure and the matter distribution on some space-like surfaces. This is implausible.

Response 2. Constraints upon matter distributions are nothing new. For instance, Maxwell’s equations constrain electric fields \(\boldsymbol{E}\) on an initial surface to be related to the (simultaneous) charge density distribution \(\varrho\) by the equation \(\varrho = \text{div}(\boldsymbol{E})\). (If we assume that the \(E\) field is generated solely by the charge distribution, this conditions amounts to requiring that the \(E\) field at any point in space simply be the one generated by the charge distribution according to Coulomb’s inverse square law of electrostatics.) This is not implausible divine harmony. Such constraints can hold as a matter of physical law. Moreover, if we had inferred from the apparent free variation of conditions on spatial regions that there could be no such constraints we would have mistakenly inferred that \(\varrho = \text{div}(\boldsymbol{E})\) could not be a law of nature.

Counterresponse 2. The constraints imposed by the existence of closed time-like lines are of quite a different character from the constraint imposed by \(\varrho = \text{div}(\boldsymbol{E})\). The constraints imposed by \(\varrho = \text{div}(\boldsymbol{E})\) on the state on a space-like hypersurface are:

• local constraints (i.e., to check whether the constraint holds in a region you just need to see whether it holds at each point in the region),
• quite independent of the global space-time structure,
• quite independent of how the space-like surface in question is embedded in a given space-time, and
• very simply and generally stateable.

On the other hand, the consistency constraints imposed by the existence of closed time-like curves (i) are not local, (ii) are dependent on the global structure of space-time, (iii) depend on the location of the space-like surface in question in a given space-time, and (iv) appear not to be simply stateable other than as the demand that the state on that space-like surface embedded in such and such a way in a given space-time, do not lead to inconsistency. On some views of laws (e.g., David Lewis’ view) this plausibly implies that such constraints, even if they hold, could not possibly be laws. But even if one does not accept such a view of laws, one could claim that the bizarre features of such constraints imply that it is implausible that such constraints hold in our world or in any world remotely like ours.

Response 3. It would be strange if there are constraints in the non-time travel region. It is not strange if there are constraints in the time travel region. They should be explained in terms of the strange, self-interactive, character of time travel regions. In this region there are time-like trajectories from points to themselves. Thus the state at such a point, in such a region, will, in a sense, interact with itself. It is a well-known fact that systems that interact with themselves will develop into an equilibrium state, if there is such an equilibrium state, or else will develop towards some singularity. Normally, of course, self-interaction isn’t true instantaneous self-interaction, but consists of a feed-back mechanism that takes time. But in time travel regions something like true instantaneous self-interaction occurs. This explains why constraints on states occur in such time travel regions: the states “ ab initio ” have to be “equilibrium states”. Indeed in a way this also provides some picture of why indeterminism occurs in time travel regions: at the onset of self-interaction states can fork into different equi-possible equilibrium states.

Counterresponse 3. This is explanation by woolly analogy. It all goes to show that time travel leads to such bizarre consequences that it is unlikely that it occurs in a world remotely like ours.

Response 4. All of the previous discussion completely misses the point. So far we have been taking the space-time structure as given, and asked the question whether a given time travel space-time structure imposes constraints on states on (parts of) space-like surfaces. However, space-time and matter interact. Suppose that one is in a space-time with closed time-like lines, such that certain counterfactual distributions of matter on some neighborhood of a point \(p\) are ruled out if one holds that space-time structure fixed. One might then ask

Why does the actual state near \(p\) in fact satisfy these constraints? By what divine luck or plan is this local state compatible with the global space-time structure? What if conditions near \(p\) had been slightly different?

And one might take it that the lack of normal answers to these questions indicates that it is very implausible that our world, or any remotely like it, is such a time travel universe. However the proper response to these question is the following. There are no constraints in any significant sense. If they hold they hold as a matter of accidental fact, not of law. There is no more explanation of them possible than there is of any contingent fact. Had conditions in a neighborhood of \(p\) been otherwise, the global structure of space-time would have been different. So what? The only question relevant to the issue of constraints is whether an arbitrary state on an arbitrary spatial surface \(S\) can always be embedded into a space-time such that that state on \(S\) consistently extends to a solution on the entire space-time.

But we know the answer to that question. A well-known theorem in general relativity says the following: any initial data set on a three dimensional manifold \(S\) with positive definite metric has a unique embedding into a maximal space-time in which \(S\) is a Cauchy surface (see, e.g., Geroch & Horowitz 1979: 284 for more detail), i.e., there is a unique largest space-time which has \(S\) as a Cauchy surface and contains a consistent evolution of the initial value data on \(S\). Now since \(S\) is a Cauchy surface this space-time does not have closed time like curves. But it may have extensions (in which \(S\) is not a Cauchy surface) which include closed timelike curves, indeed it may be that any maximal extension of it would include closed timelike curves. (This appears to be the case for extensions of states on certain surfaces of Taub-NUT space-times. See Earman, Smeenk, & Wüthrich 2009). But these extensions, of course, will be consistent. So properly speaking, there are no constraints on states on space-like surfaces. Nonetheless the space-time in which these are embedded may or may not include closed time-like curves.

Counterresponse 4. This, in essence, is the stonewalling answer which we indicated in section 1. However, whether or not you call the constraints imposed by a given space-time on distributions of matter on certain space-like surfaces “genuine constraints”, whether or not they can be considered lawlike, and whether or not they need to be explained, the existence of such constraints can still be used to argue that time travel worlds are so bizarre that it is implausible that our world or any world remotely like ours is a time travel world.

Suppose that one is in a time travel world. Suppose that given the global space-time structure of this world, there are constraints imposed upon, say, the state of motion of a ball on some space-like surface when it is treated as a test particle, i.e., when it is assumed that the ball does not affect the metric properties of the space-time it is in. (There is lots of other matter that, via the Einstein equation, corresponds exactly to the curvature that there is everywhere in this time travel worlds.) Now a real ball of course does have some effect on the metric of the space-time it is in. But let us consider a ball that is so small that its effect on the metric is negligible. Presumably it will still be the case that certain states of this ball on that space-like surface are not compatible with the global time travel structure of this universe.

This means that the actual distribution of matter on such a space-like surface can be extended into a space-time with closed time-like lines, but that certain counterfactual distributions of matter on this space-like surface can not be extended into the same space-time. But note that the changes made in the matter distribution (when going from the actual to the counterfactual distribution) do not in any non-negligible way affect the metric properties of the space-time. (Recall that the changes only effect test particles.) Thus the reason why the global time travel properties of the counterfactual space-time have to be significantly different from the actual space-time is not that there are problems with metric singularities or alterations in the metric that force significant global changes when we go to the counterfactual matter distribution. The reason that the counterfactual space-time has to be different is that in the counterfactual world the ball’s initial state of motion starting on the space-like surface, could not “meet up” in a consistent way with its earlier self (could not be consistently extended) if we were to let the global structure of the counterfactual space-time be the same as that of the actual space-time. Now, it is not bizarre or implausible that there is a counterfactual dependence of manifold structure, even of its topology, on matter distributions on spacelike surfaces. For instance, certain matter distributions may lead to singularities, others may not. We may indeed in some sense have causal power over the topology of the space-time we live in. But this power normally comes via the Einstein equations. But it is bizarre to think that there could be a counterfactual dependence of global space-time structure on the arrangement of certain tiny bits of matter on some space-like surface, where changes in that arrangement by assumption do not affect the metric anywhere in space-time in any significant way . It is implausible that we live in such a world, or that a world even remotely like ours is like that.

Let us illustrate this argument in a different way by assuming that wormhole time travel imposes constraints upon the states of people prior to such time travel, where the people have so little mass/energy that they have negligible effect, via the Einstein equation, on the local metric properties of space-time. Do you think it more plausible that we live in a world where wormhole time travel occurs but it only occurs when people’s states are such that these local states happen to combine with time travel in such a way that nobody ever succeeds in killing their younger self, or do you think it more plausible that we are not in a wormhole time travel world? [ 5 ]

An alternative approach to time travel (initiated by Deutsch 1991) abstracts away from the idealized toy models described above. [ 6 ] This computational approach considers instead the evolution of bits (simple physical systems with two discrete states) through a network of interactions, which can be represented by a circuit diagram with gates corresponding to the interactions. Motivated by the possibility of CTCs, Deutsch proposed adding a new kind of channel that connects the output of a given gate back to its input —in essence, a backwards-time step. More concretely, given a gate that takes \(n\) bits as input, we can imagine taking some number \(i \lt n\) of these bits through a channel that loops back and then do double-duty as inputs. Consistency requires that the state of these \(i\) bits is the same for output and input. (We will consider an illustration of this kind of system in the next section.) Working through examples of circuit diagrams with a CTC channel leads to similar treatments of Consistency and Underdetermination as the discussion above (see, e.g., Wallace 2012: § 10.6). But the approach offers two new insights (both originally due to Deutsch): the Easy Knowledge paradox, and a particularly clear extension to time travel in quantum mechanics.

