No, the space being shown here remains entirely flat. There is length contraction and time dilation at play, but that’s a uniform effect. The reason the image appears distorted is because we have more time to catch up to light rays emitted from farther away. This visual phenomenon is called Terrell rotation.
It’s based entirely on special relativity—not to be confused with general relativity, which deals with curved spacetime in the presence of gravitational fields.
Submitted title was "Website to observe how space is curved the closer you get to the speed of light". We got complaints about that, so have reverted to the web page's own title.
Also check out the game "A Slower Speed of Light" [0] if you are interested in visualization of relativistic effects. It includes effects like Doppler shifting of colors, perceived warping of space and time dilation. Good luck at not getting nauseous.
Although if you’re on macOS Catalina or higher, the game no longer runs. And since the team abandoned it without open sourcing it[0], it can’t be recompiled for 64-bit.
[0] Although they did open source some of their scripts and shaders as a Unity plugin called OpenRelativity, which was cool.
You could make different player’s in-game clocks appear slower or faster, but you obviously couldn’t affect the players’ actual subjective clocks, so you obviously couldn’t do any of the interesting things like the twin paradox, unless the entire in-game simulation was sped up significantly and you could do something interesting with in-game characters aging at different rates.
Something I found very interesting when I learned about it several years ago: it's possible to formulate SR and GR with the Euclidean (++++) metric instead of the Minkowski (+---) or (-+++) metric. Such a formulation (there is a variety of them) is sometimes called Euclidean Relativity (ER).
A new description of gravitational motion will be proposed. It is part of the proper time formulation of physics as presented on the IARD 2000 conference. According to this formulation the proper time of an object is taken as its fourth coordinate. As a consequence, one obtains a circular space–time diagram where distances are measured with the Euclidean metric. The relativistic factor turns out to be of simple goniometric origin. It further follows that the Lagrangian for gravitational dynamics does not require an interpretation in terms of curvature of space–time. The flat space model for gravitational dynamics leads to the correct predictions for the bending of light, the perihelion shift of Mercury and gravitational red-shift. The new theory is free of singularities.
A really excellent series if you like math and physics. It gets bad reviews because most readers aren’t looking for a physics text disguised as a novel. Personally, I love it.
Looks nice, I used a more complicated version during undergrad for a physics lab. It was great as you could explore length contraction, time dilation etc, and also had toggles for enabling some of the really crazy relativistic effects. https://people.physics.anu.edu.au/~cms130/RTR/
Some of the funny effects seen here come not from relativity but from the finite time of propogation. In fact, relativity _reduces_ the effect of you see from time of propogation. An example is that objects seem to be curved, because it takes more time for the light from there to get to you, and you move in that time. With relativity, this apparent curvature is less.
Somewhat related, the relativistic rocket equation itself is pretty fascinating. I've written some code that lets one play around with it: https://github.com/the80srobot/gorocket
It's only when you try simulating relativistic physics yourself that some points become apparent. For example, I didn't remember from school that all observers agree on acceleration, and in the first implementation I treated it as happening over time experienced by the accelerating frame. By having all of my unit tests spit out nonsense and figuring out what the problem was, it finally "clicked" for me.
If I have a point (do I?) it is this: if you're trying to learn physics, I highly recommend trying to code some simple simulations yourself. It's amazing how much better one can understand stuff that way, than reading from a book.
Have you looked at SICM? (Structure and Interpretation of Classical Mechanics, the far less popular half-sibling of the SICP) https://mitpress.mit.edu/books/structure-and-interpretation-... -it has you derive classical mechanics, which is to say most() of Newtonian physics up to around 1900, by writing a giant pile of scheme that drives graphical simulations.
() For a curious value of "most" that elides thermodynamics, electromagnetism, etc..
Why does the slider conflate position with velocity? Leave it at 0.95c for a minute, put it back to zero, then watch as your position is re-set back to 0. Subsequently slide it back to 0.95c, your position is magically fast-forwarded to your previous position, along with resumption of velocity.
OK, so here's a question that I've never been able to find a clear answer for (that I understood)...
Say I'm sitting on the bridge of a spaceship travelling N-times the speed of light. I'm facing forward. What do I see? Am I blinded because photons from far off stars are hitting my eyes at an increased rate?
Also, if I look to the left and the right, and behind me? What do I see ?
In Star Trek, it's all stripy-stars, and I'm sure that's not correct.
But what you can do is imagine what would happen if you reached the speed of light.
Length contraction means that while you and your ship appear to be the normal size, the universe around you shrinks along the direction of travel. The faster you go, the less distance there is in front and behind you. At the speed of light, the entire width of the universe shrinks to zero.
