faster than light time travel

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:

This Trick Flips Space and Time

By Meddling With Spacetime Dimensions, We Could Finally Reach Warp Speed

New research shows that the “superluminal observer” needs three separate time dimensions for a warp-speed math trick that would please even Galileo.

✅ Quick Facts:

• In new research, the lead scientist explains why just one space and one time aren’t enough for this scenario.
• Symmetry is a physics concept that goes all the way back to Galileo’s time.

The secret to faster-than-light physics could be to double down on the number of dimensions. Specifically, the solution may lie in three dimensions of time , with just one representing space. The math is deep and complicated, but the ideas may be within our grasp after all. And there’s one math trick at superspeeds that may just “flip” your lid.

The key idea at play is that of a “superluminal observer,” according to research published in December 2022 in the journal Classical and Quantum Gravity. “Superluminal” means faster than light, from super - meaning “more” or “most,” and - luminal like, well, Lumière from Beauty and the Beast, and the lumens that power your home movie projector. The superluminal observer is a hypothetical thing that is looking at the universe while traveling faster than light. It’s you in your Star Trek warp-speed shuttle.

Superluminal observers are cool because, in a way, they marry together two very different sides of physics: general relativity and quantum mechanics . General relativity is the work embodied by Albert Einstein, which governs how spacetime functions as bodies move around the universe at subluminal, or slower than light, speeds. Quantum mechanics explains how subatomic particles behave, or don’t behave, in very strange ways on the smallest of scales.

The research team—led by theoretical physicist Andrzej Dragan of the University of Warsaw and the National University of Singapore—has theorized that many parts of quantum physics, like indeterminism and superposition , can be explained if you take general relativity and apply its principles to the superluminal observer. In other words, how messy does spacetime get if we take our shuttle up to warp speed? Is everything suddenly in multiple places at once?

Dragan’s new work indicates that it’s at least a possibility. Perhaps more interestingly, the way general relativity becomes quantum phenomena at speeds greater than light doesn’t seem to introduce any causal paradoxes. In earlier work , published in the New Journal of Physics in March 2020, Dragan and his coauthor studied “just” one space dimension and one time dimension, known as 1+1. In the new paper, the researchers upped the ante to include one space dimension and three time dimensions, or 1+3.

When Time and Space Flip Math

Why do we need three time dimensions? To understand, we have to talk about some math. “[D]espite our common perception, time and space are strikingly similar according to relativity, and mathematically the only difference between them is the minus sign somewhere in the equations,” Dragan explains to Popular Mechanics in an email. That’s a small difference in complicated math, but think of the algebra example of the difference of two squares: x² - 16, for example, is the result of (x - 4)(x + 4). With one flipped sign, the middle term in the polynomial falls away.

But when the observer is going faster than the speed of light, the difference in signs also changes. That’s because time and space must flip in the math. “The time of the superluminal observer becomes space of the subluminal one, and their space becomes time,” Dragan says. In other words, the regular, non-light-speed observer’s space and time turn into the time and space, relatively, of the faster-than-light observer. “So their corresponding signs have to interchange.”

In a 1+1 scenario, that means the two dimensions are the same, making it redundant. If 50 = 50, does it matter which 50 is which? (In logic, we call this a tautology.) That means that if we want to truly study space and time as different things, we have to add a second “set” of two dimensions: space and time 1, together, represent space; while time 2 and time 3, together, represent time . It’s not quite the difference of two squares, but we have two balanced sets of dimensions.

The Symmetry in Physics

There’s another interesting aspect to this research, because Dragan’s team wants to show that even at superluminal speeds, physics shows symmetry.

“The idea of symmetry in physics can be traced back to Galileo,” Dragan says. “He noticed that no matter what velocity we move at, as long as that velocity is constant, our physics remains the same. A parrot flying in a moving ship experiences the same dynamical laws as at ‘rest’ on Earth.”

✅ Galileo Galilei was an influential Italian scientist who lived during the 16th and 17th centuries. As an elderly man, he received a life sentence for going public with his belief that Earth orbited the sun!

But our conceptions of physics are limited by the long-running (and reasonable!) belief that nothing can travel faster than light, Dragan explains. That means the superluminal observer, by definition, exists as a kind of exception into which we must work to extend the idea of symmetry. Does it make sense that a superluminal observer would still be subject to symmetry? Is the parrot traveling faster than light still the same as the parrot in the ship or on Earth?

“We argued that this additional limiting assumption isn’t necessary,” Dragan says. He believes symmetry may extend into faster-than-light speeds, and our parrot friend would be just as affected by the same laws of physics while traveling in the warp-speed shuttle.

Toward a Grand Unified Theory

So, this paper isn’t about traveling at warp speed, but instead an analysis of physics to show how we can bring two very different physics branches together. Why is that, itself, so important?

“The idea of more than one time dimension has been considered by others over the years, so that particular premise is not novel,” Harold “Sonny” White, a onetime NASA physicist and the founder of the Limitless Space Institute (LSI), a group that funds and promotes far-out space travel and physics research, tells Popular Mechanics . “But the mathematical framework developed by the authors in this published paper is unique. It would seem the authors’ perceived benefit from the effort is that it establishes a mathematical basis for why we need a field theoretical framework.”

What is a field theoretical framework? It’s the big picture of physics that can bring everything together. “[I]f we envision the standard models of physics as a Venn diagram, there would be two circles side-by-side that touch at a single tangent point,” White explains. “The idea of a grand unified field theory might be envisioned as a larger circle that encircles both the smaller circles.”

By showing their work, these researchers have pointed out a really specific way in which one big basket of physics—rather than two baskets that we aren’t sure how to carry at the same time—would make more sense in practical and mathematical terms.

Okay, sure, you may be thinking: all this superluminal jabberwocky is interesting. But warp speed itself is science fiction, right? (At least for now: White’s LSI funds education that may eventually lead us elsewhere.) The superluminal observer is just a thought exercise ... right?

Dragan isn’t so sure. “The last remaining question is whether superluminal objects are only a mathematical possibility, or they actually exist in reality,” he concludes. “We believe the latter to be that case, and that is the purpose of our further research.”

That means our warp-speed shuttle, once the most far-out thing science fiction writers could even imagine, could embody an elegant theory that brings together two very different kinds of physics. Indeed, objects in the superluminal mirror may be closer than they appear.

Caroline Delbert is a writer, avid reader, and contributing editor at Pop Mech. She's also an enthusiast of just about everything. Her favorite topics include nuclear energy, cosmology, math of everyday things, and the philosophy of it all. 

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March 9, 2021

Breaking the warp barrier for faster-than-light travel

by University of Göttingen

If travel to distant stars within an individual's lifetime is going to be possible, a means of faster-than-light propulsion will have to be found. To date, even recent research about superluminal (faster-than-light) transport based on Einstein's theory of general relativity would require vast amounts of hypothetical particles and states of matter that have 'exotic' physical properties such as negative energy density. This type of matter either cannot currently be found or cannot be manufactured in viable quantities. In contrast, new research carried out at the University of Göttingen gets around this problem by constructing a new class of hyper-fast 'solitons' using sources with only positive energies that can enable travel at any speed. This reignites debate about the possibility of faster-than-light travel based on conventional physics. The research is published in the journal Classical and Quantum Gravity .

The author of the paper, Dr. Erik Lentz, analyzed existing research and discovered gaps in previous 'warp drive' studies. Lentz noticed that there existed yet-to-be explored configurations of space-time curvature organized into 'solitons' that have the potential to solve the puzzle while being physically viable. A soliton—in this context also informally referred to as a 'warp bubble'—is a compact wave that maintains its shape and moves at constant velocity. Lentz derived the Einstein equations for unexplored soliton configurations (where the space-time metric's shift vector components obey a hyperbolic relation), finding that the altered space-time geometries could be formed in a way that worked even with conventional energy sources. In essence, the new method uses the very structure of space and time arranged in a soliton to provide a solution to faster-than-light travel , which—unlike other research—would only need sources with positive energy densities. No exotic negative energy densities needed.

If sufficient energy could be generated, the equations used in this research would allow space travel to Proxima Centauri, our nearest star, and back to Earth in years instead of decades or millennia. That means an individual could travel there and back within their lifetime. In comparison, the current rocket technology would take more than 50,000 years for a one-way journey. In addition, the solitons (warp bubbles) were configured to contain a region with minimal tidal forces such that the passing of time inside the soliton matches the time outside: an ideal environment for a spacecraft. This means there would not be the complications of the so-called 'twin paradox' whereby one twin traveling near the speed of light would age much more slowly than the other twin who stayed on Earth: in fact, according to the recent equations both twins would be the same age when reunited.

