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Let's say I want to write about a living thing that can naturally go to 99% the speed of light in just one second of acceleration.

I would like to write what this being would experience at such speed realistically (Of course, ignoring the possible collateral damage and where it gets so much energy from, that would be a separate problem, maybe is a robot) but nevertheless, every time I see documentaries about things going "almost to speed of light" I see examples of two effects that are both supposed to be realistic but I don't understand how they are both possible at the same time

-That at such a speed time seems to stop

-That when the faster your relativistic speed gets, the greater your relativistic mass gets, and therefore when you get to another point, much more time will have passed than you felt

I don't understand, how are both effects supposed to work at the same time?

Why would have passed more time than the one you felt when you arrive at your destination if time is supposed to have almost stopped in your point of view?

Or is "seeing things stopped in time" just a fanciful example of what would happen if someone could react at near light speed?

The effects of moving at 99% the speed of light become more prominent the further you travel? (for example, the living being using his speed to travel a 100 km road vs. him traveling to the nearest star)

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    $\begingroup$ Time will never "seem to stop" except at exactly the speed of light, per special relativity. Additionally, you can only tell there is a difference in time by comparing with a clock not traveling at 99% of the speed of light with you (i.e. time is relative). You and your own clock would appear to tick happily along as if nothing was happening. $\endgroup$
    – stix
    Dec 21, 2022 at 20:45
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    $\begingroup$ In the own frame of reference of any observer, time flows at a rate of one second per second; because in its own frame of reference the speed of the creature is zero. Those effects you have heard of are always from the point of view of other observers who are looking at the creature. $\endgroup$
    – AlexP
    Dec 21, 2022 at 20:49
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    $\begingroup$ The Lorentz factor at .99c is "only" 7... more than high enough for weird relativistic effects, but a time-dilation factor of 7 is quite a long way from "time stopping". Also, be careful about the term "relativistic mass" which is a measure of the total mass-energy of a system, not about things getting heavier as they go faster. $\endgroup$ Dec 21, 2022 at 21:55
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    $\begingroup$ Obligatory XKCD "RELATIVISTIC BASEBALL" link what-if.xkcd.com/1 $\endgroup$ Dec 22, 2022 at 13:51
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    $\begingroup$ keep in mind at those speeds even running into AIR will trigger nuclear fusion. so really the only thing they see is a washout of light and gamma radiation $\endgroup$
    – John
    Dec 22, 2022 at 21:32

8 Answers 8

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So far all answers have got the effects of relativity wrong resulting in incorrect and backwards results.

The principle of relativity states that there is no privileged reference frame, and that the laws of physics take the same form in all inertial reference frames (i.e. the reference frames of free-falling objects).

It follows from this that for a free-falling spaceship (i.e. one not being significantly slowed by interstellar drag, and not accelerating with its engines etc) passing by a planet at a significant fraction of the speed of light the spaceship will see the planet's clocks speed up or slow down by the exact same factor that the people on the planet will see the spaceship's clocks speed up or slow down.

One of the other postulates of relativity is that light always travels at the same speed in all reference frames.

From these two facts together we get length contraction and time dilation.

Length contraction means that the people on the planet see the ship compressed along its length (and by the principle of relativity, people on the ship see the planet compressed along the direction of travel).

Time dilation means that the people on the planet see the ship's clocks tick slower than their own (and by the principle of relativity, people on the ship see the planet's clocks ticking slower than their own).

The relevant factor here is the Lorentz factor: γ=1/sqrt(1-v^2/c^2)

This factor is always greater than or equal to 1.

An observer on the spaceship will count this many ticks of their own clock for every tick of the planet's clock, whilst by the principle of relativity an observer on the planet will count this many ticks of their own clock for every tick of the spaceship's clock.

Conversely, the observer on the spaceship will see this many of the planet's metre rulers fitting within the same distance as one of their own (on the spaceship), and of course, vice versa for the observer on the planet.

This appears paradoxical because we are used to living in a Newtonian world where time and distance are absolute quantities, but this is not the case in Relativity.

Most of these paradoxes can be resolved by giving up such Newtonian ideas.