A computer equipped with a CTC channel can exploit the need to find consistent evolution to solve remarkably hard problems. (This is quite different than the first idea that comes to mind to enhance computational power: namely to just devote more time to a computation, and then send the result back on the CTC to an earlier state.) The gate in a circuit incorporating a CTC implements a function from the input bits to the output bits, under the constraint that the output and input match the i bits going through the CTC channel. This requires, in effect, finding the fixed point of the relevant function. Given the generality of the model, there are few limits on the functions that could be implemented on the CTC circuit. Nature has to solve a hard computational problem just to ensure consistent evolution. This can then be extended to other complex computational problems—leading, more precisely, to solutions of NP -complete problems in polynomial time (see Aaronson 2013: Chapter 20 for an overview and further references). The limits imposed by computational complexity are an essential part of our epistemic situation, and computers with CTCs would radically change this.

We now turn to the application of the computational approach to the quantum physics of time travel (see Deutsch 1991; Deutsch & Lockwood 1994). By contrast with the earlier discussions of constraints in classical systems, they claim to show that time travel never imposes any constraints on the pre-time travel state of quantum systems. The essence of this account is as follows. [ 7 ]

A quantum system starts in state \(S_1\), interacts with its older self, after the interaction is in state \(S_2\), time travels while developing into state \(S_3\), then interacts with its younger self, and ends in state \(S_4\) (see figure 10 ).

Figure 10 [An extended description of figure 10 is in the supplement.]

Deutsch assumes that the set of possible states of this system are the mixed states, i.e., are represented by the density matrices over the Hilbert space of that system. Deutsch then shows that for any initial state \(S_1\), any unitary interaction between the older and younger self, and any unitary development during time travel, there is a consistent solution, i.e., there is at least one pair of states \(S_2\) and \(S_3\) such that when \(S_1\) interacts with \(S_3\) it will change to state \(S_2\) and \(S_2\) will then develop into \(S_3\). The states \(S_2, S_3\) and \(S_4\) will typically be not be pure states, i.e., will be non-trivial mixed states, even if \(S_1\) is pure. In order to understand how this leads to interpretational problems let us give an example. Consider a system that has a two dimensional Hilbert space with as a basis the states \(\vc{+}\) and \(\vc{-}\). Let us suppose that when state \(\vc{+}\) of the young system encounters state \(\vc{+}\) of the older system, they interact and the young system develops into state \(\vc{-}\) and the old system remains in state \(\vc{+}\). In obvious notation:

Similarly, suppose that:

Let us furthermore assume that there is no development of the state of the system during time travel, i.e., that \(\vc{+}_2\) develops into \(\vc{+}_3\), and that \(\vc{-}_2\) develops into \(\vc{-}_3\).

Now, if the only possible states of the system were \(\vc{+}\) and \(\vc{-}\) (i.e., if there were no superpositions or mixtures of these states), then there is a constraint on initial states: initial state \(\vc{+}_1\) is impossible. For if \(\vc{+}_1\) interacts with \(\vc{+}_3\) then it will develop into \(\vc{-}_2\), which, during time travel, will develop into \(\vc{-}_3\), which inconsistent with the assumed state \(\vc{+}_3\). Similarly if \(\vc{+}_1\) interacts with \(\vc{-}_3\) it will develop into \(\vc{+}_2\), which will then develop into \(\vc{+}_3\) which is also inconsistent. Thus the system can not start in state \(\vc{+}_1\).

But, says Deutsch, in quantum mechanics such a system can also be in any mixture of the states \(\vc{+}\) and \(\vc{-}\). Suppose that the older system, prior to the interaction, is in a state \(S_3\) which is an equal mixture of 50% \(\vc{+}_3\) and 50% \(\vc{-}_3\). Then the younger system during the interaction will develop into a mixture of 50% \(\vc{+}_2\) and 50% \(\vc{-}_2\), which will then develop into a mixture of 50% \(\vc{+}_3\) and 50% \(\vc{-}_3\), which is consistent! More generally Deutsch uses a fixed point theorem to show that no matter what the unitary development during interaction is, and no matter what the unitary development during time travel is, for any state \(S_1\) there is always a state \(S_3\) (which typically is not a pure state) which causes \(S_1\) to develop into a state \(S_2\) which develops into that state \(S_3\). Thus quantum mechanics comes to the rescue: it shows in all generality that no constraints on initial states are needed!

One might wonder why Deutsch appeals to mixed states: will superpositions of states \(\vc{+}\) and \(\vc{-}\) not suffice? Unfortunately such an idea does not work. Suppose again that the initial state is \(\vc{+}_1\). One might suggest that that if state \(S_3\) is

one will obtain a consistent development. For one might think that when initial state \(\vc{+}_1\) encounters the superposition

it will develop into superposition

and that this in turn will develop into

as desired. However this is not correct. For initial state \(\vc{+}_1\) when it encounters

will develop into the entangled state

In so far as one can speak of the state of the young system after this interaction, it is in the mixture of 50% \(\vc{+}_2\) and 50% \(\vc{-}_2\), not in the superposition

So Deutsch does need his recourse to mixed states.

This clarification of why Deutsch needs his mixtures does however indicate a serious worry about the simplifications that are part of Deutsch’s account. After the interaction the old and young system will (typically) be in an entangled state. Although for purposes of a measurement on one of the two systems one can say that this system is in a mixed state, one can not represent the full state of the two systems by specifying the mixed state of each separate part, as there are correlations between observables of the two systems that are not represented by these two mixed states, but are represented in the joint entangled state. But if there really is an entangled state of the old and young systems directly after the interaction, how is one to represent the subsequent development of this entangled state? Will the state of the younger system remain entangled with the state of the older system as the younger system time travels and the older system moves on into the future? On what space-like surfaces are we to imagine this total entangled state to be? At this point it becomes clear that there is no obvious and simple way to extend elementary non-relativistic quantum mechanics to space-times with closed time-like curves: we apparently need to characterize not just the entanglement between two systems, but entanglement relative to specific spacetime descriptions.

How does Deutsch avoid these complications? Deutsch assumes a mixed state \(S_3\) of the older system prior to the interaction with the younger system. He lets it interact with an arbitrary pure state \(S_1\) younger system. After this interaction there is an entangled state \(S'\) of the two systems. Deutsch computes the mixed state \(S_2\) of the younger system which is implied by this entangled state \(S'\). His demand for consistency then is just that this mixed state \(S_2\) develops into the mixed state \(S_3\). Now it is not at all clear that this is a legitimate way to simplify the problem of time travel in quantum mechanics. But even if we grant him this simplification there is a problem: how are we to understand these mixtures?

If we take an ignorance interpretation of mixtures we run into trouble. For suppose that we assume that in each individual case each older system is either in state \(\vc{+}_3\) or in state \(\vc{-}_3\) prior to the interaction. Then we regain our paradox. Deutsch instead recommends the following, many worlds, picture of mixtures. Suppose we start with state \(\vc{+}_1\) in all worlds. In some of the many worlds the older system will be in the \(\vc{+}_3\) state, let us call them A -worlds, and in some worlds, B -worlds, it will be in the \(\vc{-}_3\) state. Thus in A -worlds after interaction we will have state \(\vc{-}_2\) , and in B -worlds we will have state \(\vc{+}_2\). During time travel the \(\vc{-}_2\) state will remain the same, i.e., turn into state \(\vc{-}_3\), but the systems in question will travel from A -worlds to B -worlds. Similarly the \(\vc{+}\) \(_2\) states will travel from the B -worlds to the A -worlds, thus preserving consistency.

Now whatever one thinks of the merits of many worlds interpretations, and of this understanding of it applied to mixtures, in the end one does not obtain genuine time travel in Deutsch’s account. The systems in question travel from one time in one world to another time in another world, but no system travels to an earlier time in the same world. (This is so at least in the normal sense of the word “world”, the sense that one means when, for instance, one says “there was, and will be, only one Elvis Presley in this world.”) Thus, even if it were a reasonable view, it is not quite as interesting as it may have initially seemed. (See Wallace 2012 for a more sympathetic treatment, that explores several further implications of accepting time travel in conjunction with the many worlds interpretation.)

We close by acknowledging that Deutsch’s starting point—the claim that this computational model captures the essential features of quantum systems in a spacetime with CTCs—has been the subject of some debate. Several physicists have pursued a quite different treatment of evolution of quantum systems through CTC’s, based on considering the “post-selected” state (see Lloyd et al. 2011). Their motivations for implementing the consistency condition in terms of the post-selected state reflects a different stance towards quantum foundations. A different line of argument aims to determine whether Deutsch’s treatment holds as an appropriate limiting case of a more rigorous treatment, such as quantum field theory in curved spacetimes. For example, Verch (2020) establishes several results challenging the assumption that Deutsch’s treatment is tied to the presence of CTC’s, or that it is compatible with the entanglement structure of quantum fields.

What remains of the grandfather paradox in general relativistic time travel worlds is the fact that in some cases the states on edgeless spacelike surfaces are “overconstrained”, so that one has less than the usual freedom in specifying conditions on such a surface, given the time-travel structure, and in some cases such states are “underconstrained”, so that states on edgeless space-like surfaces do not determine what happens elsewhere in the way that they usually do, given the time travel structure. There can also be mixtures of those two types of cases. The extent to which states are overconstrained and/or underconstrained in realistic models is as yet unclear, though it would be very surprising if neither obtained. The extant literature has primarily focused on the problem of overconstraint, since that, often, either is regarded as a metaphysical obstacle to the possibility time travel, or as an epistemological obstacle to the plausibility of time travel in our world. While it is true that our world would be quite different from the way we normally think it is if states were overconstrained, underconstraint seems at least as bizarre as overconstraint. Nonetheless, neither directly rules out the possibility of time travel.