"This work has moved the problem of faster-than-light travel one step away from theoretical research in fundamental physics and closer to engineering. The next step is to figure out how to bring down the astronomical amount of energy needed to within the range of today's technologies, such as a large modern nuclear fission power plant. Then we can talk about building the first prototypes," says Lentz.

Currently, the amount of energy required for this new type of space propulsion drive is still immense. Lentz explains, "The energy required for this drive traveling at light speed encompassing a spacecraft of 100 meters in radius is on the order of hundreds of times of the mass of the planet Jupiter. The energy savings would need to be drastic, of approximately 30 orders of magnitude to be in range of modern nuclear fission reactors." He goes on to say: "Fortunately, several energy-saving mechanisms have been proposed in earlier research that can potentially lower the energy required by nearly 60 orders of magnitude." Lentz is currently in the early-stages of determining if these methods can be modified, or if new mechanisms are needed to bring the energy required down to what is currently possible.

Provided by University of Göttingen

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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.

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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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What is the speed of light? Here’s the history, discovery of the cosmic speed limit

On one hand, the speed of light is just a number: 299,792,458 meters per second. And on the other, it’s one of the most important constants that appears in nature and defines the relationship of causality itself.

As far as we can measure, it is a constant. It is the same speed for every observer in the entire universe. This constancy was first established in the late 1800’s with the experiments of Albert Michelson and Edward Morley at Case Western Reserve University . They attempted to measure changes in the speed of light as the Earth orbited around the Sun. They found no such variation, and no experiment ever since then has either.

Observations of the cosmic microwave background, the light released when the universe was 380,000 years old, show that the speed of light hasn’t measurably changed in over 13.8 billion years.

In fact, we now define the speed of light to be a constant, with a precise speed of 299,792,458 meters per second. While it remains a remote possibility in deeply theoretical physics that light may not be a constant, for all known purposes it is a constant, so it’s better to just define it and move on with life.

How was the speed of light first measured?

In 1676 the Danish astronomer Ole Christensen Romer made the first quantitative measurement of how fast light travels. He carefully observed the orbit of Io, the innermost moon of Jupiter. As the Earth circles the Sun in its own orbit, sometimes it approaches Jupiter and sometimes it recedes away from it. When the Earth is approaching Jupiter, the path that light has to travel from Io is shorter than when the Earth is receding away from Jupiter. By carefully measuring the changes to Io’s orbital period, Romer calculated a speed of light of around 220,000 kilometers per second.

Observations continued to improve until by the 19 th century astronomers and physicists had developed the sophistication to get very close to the modern value. In 1865, James Clerk Maxwell made a remarkable discovery. He was investigating the properties of electricity and magnetism, which for decades had remained mysterious in unconnected laboratory experiments around the world. Maxwell found that electricity and magnetism were really two sides of the same coin, both manifestations of a single electromagnetic force.

As Maxwell explored the consequences of his new theory, he found that changing magnetic fields can lead to changing electric fields, which then lead to a new round of changing magnetic fields. The fields leapfrog over each other and can even travel through empty space. When Maxwell went to calculate the speed of these electromagnetic waves, he was surprised to see the speed of light pop out – the first theoretical calculation of this important number.

What is the most precise measurement of the speed of light?

Because it is defined to be a constant, there’s no need to measure it further. The number we’ve defined is it, with no uncertainty, no error bars. It’s done. But the speed of light is just that – a speed. The number we choose to represent it depends on the units we use: kilometers versus miles, seconds versus hours, and so on. In fact, physicists commonly just set the speed of light to be 1 to make their calculations easier. So instead of trying to measure the speed light travels, physicists turn to more precisely measuring other units, like the length of the meter or the duration of the second. In other words, the defined value of the speed of light is used to establish the length of other units like the meter.

How does light slow down?

Yes, the speed of light is always a constant. But it slows down whenever it travels through a medium like air or water. How does this work? There are a few different ways to present an answer to this question, depending on whether you prefer a particle-like picture or a wave-like picture.

In a particle-like picture, light is made of tiny little bullets called photons. All those photons always travel at the speed of light, but as light passes through a medium those photons get all tangled up, bouncing around among all the molecules of the medium. This slows down the overall propagation of light, because it takes more time for the group of photons to make it through.

In a wave-like picture, light is made of electromagnetic waves. When these waves pass through a medium, they get all the charged particles in motion, which in turn generate new electromagnetic waves of their own. These interfere with the original light, forcing it to slow down as it passes through.

Either way, light always travels at the same speed, but matter can interfere with its travel, making it slow down.

Why is the speed of light important?

The speed of light is important because it’s about way more than, well, the speed of light. In the early 1900’s Einstein realized just how special this speed is. The old physics, dominated by the work of Isaac Newton, said that the universe had a fixed reference frame from which we could measure all motion. This is why Michelson and Morley went looking for changes in the speed, because it should change depending on our point of view. But their experiments showed that the speed was always constant, so what gives?

Einstein decided to take this experiment at face value. He assumed that the speed of light is a true, fundamental constant. No matter where you are, no matter how fast you’re moving, you’ll always see the same speed.

This is wild to think about. If you’re traveling at 99% the speed of light and turn on a flashlight, the beam will race ahead of you at…exactly the speed of light, no more, no less. If you’re coming from the opposite direction, you’ll still also measure the exact same speed.

This constancy forms the basis of Einstein’s special theory of relativity, which tells us that while all motion is relative – different observers won’t always agree on the length of measurements or the duration of events – some things are truly universal, like the speed of light.

Can you go faster than light speed?

Nope. Nothing can. Any particle with zero mass must travel at light speed. But anything with mass (which is most of the universe) cannot. The problem is relativity. The faster you go, the more energy you have. But we know from Einstein’s relativity that energy and mass are the same thing. So the more energy you have, the more mass you have, which makes it harder for you to go even faster. You can get as close as you want to the speed of light, but to actually crack that barrier takes an infinite amount of energy. So don’t even try.

How is the speed at which light travels related to causality?

If you think you can find a cheat to get around the limitations of light speed, then I need to tell you about its role in special relativity. You see, it’s not just about light. It just so happens that light travels at this special speed, and it was the first thing we discovered to travel at this speed. So it could have had another name. Indeed, a better name for this speed might be “the speed of time.”

Related: Is time travel possible? An astrophysicist explains

We live in a universe of causes and effects. All effects are preceded by a cause, and all causes lead to effects. The speed of light limits how quickly causes can lead to effects. Because it’s a maximum speed limit for any motion or interaction, in a given amount of time there’s a limit to what I can influence. If I want to tap you on the shoulder and you’re right next to me, I can do it right away. But if you’re on the other side of the planet, I have to travel there first. The motion of me traveling to you is limited by the speed of light, so that sets how quickly I can tap you on the shoulder – the speed light travels dictates how quickly a single cause can create an effect.

The ability to go faster than light would allow effects to happen before their causes. In essence, time travel into the past would be possible with faster-than-light travel. Since we view time as the unbroken chain of causes and effects going from the past to the future, breaking the speed of light would break causality, which would seriously undermine our sense of the forward motion of time.

Why does light travel at this speed?

No clue. It appears to us as a fundamental constant of nature. We have no theory of physics that explains its existence or why it has the value that it does. We hope that a future understanding of nature will provide this explanation, but right now all investigations are purely theoretical. For now, we just have to take it as a given.

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[Physics FAQ] - [Copyright]

By Philip Gibbs, 1997, 1998.

It might be thought that special relativity provides a short negative answer to this question.  In actual fact, there are many trivial ways in which things can be going faster than light (FTL) in a sense, and there may be other more genuine possibilities.  On the other hand, there are also good reasons to believe that real FTL travel and communication will always be unachievable.  This article is not a full answer to the question (which no doubt will continue to be discussed in the newsgroups for the foreseeable future), but it does cover some of the more common points that are repeatedly made.

