# Kurzgesagt – In a Nutshell

## Sources – Time Travel

We thank our expert for their feedback:

—We think our universe is four dimensional, with three spatial and one time dimension - smooshed together into a fancy thing we call spacetime.

#Encyclopaedia Britannica: “Space-time” (retrieved 2024)

Quote: Space-time, in physical science, single concept that recognizes the union of space and time, first proposed by the mathematician Hermann Minkowski in 1908 as a way to reformulate Albert Einstein’s special theory of relativity (1905).

—Ok. So there is a very strange rule: Everything in our universe moves at the speed of light through four dimensional spacetime. Your speed through spacetime is the sum of your separate speeds through time and space. It is impossible for you to stay still. Even if you are not moving through space dimensions, you are moving through the time dimension, blasting face first into the future.

#Lincoln, Don (2014): “Proving special relativity: episode 4” FermiLab Today

Quote:All things travel at just one speed, the speed of light. In fact, as you sit there, perhaps eating a muffin on your morning coffee break, you are traveling at the speed of light. [...] The idea that you are traveling at such an incredible speed seems absurd, but wait for the catch: You are traveling at that speed through time. That is, assuming that you are not moving at all through space, your motion is exclusively through time.[...] In relativity, space and time should be thought of as equivalent in the same way that the north-south direction is relatable to the east-west direction. Then it becomes easy to see how an object with a single speed can travel entirely through time, entirely through space or in a mixture.

—You can slow down in the time dimension, by moving faster through the space dimensions but in total, you will always move at the speed of light through spacetime. If you could somehow truly stand still in space – you would move through time at the speed of light. And the other way around.

Of course, no one can really “stand still in space”, since who is still and who moves depends on the observer. If you’re reading on the train, the book in your hand does not seem to be moving to you, but it is moving for someone waiting on the station. Here, we say “stay still in space", to mean “stay still for a particular observer”. If we follow our rule of having all objects move through spacetime at c, objects that don’t move from my point of view don’t have any speed through space, so all of their spacetime speed will go to their “time” coordinate. We omit the mention of an observer here for readability, but we are aware that the importance of the observer is a key insight of relativity, and that there is no one that “stands still” for everyone.

—Photons, light particles, move at the speed of light through space. They don’t experience any time passing because their speed in that time dimension is 0. In the time dimension they are frozen in place. If you see light on earth, from the photon’s perspective it just was on the surface of the sun and then suddenly crashed into your eye with nothing happening in between.

There are no inertial reference frames in which the photon is at rest, so one cannot properly define the reference frame of a photon or describe a photon’s “experience” or its “4-vector”. However, if we consider an object moving arbitrarily close to the speed of light in our frame of reference, following our rule, the object has increasingly less “budget” left in their 4-vector speed to traverse through time, which can be understood as them not experiencing the passage of time in the limit.

—The story that is usually told to demonstrate this, is to get twins, force one of them into a rocket against their will, shoot them through space super fast while the other twin chills on earth. And because as one twin moves very fast through space while the other moves slowly on earth, they move at different speeds through time. When the rocket finally gets home, they are no longer the same age and the younger space twin is ready to start years of therapy for being abducted by theoretical physicists.

#CalTech (1963): “The Feynman Lectures on Physics”, vol. I, Ch. 6(2)

Quote: “To continue our discussion of the Lorentz transformation and relativistic effects, we consider a famous so-called “paradox” of Peter and Paul, who are supposed to be twins, born at the same time. When they are old enough to drive a space ship, Paul flies away at very high speed. Because Peter, who is left on the ground, sees Paul going so fast, all of Paul’s clocks appear to go slower, his heart beats go slower, his thoughts go slower, everything goes slower, from Peter’s point of view. Of course, Paul notices nothing unusual, but if he travels around and about for a while and then comes back, he will be younger than Peter, the man on the ground! That is actually right; it is one of the consequences of the theory of relativity which has been clearly demonstrated. Just as the muons last longer when they are moving, so also will Paul last longer when he is moving. This is called a “paradox” only by the people who believe that the principle of relativity means that all motion is relative; they say, “Heh, heh, heh, from the point of view of Paul, can’t we say that Peter was moving and should therefore appear to age more slowly? By symmetry, the only possible result is that both should be the same age when they meet.” But in order for them to come back together and make the comparison, Paul must either stop at the end of the trip and make a comparison of clocks or, more simply, he has to come back, and the one who comes back must be the man who was moving, and he knows this, because he had to turn around. When he turned around, all kinds of unusual things happened in his space ship—the rockets went off, things jammed up against one wall, and so on—while Peter felt nothing.