Also, you are at the same time experiencing time dilation. Although time on board your ship advances at the normal rate, time outside the ship appears to slow down. When you reach the speed of light, the rate of time passing outside the ship goes completely to zero.
Together these mean that the universe outside your ship effectively vanishes! It occupies no volume, and has no events in it. At the speed of light, your current position and your destination are the _same place_, because there is no distance and no time separating them.
This is why you cannot go faster than the speed of light. There aren’t any speeds faster than that.
> The faster you go, the less distance there is in front and behind you. At the speed of light, the entire width of the universe shrinks to zero.
Since you could get to anywhere in the universe almost instantly by travelling sufficiently close to the speed of light, why do many science fiction writers and science fiction movies want to introduce faster than light travel? It doesn’t seem necessary; just tell the readers that the spaceship was travelling at 0.99999c to get to the other size of the galaxy in a week or at 0.99999999c to get there in a minute. (I didn’t do the calculation, but you can imagine what I mean.)
I’m going to guess that it’s easier to move the story along by saying “faster than light” than it is to explain the above. Most people would think the author made a goof by saying that something travelled 100,000 light years in less than 100,000 years if travelling at less than the speed of light. (Talking from the traveller’s perspective of course.)
> why do many science fiction writers and science fiction movies want to introduce faster than light travel?
Because this way you keep the human timescales for all characters. It allows you to tell stories more familiar to your audience while introducing elements that we wouldn’t be able to introduce without this plot device.
If you embark on a relativistic trip to Kepler-186f, when you return you will find a completely changed planet. The only way this would work is if every character spends most of the time at relativistic speeds reuniting from time to time as the whole universe ages around them.
Most writers did not take science classes in college; they got a liberal arts degree and not a physics degree. On the other hand there are a few writers who do a better job of things.
Vernor Vinge does a great job in A Deepness In The Sky of creating a human space–fairing society that has to deal with some degree of relativity. Their ships only manage a 0.3× the speed of light, but they also use suspended animation to hibernate for most of their voyages. A trip where you age a year might mean that hundreds of years pass on the planet you’re going to. One character founded a vast trading coalition that was enormously successful in spite of this and other handicaps.
Greg Egan wrote a book called The Clockwork Rocket that is set in a universe where the space–time metric is different. This has huge effects on all aspects of physics from relativity to quantum mechanics, and he worked out all of those implications before writing the story. You can learn a lot about our universe just by contemplating all of the ways that this fictional Riemannian universe is different from our own Lorentzian universe. For example, in the Riemannian universe there is no fixed upper bound on speeds, light travels at different speeds based on its color, and thermodynamics is backwards so plants gain energy not by absorbing light but by emitting it.
> Since you could get to anywhere in the universe almost instantly by travelling sufficiently close to the speed of light
But the universe is billions of light years across - if someone is travelling at just under the speed of light, wouldn't that mean it would take them billions of years (as experienced on the ship) to traverse the universe?
> why do many science fiction writers and science fiction movies want to introduce faster than light travel?
My thought on this, from a purely sci-fi perspective, is that accelerating close to light speed would use a phenomenonal amount of energy, and take a long time to do. Furthermore, time is experienced differently for those on the ship and those outside it. So with these points in mind, some kind of "hack" that allows you to fold spacetime and jump several lightyears instantaneously (as experienced by everyone) makes sense.
I get that time passes slower for those outwith the ship, but I'm struggling to wrap my head around how long it would take those on the ship to travel large distances at close to light speed - whenever I think on this topic, my head almost bursts with awe and wonder!
Let's consider a ship, travelling from Earth, and say it somehow accelerates almost instantly to just below light speed, and travels for a distance of 1 light year. How much time would pass for those still on Earth, and for those on the ship?
Ursula Le Guin's Hainish Cycle explores how an interstellar society would function if people could travel this way: an instant for the traveler, but decades back home. Despite glossing over all the technobabble that other scifi finds so fascinating, these books, more than any others I've read, show just how great the distances are between stars.
Funny thing is that this difference of passed time that remains after the spaceship slows down has more to do with acceletation and GR than speed and SR.
The fact that you can describe this effect from the point of SR (by swuinting a bit) means that you can get GR time dilatation from SR time dilatation with no additional input.
The moment that we knew that the acceleration is the same as the gravity and that the speed of light in vacuum is constant we only had to think long and hard to see that gravity causes time to flow differently in different places.
OTOH, by the time the Death Star arrives at Yavin, the Rebel civilisation will have collapsed a couple times and won’t even remember why they even got there in the first place.