If time travel entailed contradictions then the issue would be settled. And indeed, most of the stories employing time travel in popular culture are logically incoherent: one cannot “change” the past to be different from what it was, since the past (like the present and the future) only occurs once. But if the only requirement demanded is logical coherence, then it seems all too easy. A clever author can devise a coherent time-travel scenario in which everything happens just once and in a consistent way. This is just too cheap: logical coherence is a very weak condition, and many things we take to be metaphysically impossible are logically coherent. For example, it involves no logical contradiction to suppose that water is not molecular, but if both chemistry and Kripke are right it is a metaphysical impossibility. We have been interested not in logical possibility but in physical possibility. But even so, our conditions have been relatively weak: we have asked only whether time-travel is consistent with the universal validity of certain fundamental physical laws and with the notion that the physical state on a surface prior to the time travel region be unconstrained. It is perfectly possible that the physical laws obey this condition, but still that time travel is not metaphysically possible because of the nature of time itself. Consider an analogy. Aristotle believed that water is homoiomerous and infinitely divisible: any bit of water could be subdivided, in principle, into smaller bits of water. Aristotle’s view contains no logical contradiction. It was certainly consistent with Aristotle’s conception of water that it be homoiomerous, so this was, for him, a conceptual possibility. But if chemistry is right, Aristotle was wrong both about what water is like and what is possible for it. It can’t be infinitely divided, even though no logical or conceptual analysis would reveal that.

Similarly, even if all of our consistency conditions can be met, it does not follow that time travel is physically possible, only that some specific physical considerations cannot rule it out. The only serious proof of the possibility of time travel would be a demonstration of its actuality. For if we agree that there is no actual time travel in our universe, the supposition that there might have been involves postulating a substantial difference from actuality, a difference unlike in kind from anything we could know if firsthand. It is unclear to us exactly what the content of possible would be if one were to either maintain or deny the possibility of time travel in these circumstances, unless one merely meant that the possibility is not ruled out by some delineated set of constraints. As the example of Aristotle’s theory of water shows, conceptual and logical “possibility” do not entail possibility in a full-blooded sense. What exactly such a full-blooded sense would be in case of time travel, and whether one could have reason to believe it to obtain, remain to us obscure.

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How to cite this entry . Preview the PDF version of this entry at the Friends of the SEP Society . Look up topics and thinkers related to this entry at the Internet Philosophy Ontology Project (InPhO). Enhanced bibliography for this entry at PhilPapers , with links to its database.

• Adlam, Emily, unpublished, “ Is There Causation in Fundamental Physics? New Insights from Process Matrices and Quantum Causal Modelling ”, 2022, arXiv: 2208.02721. doi:10.48550/ARXIV.2208.02721
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Is time travel possible? Why one scientist says we 'cannot ignore the possibility.'

A common theme in science-fiction media , time travel is captivating. It’s defined by the late philosopher David Lewis in his essay “The Paradoxes of Time Travel” as “[involving] a discrepancy between time and space time. Any traveler departs and then arrives at his destination; the time elapsed from departure to arrival … is the duration of the journey.”

Time travel is usually understood by most as going back to a bygone era or jumping forward to a point far in the future . But how much of the idea is based in reality? Is it possible to travel through time? 

Is time travel possible?

According to NASA, time travel is possible , just not in the way you might expect. Albert Einstein’s theory of relativity says time and motion are relative to each other, and nothing can go faster than the speed of light , which is 186,000 miles per second. Time travel happens through what’s called “time dilation.”

Time dilation , according to Live Science, is how one’s perception of time is different to another's, depending on their motion or where they are. Hence, time being relative. 

Learn more: Best travel insurance

Dr. Ana Alonso-Serrano, a postdoctoral researcher at the Max Planck Institute for Gravitational Physics in Germany, explained the possibility of time travel and how researchers test theories. 

Space and time are not absolute values, Alonso-Serrano said. And what makes this all more complex is that you are able to carve space-time .

“In the moment that you carve the space-time, you can play with that curvature to make the time come in a circle and make a time machine,” Alonso-Serrano told USA TODAY. 

She explained how, theoretically, time travel is possible. The mathematics behind creating curvature of space-time are solid, but trying to re-create the strict physical conditions needed to prove these theories can be challenging. 

“The tricky point of that is if you can find a physical, realistic, way to do it,” she said. 

Alonso-Serrano said wormholes and warp drives are tools that are used to create this curvature. The matter needed to achieve curving space-time via a wormhole is exotic matter , which hasn’t been done successfully. Researchers don’t even know if this type of matter exists, she said.

“It's something that we work on because it's theoretically possible, and because it's a very nice way to test our theory, to look for possible paradoxes,” Alonso-Serrano added.

“I could not say that nothing is possible, but I cannot ignore the possibility,” she said. 

She also mentioned the anecdote of  Stephen Hawking’s Champagne party for time travelers . Hawking had a GPS-specific location for the party. He didn’t send out invites until the party had already happened, so only people who could travel to the past would be able to attend. No one showed up, and Hawking referred to this event as "experimental evidence" that time travel wasn't possible.

What did Albert Einstein invent?: Discoveries that changed the world

Just Curious for more? We've got you covered

USA TODAY is exploring the questions you and others ask every day. From "How to watch the Marvel movies in order" to "Why is Pluto not a planet?" to "What to do if your dog eats weed?" – we're striving to find answers to the most common questions you ask every day. Head to our Just Curious section to see what else we can answer for you. 

October 21, 1999

According to current physical theory, is it possible for a human being to travel through time?

As several respondents noted, we constantly travel through time--just forward, and all at the same rate. But seriously, time travel is more than mere fantasy, as noted by Gary T. Horowitz, a professor of physics at the University of California at Santa Barbara:

"Perhaps surprisingly, this turns out to be a subtle question. It is not obviously ruled out by our current laws of nature. Recent investigations into this question have provided some evidence that the answer is no, but it has not yet been proven to be impossible."

Even the slight possibility of time travel exerts such fascination that many physicists continue to study not only whether it may be possible but also how one might do it.

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One of the leading researchers in this area is William A. Hiscock, a professor of physics at Montana State University. Here are his thoughts on the matter:

"Is it possible to travel through time? To answer this question, we must be a bit more specific about what we mean by traveling through time. Discounting the everyday progression of time, the question can be divided into two parts: Is it possible, within a short time (less than a human life span), to travel into the distant future? And is it possible to travel into the past?

"Our current understanding of fundamental physics tells us that the answer to the first question is a definite yes, and to the second, maybe.

"The mechanism for traveling into the distant future is to use the time-dilation effect of Special Relativity, which states that a moving clock appears to tick more slowly the closer it approaches the speed of light. This effect, which has been overwhelmingly supported by experimental tests, applies to all types of clocks, including biological aging.

"If one were to depart from the earth in a spaceship that could accelerate continuously at a comfortable one g (an acceleration that would produce a force equal to the gravity at the earth's surface), one would begin to approach the speed of light relative to the earth within about a year. As the ship continued to accelerate, it would come ever closer to the speed of light, and its clocks would appear to run at an ever slower rate relative to the earth. Under such circumstances, a round trip to the center of our galaxy and back to the earth--a distance of some 60,000 light-years--could be completed in only a little more than 40 years of ship time. Upon arriving back at the earth, the astronaut would be only 40 years older, while 60,000 years would have passed on the earth. (Note that there is no 'twin paradox,' because it is unambiguous that the space traveler has felt the constant acceleration for 40 years, while a hypothetical twin left behind on a spaceship circling the earth has not.)

"Such a trip would pose formidable engineering problems: the amount of energy required, even assuming a perfect conversion of mass into energy, is greater than a planetary mass. But nothing in the known laws of physics would prevent such a trip from occurring.

"Time travel into the past, which is what people usually mean by time travel, is a much more uncertain proposition. There are many solutions to Einstein's equations of General Relativity that allow a person to follow a timeline that would result in her (or him) encountering herself--or her grandmother--at an earlier time. The problem is deciding whether these solutions represent situations that could occur in the real universe, or whether they are mere mathematical oddities incompatible with known physics. No experiment or observation has ever indicated that time travel is occurring in our universe. Much work has been done by theoretical physicists in the past decade to try to determine whether, in a universe that is initially without time travel, one can build a time machine--in other words, if it is possible to manipulate matter and the geometry of space-time in such a way as to create new paths that circle back in time.

"How could one build a time machine? The simplest way currently being discussed is to take a wormhole (a tunnel connecting spatially separated regions of space-time) and give one mouth of the wormhole a substantial velocity with respect to the other. Passage through the wormhole would then allow travel to the past.

"Easily said--but where does one obtain a wormhole? Although the theoretical properties of wormholes have been extensively studied over the past decade, little is known about how to form a macroscopic wormhole, large enough for a human or a spaceship to pass through. Some speculative theories of quantum gravity tell us that space-time has a complicated, foamlike structure of wormholes on the smallest scales--10^-33 centimeter, or a billion billion times smaller than an electron. Some physicists believe it may be possible to grab one of these truly microscopic wormholes and enlarge it to usable size, but at present these ideas are all very hypothetical.

"Even if we had a wormhole, would nature allow us to convert it into a time machine? Stephen Hawking has formulated a "Chronology Protection Conjecture," which states that the laws of nature prevent the creation of a time machine. At the moment, however, this is just a conjecture, not proven.