It is sometimes objected that "they said no-one would ever go faster than sound and they were wrong.  Now they say no-one will ever go faster than light..."   Actually it is probably not true that anybody said it was impossible to go faster than sound.  It was known that rifle bullets go faster than sound long before an aircraft did.  The truth is that some engineers once said that controlled flight faster than sound might be impossible, and they were wrong about that.  FTL travel is a very different matter.  It was inevitable that someone would one day succeed in flying faster than sound, once technology got around the problems.  It is not inevitable that one day technology will enable us to go faster than light.  Relativity has a lot to say about this.  If FTL travel or FTL communication were possible, then causality would probably be violated and some very strange situations would arise.

First we will cover the trivial ways in which things can go FTL.  These points are mentioned not because they are interesting, but because they come up time and time again when FTL is being discussed, and so they are necessary to deal with.  Then we will think about what we mean by non-trivial FTL travel/communication and examine some of the arguments against it.  Finally, we will look at some of the more serious proposals for real FTL.  Many of these things are discussed in more detail elsewhere in the FAQ and hyper-links are provided.  The sections are numbered so that they can be referred to individually.

Trivial FTL Travel

1. cherenkov effect.

One way to go faster than light is to make the light slow down!  Light in vacuum travels at a speed c which is a universal constant (see the FAQ entry Is the speed of light constant? ), but in a dense medium such as water or glass, light slows down to c/n where n is the refractive index of the medium (1.0003 for air, 1.4 for water).  It is certainly possible for particles to travel through air or water faster than light travels in that medium, and Cherenkov radiation is produced as a result.  See the FAQ entry Is there an equivalent of the sonic boom for light? .

When we discuss moving faster than light, we are really talking about exceeding the speed of light in vacuum c (299,792,458 m/s).  The Cherenkov effect is thus not considered to be a real example of FTL travel.

2. Third-Party Observers

If a rocket A is travelling away from me at 0.6c in a westerly direction, and another B is travelling away from me at 0.6c in an easterly direction, then the total distance between A and B as seen in my frame of reference is increasing at 1.2c .  An apparent relative speed greater than c can be observed by a third person in this way.

But this is not what is normally meant by relative speeds.  The true speed of rocket A relative to rocket B is the speed at which an observer in rocket B observes his distance from A to be increasing.  The two speeds must be added using the relativistic formula for addition of velocities.  (See the FAQ entry How do You Add Velocities in Special Relativity? )  In this case the relative speed is actually about 0.88c , so this is not an example of FTL travel.

3. Shadows and Light Spots

Think about how fast a shadow can move.  If you project the shadow of your finger using a nearby lamp onto a distant wall and then wag your finger, the shadow will move much faster than your finger.  If your finger moves parallel to the wall, the shadow's speed will be multiplied by a factor D/d where d is the distance from the lamp to your finger, and D is the distance from the lamp to the wall.  The speed can even be much faster than this if the wall is at an angle to your finger's motion.  If the wall is very far away, the movement of the shadow will be delayed because of the time it takes light to get there, but the shadow's speed is still increased by the same ratio.  The speed of a shadow is therefore not restricted to be less than the speed of light.

This behaviour of a shadow is all about the arrival of successive "pieces of light" (photons, if you will) at a screen.  It is really no different to the faster-than-light speed of a spot on the Moon's surface caused by a laser that has been aimed at that surface and is being waved around on Earth.  Given that the distance to the Moon is 385,000 km, try working out the speed of that spot if you wave the laser at a gentle speed.  You might also like to think about a water wave arriving obliquely at a long straight beach.  How fast can the point at which the wave is breaking travel along the beach?

This sort of thing turns up in Nature; for example, the beam of light from a pulsar can sweep across a dust cloud.  A bright explosion emits an expanding spherical shell of light or other radiation.  When this shell intersects a surface, it creates a circle of light which expands faster than light.  A natural example of this has been observed when an electromagnetic pulse from a lightning flash hits an upper layer of the atmosphere.

These are all examples of "things" that seem to be moving faster than light.  In reality, no object or signal is moving faster that light here.  For a more prosaic example, imagine squirting water from a garden hose at a fence, and moving your aim from one end of the fence to the other.  The intersection point of water stream and fence moves quickly, but of course no thing or signal is really moving along the fence.  A succession of water molecules strikes the fence, but their speed of travel has nothing to do with how quickly you move the hose.  It is a kind of optical illusion for us to think that the wet spot advancing along the fence is a moving object or signal.  The ban in relativity against faster-than-light travel actually concerns the speed of signals (which includes material objects and waves): in a vacuum, no signal is allowed to move faster than light moves in its vicinity.  Neither a moving shadow, nor a laser spot, nor a wet spot on a fence, constitute a signal that is being sent from the initial position of those spots to the final position.  Since these moving spots don't constitute a signal, they are all allowed to move faster than light.  This is not really what we mean by faster-than-light travel, although it shows how difficult it is to define what we really do mean by faster-than-light travel.  See also the FAQ The Superluminal Scissors .

4. Rigid Bodies

If you have a long rigid stick and you hit one end, wouldn't the other end have to move immediately?  Would this not provide a means of FTL communication?

Well, it would if there were such things as perfectly rigid bodies.  In practice the effect of hitting one end of the stick propagates along it at the speed of sound in the material; this speed depends on the stick's elasticity and density.  Relativity places an absolute limit on material rigidity in such a way that the speed of sound in the material will not be greater than c .

The same principle applies if you hold a long string or rod vertically in a gravitational field and let go of the top end.  The point at which you let go will start to move immediately, but the lower end cannot move until the effect has propagated down the length.  That speed of propagation depends on the nature of the material and the strength of the gravitational field.

It is difficult to formulate a general theory of elastic materials in relativity, but the general principle can be illustrated with newtonian mechanics.  The equation for longitudinal motion in an ideal elastic body can be derived from Hooke's law.  In terms of the mass per unit length p and Young's modulus of elasticity Y , the longitudinal displacement X satisfies a wave equation (see for example Goldstein's "Classical Mechanics"):

Plane wave solutions travel at the speed of sound s where s 2 = Y/p .  This wave equation does not allow any causal effect to propagate faster than s .  Relativity therefore imposes a limit on elasticity: Y < pc 2 .  In practice, no known material comes anywhere near this limit.  Note that even if the speed of sound is near c , the matter does not necessarily move at relativistic speeds.  But how can we know that no material can possibly exceed this limit?  The answer is that all materials are made of particles whose interaction are governed by the standard model of particle physics, and no influence faster than light can propagate in that model (see the section on Quantum Field Theory below).

So although there is no such thing as a rigid body, there is such a thing as rigid body motion; but this is another example in the same category as the shadows and light spots described above which do not give FTL communication.  (See also the FAQ articles The Superluminal Scissors and The Rigid Rotating Disk in Relativity ).

5. Phase, Group, and Signal Velocities

Look at this wave equation:

This has solutions of the form:

These solutions are sine waves propagating with a speed

But this is faster than light, so is this the equation for a tachyon field?  (See the paragraph on tachyons below ).  No, it is the usual relativistic equation for an ordinary particle with mass!

Superluminal speeds such as this present no problem once we recognise three types of speed associated with wave motion: phase velocity , group velocity , and signal velocity .  Phase velocity is the velocity of waves that have well-defined wavelengths, and it often varies as a function of this wavelength.  We can combine ("superpose") waves of different wavelengths to build a wave packet , a blob of some specified extent over which the wave disturbance is not small.  This packet does not have a well-defined wavelength, and because it usually spreads out as it travels, it doesn't have a well-defined velocity either; but it does have representative velocity, and this is called its group velocity, which will usually be less than c .  Each of the packet's constituent wave trains travels with its own individual phase velocity, which in some instances will be greater than c .  But it is only possible to send information with such a wave packet at the group velocity (the velocity of the blob), so the phase velocity is yet another example of a speed faster than light that cannot carry a message.

In some situations, we can build a fairly exotic wave packet whose group velocity is greater than c .  Does this then constitute an example of information being sent at a speed faster than light?  It turns out that for these packets, information does not travel at the group velocity; instead, it travels at the signal velocity , which has to do with the time of arrival of the initial rise of the wave front as it reaches its destination.  You might not now be surprised to learn that the signal velocity turns out always to be less than c .

6. Superluminal Galaxies

If something is coming towards you at nearly the speed of light and you measure its apparent speed without taking into account the diminishing time it takes light to reach you from the object, you can get an answer that is faster than light.  This is an optical illusion, and is not due to the object's moving at FTL.  See the FAQ Apparent Superluminal Velocity of Galaxies .