Now for other effects.

Relativistic mass isn't really a concept used much these days, as it leads to incorrect assumptions down the road. Instead, we include the Lorentz factor explicitly, with E=mγc^2, p=mγv etc. Unfortunately pop-science books and TV shows love it.

The main other noticeable effects would be the Relativistic Doppler Effect & Relativistic Aberration. The Doppler effect is similar in relativity to that of Newtonian mechanics, so you'd see objects ahead of you look bluer (or depending on the speed, possibly shifted into the ultraviolet or gamma spectrum) than normal, and ones behind look redder (again depending on the speed, possibly being shifted outside the visible range into the infrared or radio spectrum), but unlike the classical effect, objects perceived as directly to your side will also appear redshifted. The diagram below shows how the colour of uniform distant yellow stars will appear in different directions for an observer moving to the right with the Relativistic Doppler Effect applied on the top, and only the classical one on the bottom.

relativistic doppler

Additionally, Relativistic Aberration (which is closely related to the Relativistic Doppler Effect) will cause objects to appear to be closer to the point directly in line with the direction of travel (i.e. directly in front, or directly behind).

By the principle of relativity, the observers on the planet will also see the spaceship to be relativistically Doppler shifted (including being redshifted as it moves perpendicular to the planet), and to appear closer to the point directly in line with the direction of travel (i.e. further away than it is as it approaches, and nearer than it is as it departs).

Note: so far I have only considered Special Relativity. This is sufficient to cover the case described in the OP, as special-relativistic effects will be much stronger than any general-relativistic ones. Special relativity applies to any motion on a "flat" spacetime (one where the gravity is weak compared to the scale of the experiment). If you start going near black holes or doing long-term observations at low speeds in gravitational wells you'll start getting other effects coming in (e.g. gravitational time dilation where clocks lower down a gravity well tick more slowly than those higher up).

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  • $\begingroup$ you're misleading people. You can say that your opinion is as good as mine, but I have real-world examples to back my side up. You apply "no privileged frame of reference" like libertarians apply gun ownership. You take it further than it was ever meant to go. There IS a privileged frame of reference. If there weren't, then deceleration couldn't exist. "An observer on the spaceship will count this many ticks of their own clock for every tick of the planet's clock" If this were true, then the GPS satellites would have to change their clocks in the other direction. $\endgroup$ Dec 23, 2022 at 18:45
  • $\begingroup$ @RobertRapplean: No, there is no such thing as a privileged inertial frame of reference. If a body is accelerating, then it will be observed as accelerating in all inertial frames of reference. The answer explicitly says that is applies to a spaceship in free fall, i.e., not accelerating. And GPS satellites, which are not in an inertial frame of reference because they move on closed orbits, correct for both special-relativity effects and general-relativity effects. Yes, those two corrections cancel out in part, but not completely. $\endgroup$
    – AlexP
    Dec 24, 2022 at 9:05
  • $\begingroup$ The point being that you don't have the situation where both points perceive that the other guy's is moving slower. The earthbound move 45ms per day slower than the satellite because we're deeper in the gravity well, but 7ms per day faster because we're not zipping around the planet. It's a concrete, measurable quantity. There is no paradoxical relative reciprocity mumbo jumbo. $\endgroup$ Dec 24, 2022 at 19:57
  • $\begingroup$ @AlexP GPS satellites are in an inertial reference frame (they are in free-fall), the fact they're in closed orbits is irrelevant. It's the people on the surface who aren't in an inertial reference frame (because we're not freefalling). Otherwise yes, you are correct that it is that no inertial reference frame is privileged over any other inertial reference frame $\endgroup$
    – Tristan
    Dec 27, 2022 at 15:34
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Q: "Would a living being moving at 99% the speed of light see time stop, or would it see time move faster?"

Your own experience of time will remain the same

Living beings like humans don't "see time", we have no sense for it. The little beeper for time that exists in our brain will just pulse at some arbitrary, but regular interval, like a clock does. That is sufficient clue to provide the impression of time going by. It is regular, but you get deviations in time experience, when you are sleeping, dreaming, working, ageing, etc.