So the way to state the rule is to say that the man who has felt the accelerations, who has seen things fall against the walls, and so on, is the one who would be the younger; that is the difference between them in an “absolute” sense, and it is certainly correct.”

—Massive objects bend space time, causing time to go slower near them.

#Max Planck Institute for Gravitational Physics: “Time dilation” Einstein Online ´: Glossary (retrieved 2024)

Quote:In general relativity, there is the phenomenon of gravitational time dilation: Roughly speaking, clocks in the vicinity of a mass or other source of gravity run more slowly than clocks which are farther away. This phenomenon is closely related to the gravitational redshift.

—On Earth the effect is tiny - the gravity of our planet makes time pass 0.00000007% slower than in deep space, far from any gravitational fields. Hardly useful for time travel, but it’s a start.

#Hamilton, Andrew (2016): “More about the Schwarzschild Geometry” (retrieved 2024)

https://jila.colorado.edu/~ajsh/bh/schwp.html

Quote: “One of the remarkable predictions of Schwarzschild’s geometry was that if a mass

M were compressed inside a critical radius rs, nowadays called the Schwarzschild radius, then its gravity would become so strong that not even light could escape. The Schwarzschild radius

rs of a mass M is given by

rs= 2GM/c2

[...]

In the case of the Schwarzschild metric, the proper time, the actual time measured by an observer at rest at radius r, during an interval dt of universal time is sqrt(1-r/rs) dt

which is less than the universal time interval dt. Thus a distant observer at rest will observe the clock of an observer at rest at radius r to run more slowly than the distant observer’s own clock, by a factor

sqrt(1-r/rs) “

#NASA: “Earth fact Sheet” (retrieved 2024)

—If you move into a really strong gravitational field, like around a black hole, the closer you get to the event horizon, the slower time passes for you. If we kidnap our twin again, they won’t notice it at all - their watch ticks as fast as it always does. But from the outside they seem to almost stand still. Only when the twin leaves the gravitational field and comes back to earth do they realize they time traveled.

#Harvard Smithsonian Center for Astrophysics (2004): ”What are Black Holes?” Universe Forum archival site

Quote: Near a black hole, the slowing of time is extreme. From the viewpoint of an observer outside the black hole, time stops. For example, an object falling into the hole would appear frozen in time at the edge of the hole.

We have covered some of the strange things that happen when you get close to (and fall in) a black hole in another video:

#Kurzgesagt – In a Nutshell (2021): “What If You Fall into a Black Hole?”

—The theory of relativity, which may be the most solid scientific theory we know, does NOT forbid faster than light motion through space.

#Bilaniuk, Olexa-Myron; Sudarshan, E. C. George  (1962): “Particles beyond the light barrier”

Physics Today, vol. 22, 5 , 43–51

Quote:Some time ago we reexamined this point and concluded that existence of superluminal particles is in no way precluded by Einstein's theory. On the contrary, it is this very theory that

suggests the possibility. Other physicists, notably Yakov P. Terletskii and Gerald Feinberg, have reiterated this same conclusion.”

—Actually, scientists have been looking for superluminal particles and given them a name: “tachyons”. They could exist and would have wild properties like getting faster when they lose energy and of course, traveling backwards in time.

#Encyclopaedia Britannica: “Tachyon” (retrieved 2024)

Quote:Tachyon, hypothetical subatomic particle whose velocity always exceeds that of light. The existence of the tachyon, though not experimentally established, appears consistent with the theory of relativity, which was originally thought to apply only to particles traveling at or less than the speed of light. Just as an ordinary particle such as an electron can exist only at speeds less than that of light, so a tachyon could exist only at speeds above that of light, at which point its mass would be real and positive. Upon losing energy, a tachyon would accelerate; the faster it traveled, the less energy it would have.

#Norton, John D: “Spacetime, Tachyons, Twins and Clocks” (retrieved 2024)

Quote:One of the most intriguing entities in relativity theory are tachyons. They are hypothetical particles that travel faster than light. They are distinguished from "bradyons," particles that travel at less than the speed of light. While bradyons are familiar and include protons, electrons and neutrons, tachyons have never been observed. For present purposes, the interesting fact is a curious property: for some observers tachyons travel backwards in time.

— But now for the first time, some observers could actually see tachyons literally traveling backwards in time. Which means they could be used to directly interact with the past. In theory you could use them to send messages to your past self and change all sorts of things that have already happened

#Buckley, Matthew B. (2016): “Why FTL implies time travel”

Quote:  “Let's say we on Earth have built a FTL [(faster than light)] communication device that let's us talk to the inhabitants of the planet Proxima Centauri B, 4.25 lightyears away. Again, this is what a FTL and slower-than-light set of communications would appear like in a spacetime diagram.