7. Relativistic Rocket

A controller based on Earth is monitoring a space ship moving away at a speed 0.8c .  According to the theory of relativity, he will observe a time dilation that slows the ship's clocks by a factor of 5/3, even after he has taken into account the Doppler shift of signals coming from the space ship.  If he works out the distance moved by the ship divided by the time elapsed as measured by the onboard clocks, he will get an answer of 4/3 c .  He infers from this that the ship's occupants determine themselves to be traversing the distances between stars at speeds greater than the speed of light when measured with their clocks.  From the point of view of the occupants their clocks undergo no slowing; rather, they maintain that it is the distance between the stars which has contracted by a factor of 5/3.  So they also agree that they are covering the known distances between stars at 4/3 c .

This is a real effect which in principle could be used by space travellers to cover very large distances in their lifetimes.  If they accelerate at a constant acceleration equal to the acceleration due to gravity on Earth, they would not only have a perfect artificial gravity on their ship, but would also be able to cross the galaxy in only about 12 years of their own "proper time": that is, they would age 12 years during the journey.  See the FAQ What are the Equations for the Relativistic Rocket?

Nevertheless, this is not true FTL travel.  The effective speed calculated used the distance in one reference frame and the time in another.  This is no way to calculate a speed.  Only the occupants of the ship benefit from this effective speed.  The controller will not measure them to be travelling large distances in his own lifetime.

8. Speed of Gravity

Some people have argued that the speed of gravity in a gravitationally bound system is much greater than c or even infinite.  In fact, gravitational effects and gravitational waves travel at the speed of light c .  See the articles Does Gravity Travel at the Speed of Light? and What is Gravitational Radiation? for the explanation.

9. EPR Paradox

In 1935 Einstein, Podolsky, and Rosen published a thought experiment that seemed to produce a paradox in quantum mechanics, as well as demonstrating that it was incomplete.  Their argument used the fact that there can be an apparent instantaneous interaction in the measurement of two separated particles that have been prepared in a certain "entangled" manner.  Einstein called it "spooky action at a distance".  It has been shown by Eberhard that no information can be passed using this effect; so there is no FTL communication, but the paradox is still very controversial.  See the FAQ article The EPR Paradox and Bell's Inequality for more details.

10. Virtual Photons

In quantum field theory forces are mediated by "virtual particles".  The Heisenberg Uncertainty Principle allows these virtual particles to move faster than light.  But virtual particles are not called "virtual" for nothing.  They are only part of a convenient mathematical notation, and once again, no real FTL travel or communication is possible.  See the FAQ Virtual Particles .

11. Quantum Tunnelling

Quantum Tunnelling is the quantum mechanical effect that permits a particle to pass through a barrier when it does not have enough energy to do so classically.  You can do a calculation of the time it takes a particle to tunnel through such a barrier.  The answer you get can come out less than the time it takes light to cover the distance at speed c .  Does this provide a means of FTL communication? Ref: T. E. Hartman, J. Appl. Phys. 33 , 3427 (1962).

The answer must surely be "No!"—otherwise our understanding of QED is very suspect.  Yet a group of physicists have performed experiments that seem to suggest that FTL communication by quantum tunneling is possible.  They claim to have transmitted Mozart's 40th Symphony through a barrier 11.4cm wide at a speed of 4.7 c .  Their interpretation is, of course, very controversial.  Most physicists say this is a quantum effect where no information can actually be passed at FTL speeds.  If the effect is real it is difficult to see why it should not be possible to transmit signals into the past by placing the apparatus in a fast-moving frame of reference. Refs: W. Heitmann and G. Nimtz, Phys. Lett. A196 , 154 (1994); A. Enders and G. Nimtz, Phys. Rev. E48 , 632 (1993).

Terence Tao has pointed out that apparent FTL transmission of an audio signal over such a short distance is not very impressive.  The signal takes less than 0.4 ns to travel the 11.4 cm at light speed, but it is quite easy to anticipate an audio signal ahead of time by up to 1000 ns simply by extrapolating the signal waveform.  Although this is not what is being done in the above experiments, it does illustrate that the experimenters will need to use a much higher frequency random signal, or transmit over much larger distances, if they are to demonstrate FTL information transfer convincingly.

The likely conclusion is that there is no real FTL communication taking place, and that the effect is another manifestation of the Heisenberg Uncertainty Principle.

12. Casimir Effect

The Casimir Effect describes the fact that a very small but measurable force exists between two uncharged conducting plates when they are very close together.  It is due to the existence of vacuum energy (see the FAQ article on the Casimir Effect ).  A surprising calculation by Scharnhorst suggests that photons travelling across the gap between the plates in the Casimir Effect must go faster than c by a very very small amount (at best 1 part in 10 24 for a 1 nanometre gap.) It has been suggested that in certain cosmological situations, such as in the vicinity of cosmic strings if they exist, the effect could be much more pronounced.  Even so, further theoretical investigations have shown that, once again, there is no possibility of FTL communication using this effect. Refs: K. Scharnhorst, Physics Letters B236 , 354 (1990) S. Ben-Menahem, Physics Letters B250 , 133 (1990) Andrew Gould (Princeton, Inst. Advanced Study). IASSNS-AST-90-25 Barton & Scharnhorst, J. Phys. A26 , 2037 (1993).

13. Expansion of the Universe

According to Hubble's Law, two galaxies that are a distance D apart are moving away from each other at a speed HD , where H is Hubble's constant.  So this interpretation of Hubble's Law implies that two galaxies separated by a distance greater than c/H must be moving away from each other faster than light.  Actually, the modern viewpoint describes this situation differently: general relativity takes the galaxies as being at rest relative to one another, while the space between them is expanding.  In that sense, the galaxies are not moving away from each other faster than light; they are not moving away from each other at all!  This change of viewpoint is not arbitrary; rather, it's in accord with the different but very fruitful view of the universe that general relativity provides.  So the distance between two objects can be increasing faster than light because of the expansion of the universe, but this does not mean, in fact, that their relative speed is faster than light.

As was mentioned above, in special relativity it is possible for two objects to be moving apart by speeds up to twice the speed of light as measured by an observer in a third frame of reference.  In general relativity even this limit can be surpassed, but it will not then be possible to observe both objects at the same time.  Again, this is not real faster-than-light travel; it will not help anyone to travel across the galaxy faster than light.  All that is happening is that the distance between two objects is increasing faster when taken in some cosmological reference frame.

14. The Moon revolves round my head faster than light!

Stand up in a clear space and spin round.  It is not too difficult to turn at one revolution each two seconds.  Suppose the Moon is on the horizon.  How fast is it spinning round your head?  It is about 385,000 km away, so the answer is 1.21 million km/s, which is more than four times the speed of light!  It might sound ridiculous to say that the Moon is going round your head when really it is you who is turning, but according to general relativity all co-ordinate systems are equally valid, including rotating ones.  So isn't the Moon going faster than light?

What it comes down to is the fact that velocities in different places cannot be compared directly in general relativity.  Notice that the Moon is not overtaking any light in its own locality.  The speed of the Moon can only be compared to the speeds of other objects in its own locality.  Indeed, the concept of speed is not a very useful one in general relativity, and this makes it difficult to define what "faster than light" means.  Even the statement that "the speed of light is constant" is open to interpretation in general relativity.  Einstein himself, on page 76 of his book "Relativity: the Special and the General Theory", wrote that the statement cannot claim unlimited validity.  When there is no absolute definition of time and distance it is not so clear how speeds should be determined.

Nevertheless, the modern interpretation is that the speed of light is constant in general relativity and this statement is a tautology given that standard units of distance and time are tied together using the speed of light.  The Moon is given to be moving slower than light because it remains within the "future light cone" propagating from its position at any instant.

Relativity Arguments Against FTL Travel

15. what does "faster than light" mean.

The cases given so far only demonstrate how difficult it is to pin down exactly what we mean by FTL travel or communication.  If we do not include things such as moving shadows, then what exactly do we mean by FTL?

In relativity there is no such thing as absolute velocity, only relative velocity; but there is a clear distinction between "world lines" that are "timelike", "lightlike", and "spacelike".  By "world line" we mean a curve traced out in the four dimensions of space-time.  Such a curve is the set of all events that make up the history of a particle.  If a world line is spacelike then it describes something moving faster than light.  So there is a clear meaning of what is meant by a "faster-than-light" speed which does not depend on the existence of third-party observers.