When you move at 99% of c, you won't experience anything different. In a space ship built on Earth, you'll probably eat and sleep in a 24h time interval, because the ship's design is adjusted to Earthlings.

Now suppose, you'd orbit Earth at 0.99 c in some wonder ship: you are not getting crunched because the wonder ship keeps you alive..

Observing

As a pilot.. you'll notice there's something "wrong" with time when

Analogy 1: ..you try to communicate using a wonder phone, with people on Earth. For them, time will elapse in their pace and because of your relativistic speed, you get squeeking responses, very quickly. It seems they don't need any time to answer your questions. When you play chess with them, they will be very strong, because they have 7x the amount of time you have.

Analogy 2: ..you look at people on Earth. A place with people would seem like an ants nest, folks seem to move 7x as fast. When you would land after 4 years, 28 years of time went by on the planet. You'll meet your friends again, they are old people

Observers

When people on Earth..

Analogy 1: ..contact you to communicate using a wonder phone, it will take a lot of waiting time on their part, before you answer. When you answer, the sound you seem to produce is low frequency. When they play chess with you, they have to wait for ages.

Analogy 2: When people look up to you, suppose there's a wonder telescope for that purpose as well, you would seem to be frozen in time, moving 7x as slow as the average pilot. When you land after 4 years, you'll meet your friends again, and they wonder why you did not age ! you are the same young person that went to space 28 years ago.

Backgrounds in-depth:

https://physics.stackexchange.com/questions/634924/i-am-confused-about-the-passage-of-time-for-an-outside-observer-versus-an-observ

https://physics.stackexchange.com/questions/109776/how-long-would-it-take-me-to-travel-to-a-distant-star

https://en.wikipedia.org/wiki/Twin_paradox

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    $\begingroup$ This answer is somewhat misleading, because in the example used - "Now suppose, you'd orbit Earth at 0.99 c in some wonder ship" - the spaceship would be under constant, massive acceleration (perpendicular to the direction of motion) to maintain that "orbit". The acceleration changes things a lot; without the acceleration, someone in a spaceship moving at .99c relative to Earth would see time appear to move slowly for people on Earth, just as people on Earth would see time appear to move slowly for the observer on the spaceship. $\endgroup$ Dec 22, 2022 at 13:27
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    $\begingroup$ I think it would depend on whether you were looking forward with your telescope or backward, no? $\endgroup$
    – workerjoe
    Dec 22, 2022 at 14:20
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    $\begingroup$ "folks seem to move 7x as fast" this is incorrect. Time dilation appears symmetrically as neither reference frame is privileged over the other. Both observers always see the other observer as moving slower. The reason the twin paradox occurs is that the symmetry is broken by one of the twins returning to the other, whilst at each moment each twin sees the other aging more slowly, the twin in the ship will see the other catch up, and overtake them as they turn around $\endgroup$
    – Tristan
    Dec 22, 2022 at 15:24
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    $\begingroup$ @Goodies, your wondertools are time-travel devices. The shift is simple. A 2x faster time frame perceives light at half the normal frequency. This would shift the low end of ultraviolet to the low end of red. $\endgroup$ Dec 22, 2022 at 20:06
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    $\begingroup$ @RobertRapplean It's not because the physics in the answer is wrong; it's because the answer answers a (subtly) different question, and doesn't highlight that fact. (The comments suggest this might be because Goodies doesn't fully understand relativity.) $\endgroup$
    – wizzwizz4
    Dec 22, 2022 at 21:20
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Aspects of your question have been discussed via a couple of questions I've previously asked, and they're worth looking at

Here's a summary

One of the things that makes relativity difficult to understand is the all-too-human desire to see everything "from my point of view." Why this makes relativity difficult is easy: it's all about seeing things "from another point of view."

Let's assume for convenience that your creature needs a single hour to accelerate from a planetary orbit to the speed of light. That's a breathtaking amount of acceleration that's likely to kill the creature long before it gets to the speed of light (i.e., within the first few seconds of acceleration), but we'll ignore that. One hour to leave orbit and hit the speed of light.