"Theoretical physicists have studied various aspects of physics to determine whether this law or that might protect chronology and forbid the building of a time machine. In all the searching, however, only one bit of physics has been found that might prohibit using a wormhole to travel through time. In 1982, Deborah A. Konkowski of the U.S. Naval Academy and I showed that the energy in the vacuum state of a massless quantized field (such as the photon) would grow without bound as a time machine is being turned on, effectively preventing it from being used. Later studies by Hawking and Kip S. Thorne of Caltech have shown that it is unclear whether the growing energy would change the geometry of space-time rapidly enough to stop the operation of the time machine. Recent work by Tsunefumi Tanaka of Montana State University and myself, along with independent research by David Boulware of the University of Washington, has shown that the energy in the vacuum state of a field having mass (such as the electron) does not grow to unbounded levels; this finding indicates there may be a way to engineer the particle physics to allow a time machine to work.

"Perhaps the biggest surprise of the work of the past decade is that it is not obvious that the laws of physics forbid time travel. It is increasingly clear that the question may not be settled until scientists develop an adequate theory of quantum gravity."

John L. Friedman of the physics department at the University of Wisconsin at Milwaukee has also given this subject a great deal of consideration:

"Special relativity implies that people or clocks at rest (or not accelerating) age more quickly than partners traveling on round-trips in which one changes direction to return to one's partner. In the world's particle accelerators, this prediction is tested daily: Particles traveling in circles at nearly the speed of light decay more slowly than those at rest, and the decay time agrees with theory to the high precision of the measurements.

"Within the framework of Special Relativity, the fact that particles cannot move faster than light prevents one from returning after a high-speed trip to a time earlier than the time of departure. Once gravity is included, however, spacetime is curved, so there are solutions to the equations of General Relativity in which particles can travel in paths that take them back to earlier times. Other features of the geometries that solve the equations of General Relativity include gravitational lenses, gravitational waves and black holes; the dramatic explosion of discoveries in radio and X-ray astronomy during the past two decades has led to the observation of gravitational lenses and gravitational waves, as well as to compelling evidence for giant black holes in the centers of galaxies and stellar-sized black holes that arise from the collapse of dying stars. But there do not appear to be regions of spacetime that allow time travel, raising the fundamental question of what forbids them--or if they really are forbidden.

"A recent surprise is that one can circumvent the 'grandfather paradox,' the idea that it is logically inconsistent for particle paths to loop back to earlier times, because, for example, a granddaughter could go back in time to do away with her grandfather. For several simple physical systems, solutions to the equations of physics exist for any starting condition. In these model systems, something always intervenes to prevent inconsistency analogous to murdering one's grandfather.

"Then why do there seem to be no time machines? Two different answers are consistent with our knowledge. The first is simply that the classical theory has a much broader set of solutions than the correct theory of quantum gravity. It is not implausible that causal structure enters in a fundamental way in quantum gravity and that classical spacetimes with time loops are spurious--in other words, that they do not approximate any states of the complete theory. A second possible answer is provided by recent results that go by the name chronology protection: One supposes that quantum gravity allows microscopic structures that violate causality, and one shows that the character of macroscopic matter forbids the existence of regions with macroscopically large time loops. To create a time machine would require negative energy, and quantum mechanics appears to allow only extremely small regions of negative energy. And the forces needed to create an ordinary-sized region with time loops appear to be extremely large.

"To summarize: It is very likely that the laws of physics rule out macroscopic time machines, but possible that spacetime is filled with microscopic time loops.

Time Travel

Arguably, we are always travelling though time, as we move from the past into the future. But time travel usually refers to the possibility of changing the rate at which we travel into the future, or completely reversing it so that we travel into the past. Although a plot device in fiction since the 19 th Century (see the section on Time in Literature ), time travel has never been practically demonstrated or verified, and may still be impossible.

Time travel is not possible in Newtonian absolute time (we move deterministically and linearly forward into the future). Neither is it possible according to special relativity (we are constrained by our light cones). But general relativity does raises the prospect (at least theoretically) of travel through time, i.e. the possibility of movement backwards and/or forwards in time, independently of the normal flow of time we observe on Earth, in much the same way as we can move between different points in space.

Time travel is usually taken to mean that a person’s mind and body remain unchanged, with their memories intact, while their location in time is changed. If the traveller’s body and mind reverted its condition at the destination time, then no time travel would be perceptible.

Time Travel Scenarios

Although, in the main, differing fundamentally from the H.G. Wells concept of a physical machine with levers and dials, many different speculative time travel solutions and scenarios have been put forward over the years. However, the actual physical plausibility of these solutions in the real world remains uncertain.

At its simplest, as we have seen in the section on Relativistic Time , if one were to travel from the Earth at relativistic speeds and then return, then more time would have passed on Earth than for the traveller, so the traveller would, from his perspective, effectively have “travelled into the future”. This is not to say that the traveller suddenly jumped into the Earth’s future, in the way that time travel is often envisioned, but that, as judged by the Earth’s external time, the traveller has experienced less passage of time than his twin who remained on Earth. This is not real time travel, though, but more in the nature of “fast-forwarding” through time: it is a one-way journey forwards with no way back.

There does, however, appear to be some scientific basis within the Theory of Relativity for the possibility of real time travel in certain scenarios. Kurt Gödel showed, back in the early days of relativity, that there are some solutions to the field equations of general relativity that describe space-times so warped that they contain “ closed time-like curves ”, where an individual time-cone twists and closes in on itself, allowing a path from the present to the distant future or the past. Gödel’s solution was the first challenge in centuries to the dominant idea of linear time on which most of physics rests. Although a special case solution, based on an infinite, rotating universe (not the finite, non-rotating universe we actually find ourselves in), other time travel solution have been identified since then that do not require an infinite, rotating universe, but they remain contentious.

In the 1970s, controversial physicist Frank Tipler published his ideas for a “time machine”, using an infinitely long cylinder which spins along its longitudinal axis, which he claimed would allow time travel both forwards and backwards in time without violating the laws of physics, although Stephen Hawking later disproved Tipler’s ideas.

In 1994, Miguel Alcubierre proposed a hypothetical system whereby a spacecraft would contract space in front of it and expand space behind it, resulting in effective faster-than-light travel and therefore (potentially) time travel, but again the practicalities of constructing this kind of a “ warp drive ” remain prohibitive.

Other theoretical physicists like Kip Thorne and Paul Davies have shown how a wormhole in space-time could theoretically provide an instantaneous gateway to different time periods, in much the same way as general relativity allows the theoretical possibility of instantaneous spatial travel through wormholes. Wormholes are tubes or conduits or short-cuts through space-time, where space-time is so warped that it bends back on itself, another science fiction concept made potential reality by the Theory of Relativity. The drawback is that unimaginable amounts of energy would be required to bring about such a wormhole, although experiments looking into the possibility of creating mini-wormholes and mini-black holes are being carried out at the particle accelerator at CERN in Switzerland. It also seems likely that such a wormhole would collapse instantly into a black hole unless some method of holding it open were devised (possibly so-called “negative energy”, which is known to be theoretically possible, but which is not yet practically feasible). Stephen Hawking has suggested that radiation feedback, analogous to feedback in sound, would destroy the wormhole, which would therefore not last long enough to be used as a time machine. Actually controlling where (and when) a wormhole exits is another pitfall.

Another potential time travel possibility, although admittedly something of a long shot, relates to cosmic strings (or quantum strings ), long shreds of energy left over after the Big Bang, thinner than an atom but incredibly dense, that weave through the entire universe. Richard Gott has suggested that if two such cosmic strings were to pass close to each other, or even close to a black hole, the resulting warpage of space-time could well be so severe as to create a closed-time-like curve. However, cosmic strings remain speculative and the chances of finding such a phenomenon are vanishingly small (and, even if it were possible, such a loop may well find itself trapped inside a rotating black hole).

Physicist Ron Mallet has been looking into the possibility of using lasers to control extreme levels of gravity, which could then potentially be used to control time. According to Mallet, circulating beams of laser-controlled light could create similar conditions to a rotating black hole, with its frame-dragging and potential time travel properties.

Others are looking to quantum mechanics for a solution to time travel. In quantum physics, proven concepts such as superposition and entanglement effectively mean that a particle can be in two (or more) places at once. One interpretation of this (see the section on Quantum Time ) is the “ many worlds ” view in which all the different quantum states exist simultaneously in multiple parallel universes within an overall multiverse. If we could gain access to these alternative parallel universes, a form of time travel might then be possible.

At the sub-sub-microscopic level – at the level of so-called quantum foam , tiny bubbles of matter a billion-trillion-trillionths of a centimetre in length, perpetually popping into and out of existence – it is speculated that tiny tunnels or short-cuts through space-time are constantly forming, disappearing and reforming. Some scientists believe that it may be possible to capture such a quantum tunnel and enlarge it many trillions of times to the human scale. However, the idea is still at a very speculative stage,

It should be noted that, with all of these schemes and ideas, it does not look to be possible to travel any further back in time that the time at which the travel technology was devised.

Faster-Than-Light Particles

The equations of relativity imply that faster-than-light ( superluminal ) particles, if they existed, would theoretically travel backwards in time. Therefore, they could, again theoretically, be used to build a kind of “ antitelephone ” to send signals faster than light, and thus communicate backwards in time. Although the Theory of Relativity disallows particles from accelerating from sub-light speed to the speed of light (among other effects, time would slow right down and effectively stop for such a particle, and its mass would increase to infinity), it does not preclude the possibility of particles that ALWAYS travel faster than light. Therefore, the possibility does still exist in theory for faster-than-light travel in the case of a particle with such properties.