Critically, I've drawn the time axis for the Proximal Centaurians parallel to our own time. This is because Proxima Centauri is moving at essentially the same velocity as Earth (the differences are small compared to the speed of light). Thus, there are no big relativistic effects between our counting of time and the Proximal Centaurians.

Now, let's imagine that some event occurs away from Earth, oriented in such a way that the light from the event hits us before it reaches Proxima Centauri. The spacetime diagram for that would look like what I've shown. First we see the light, then the light reaches Proxima Centauri. Notice I've drawn the light rays from the event traveling at 45 degrees to my time axis. After all, it is light, and light travels at 45 degrees on spacetime diagrams.

So, now, let's add in FTL communication. We see the event, we get on the FTL phone, and we tell the Proximal Centaurians. They get the phone call, and now have years to prepare for the arrival of the light from whatever the event is (let's say it's a supernovae, or the launch of relativistic attack vehicles. We are playing with sci-fi tropes here).

Now, this is the image most people have of FTL communication. There appears to be no problem: we all agree that the event happened "first," then Earth calls Proxima Centauri, then the light reaches Proxima Centauri. No problem: though the Proximal Centaurians hear about the event "early," no causality has been violated. After all, we all agree on what happened first, don't we? No effect precedes its cause.

Right?

But we've forgotten relativity. This only works when everyone is moving in the same frame of reference, like us and Proxima Centauri (really we're not in the same rest frame, but its close enough not to matter). So, to see the problem, let's add a new observer, moving at high speeds relative to Earth and Proxima Centauri. It's sci-fi, so we add a relativistic spaceship. It's moving with v<c but v>>0, so it's trajectory on my spacetime diagram is highly skewed relative to my time axis: it's nearly moving at the speed of light.

Here's where the relativistic effects start coming into play. Relativity tells us that everyone moving with constant velocity is totally justified in saying they are stationary. Thus, we think we're stationary (ignore the rotation of the Earth, or its orbit around the Sun). The Proximal Centaurians think they're at rest. The people on the relativistic spaceship think they are at rest. So they can draw their spacetime diagram, with their own time axis. That time axis, like mine, is always where they are: on the ship. So I think their time axis is aligned with the ship trajectory.

In addition, they have a space-axis, just like I do. Relativity mixes up space and time, so their space axis I perceive as slanted - just like their time axis is skewed. It turns out that the space axis is flipped across the 45 degree null line, but I'm not going to prove that. This weird mixture of space and time of observers I perceive as moving is a necessary part of relativity. It is the only way everyone can agree that light moves at c.

[...]

So what happens now. Let's ask when the spaceship sees the various events in this diagram. To do that, we need to know the lines of constant time for the ship. That's not too hard: lines of constant time for us are lines in the spacetime diagram parallel to the space axis. So it is for the spaceship. Their lines of constant time look like this:

Now do you see the problem?

According to us, on Earth, the order of events is thus: we see the light from the event hit us. We call Proxima Centauri on the FTL phone. The Proximal Centaurians do whatever they want to do in response to that call, and then they see the light of the event.

What does the ship see? They see the phone call received on Proxima Centauri. Then they see the phone call placed from Earth.

Effect precedes cause: causality is violated. In fact, if the ship had a FTL phone set up in the right way, they could call Earth before Earth placed the call. They could even tell Earth "hey, don't make that call to Proxima Centauri we just saw you make."

—It seems like our universe has different realms of reality that are impossible to mix.

These “realms of reality” refer to the class of particles deemed as Class I (subluminal matter like electrons) , Class II (particles moving at the speed of light like photons. Neutrinos were previously thought to belong in this class.) and Class III (superluminal particles, the hypothesized tachyons) by Bilaniuk y Sudarshan. As explained in their paper below, particles of one class cannot be accelerated into another class.

#Bilaniuk, Olexa-Myron; Sudarshan, E. C. George  (1962): “Particles beyond the light barrier”

Physics Today, vol. 22, 5 , 43–51

—Unfortunately the theory of relativity, specifically forbids anything that starts out traveling slower than the speed of light, to reach the speed of light. Because moving faster through space requires energy and the energy required to reach the speed of light is literally infinite.

#Bilaniuk, Olexa-Myron; Sudarshan, E. C. George  (1962): “Particles beyond the light barrier”

Physics Today, vol. 22, 5 , 43–51

Quote: “even if we could supply a particle with an arbitrarily large amount of energy, its

velocity with respect to us would still be bounded by the value of c

#OpenStax: “University Physics” vol.3 Ch. 5 (9)

Quote:An infinite amount of work (and, hence, an infinite amount of energy input) is required to accelerate a mass to the speed of light.”