But what do we mean by an "object" if we don't want to include shadows?  We could define an object to be anything that carries energy, charge, spin, or information; or perhaps just that it must be made of atoms, but there are technical problems in each case.  In general relativity energy cannot be localised, so we had better avoid using energy in our definition.  Charge and spin can be localised, but not every object need have charge or spin.  Using the concept of information is better but tricky to define, and sending information faster than light is really just FTL communication—not FTL travel.  Another difficulty is knowing whether an object seen at A is the same as the one that was earlier seen at B when we claim that it has travelled across the gap faster than light.  Could it not be a duplicate?  It could even be argued that FTL communication makes FTL travel possible, because you can send the blueprint for an object FTL as advance information, and then reconstruct the object—although not everyone would accept such teleportation as FTL travel.

The problems of specifying just what we mean by FTL are more difficult in general relativity.  A valid form of FTL travel may mean distorting space-time (e.g. making a worm hole) to get from A to B without going on a spacelike curve locally.  There is a distinction between going faster than light locally and getting from A to B faster than light globally .  When a gravitational lens bends the light coming from a distant galaxy asymmetrically, the light coming round the galaxy on one side reaches us later than light that left at the same time and went round the other side.  We must avoid a definition of FTL travel that says a particle going from A to B gets there before light that has made the same journey along a lightlike geodesic.  This makes it very difficult, perhaps impossible, to define global FTL travel unambiguously.

If you were expecting me to finish this section with a precise definition of what is meant by FTL travel and FTL communication, I am afraid I must disappoint you!  The above difficulties are insurmountable.  Nonetheless, you will probably recognise the real thing when confronted with it now that I have given some examples of what would not be FTL travel.

16. The Infinite-Energy Argument

When Einstein wrote down his postulates for special relativity, he did not include the statement that you cannot travel faster than light.  There is a misconception that it is possible to derive it as a consequence of the postulates he did give.  Incidentally, it was Henri Poincare who said "Perhaps we must construct a new mechanics [...] in which the speed of light would become an impassable limit."  That was in an address to the International Congress of Arts and Science in 1904—before Einstein announced special relativity in 1905.

It is a consequence of relativity that the energy of a particle of rest mass m moving with speed v is given by

As the speed approaches the speed of light, the particle's energy approaches infinity.  Hence it should be impossible to accelerate an object with rest mass to the speed of light; also, particles with zero rest mass must always move at exactly the speed of light, since otherwise they would have no energy.  This is sometimes called the "light speed barrier", but it is very different from the "sound speed barrier".  As an aircraft approaches the speed of sound it starts to feel pressure waves which indicate that it is moving close to the speed of sound, and before the existence and effects of these waves were well understood, they destroyed several aircraft in the mid 20th century; hence the old name of sound "barrier".  In fact, with more thrust and the right aerodynamics, an aircraft can certainly pass through the sound barrier.

The situation is different for light.  As the light speed barrier is approached (in a perfect vacuum) there are no such waves according to relativity (destructive or otherwise).  Moving at 0.999 c is just like standing still with everything rushing past you at −0.999 c .  Particles are routinely pushed to these speeds and beyond in accelerators, so the theory is well established.  Trying to attain the speed of light in this way is a matter of chasing something that is forever just out of your reach.

This explains why it is not possible to exceed the speed of light by ordinary mechanical means.  But it does not in itself rule out FTL travel.  It is really just one way in which things cannot be made to go faster than light, rather than a proof that there is no way to do so.  Particles are known to decay instantly into other particles which fly off at high speed.  It is not necessary to think in terms of the particles' having been accelerated, so how could we say that they could not go faster than light?  What about the possibility of particles that might always have been moving faster than light, and which might be used to send information if they can be detected without ever slowing down to less than the speed of light?  Even if such "tachyons" don't exist (and we don't believe that they do exist), there may be ways of moving matter from A to B faster than light is able to travel from A to B by the usual route, but without anything having to go at a FTL speed locally.  See the paragraph on tachyons below .

17. Quantum Field Theory

Except for gravity, all physical phenomena are observed to comply with the "Standard Model" of particle physics.  The Standard Model is a relativistic quantum field theory which incorporates the nuclear and electromagnetic forces as well as all the observed particles.  In this theory, any pair of operators corresponding to physical observables at space-time events separated by a spacelike interval "commute" (i.e. their order can be reversed).  In principle, this implies that effects cannot propagate faster than light in the standard model, and it can be regarded as the quantum field theory equivalent of the infinite energy argument.

But no completely rigorous proofs of anything exist in the quantum field theory of the Standard Model, since no one has yet succeeded in showing that the theory is completely self consistent; and in fact, most likely it is not!  In any case, there is no guarantee that there are not other undiscovered particles and forces that disobey the no-FTL rule.  Nor is there any generalisation that takes gravity and general relativity into account.  Many physicists working on quantum gravity doubt that such simplistic expressions of causality and locality will be generalised.  All told, there is no guarantee that light speed will be meaningful as a speed limit in a more complete theory that might arise in the future.

18. Grandfather Paradox

A better argument against FTL travel is the Grandfather Paradox.  In special relativity, a particle moving FTL in one frame of reference will be travelling back in time in another.  FTL travel or communication should therefore also give the possibility of travelling back in time or sending messages into the past.  If such time travel is possible, you would be able to go back in time and change the course of history by killing your own grandfather.  This is a very strong argument against FTL travel, but it leaves open the perhaps-unlikely possibility that we may be able to make limited journeys at FTL speed that did not allow us to come back.  Or it may be that time travel is possible and causality breaks down in some consistent fashion when FTL travel is achieved.  That is not very likely either, but if we are discussing FTL then we had better keep an open mind.

Conversely, if we could travel back in time we might also claim the ability to travel FTL, because we can go back in time and then travel at a slow speed to arrive somewhere before light got there by the usual route.  See the FAQ article on Time Travel for more on this subject.

Open Possibilities for FTL Travel

In this last section I give a few of the speculative but serious suggestions for possible faster-than-light travel.  These are not the kinds of thing usually included in the FAQ because they raise more questions than answers.  They are included merely to make the point that serious research is being done in this direction.  Only a brief introduction to each topic is given; more information can be found all over the Internet (and should, like almost everything on the Internet, be taken with a huge grain of salt!).

19. Tachyons

Tachyons are hypothetical particles that travel faster than light locally.  Their mass must take on imaginary values (i.e. to do with the square root of −1) to be able to do so, but they have real-valued energy and momentum.  Sometimes people imagine that such FTL particles would be impossible to detect, but there is no reason to think so.  Shadows and spotlights suffice to show that there is no logic in this suggestion, because they can certainly go FTL and still be seen.

No tachyons have definitely been found and most physicists doubt their existence.  There has been a claim that experiments to measure neutrino mass in tritium beta decay indicated that the neutrinos were tachyonic. ; while this is very doubtful, it is not entirely ruled out.  Tachyon theories have problems because, apart from the possibility of causality violations, they destabilise the vacuum.  It may be possible to get around such difficulties—but then we would not be able to use tachyons for the kind of FTL communication that we would like.

The truth is that most physicists consider tachyons to be a sign of pathological behaviour in field theories, and the interest in them among the wider public stems mostly from the fact that they are used so often in science fiction.  See the FAQ article on Tachyons .

20. Worm Holes

A famous proposition for global FTL travel is to use "worm holes".  Worm holes are shortcuts through space-time from one place in the universe to another which would permit you to go from one end to the other in a shorter time than it would take light passing by the usual route.  Worm holes are a feature of classical general relativity, but to create them you have to change the topology of space-time.  That might be possible within a theory of quantum gravity.

To keep a worm hole open, regions of negative energy would be needed.  Misner and Thorne have suggested using the Casimir Effect on a grand scale to generate the negative energy, while Visser has proposed a solution involving cosmic strings.  These are very speculative ideas which may simply not be possible.  Exotic matter with negative energy may not exist in the form required.