There is a rather strange theoretical particle in physics called the tachyon that routinely travels faster than light, with the corollary that such a particle would naturally travel backwards in time as we know it. So, in theory, one could never see such a particle approaching, only leaving, and the particle could even violate the normal order of cause and effect. For a tachyon, the speed of light is the lower speed limit, while the upper speed limit is infinity, and its speed increases as its energy decreases. Even stranger, the mass of a tachyon would technically be an imaginary number (i.e. the number squared is negative), whatever that might actually mean in practice.

It should be stressed that there is no experimental evidence to suggests that tachyons actually exist, and many physicists deny even the possibility. A tachyon has never been observed or recorded (although the search continues, particularly through analysis of cosmic rays and in particle accelerators), and neither has one ever been created, so they remain hypothetical, although theory strongly supports their existence.

Research using MINOS and OPERA detectors has suggested that tiny particles called neutrinos may travel faster than light. Other more recent research from CERN, however, has put the findings into dispute, and the matter remains inconclusive. Neutrinos are not merely hypothetical particles like tachyons, but a well-known part of modern particle physics. But they are tiny, almost-massless, invisible, electrically neutral, weakly-interacting particles that pass right through normal matter, and consequently are very difficult to measure and deal with (even their mass has never been measured accurately).

Time Travel Paradoxes

The possibility of travel backwards in time is generally considered by scientists to be much more unlikely than travel into the future. The idea of time travel to the past is rife with problems, not least the possibility of temporal paradoxes resulting from the violation of causality (i.e. the possibility that an effect could somehow precede its cause). This is most famously exemplified by the grandfather paradox : if a hypothetical time traveller goes back in time and kills his grandfather, the time traveller himself would never be born when he was meant to be; if he is never born, though, he is unable to travel through time and kill his grandfather, which means that he WOULD be born; etc, etc.

Some have sought to justify the possibility of time travel to the past by the very fact that such paradoxes never actually arise in practice. For example, the simple fact that the time traveller DOES exist at the start of his journey is itself proof that he could not kill his grandfather or change the past in any way, either because free will ceases to exist in the past, or because the outcomes of such decisions are predetermined. Or, alternatively, it is argued, any changes made by a hypothetical future time traveller must already have happened in the traveller’s past, resulting in the same reality that the traveller moves from.

Theoretical physicist Stephen Hawking has suggested that the fundamental laws of nature themselves – particularly the idea that causes always precede effects – may prevent time travel in some way. The apparent absence of “tourists from the future” here in our present is another argument, albeit not a rigorous one, that has been put forward against the possibility of time travel, even in a technologically advanced future (the assumption here is that future civilizations, millions of years more technologically advanced than us, should be capable of travel).

Some interpretations of time travel, though, have tried to resolve such potential paradoxes by accepting the possibility of travel between “ branch points ”, parallel realities or parallel universes , so that any new events caused by a time traveller’s visit to the past take place in a different reality and so do not impact on the original time stream. The idea of parallel universes, first put forward by Hugh Everett III in his “ many worlds ” interpretation of quantum theory in the 1950s, is now quite mainstream and accepted by many (although by no means all) physicists.

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Physics of Time

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Is Time Travel Possible?

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Stories regarding travel into the past and the future have long captured our imagination, but the question of whether time travel is possible is a thorny one that gets right to the heart of understanding what physicists mean when they use the word "time." 

Modern physics teaches us that time is one of the most mysterious aspects of our universe, though it may at first seem straightforward. Einstein revolutionized our understanding of the concept, but even with this revised understanding, some scientists still ponder the question of whether or not ​ time actually exists or whether it is a mere "stubbornly persistent illusion" (as Einstein once called it). Whatever time is, though, physicists (and fiction writers) have found some interesting ways to manipulate it to consider traversing it in unorthodox ways.

Time and Relativity

Though referenced in H.G. Wells' The Time Machine (1895), the actual science of time travel didn't come into being until well into the twentieth century, as a side-effect of Albert Einstein 's theory of general relativity (developed in 1915). Relativity describes the physical fabric of the universe in terms of a 4-dimensional spacetime, which includes three spatial dimensions (up/down, left/right, and front/back) along with one time dimension. Under this theory, which has been proven by numerous experiments over the last century, gravity is a result of the bending of this spacetime in response to the presence of matter. In other words, given a certain configuration of matter, the actual spacetime fabric of the universe can be altered in significant ways.

One of the amazing consequences of relativity is that movement can result in a difference in the way time passes, a process known as time dilation . This is most dramatically manifested in the classic Twin Paradox . In this method of "time travel," you can move into the future faster than normal, but there's not really any way back. (There's a slight exception, but more on that later in the article.)

Early Time Travel

In 1937, Scottish physicist W. J. van Stockum first applied general relativity in a way that opened the door for time travel. By applying the equation of general relativity to a situation with an infinitely long, extremely dense rotating cylinder (kind of like an endless barbershop pole). The rotation of such a massive object actually creates a phenomenon known as "frame dragging," which is that it actually drags spacetime along with it. Van Stockum found that in this situation, you could create a path in 4-dimensional spacetime which began and ended at the same point - something called a closed timelike curve - which is the physical result that allows time travel. You can set off in a space ship and travel a path which brings you back to the exact same moment you started out at.

Though an intriguing result, this was a fairly contrived situation, so there wasn't really much concern about it taking place. A new interpretation was about to come along, however, which was much more controversial.

In 1949, the mathematician Kurt Godel - a friend of Einstein's and a colleague at Princeton University's Institute for Advanced Study - decided to tackle a situation where the whole universe is rotating. In Godel's solutions, time travel was actually allowed by the equations if the universe were rotating. A rotating universe could itself function as a time machine.

Now, if the universe were rotating, there would be ways to detect it (light beams would bend, for example, if the whole universe were rotating), and so far the evidence is overwhelmingly strong that there is no sort of universal rotation. So again, time travel is ruled out by this particular set of results. But the fact is that things in the universe do rotate, and that again opens up the possibility.

Time Travel and Black Holes

In 1963, New Zealand mathematician Roy Kerr used the field equations to analyze a rotating black hole , called a Kerr black hole, and found that the results allowed a path through a wormhole in the black hole, missing the singularity at the center, and make it out the other end. This scenario also allows for closed timelike curves, as theoretical physicist Kip Thorne realized years later.

In the early 1980s, while Carl Sagan worked on his 1985 novel Contact , he approached Kip Thorne with a question about the physics of time travel, which inspired Thorne to examine the concept of using a black hole as a means of time travel. Together with the physicist Sung-Won Kim, Thorne realized that you could (in theory) have a black hole with a wormhole connecting it to another point in space held open by some form of negative energy.

But just because you have a wormhole doesn't mean that you have a time machine. Now, let's assume that you could move one end of the wormhole (the "movable end). You place the movable end on a spaceship, shooting it off into space at nearly the speed of light . Time dilation kicks in, and the time experienced by the movable end is much less than the time experienced by the fixed end. Let's assume that you move the movable end 5,000 years into the future of the Earth, but the movable end only "ages" 5 years. So you leave in 2010 AD, say, and arrive in 7010 AD.

However, if you travel through the movable end, you will actually pop out of the fixed end in 2015 AD (since 5 years have passed back on Earth). What? How does this work?

Well, the fact is that the two ends of the wormhole are connected. No matter how far apart they are, in spacetime, they're still basically "near" each other. Since the movable end is only five years older than when it left, going through it will send you back to the related point on the fixed wormhole. And if someone from 2015 AD Earth steps through the fixed wormhole, they'd come out in 7010 AD from the movable wormhole. (If someone stepped through the wormhole in 2012 AD, they'd end up on the spaceship somewhere in the middle of the trip and so on.)

Though this is the most physically reasonable description of a time machine, there are still problems. No one knows if wormholes or negative energy exist, nor how to put them together in this way if they do exist. But it is (in theory) possible.

• Can We Travel Through Time to the Past?
• Closed Timelike Curve
• Wormholes: What Are They and Can We Use Them?
• Time Travel: Dream or Possible Reality?
• What Is the Twin Paradox? Real Time Travel
• Einstein's Theory of Relativity
• The Science of Star Trek
• What Is Time? A Simple Explanation
• Understanding Time Dilation Effects in Physics
• Is Warp Drive From 'Star Trek' Possible?
• Understanding Cosmology and Its Impact
• An Introduction to Black Holes
• Cosmos Episode 4 Viewing Worksheet
• The History of Gravity
• Black Holes and Hawking Radiation
• Spiral Galaxies

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time travel

• hypothetical transport through time into the past or the future.

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The Ethics and Morals of Time Travel: Tackling the Time Traveler’s Dilemma

The ethical and moral implications of time travel are complex and multi-layered. In recent years, discussions about the feasibility of time travel have become more prevalent, leading to questions about whether or not it would be ethical to travel through time.

Many experts argue that traveling through time could have far-reaching implications, such as altering the course of history, causing paradoxes, and creating significant ethical dilemmas. Some argue that time travel could allow for the correction of past injustices, while others argue that it could create new ones.