From the point of view of someone watching your creature, they see it disappear from sight very quickly. Then it's gone for however many years are required to get from the observer's sun to the next solar system. Let's assume that same observer could know when the creature appeared at its destination (don't ask how, it's basically magic from the perspective of science). The observer would see the creature (quite literally) suddenly appear and move into orbit around a planet in that system. Remember, total time experienced by the observer is the number of years represented by the distance between the two stars in light-years.

From the point of view of the creature it spent about 30 minutes accelerating, about 30 minutes decelerating, and was happily around the new star. An hour of its time.

If the first observer were magically able to see the creature while it's fully accelerated (which the observer can't, but work with me), the creature would appear frozen in time. The creature, of course, can't magically see the observer (who would appear to be moving really, really, really fast!) because time has stopped for the creature from the point of view of the observer. The creature, of course, is aware of none of this. Time seemed to flow normally for it, it just happened to pass through a blistering distance in the proverbial blink of an eye.

This is the nature of relativity you're seeking to understand. The faster you go, the slower time appears to flow compared to an observer still experiencing life at the location where you started from. But your experience is very different. From your point of view, nothing changed! What happened from your point of view is that a bunch of distance just... passed by... you didn't even notice it.

The real problem is, what's happening during transit?

A challenge that you need to face (one that's discussed in the first question linked above) is what happens while your creature is traveling? Your creature experiences infinite velocity or zero time from the moment it hits light speed to the moment it exits light speed. But things are happening while the creature passes through those vast reaches of space. It's a complicated subject, but think of it this way: the creature will have some number of photons that strike it during transit. Over the distance covered, that could be a whomping lot of photons. Anything from a suntan to being burned to a tendril of smoke could happen.

The creature is also impacting atoms, molecules, and dust. All that is completely irrelevant at our very slow speed of space flight, but at the speed of light and over those distances, those impacts add up. Anything from having the leading edge of the creature abraded (e.g., rubbed lightly with sandpaper) to that tendril of smoke we just spoke about.

The creature may even have trouble with gravity. At those speeds the gentle ebb and flow of gravity suddenly becomes a series of speed bumps, or waves being smashed through... or walls. I might have been a bit dramatic there, but I'd be curious if there's research into what gravity would "look like" to an accelerated object. I know what it's like to hit speed bumps with my car. I also know (to my everlasting shame) what it's like to hit a curb.

But here's the rub... your creature won't consciously experience any of that. It's all happening during the time that "time has stopped" for your creature. Your creature isn't aware of time passing while its accelerated because time doesn't flow as we know it when accelerated. In the blink of an eye, it suddenly has a nasty sunburn, a big gash down one side of it, and a blinding headache. That's all it knows, assuming it survived the trip at all (it's your world, so it certainly can survive!).

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  • $\begingroup$ If you replace "at the speed of light" with "very close to the speed of light", I don't think there are problems with this answer. As-is, though, this doesn't describe real-world physics. $\endgroup$
    – wizzwizz4
    Dec 22, 2022 at 21:28
  • $\begingroup$ @wizzwizz4 You're certainly welcome to step off the comment chain (you've left several complaining about other people's attempts to answer the question) and write one yourself. The OP and others would benefit from your mastery of Real World physics. $\endgroup$
    – JBH
    Dec 23, 2022 at 3:16
  • $\begingroup$ If I could write a better one than yours, I would've done so. :-) My comment on your answer is basically just a repeat of this one – but your answer's very intuitive. $\endgroup$
    – wizzwizz4
    Dec 23, 2022 at 13:29
  • $\begingroup$ @wizzwizz4 You can't write a better answer but your sure I'm wrong? Odd.... $\endgroup$
    – JBH
    Dec 23, 2022 at 14:06
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    $\begingroup$ @wizzwizz4 That's actually a common mistake. "Physics" here on Worldbuilding refers to the physics of the OP's world. The Real World only affects the OP's world when specifically asked for. $\endgroup$
    – JBH
    Dec 23, 2022 at 16:18
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The answer seems to be, unintuitively, "yes".