Thorne has found that if worm holes can be created, then they can be used to construct closed timelike loops in space-time which would imply the possibility of time travel.  It has been suggested that the "multiverse" interpretation of quantum mechanics (many universes co-existing) gets you out of trouble by allowing time to evolve differently if you succeed in going back to a previous time.  But multiverses are entirely out of keeping with the Ockham's Razor approach to doing science, and constitute more of a popular interpretation of quantum mechanics than a serious physical theory.  Hawking says that worm holes would simply be unstable and therefore unusable.  The subject remains a fertile area for thought experiments that help clarify what is and what is not possible according to known and suggested laws of physics. Refs: W. G. Morris and K. S. Thorne, American Journal of Physics 56 , 395–412 (1988) W. G. Morris, K. S. Thorne, and U. Yurtsever, Phys. Rev. Letters 61 , 1446–9 (1988) Matt Visser, Physical Review D39 , 3182–4 (1989) See also "Black Holes and Time Warps", Kip Thorne, Norton & co. (1994) For an explanation of the multiverse see "The Fabric of Reality" David Deutsch, Penguin Press.

21. Warp Drives

A "warp drive" such as used in the Star Trek science fiction series would be a mechanism for warping space-time in such a way that an object could move faster than light.  Miguel Alcubierre made himself famous by working out a space-time geometry which describes such a warp drive.  The warp in space-time makes it possible for an object to go FTL while remaining on a timelike curve.  The main catch is the same one that may stop us making large worm holes.  To make such a warp, you would need exotic matter with negative energy density.  Even if such exotic matter can exist, it is not clear how it could be deployed to make the warp drive work. Ref.   M. Alcubierre, Classical and Quantum Gravity, 11 , L73–L77, (1994). Ref.   S. Finazzi, S. Liberati, C. Barcel�, Semiclassical instability of dynamical warp drives at arxiv.org.

• To begin with, it is rather difficult to define exactly what is really meant by FTL travel and FTL communication.  Many things such as shadows can go FTL, but not in a useful way that can carry information.
• There are several serious possibilities for real FTL which have been proposed in the scientific literature, but these always come with technical difficulties.
• The Heisenberg Uncertainty Principle tends to stop the use of apparent FTL quantum effects for sending information or matter.
• In general relativity there are potential means of FTL travel, but they may be impossible to make work.  It is thought highly unlikely that engineers will be building space ships with FTL drives in the foreseeable future, if ever, but it is curious that theoretical physics as we presently understand it seems to leave the door open to the possibility.
• FTL travel of the sort science fiction writers would like is almost certainly impossible.  For physicists the interesting question is "why is it impossible and what can we learn from that?"

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What If You Traveled Faster Than the Speed of Light?

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When we were kids, we were amazed that Superman could travel "faster than a speeding bullet." We could even picture him, chasing down a projectile fired from a weapon, his right arm outstretched, his cape rippling behind him. If he traveled at half the bullet 's speed, the rate at which the bullet moved away from him would halve. If he did indeed travel faster than the bullet, he would overtake it and lead the way. Go, Superman!

In other words, Superman's aerial antics obeyed Newton's views of space and time : that the positions and motions of objects in space should all be measurable relative to an absolute, nonmoving frame of reference [source: Rynasiewicz ].

In the early 1900s, scientists held firm to the Newtonian view of the world. Then a German-born mathematician and physicist by the name of Albert Einstein came along and changed everything. In 1905, Einstein published his theory of special relativity , which put forth a startling idea: There is no preferred frame of reference. Everything, even time, is relative.

Two important principles underpinned his theory. The first stated that the same laws of physics apply equally in all constantly moving frames of reference. The second said that the speed of light — about 186,000 miles per second (300,000 kilometers per second) — is constant and independent of the observer's motion or the source of light. According to Einstein, if Superman were to chase a light beam at half the speed of light, the beam would continue to move away from him at exactly the same speed [source: Stein , AMNH.org ].

These concepts seem deceptively simple, but they have some mind-bending implications. One of the biggest is represented by Einstein's famous equation, E = mc², where E is energy, m is mass and c is the speed of light.

According to this equation, mass and energy are the same physical entity and can be changed into each other. Because of this equivalence, the energy an object has due to its motion will increase its mass. In other words, the faster an object moves, the greater its mass. This only becomes noticeable when an object moves really quickly. If it moves at 10 percent the speed of light, for example, its mass will only be 0.5 percent more than normal. But if it moves at 90 percent the speed of light, its mass will double [source: LBL.gov ].

As an object approaches the speed of light, its mass rises precipitously. If an object tries to travel 186,000 miles per second, its mass becomes infinite, and so does the energy required to move it. For this reason, no normal object can travel as fast or faster than the speed of light.

That answers our question, but let's have a little fun and modify the question slightly.

Almost As Fast As the Speed of Light?

We covered the original question, but what if we tweaked it to say, "What if you traveled almost as fast as the speed of light?" In that case, you would experience some interesting effects. One famous result is something physicists call time dilation , which describes how time runs more slowly for objects moving very rapidly. If you flew on a rocket traveling 90 percent of light-speed, the passage of time for you would be halved. Your watch would advance only 10 minutes, while more than 20 minutes would pass for an Earthbound observer [source: May ]

You would also experience some strange visual consequences. One such consequence is called aberration , and it refers to how your entire field of view would shrink down to a tiny, tunnel-shaped "window" out in front of your spacecraft. This happens because photons (those exceedingly tiny packets of light) — even photons behind you — appear to come in from the forward direction.

In addition, you would notice an extreme Doppler effect , which would cause light waves from stars in front of you to crowd together, making the objects appear blue. Light waves from stars behind you would spread apart and appear red. The faster you go, the more extreme this phenomenon becomes until all visible light from stars in front of the spacecraft and stars to the rear become completely shifted out of the known visible spectrum (the colors humans can see). When these stars move out of your perceptible wavelength, they simply appear to fade to black or vanish against the background.

Of course, if you want to travel faster than a speeding photon, you'll need more than the same rocket technology we've been using for decades.

In a March 2021 paper published in the journal Classical and Quantum Gravity , astrophysicist Erik Lentz of the University of Göttingen in Germany proposed the idea of rearranging space-time to create a warp bubble, inside which a spacecraft might be able to travel at faster-than-light speeds.

Speed of Light FAQ

Is there anything faster than the speed of light, how fast is the speed of light in miles, why is "c" the speed of light, what is the speed of light on earth, lots more information, related articles.

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• American Museum of Natural History. "A Matter of Time. " Amnh.org. (Feb. 16, 2022) https://www.amnh.org/exhibitions/einstein/time/a-matter-of-time
• Brandeker, Alexis. "What would a relativistic interstellar traveler see?" Usenet Physics FAQ. May 2002. (Feb. 16, 2022J) http://www.desy.de/user/projects/Physics/Relativity/SR/Spaceship/spaceship.html
• Carl Sagan's Cosmos. "Travels in Space and Time." YouTube. Video uploaded Nov. 27, 2006 (Feb. 16, 2022 ) https://www.youtube.com/watch?v=2t8hUaaZVJg
• Hawking, Stephen. "The Illustrated Brief History of Time. " Bantam. 1996. (Feb. 16. 2022) https://bit.ly/367UGpZ
• EurekAlert! "Breaking the warp barrier for faster-than-light travel. " Eurekalert.org. March 9, 2021. (Feb. 16, 2022) https://www.eurekalert.org/news-releases/642756
• Lawrence Berkeley National Laboratory. "Mass, Energy, the Speed of Light – It's Not Intuitive! " Lbl.gov. 1996. (Feb. 16, 2022) https://www2.lbl.gov/MicroWorlds/teachers/massenergy.pdf
• Lemonick, Michael D. "Will We Ever Travel at the Speed of Light?" Time. Apr. 10, 2000. (Feb. 16, 2022), 2011) http://content.time.com/time/subscriber/article/0,33009,996616,00.html
• May, Andrew. "What is time dilation? " LiveScience. Nov. 17, 2021. (Feb. 16, 2022) https://www.livescience.com/what-is-time-dilation
• NOVA Physics + Math. "Carl Sagan Ponders Time Travel." NOVA. Oct. 12, 1999. (Feb. 16, 2022) http://www.pbs.org/wgbh/nova/physics/Sagan-Time-Travel.html
• Ptak, Andy. "The Speed of Light in a Rocket." NASA's Imagine the Universe: Ask An Astrophysicist. Jan. 2, 1997. (Feb. 16, 2022) http://imagine.gsfc.nasa.gov/docs/ask_astro/answers/970102c.html
• Rynasiewicz, Robert, "Newton's Views on Space, Time, and Motion."Stanford Encyclopedia of Philosophy. Summer 2014. (Feb. 16, 2022) https://plato.stanford.edu/cgi-bin/encyclopedia/archinfo.cgi?entry=newton-stm
• Stein, Vicky. "Einstein's Theory of Special Relativity. " Space.com. Sept. 20, 2021. (Feb. 16, 2022) https://www.space.com/36273-theory-special-relativity.html
• Van Zyl, Miezam (project editor)."Universe: The Definitive Visual Guide." Dorling Kindersley Limited. 2020. (Feb. 16, 2022) https://bit.ly/33q5Mpm.