Ultimately, the question of whether time travel is ethical depends on a variety of factors, including the reason for time travel, its potential consequences, and the impact it could have on individuals and society as a whole.

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The Concept Of Altering The Past

The concept of time travel has been a source of fascination for humankind for as long as we have dreamt about our future. With the advent of technology and modern science, the idea of traveling through time is gradually moving from the realm of science fiction to scientific possibility.

Altering past events may seem intriguing at first glance, but it raises significant ethical and moral dilemmas. Here are some points to keep in mind when considering the idea of changing past events:

The Butterfly Effect And Its Consequences

The butterfly effect is a concept that suggests that small changes in a complex system can have significant and unpredictable effects. In the context of time travel, this concept takes a whole new meaning. Even the slightest alteration of a past event can have an enormous impact on future events, causing unexpected and potentially dangerous consequences.

For instance, what if someone went back in time and prevented the birth of a famous inventor, such as thomas edison or steve jobs? The world, as we know it, could be vastly different, or may not even exist at all.

The consequence of the butterfly effect is not limited to the advancement of technology or history. It could also result in the loss of life, cultural changes, or the destruction of the environment. Consider the outcome if someone went back in time and killed adolf hitler before he gained power.

While it may seem like a noble act, would it fundamentally change the philosophies that fueled the nazi party? Would that same person be responsible for creating another dictator in the future? The butterfly effect raises more questions than answers, and we may never be able to predict the outcomes of our actions when we meddle with time travel.

Analysis Of The Effect Of Altering Historical Events On Society, Culture, And Moral Values

An action as seemingly innocuous as going back in time to buy a particular painting or artifact could have a profoundly negative impact on society, culture, and moral values. Imagine someone traveled back in time and took the mona lisa from the louvre in the 19th century.

While it could significantly benefit one individual, it would rob the world of a masterpiece that is enjoyed and celebrated for its beauty and cultural significance. Additionally, hypothetically speaking, if someone went back in time and saved john f. kennedy from assassination, it could set a dangerous precedent of altering historical events that changed the trajectory of our culture and values.

The Paradoxical Nature Of Changing The Past And The Resulting Confusion And Chaos

The idea of time travel inherently creates a paradox, as the ability to change the past undermines the very essence of time itself. If someone went back in time and killed their grandfather, what would happen to their existence? Would they cease to exist, or would they have created a different universe entirely?

This paradox and uncertainty surrounding the idea of time travel can lead to a world of confusion and chaos.

The concept of changing the past presents a host of ethical and moral dilemmas, including the butterfly effect, the impact of changing historical events on society and culture, and the resulting paradoxical nature of changing the past. While it may be tempting to correct our mistakes or improve our future, we may need to make peace with the fact that time is a one-way street, and changing it would bring more unknown and unintended risks than rewards.

The Responsibility Of Time Travelers

Analyzing the responsibility that time travelers bear for the consequences of their actions.

The very notion of time travel brings up several moral and ethical dilemmas that we as a society must address. One such dilemma involves analyzing the responsibility that time travelers bear for the consequences of their actions. Here are some key points to consider:

• Time travelers must recognize the impact of their actions on the course of history. Any significant deviation from the timeline can have catastrophic consequences in the present and future.
• Time travelers have a responsibility to ensure that they do not disrupt the course of natural events in a way that could cause harm to future generations.
• Time travelers must consider the implications of their actions on future generations and act accordingly to minimize negative outcomes.
• Time travelers must be prepared to accept responsibility for their actions and the consequences that may arise from them.

The Moral And Ethical Considerations Of Using Knowledge Gained From The Future For Personal Gain

Using knowledge gained from the future for personal gain is a compelling prospect, but it raises several moral and ethical questions, including:

• The question of whether it is fair to use knowledge obtained from future generations for one’s benefit in the present day.
• The question of whether this creates an unjust advantage, as knowledge of future events gives someone an unfair advantage over others who do not have access to that future information.
• The question of whether using future knowledge in the present day can change the future, impacting the lives of those who sent the traveler back in time.
• The ethical implications of using future knowledge in the present day must be carefully considered to avoid incurring future harm.

The Impact Of Time Travel On The Freedom Of Choice And The Concept Of Fate

The concept of time travel also challenges our ideas of fate and the extent of human agency. Here are some key points to consider:

• Time travel raises the question of whether our actions are predestined, or whether we have free will, as we can change the course of events in the past and future.
• This creates unique ethical challenges since our present-day actions can have a significant impact on the lives of future generations, and our choices may be seen as morally questionable by those who sent us back in time.
• The ability to time travel also means that our actions may have consequences that we cannot foresee, making it important to consider the wider ramifications of our actions.

Time travel raises complex ethical and moral considerations that require us to consider the consequences of our actions carefully. Factors like responsibility, personal gain, and the nature of time and free will all warrant careful and thoughtful reflection.

Time Travel Regulation

Time travel is undoubtedly one of the most fascinating concepts that humanity has ever come up with. With movies like back to the future and interstellar gaining global popularity, the idea of “bending” time is both exciting and unsettling. However, time travel is not just a science-fiction concept, and it carries profound ethical and moral implications.

Therefore, regulating time travel is crucial to prevent any paradoxes or unforeseen repercussions. In this section, we will analyze the current regulations and legal frameworks for time travel, the role of governments and international organizations, and the debate surrounding the need for stricter regulations and moral guidelines.

Analysis Of The Current Regulations And Legal Frameworks For Time Travel

At the moment, time travel is still a theoretical concept, and there are no explicit legal frameworks or regulations in place. However, some countries have proposed some guidelines to prevent any misuse of this technology, such as denmark’s proposed “time traveling ethics commission.

” The commission aims to investigate, analyze, and possibly regulate any possible time travel attempt. There are several reasons why we need these regulations, such as:

• The butterfly effect: The butterfly effect suggests that a tiny change in the past can cause drastic future changes. Hence, we need regulations to prevent the possibility of a paradox and any other unforeseen consequences.
• The possibility of changing history: Time travel could allow people to influence the course of history, which could be dangerous. Therefore, we need guidelines to prevent any ill-intended attempt to modify events and the course of history.

The Role Of Governments And International Organizations In Regulating Time Travel

As the concept of time travel becomes more plausible, many governments and international organizations have raised concerns about it and have attempted to introduce regulations to prevent any unforeseen consequences. Here are some of the reasons why governments and international organizations need to regulate time travel:

• National security: Time travel could compromise national security, and governments need to regulate it to prevent any potential threats.
• Human rights abuse: Time travel could also be used for human rights abuse, such as meddling in the affairs of other nations or even genocide.
• Environmental impact: Time travel could have a significant impact on the environment, especially if it affects natural resources and ecosystems. Hence, we need regulations to prevent any exploitation of natural resources.

The Debate Surrounding The Need For Stricter Regulations And Moral Guidelines

Despite the current regulations and legal frameworks, there is still a debate surrounding the need for stricter regulations and moral guidelines for time travel. Some argue that regulations are essential to prevent any misuse of this technology, while others believe that it should be entirely banned.

Here are some of the reasons why we need stricter regulations and moral guidelines:

• Preventing abuse: Stricter regulations and moral guidelines can prevent any unethical intent of time travel, such as meddling in personal affairs or changing history to suit personal interests.
• Unforeseen consequences: Stricter regulations can prevent any unforeseen consequences of time travel, such as the butterfly effect or creating alternate timelines.
• Transparency: Stricter regulations can ensure transparency concerning the development, testing, and application of time travel technology.

Time travel is a fascinating concept with significant ethical and moral implications. As we move towards making time travel a reality, we need to have strict regulations and moral guidelines to prevent any potential misuse of this technology. Governments and international organizations need to take action in creating these regulations to ensure the safety and security of all.

Frequently Asked Questions On The Time Traveler’S Dilemma: Ethics And Moral Implications

What is the time traveler’s dilemma.

The time traveler’s dilemma refers to the ethical and moral implications of time travel. It raises questions about altering the past, the butterfly effect, and the responsibility of the time traveler.

What Are The Moral Implications Of Time Travel?

Time travel can have severe moral implications, such as altering historical events, changing the course of history, and affecting innocent people’s lives. The time traveler must take responsibility for the consequences of their actions.

Can Time Travel Lead To Unintended Consequences?

Yes, time travel can lead to unintended consequences as altering even the smallest detail in the past can cause a significant impact on the present and future. The butterfly effect must be considered before taking any action in the past.

The dilemma of time travel ethics and moral implications is not a simple one. It requires a thoughtful and deliberate approach to understand the intricacies involved in such a scenario. As we have seen, the butterfly effect can have drastic consequences on the future.

It is important to be mindful of how our actions today can affect generations to come. The concept of time travel raises important questions about our responsibility towards the future. As we explore the possibility of time travel, we must also consider the implications it would have on our sense of morality and ethics.

A strong code of ethics is crucial to safeguarding the interest of humanity as a whole. We must tread carefully and thoughtfully in the realm of time travel, lest we inadvertently change the very course of history itself.

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What Are Tesseracts In A Wrinkle In Time ?

What are tesseracts in a wrinkle in time & how can i use one to travel out of this dimension.

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June 27, 2024

Latest news releases

Highway 23 detour Bock to Ogilvie remains in place through mid-July

Recent heavy rains delay project schedule.

ST. CLOUD, Minn. – Due to recent heavy rains, Highway 23 will remain closed east of Bock to Ogilvie with the detour in place through mid-July, reports the Minnesota Department of Transportation.