Think about it like this, the sun is 8 light-minutes away from earth, but due to its lack of mass, the photon emits experiences no time at all on that trip. Let's say for the sake of the illustration that it actually experiences one second. So then the photon would see 8 minutes of stuff happening within the span of one second.

But if you stand across the room and shine a flashlight at me, from the photon's point of view, no time passes either. But also to us, it seems like no time as has passed. So if we again grant the photon a second to observe its journey, then we will appear to be frozen.

Thus it seems to me that temporal compression is dependant on the distance traveled. As long as you don't ever hit 1c, then the traveler will experience some time passing. And so the amount of outside time being observed while traveling seems to be directly proportional to the distance traveled under relativistic speeds.

If your story introduced some element of being able to speed up cognition, then that perceived "one second trip" could be any length of "time" needed.

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The being would experience some things differently, but not a subjective experience of time. There would definitely be some weird effects. The being would, for instance, see length contract in very odd ways (counter-intuitively, moving forward would make length appear longer even though it would be measured shorter). However, the subjective experience of time would not change. The outside world, viewed by the being, would appear to be going very fast, so by that perspective yeah, the being would see "time slow down". But its thoughts and movements, from its perspectives, would not change.

A fascinating Youtube video was made on this very topic: https://www.youtube.com/watch?v=udqihUBGuZ8&ab_channel=TheActionLab

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    $\begingroup$ Isn't it the other way around? To the universe, the traveler is moving fast (relative to the universe), and so the traveler's clock is ticking slowly. To the traveler, the universe is moving fast (relative to the traveler), and so the universe's clock is ticking slowly. $\endgroup$
    – void_ptr
    Dec 21, 2022 at 22:57
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    $\begingroup$ @Pelinore I think what you said goes against the very principle of relativity. You are saying that time dilation works differently in different inertial frames of reference. $\endgroup$
    – void_ptr
    Dec 22, 2022 at 1:24
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    $\begingroup$ @Pelinore Your understanding is flawed and is the exact opposite of what relativity is. $\endgroup$
    – void_ptr
    Dec 22, 2022 at 4:43
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    $\begingroup$ @Pelinore: A traveler moving at .99c relative to Earth does see themselves aging faster than people on Earth, just as people on Earth see themselves aging faster than the traveler. If a traveler leaves Earth at .99c, then turns around and comes back, they see more time pass on Earth not because Earth time seems to be ticking faster the whole way, but because a lot of time seems to pass on Earth while the traveler is turning around. $\endgroup$ Dec 22, 2022 at 13:57
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    $\begingroup$ @Pelinore you are incorrect. Provided it is not accelerating, the spaceship sees the clock on the planet ticking slower, just as the people on the planet sees the clock on the ship ticking slower. That follows trivially from the principle of relativity. The reason the twin paradox occurs is that the symmetry is broken by one of the twins returning to the other, whilst at each moment each twin sees the other aging more slowly, the twin in the ship will see the other catch up, and overtake them as they turn around $\endgroup$
    – Tristan
    Dec 22, 2022 at 15:27
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The rest of the universe would be moving faster around you.

You couldn't do this on a planet because you'd be clear of the planet faster than you could blink. The base time frame would appear to you to be more than seven times your time frame. If you had a telescope and were approaching a planet, it would look like eight times because you'd be seeing events that happened in a decreasing amount of the past.

However, everything would be "foreshortened." Stars that you passed would look like pancakes, adjusted by the same 7:1 ratio that time was adjusted by.