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General Relativity and Quantum Cosmology

Title: lectures on faster-than-light travel and time travel.

Abstract: These lecture notes were prepared for a 25-hour course for advanced undergraduate students participating in Perimeter Institute's Undergraduate Summer Program. The lectures cover some of what is currently known about the possibility of superluminal travel and time travel within the context of established science, that is, general relativity and quantum field theory. Previous knowledge of general relativity at the level of a standard undergraduate-level introductory course is recommended, but all the relevant material is included for completion and reference. No previous knowledge of quantum field theory, or anything else beyond the standard undergraduate curriculum, is required. Advanced topics in relativity, such as causal structures, the Raychaudhuri equation, and the energy conditions are presented in detail. Once the required background is covered, concepts related to faster-than-light travel and time travel are discussed. After introducing tachyons in special relativity as a warm-up, exotic spacetime geometries in general relativity such as warp drives and wormholes are discussed and analyzed, including their limitations. Time travel paradoxes are also discussed in detail, including some of their proposed resolutions.

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Can anything travel faster than the speed of light?

Does it matter if it's in a vacuum?

In 1676, by studying the motion of Jupiter's moon Io, Danish astronomer Ole Rømer calculated that light travels at a finite speed. Two years later, building on data gathered by Rømer, Dutch mathematician and scientist Christiaan Huygens became the first person to attempt to determine the actual speed of light, according to the American Museum of Natural History in New York City. Huygens came up with a figure of 131,000 miles per second (211,000 kilometers per second), a number that isn't accurate by today's standards — we now know that the speed of light in the "vacuum" of empty space is about 186,282 miles per second (299,792 km per second) — but his assessment showcased that light travels at an incredible speed.

According to Albert Einstein 's theory of special relativity , light travels so fast that, in a vacuum, nothing in the universe is capable of moving faster. 

"We cannot move through the vacuum of space faster than the speed of light," confirmed Jason Cassibry, an associate professor of aerospace engineering at the Propulsion Research Center, University of Alabama in Huntsville.

Question answered, right? Maybe not. When light is not in a vacuum, does the rule still apply?

Related: How many atoms are in the observable universe?

"Technically, the statement 'nothing can travel faster than the speed of light' isn't quite correct by itself," at least in a non-vacuum setting, Claudia de Rham, a theoretical physicist at Imperial College London, told Live Science in an email. But there are certain caveats to consider, she said. Light exhibits both particle-like and wave-like characteristics, and can therefore be regarded as both a particle (a photon ) and a wave. This is known as wave-particle duality.

If we look at light as a wave, then there are "multiple reasons" why certain waves can travel faster than white (or colorless) light in a medium, de Rham said. One such reason, she said, is that "as light travels through a medium — for instance, glass or water droplets — the different frequencies or colors of light travel at different speeds." The most obvious visual example of this occurs in rainbows, which typically have the long, faster red wavelengths at the top and the short, slower violet wavelengths at the bottom, according to a post by the University of Wisconsin-Madison . 

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When light travels through a vacuum, however, the same is not true. "All light is a type of electromagnetic wave, and they all have the same speed in a vacuum (3 x 10^8 meters per second). This means both radio waves and gamma rays have the same speed," Rhett Allain, a physics professor at Southeastern Louisiana University, told Live Science in an email.

So, according to de Rham, the only thing capable of traveling faster than the speed of light is, somewhat paradoxically, light itself, though only when not in the vacuum of space. Of note, regardless of the medium, light will never exceed its maximum speed of 186,282 miles per second.

Universal look

According to Cassibry, however, there is something else to consider when discussing things moving faster than the speed of light.

"There are parts of the universe that are expanding away from us faster than the speed of light, because space-time is expanding," he said. For example, the Hubble Space Telescope recently spotted 12.9 billion year-old light from a distant star known as Earendel. But, because the universe is expanding at every point, Earendel is moving away from Earth and has been since its formation, so the galaxy is now 28 billion light years away from Earth.

In this case, space-time is expanding, but the material in space-time is still traveling within the bounds of light speed.

Related: Why is space a vacuum?

So, it's clear that nothing travels faster than light that we know of, but is there any situation where it might be possible? Einstein's theory of special relativity, and his subsequent theory of general relativity, is "built under the principle that the notions of space and time are relative," de Rham said. But what does this mean? "If someone [were] able to travel faster than light and carry information with them, their notion of time would be twisted as compared to ours," de Rham said. "There could be situations where the future could affect our past, and then the whole structure of reality would stop making sense."

This would indicate that it would probably not be desirable to make a human travel faster than the speed of light. But could it ever be possible? Will there ever be a time when we are capable of creating craft that could propel materials — and ultimately humans — through space at a pace that outstrips light speed? "Theorists have proposed various types of warp bubbles that could enable faster-than-light travel," Cassibry said.

But is de Rham convinced?

"We can imagine being able to communicate at the speed of light with systems outside our solar system ," de Rham said. "But sending actual physical humans at the speed of light is simply impossible, because we cannot accelerate ourselves to such speed.

"Even in a very idealistic situation where we imagine we could keep accelerating ourselves at a constant rate — ignoring how we could even reach a technology that could keep accelerating us continuously — we would never actually reach the speed of light," she added. "We could get close, but never quite reach it."

Related: How long is a galactic year?

This is a point confirmed by Cassibry. "Neglecting relativity, if you were to accelerate with a rate of 1G [Earth gravity], it would take you a year to reach the speed of light. However, you would never really reach that velocity because as you start to approach lightspeed, your mass energy increases, approaching infinite. "One of the few known possible 'cheat codes' for this limitation is to expand and contract spacetime, thereby pulling your destination closer to you. There seems to be no fundamental limit on the rate at which spacetime can expand or contract, meaning we might be able to get around this velocity limit someday."

— What would happen if the speed of light were much lower?

— What if the speed of sound were as fast as the speed of light?

— How does the rubber pencil illusion work?

Allain is similarly confident that going faster than light is far from likely, but, like Cassibry, noted that if humans want to explore distant planets, it may not actually be necessary to reach such speeds. "The only way we could understand going faster than light would be to use some type of wormhole in space," Allain said. "This wouldn't actually make us go faster than light, but instead give us a shortcut to some other location in space."

Cassibry, however, is unsure if wormholes will ever be a realistic option.

"Wormholes are theorized to be possible based on a special solution to Einstein's field equations," he said. "Basically, wormholes, if possible, would give you a shortcut from one destination to another. I have no idea if it's possible to construct one, or how we would even go about doing it." Originally published on Live Science.

Joe Phelan is a journalist based in London. His work has appeared in VICE, National Geographic, World Soccer and The Blizzard, and has been a guest on Times Radio. He is drawn to the weird, wonderful and under examined, as well as anything related to life in the Arctic Circle. He holds a bachelor's degree in journalism from the University of Chester. 

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Breaking the speed limit: is faster-than-light travel possible.

Traveling faster than light – or as scientists call it, FTL – has long been a staple of science fiction; but according to Einstein’s theory of relativity, it’s an impossible task. However, new research proposes several methods through which FTL travel might be possible . While these ideas are exciting, there are significant hurdles to overcome. Let’s delve deeper into this fascinating concept and explore the challenges that lie ahead in making FTL travel a reality!

What is Faster-Than-Light Travel?

Imagine stretching a rubber sheet flat. That sheet represents the fabric of spacetime, according to Einstein’s theory of relativity. Everything in the universe, from tiny particles to massive stars, are like marbles sitting on this sheet, some much larger than others. Each marble causes the sheet of spacetime to curve and bend (Skruse, 2). Most propositions for FTL travel propose a way to manipulate this spacetime fabric itself, creating a kind of warp or shortcut that would allow a spacecraft to travel faster than the speed of light, which is currently considered the cosmic speed limit. In essence, FTL wouldn’t be about the spacecraft pushing itself to faster speeds than light, which is considered impossible, but rather about warping spacetime around it to create a faster path or a shortcut.