The $6.5 million project to resurface and improve 12 miles of Highway 23 between Mille Lacs County Road 2 in east Milaca and the Groundhouse River east of Ogilvie, Kanabec County, began in mid-May. Crews are completing work in two segments—first, east of Bock to Ogilvie; then, east of Bock to Milaca.

Here’s the adjusted plan for Highway 23 Milaca to Ogilvie:

East of Bock to Ogilvie

• Detour through mid-July: Highway 23 will remain closed and detoured between Mille Lacs County Road 24 and north junction Highway 47 in Ogilvie. The detour goes north of Highway 23 via Mille Lacs County Road 24 east of Bock, Kanabec County Road 26 to Highway 47 back to Ogilvie.
• Local traffic: Expect segments of lane closures, alternate one-way traffic, flaggers and pilot car from sunrise to sunset on good weather days. Follow signs and enter/exit the work zone nearest to your destination to avoid delays.

East of Milaca to Bock

• Detour mid-July to mid-September: Work on the second segment will begin and Highway 23 will close between Mille Lacs County Road 2 in Milaca and Mille Lacs County Road 24 east of Bock. Motorists will be detoured along Mille Lacs County Road 2, County Road 4 and County Road 1.
• Lane closures Mid-September to early October: Travelers to encounter alternate one-way traffic with flaggers and pilot car.
• Local traffic: Highway 23 will remain open to those who live, work or visit those along the work zone; however, expect changes and use of alternate accesses. Hard closures will occur to replace box bridges. Follow signs and enter/exit the nearest to your destination to avoid delays.  

All traffic impacts are tentative and weather dependent.

For more information, to view detour maps, sign up for email updates or contact MnDOT, visit the Highway 23 project web page .

For your safety and ours— please stay out of barricaded areas, be prepared for delay, add time to your commute or seek alternative routes; expect slow moving trucks entering/exiting work areas in the work zone.

When all lanes open in early October, motorists will benefit from a smoother road surface, updated drainage, and improved access and safety along 12 miles of Highway 23.

For current road conditions in central Minnesota, visit 511mn.org .

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TSA checkpoints at Newark Liberty International Airport now equipped with new state-of-the-art 3-D checkpoint scanners to improve explosives detection in time for summer travel season

NEWARK, N.J. – The Transportation Security Administration (TSA) is prepared for the highest passenger volumes the agency has seen at airport security checkpoints nationwide during this summer’s travel season, which runs through Labor Day, and that includes individuals who are planning to fly out of Newark Liberty International Airport.

Since mid-May, TSA has seen multiple days break into the top 10 busiest days in the agency’s 22-year history. Typically, TSA had been screening approximately 2.5 million people per day nationwide, however since last month, the number of people screened has increased by several hundred thousand per day, with TSA officers screening more than 3 million individuals at checkpoints for the very first time.

“Here at Newark we already have seen a notable increase in checkpoint volume,” said Thomas Carter, TSA’s Federal Security Director for New Jersey. “We have been in close coordination with our airport, airline and travel partners, and we are more than ready to handle this summer’s increased travel volumes as we head into the July 4th holiday travel period,” he said.

“Knowing that travel volume will be high is why it is vital to give yourself plenty of time to park or return a rental car, check in with your airline to check bags and prepare for the security checkpoint. If you find yourself in a checkpoint line, travelers can save time by removing items from their pockets and placing them in a carry-on bag, instead of putting items directly into bins at the conveyor belt. My advice is to get into the airport two hours prior to your scheduled departure time.”

TSA is has installed eleven new computed tomography (CT) scanners in Terminal B in time for the summer travel season. These new state-of-the-art advanced CT scanners provide 3-D imaging that provide for TSA officers to enhance explosives detection capabilities for screening carry-on items.

“TSA is committed to getting the best technology to enhance security and improve the screening experience,” Carter said.  “Our officers’ use of CT technology substantially improves our threat detection capability at the checkpoint. The CT technology applies advanced algorithms for the detection of explosives, including liquid explosives and other threat items.”  

The system applies sophisticated algorithms for the detection of explosives by creating a 3-D image that can be viewed and rotated 360 degrees on three axes for thorough visual image analysis by a transportation security officer. This new technology creates such a clear image of a bag’s contents that the system can automatically detect explosives, including liquids, by shooting hundreds of images with an X-ray camera spinning around the conveyor belt to provide TSA officers with the three-dimensional views of the contents of a carry-on bag.

It takes a few extra seconds for the TSA officer to view the image and rotate it to get a better understanding of its contents, however in most instances, rotating the image allows the TSA officer to identify an item inside the bag and clear it without a need to open it for inspection. Checkpoint CT technology results in fewer bag checks. However, if a bag requires further screening, a TSA officer will inspect it to ensure that a threat item is not contained inside.

As an added passenger convenience, with the use of these new CT units, travelers may now leave their laptops and other electronic devices in their carry-on bags along with their small 3-1-1 liquids .

Since traveler volume will be high this summer, it is even more important for travelers to come to the airport prepared to go through the security screening process. Passengers need to make sure that there are no prohibited items among their carry-on items. Prohibited items will result in a need for TSA officers to open and inspect a bag to determine what triggered the alarm. This process takes a few minutes and will slow down someone’s trip through the checkpoint.

When packing, it is recommended to start to pack with an empty bag, so that travelers are well aware of the contents of their bags. Prior to packing that empty bag, individuals can check TSA’s “What Can I Bring?” tool to know what is prohibited. Individuals who are heading to the beach, may wonder how to pack their sunscreen. Any liquids, sunscreen containers and alcohol over 3.4 ounces must be packed in a checked bag. Liquids, aerosols, gels, creams and pastes are allowed in carry-on bags as long as each item is 3.4 ounces or less and placed in one quart-sized bag . Each passenger is limited to one quart-size bag of liquids, aerosols, gels, creams and pastes.

It is important for individuals who own firearms to remember that they are prohibited to pass through security checkpoints, even if a passenger has a concealed carry permit or is in a constitutional carry jurisdiction. Passengers may travel with a firearm, but it must be secured in the passenger’s checked baggage; packed unloaded; locked in a hard-sided case; and declared to the airline when checking in at the airline ticket counter. If a passenger brings a firearm to the security checkpoint on their person or in their carry-on luggage, TSA will contact local law enforcement to safely unload and take possession of the firearm. Law enforcement may also arrest or cite the passenger, depending on local law. TSA may impose a civil penalty up to $15,000 when weapons are intercepted, and passengers will lose TSA PreCheck® eligibility.

TSA PreCheck® members should make sure that their known traveler number (KTN) is in their airline  reservation. It is essential that airline reservations have the passenger’s correct KTN, full name and date of birth so they can receive the program’s benefits. Those who fly with multiple airlines should ensure their KTN is updated in each of their airline profiles every time they travel. TSA PreCheck passengers are low-risk travelers who do not need to remove shoes, belts, 3-1-1 liquids, food, laptops and light jackets at the TSA checkpoint. TSA’s wait time standards for TSA PreCheck lanes are under 10 minutes and less than 30 minutes for standard lanes. Travelers may visit https://www.tsa.gov/precheck for more information about enrolling or renewing in TSA PreCheck and to find enrollment locations and pricing information for all TSA PreCheck enrollment providers.

“It is also important to remember that our TSA officers are working throughout the summer, including the upcoming July 4th holiday, so respect TSA and other frontline airport and airline employees,” Carter said. “Our officers along with all frontline airport and airline employees and local law enforcement, are working together to ensure safe and secure travel. Consider offering them a kind word of thanks.” 

TSA also reminds travelers that starting on May 7, 2025, if you plan to use your state-issued ID or driver’s license to fly within the U.S., make sure you have a REAL ID or another acceptable form of ID. If you are not sure if you have a REAL ID, check with the New Jersey Motor Vehicle Commission .  For questions on acceptable IDs, visit TSA’s web site. “Put REAL ID on your summer to do list,” Carter recommended.

Travelers can contact TSA with questions may contact TSA by sending a text directly to 275-872 (“AskTSA”) on any mobile device or over social media by sending a message to @AskTSA on X or Facebook Messenger. An automated virtual assistant is available 24/7 to answer commonly asked questions, and AskTSA staff are available 365 days a year from 8 a.m. to 6 p.m. ET for more complicated questions. Travelers may also reach the TSA Contact Center at 866-289-9673. An automated service is available 24/7.

TSA encourages all passengers to remain vigilant. If You See Something. Say Something®.

Why does time change when traveling close to the speed of light? A physicist explains

Assistant Professor of Physics and Astronomy, Rochester Institute of Technology

Disclosure statement

Michael Lam does not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.

Rochester Institute of Technology provides funding as a member of The Conversation US.

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Curious Kids is a series for children of all ages. If you have a question you’d like an expert to answer, send it to [email protected] .

Why does time change when traveling close to the speed of light? – Timothy, age 11, Shoreview, Minnesota

Imagine you’re in a car driving across the country watching the landscape. A tree in the distance gets closer to your car, passes right by you, then moves off again in the distance behind you.

Of course, you know that tree isn’t actually getting up and walking toward or away from you. It’s you in the car who’s moving toward the tree. The tree is moving only in comparison, or relative, to you – that’s what we physicists call relativity . If you had a friend standing by the tree, they would see you moving toward them at the same speed that you see them moving toward you.