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    $\begingroup$ "If you had a telescope and were approaching a planet, it would look like eight times because you'd be seeing events that happened in a decreasing amount of the past." - while the "you'd be seeing events that happened in a decreasing amount of the past" part is true, it is a separate effect from time dilation. Time dilation happens regardless of whether an observer is approaching an object, moving away, or passing by. $\endgroup$ Dec 22, 2022 at 13:57
  • $\begingroup$ this is incorrect. Time dilation appears symmetrically as neither reference frame is privileged over the other. Both observers always see the other observer as moving slower. The reason the twin paradox occurs is that the symmetry is broken by one of the twins returning to the other, whilst at each moment each twin sees the other aging more slowly, the twin in the ship will see the other catch up, and overtake them as they turn around $\endgroup$
    – Tristan
    Dec 22, 2022 at 15:24
  • $\begingroup$ Sorry, @Tristan. That's a common misconception that's disproven by our world's GPS systems. The GPS satellites don't see us moving slightly slower, they see us moving slightly faster, and have to slow their clock rate to match. $\endgroup$ Dec 22, 2022 at 16:19
  • $\begingroup$ @RobertRapplean GPS satellites are not moving at a significant fraction of the speed of light and do not need to make corrections for special relativity. Instead they need to make corrections for general relativity due to the earth's gravity well (which is indeed asymmetric). In the situation described in the OP special relativistic effects will clearly dominate, and we can neglect gravitational time dilation $\endgroup$
    – Tristan
    Dec 22, 2022 at 16:22
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    $\begingroup$ They have to adjust for both. physicstoday.scitation.org/doi/10.1063/1.1485583 $\endgroup$ Dec 22, 2022 at 16:28
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The speed of light is badly named because that speed is the limit on pretty much everything. I like to think of it instead as the speed of causality. As for what it would likely see, think of it this way:

If you started running forward and one of your friends was in front of you and started running perpendicular to you, they would catch you only if they were faster or the same speed. Most things you interact with would work the same way. The faster you travel, the less things can interact with you because by the time they get there, you're gone.

If you are going a significant fraction of the speed of causality it's likely that what you "see" would be altered a bit. As mentioned elsewhere here, stuff in front of you would start to look bluer and bluer in to indigo, deep purple and then push on in to the UV range and beyond. Light coming at you is having its wavelength reduced because you're getting there faster. If this was a biological creature, it would need to be able to see very high frequency EM to steer at speed. It should be able to see radio, microwave and well beyond. It may have a multiplex eye with different parts for different wavelengths or different sets of eyes that work in different ranges. If it always kept its eyes open, inhabited planets and ships would look like a disco ball of various types of radiation.

It wouldn't feel time moving faster or slower, however whenever it slowed down to non-relativistic speeds, it would discover that way more time passed for everyone else than it. Time and space are like the numerator and denominator of a fraction in a fixed ratio. If you have 1/2 and want to double the numerator, but also keep the ratio the same, the denominator needs to double as well. Moving through space slows down your movement through time and vice versa. While moving at high rate time is ticking slower for you than everyone else. You don't feel it because to detect something there has to be a difference. The reason a ruler works is that you can hold it up to something of a different length. If everything was the same length, a ruler wouldn't help, or be necessary. Time affects all of you the same way whether you are moving through it faster or slower. This would however have interesting effects.

It likely wouldn't have a strong concept of time. Time and distance are two sides of the same equation. It would need some other way to mark the passage of its personal time and experienced age. Maybe there are certain physiological changes (turning gray?) that demarcate their felt age. Maybe if they can see strong EM they can do a type of sight-based carbon dating. Watching the rate of radioactive decay (if it can see EM) in some object could tell it how much time the object (or creature) has experienced.

If sentient, it would useful to be telepathic. Languages would change so quickly (in its experience) that it would never be able to keep up. Social norms and culture could also skew wildly after only a little relativistic time. These creatures would likely be fairly insular as they grew older, since everything passes.

It would need very good sight, likely some type of precognition, in order to make sure it didn't collide with anything during a high-speed jaunt. If it is traveling close to the speed of light, it likely wouldn't have time to react to "seeing" something before hitting it.

It would need some type of protection against contact with - anything at high speed. A tiny fleck of dust can impact with massive energy at relativistic speed.

It would be very difficult to tick all those boxes biologically. This critter had to somehow need that ability to survive. To accomplish relativistic travel it needs to essentially be a god. It needs to be able to survive massive impacts, see nearly all wavelengths, be precognisant (likely telepathic if it needs to communicate with other species) and be able to generate massive amounts of power. The farther you get from the speed of causality the less these issues matter.

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There is no relativity, special or general.