The Warp Drive Theory

So how could one actually do this? One theory involves folding and unfolding the rubber sheet in a specific way. (Figure 1) The marble on the sheet, representing a spaceship, wouldn’t move very quickly on its own, but by riding the folds and unfolds of the sheet, (Baron, 1) it could travel vast distances very quickly. However, at the moment, we have no method to actually bend spacetime, so this idea still remains a theory.

This concept is a simplified version of “warp drive” but there also exist other contenders for FTL travel. Other theories explore ideas like utilizing negative energy or manipulating phenomena like wormholes, which are shortcuts through spacetime that could connect distant points in the universe. (Lewis, 3)

Visualization of Warp Drive

Source: Omspace Rocket and Exploration

Negative Energy: Fuel for FTL Dreams or Nightmares?

Another intriguing idea involves negative energy, a hypothetical form of energy with properties opposite to our regular understanding. This is a scenario where energy isn’t just used up, but can somehow be formed – that’s the basic principle behind negative energy.

Theorists propose that negative energy could be used to create a repulsive force, counteracting the attractive nature of gravity. This, in turn, could potentially be harnessed to manipulate spacetime and create a warp bubble (Landis, 2) for FTL travel. However, there are significant challenges associated with negative energy. First and foremost, negative energy remains purely theoretical. No experiment or observation has ever confirmed its existence. Although we can theorize about its properties, there’s no concrete evidence to work with. Also, even if we could somehow generate negative energy, theories suggest it might be incredibly unstable. Negative energy might have a natural tendency to cancel out positive energy, making it difficult to control and potentially leading to catastrophic consequences if let out of control.

Despite these challenges, the allure of negative energy as a key to FTL travel persists. Scientists continue to explore theoretical models and search for any hints of its existence in the universe. For now, though, it remains a fascinating but highly speculative concept.

Wormholes: Cosmic Tunnels or Celestial Traps?

While manipulating spacetime with exotic energy sources is mind-bending, another theoretical pathway to FTL travel involves cosmic shortcuts known as wormholes. Going back to the metaphor of the universe as a vast sheet of fabric, a wormhole would be represented as a hidden tunnel piercing through it. These hypothetical tunnels wouldn’t require immense energy manipulation, but rather make use of the natural curvature of spacetime to connect two distant points. (Figure 2) Through wormholes, galaxies millions of light-years away could be within reach. However, there are several significant hurdles to consider.

First of all, theorists suggest wormholes might be inherently unstable. Like a tunnel made of wet sand, it would likely collapse on itself before anything could travel through. Similarly, a naturally occurring wormhole might be too short-lived or constantly fluctuating in size, making it incredibly dangerous to navigate. (Bambi, 5) Secondly, even if a stable wormhole existed, some theories suggest it might require a form of exotic matter with negative energy properties to keep it from collapsing. As discussed earlier, negative energy is purely hypothetical and incredibly difficult to control, making the creation or stabilization of a wormhole highly improbable with our current understanding of physics. And finally, other theories propose that wormholes might only be traversable in one direction. (Stojkovic, 1) Imagine a cosmic drain, allowing travel into another region of space but not back out. This one-way trip scenario would be a major drawback for interstellar exploration.

Despite these challenges, the possibility of wormholes continues to intrigue scientists and science fiction writers alike. Future discoveries about the nature of gravity and exotic forms of matter might shed light on the existence and stability of wormholes. For now, they remain a fascinating but still theoretical concept on the roadmap to FTL travel.

Bending Spacetime to Form a Wormhole

Source: Physics Stack Exchange

Chasing the Stars: Can We Ever Achieve FTL?

FTL travel, once relegated to the realm of science fiction, is now a concept being seriously explored by physicists. While immense challenges lie ahead, the potential rewards are equally immense. Traveling beyond the constraints of light speed would open up the vast expanse of the cosmos, allowing us to explore distant galaxies, potentially encounter new forms of life, and revolutionize our understanding of the universe.

The road to FTL travel will undoubtedly be long and arduous. It will require breakthroughs in our understanding of physics, the development of new technologies, and perhaps even the discovery of entirely new physical phenomena. However, the human spirit of exploration thrives on challenges. By continuing to push the boundaries of knowledge and explore these fascinating concepts, we inch closer to the day when humanity can truly touch the stars. The journey itself, filled with discovery and innovation, may be just as rewarding as the ultimate destination.

References and Sources

Skuse, Benjamin. (2021, March 24). Spacecraft in a “warp bubble” could travel faster than light, claims physicist. Physics World. 

Finazzi, S., Liberati, S., & Barceló, C. (2009, July 14). Semiclassical instability of dynamical warp drives. arXiv.org.

McMonigal, B., Lewis, G. F., & O’Byrne, P. (2012, February 26). The Alcubierre Warp Drive: On the matter of matter. arXiv.org.

Alcubierre, M. (2000, September 5). The Warp Drive: Hyper-fast travel within general relativity. arXiv.org.

Landis, Geoffrey. (2012, November 12). Negative Mass in Contemporary Physics, and its Application to Propulsion. National Aeronautics and Space Administration.

Bambi, Cosimo. (2021, May 8). Astrophysical Wormholes. arXiv.org.

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What is a light-year?

Light-year is the distance light travels in one year. Light zips through interstellar space at 186,000 miles (300,000 kilometers) per second and 5.88 trillion miles (9.46 trillion kilometers) per year.

We use light-time to measure the vast distances of space.

It’s the distance that light travels in a specific period of time. Also: LIGHT IS FAST, nothing travels faster than light.

How far can light travel in one minute? 11,160,000 miles. It takes 43.2 minutes for sunlight to reach Jupiter, about 484 million miles away. Light is fast, but the distances are vast . In an hour, light can travel 671 million miles.

Earth is about eight light minutes from the Sun. A trip at light-speed to the very edge of our solar system – the farthest reaches of the Oort Cloud, a collection of dormant comets way, way out there – would take about 1.87 years. Keep going to Proxima Centauri, our nearest neighboring star, and plan on arriving in 4.25 years at light speed.

When we talk about the enormity of the cosmos, it’s easy to toss out big numbers – but far more difficult to wrap our minds around just how large, how far, and how numerous celestial bodies really are.

To get a better sense, for instance, of the true distances to exoplanets – planets around other stars – we might start with the theater in which we find them, the Milky Way galaxy.

Our galaxy is a gravitationally bound collection of stars, swirling in a spiral through space. Based on the deepest images obtained so far, it’s one of about 2 trillion galaxies in the observable universe. Groups of them are bound into clusters of galaxies, and these into superclusters; the superclusters are arranged in immense sheets stretching across the universe, interspersed with dark voids and lending the whole a kind of spiderweb structure. Our galaxy probably contains 100 to 400 billion stars, and is about 100,000 light-years across. That sounds huge, and it is, at least until we start comparing it to other galaxies. Our neighboring Andromeda galaxy, for example, is some 220,000 light-years wide. Another galaxy, IC 1101, spans as much as 4 million light-years.

Based on observations by NASA’s Kepler Space Telescope, we can confidently predict that every star you see in the sky probably hosts at least one planet. Realistically, we’re most likely talking about multi-planet systems rather than just single planets. In our galaxy of hundreds of billions of stars, this pushes the number of planets potentially into the trillions. Confirmed exoplanet detections (made by Kepler and other telescopes, both in space and on the ground) now come to more than 4,000 – and that’s from looking at only tiny slices of our galaxy. Many of these are small, rocky worlds that might be at the right temperature for liquid water to pool on their surfaces.

The nearest-known exoplanet is a small, probably rocky planet orbiting Proxima Centauri – the next star over from Earth. A little more than four light-years away, or 24 trillion miles. If an airline offered a flight there by jet, it would take 5 million years. Not much is known about this world; its close orbit and the periodic flaring of its star lower its chances of being habitable.

The TRAPPIST-1 system is seven planets, all roughly in Earth’s size range, orbiting a red dwarf star about 40 light-years away. They are very likely rocky, with four in the “habitable zone” – the orbital distance allowing potential liquid water on the surface. And computer modeling shows some have a good chance of being watery – or icy – worlds. In the next few years, we might learn whether they have atmospheres or oceans, or even signs of habitability.

One of the most distant exoplanets known to us in the Milky Way is Kepler-443 b. Traveling at light speed, it would take 3,000 years to get there. Or 28 billion years, going 60 mph.

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