In his 1632 book “ Dialogue Concerning the Two Chief World Systems ,” the astronomer Galileo Galilei first described the principle of relativity – the idea that the universe should behave the same way at all times, even if two people experience an event differently because one is moving in respect to the other.

If you are in a car and toss a ball up in the air, the physical laws acting on it, such as the force of gravity, should be the same as the ones acting on an observer watching from the side of the road. However, while you see the ball as moving up and back down, someone on the side of the road will see it moving toward or away from them as well as up and down.

Special relativity and the speed of light

Albert Einstein much later proposed the idea of what’s now known as special relativity to explain some confusing observations that didn’t have an intuitive explanation at the time. Einstein used the work of many physicists and astronomers in the late 1800s to put together his theory in 1905, starting with two key ingredients: the principle of relativity and the strange observation that the speed of light is the same for every observer and nothing can move faster. Everyone measuring the speed of light will get the same result, no matter where they are or how fast they are moving.

Let’s say you’re in the car driving at 60 miles per hour and your friend is standing by the tree. When they throw a ball toward you at a speed of what they perceive to be 60 miles per hour, you might logically think that you would observe your friend and the tree moving toward you at 60 miles per hour and the ball moving toward you at 120 miles per hour. While that’s really close to the correct value, it’s actually slightly wrong.

This discrepancy between what you might expect by adding the two numbers and the true answer grows as one or both of you move closer to the speed of light. If you were traveling in a rocket moving at 75% of the speed of light and your friend throws the ball at the same speed, you would not see the ball moving toward you at 150% of the speed of light. This is because nothing can move faster than light – the ball would still appear to be moving toward you at less than the speed of light. While this all may seem very strange, there is lots of experimental evidence to back up these observations.

Time dilation and the twin paradox

Speed is not the only factor that changes relative to who is making the observation. Another consequence of relativity is the concept of time dilation , whereby people measure different amounts of time passing depending on how fast they move relative to one another.

Each person experiences time normally relative to themselves. But the person moving faster experiences less time passing for them than the person moving slower. It’s only when they reconnect and compare their watches that they realize that one watch says less time has passed while the other says more.

This leads to one of the strangest results of relativity – the twin paradox , which says that if one of a pair of twins makes a trip into space on a high-speed rocket, they will return to Earth to find their twin has aged faster than they have. It’s important to note that time behaves “normally” as perceived by each twin (exactly as you are experiencing time now), even if their measurements disagree.

You might be wondering: If each twin sees themselves as stationary and the other as moving toward them, wouldn’t they each measure the other as aging faster? The answer is no, because they can’t both be older relative to the other twin.

The twin on the spaceship is not only moving at a particular speed where the frame of references stay the same but also accelerating compared with the twin on Earth. Unlike speeds that are relative to the observer, accelerations are absolute. If you step on a scale, the weight you are measuring is actually your acceleration due to gravity. This measurement stays the same regardless of the speed at which the Earth is moving through the solar system, or the solar system is moving through the galaxy or the galaxy through the universe.

Neither twin experiences any strangeness with their watches as one moves closer to the speed of light – they both experience time as normally as you or I do. It’s only when they meet up and compare their observations that they will see a difference – one that is perfectly defined by the mathematics of relativity.

Hello, curious kids! Do you have a question you’d like an expert to answer? Ask an adult to send your question to [email protected] . Please tell us your name, age and the city where you live.

And since curiosity has no age limit – adults, let us know what you’re wondering, too. We won’t be able to answer every question, but we will do our best.

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ComArtSci Alumna Empowers Women Through Travel

Story adapted from an article originally published in Spartan Magazine , Spring 2024.  

Megan Grant is on a lifelong mission to see the world…and to change it at the same time. 

The 2016 communication alumna is the owner of Cherish Tours LLC, a woman-centric travel agency aimed at creating experiences to empower women. 

Grant grew up taking vacations to exotic destinations. A formative solo overseas trip in her teens planted the seeds of her future career. After graduation, Grant worked in the business hospitality industry, where she honed her skills as an event and conference planner.  While the experience sharpened her organizational abilities, it failed to satisfy her ingrained love of travel. 

“Conferences are in-and-out and you don’t really appreciate the places that you’re in,” Grant said. “You go to a conference center, you stay in the hotel and you don’t get anything about the culture,” she said. “Travel in that world was not the enjoyable kind. It was work travel. I was burning out on it.”  

Grant leaned into the skill sets and confidence she gained at MSU to launch her own business. Cherish LLC hosted its first tour in 2021. Her clients have traveled to overseas locations including Costa Rica, Panama, Iceland, Denmark, Tanzania and Turkey. Grant has also organized domestic tours in Utah and Alaska. 

At the core of each trip are women seeking growth and self-fulfillment. 

“There’s something powerful about bringing women from different walks of life, different ages, different communities, all of these people together in a space where they can be their most authentic self,” Grant said.  

Grant coordinates her tour packages with women-owned businesses in each destination.  She’s seen the economic benefits of women supporting women…and that’s how she intends to expand her business model. 

“There are studies that prove when you give a woman a dollar, the effect it spreads in her community is much greater than when you give it to a man,” Grant said. “I believe in the ripple effect of that. The empowerment of not only one person, but many. Supporting women and their dreams creates positive things in the world.”  

By: Kevin Lavery 

Read more on alumni.msu.edu  

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New travel deals for Amazon Prime members on cruises, rental cars, flights and more

These savings on travel come in time for any last-minute summer vacations.

Amazon Prime Day is fast approaching, and beyond viral beauty products or hot new kitchenware, the e-commerce giant is introducing savings on travel just in time for any last-minute summer vacations.

Amazon partnered with various travel companies, including Southwest Airlines, Viator, Turo, Carnival, and others, to give Prime members early access to price cuts on travel packages, car rentals, and cruises.

In a similar move last summer fellow retail competitor Walmart partnered with Expedia to give Walmart+ members the ability to earn Walmart Cash by booking vacations.

"These travel deals are sort of an extra that they can offer their members," RetailMeNot editor Kristin McGrath told ABC News. "There are plenty of ways you can save and get discounts. These membership programs can just make it a little bit easier."

Amazon Prime travel deals and discounts for Prime Day

Save 10% on Viator travel experiences Save up to 30% off Avis car rentals and earn 10% back Up to 15% Sixt car rentals Book a Carnival Cruise for to 40% off Southwest Airlines get 50% off Rapids Rewards points

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Walmart+ travel deals.

The company offers discounts on fuel and travel, plus up to 20% back in Walmart Cash for booking through their portal during Walmart+ week.

Costco travel discounts and deals

The warehouse retailer's travel arm offers everyday savings on top-quality, brand-name vacations, hotels, cruises, and rental cars, exclusively for Costco members.

Teresita Nino has used Costco to book vacation packages and told ABC News how she saved on international deals.

"My last trip that we booked was to Saint Lucia and we ended up booking the airfare and the hotel -- I ended up saving about $700," Nino said of her experience using Costco. "Nine out of ten times is Costco Travel is always giving me a better deal overall than other travel companies."

Access to Costco's travel deals require a paid membership as an extra perk for customers.

"The travel savings are the cherry on top -- but it's not necessarily the most lucrative benefit," McGrath said. "In these membership programs, you have to take the value of membership as a whole rather than just joining to save on travel."

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SME definition

Small and medium-sized enterprises (SMEs) represent 99% of all businesses in the EU. The definition of an SME is important for access to finance and EU support programmes targeted specifically at these enterprises.

What is an SME?

Small and medium-sized enterprises (SMEs) are defined in the EU recommendation 2003/361 .

The main factors determining whether an enterprise is an SME are

• staff headcount
• either turnover or balance sheet total

These ceilings apply to the figures for individual firms only. A firm that is part of a larger group may need to include staff headcount/turnover/balance sheet data from that group too.

Further details include

• The revised user guide to the SME definition (2020) (2 MB, available in all EU languages)
• Declaring your enterprise to be an SME (the form is available in all languages as an annex in the revised user guide)
• The SME self-assessment tool which you can use to determine whether your organisation qualifies as a small and medium-sized enterprise

What help can SMEs get?

There are 2 broad types of potential benefit for an enterprise if it meets the criteria

• eligibility for support under many EU business-support programmes targeted specifically at SMEs: research funding, competitiveness and innovation funding and similar national support programmes that could otherwise be banned as unfair government support ('state aid' – see block exemption regulation )
• fewer requirements or reduced fees for EU administrative compliance

Monitoring of the implementation of the SME definition

The Commission monitors the implementation of the SME definition and reviews it in irregular intervals. Pursuant to the latest evaluation, the Commission concluded that there is no need for a revision.

On 25 October 2021, we informed stakeholders by holding a webinar with presentations on the SME evaluation's results and next steps.

Supporting documents

• Study to map, measure and portray the EU mid-cap landscape (2022)
• Staff working document on the evaluation of the SME definition  (2021)
• Executive summary on the evaluation of the SME definition  (2021)
• Q&A on the evaluation of the SME definition  (2021)
• Final report on evaluation of the SME definition  (2018) (10 MB)
• Final report on evaluation of the SME definition (2012)  (1.8 MB)
• Executive summary on evaluation of the SME definition (2012)  (345 kB)
• Implementing the SME definition (2009)  (50 kB)
• Implementing the SME definition (2006)  (40 kB)

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