In your story you dont have to assume that Theory of Relativity is correct.

If you believe that the theory is correct then you also have to believe that reality is subjective. That for different observers a same object exist at different sizes. This is nut job.

Look at "barn door" paradox which refutes Theory of Relativity. Its roughly like this: suppose we make a barn or any container exactly as big as what it to contain, say a train. So, if we close the doors at 2 ends train fit exactly inside. "Exactly" here means with say 1 ft or 2 ft whatever extra capacity in the barn.

Now, if Theory of Relativity is correct then as the train approach light speed it gets contracted for some observer and stay at its original (rest time) size AT THE SAME TIME.

So, one observer sees it fitting exactly in the barn and with the doors closed. Another observer see it longer than the barn so its coming out of it at both ends. Here is the fun part, this observer also see the barn doors closed. He see no damage to the door and no damage to the train. The doors are closed yet the train extend beyond the doors.

There are many other paradoxes as well as this one. They all refute the Theory of Relativity.

What do happen is an illusion. Like a broken pencil in water. Just a mirage. The pencil is not broken.

First 400 milliseconds after big bang, universe expanded millions of times faster than speed of light? How? Now they fool you by saying that space expanded. What? Space by definition is empty space. Vacuum. Nothing. How can nothing do anything? They will say that the first 400 milliseconds after big bang universe expanded so fast that there are parts of universe you can never reach even if you travel at speed of light or even ten times that because some parts of universe right now are going away from us thousands or even millions of time faster than speed of light. What? Didnt they said that speed of light is the ultimate speed limit? How can you distinguish matter moving away from each other from space expanding.

If 100 airplanes hovering above ground in square formation with equal distance between them, say 1 km, move in such a way that they double their inner distances, you know by the planes at edges moving away 10 kms, the ones behind them 9 kms and so on, they will say that its space thats expanding, not the planes that are moving.

Show them the fumes of burnt petrol.

This is worldbuilding site, not physics site, you dont have to take Theory of Relativity as granted. You can write your story as you see fit.

The point of this answer is, OP, that there is enough ammunition to refute Theory of Relativity. Logic do. Proof by Contradiction do. People that believe in the theory do so by dogma, not by logic and not by any science. They will say "there are many experiments" but not go in detail of any experiment, because you know, they dont do science. They do theory. You can "proof" anything in theory.

You are now aware of existence of very logical and very scientific minded audience that actually do science. You can write story for them.

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    $\begingroup$ The barn door paradox doesn't refute relativity; it just says that relativity is incompatible with the existence of a perfectly rigid object. (Relativity implies some sort of "cosmic speed limit" – and if the ends of the ladder – or, in your telling, train – can react to each other's movement faster than that, you get time travel paradoxes.) $\endgroup$
    – wizzwizz4
    Dec 22, 2022 at 21:23
  • $\begingroup$ “How can you distinguish matter moving away from each other from space expanding.” By the behaviour of light, gravity, and other things that are instant. By observing the cosmic microwave background radiation – the closest thing we can see to a "stationary with respect to the universe". (The known laws of physics don't have a "stationary", but the actual objects in the universe appear to.) $\endgroup$
    – wizzwizz4
    Dec 22, 2022 at 21:26
  • $\begingroup$ General relativity is trickier to make an experiment for, but you can prove special relativity to yourself using lasers, clocks and centrifuges. Thanks to consumer electronics, that equipment is quite cheap these days! $\endgroup$
    – wizzwizz4
    Dec 22, 2022 at 21:27
  • $\begingroup$ No, general relativity dont make any special treatment for any kind of object. It claims to be a universal law. Dont use "perfect" to confuse. Perfectly rigid objects dont exist and it dont matter. The barn door refutal still works. $\endgroup$
    – Atif
    Dec 23, 2022 at 1:57
  • 1
    $\begingroup$ @atif the barn door paradox also relies on simultaneity being absolute. It is not. If the doors are closed simultaneously in the reference frame of the barn, they will not appear to close simultaneously in the reference frame of the train, and no paradox occurs $\endgroup$
    – Tristan
    Dec 23, 2022 at 9:31

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