Is this the foundation for the "holographic" description of the universe? Photons, traveling at the speed of light, effectively don't see one of the dimensions, so can be described using "N-1" dimensions. (Edit: Or does zero rest mass make them a special case?)
Can someone also confirm whether the following thinking is valid? The expansion of space means that the edge of the observable universe appears to be receding at the speed of light. As such, it has "N-1" dimensions and that is where the idea of a holographic boundary comes from? The same reasoning applies to the "N-1" dimensions of the event horizon in a black hole?
What made it click for me was that the speed of light isn't just the speed of light, but actually the speed of information/causality.
So if you're traveling at the speed of causality, everything you "hit" or go past happens instantly, because you're traveling "with" causality/information itself.
With a ship going the speed of light you could travel from galaxy to galaxy instantaneously. Zero distance. Though time on the other hand... If you travel to a star 4 light years away and then back, what would be no time for you, everyone on Earth would be 8 years older.
It ends up being worse than that once you plug in general relativity. You're only using special relativity, but that doesn't hold when acceleration is involved (as would be required to go from 0 to 0.99999999c).
"It's a common misconception that special relativity cannot handle accelerating objects or accelerating reference frames. Sometimes it's claimed that general relativity is required for these situations, the reason being given that special relativity only applies to inertial frames. This is not true. Special relativity treats accelerating frames differently from inertial frames, but can still deal with accelerating frames. And accelerating objects can be dealt with without even calling upon accelerating frames.
This idea that special relativity cannot handle acceleration or accelerated frames often comes up in the context of the twin paradox, when people claim that it can only be resolved in general relativity because of the acceleration present. Their claim is wrong."
Interesting, but the point remains that the answer is different from the 8 years mentioned given that you do have to accelerate up to near-c (at gees the human body can survive in) and then decelerate from it. You can't just instantly go up to near-c and then back down to zero. Whether it's special/general relativity that's necessary for this calculation, it's a materially different result.
Probably quite risky. You have little reaction time, every maneuver is 10× more expensive because your effective mass has gone up so much, and even collisions with small objects will release fantastic amounts of energy.
You don’t perceive the mass from inside the ship as its engines and attitude control are not relativistic in relation to you. You’ll see the object approaching at a relativistic speed, however, and it will release a very non Newtonian amount of energy if it hits.
I don't think you will - need to do the math though - but my impression is that the distorted time and space from the ship's frame of reference will account for the observed energy expended.
You cannot travel at or faster than the speed of light. I know this isn't satisfying, but that's why you've never had a clear answer.
As you approach the speed of light, (.9c, .99c, .999c...) two things happen.
1. Everything gets blue shifted. Light that would normally be coming at you in pretty shades of blue, green, and red become shades of ultra violet, then shades of x-rays, then shades of gamma rays.
2. More and more light arrives. As a result of length contraction/time dilation, you might get a century's worth of starlight in a second.
Depending on how fast you're going, the light coming in from in front of you might be extremely dangerous. Even a dim, cool Sun-like star might kill you with intense high energy gamma rays.
Left and right of you things would appear fairly normal.
Behind you, you'd have the opposite effect of what you see in front of you. Everything would be redshifted, and much lower intensity.
To ground the intuition with the amount of starlight, imagine all the light in the universe is a bunch of falling rain, and your rocket is barrelling through the entire volume of it at .99c. It's a lotta light.
Since you can’t travel faster than light in continuous space time there is no way to answer this. At the speed of light relativistic distortions lead to a singularity, so bye bye spacetime.
The one even faint possibility we know of, the Alcubier effect, puts you in a bubble of space time and warps that so it propagates at FTL speeds, but within that space time bubble you are stationary. You wouldn’t see anything outside the bubble though as it’s beyond an extreme distortion of space time that light cannot penetrate.
The Relativity prohibition is that anything with mass can not travel as fast as light because approaching c, mass increases requiring more and more energy while time slows, such traveling at c increases apparent mass to infinity, requires infinite energy, and time slows to a stop. The same thing could be said for anything moving FTL, as it approaches c, mass increases and time slows to zero. Relativity does not prohibit FTL travel, only travel at c.
The problem is a bit deeper than that, it doesn't just require infinite energy there simply is no isometry of space that can transform something faster than the speed of light into something slower than the speed of light and vice-versa. So really there's no way to map the laws of physics for something faster than light onto those for something moving slower than light. For similar reasons there are no known elementary particles that can maintain their existence in a superluminal trajectory.
Right, so the maths works for superluminal trajectories, but that doesn’t mean it corresponds to anything physical and to get ‘there’ from ‘here’ you need to get past that singularity.
Well saying the math 'works' is not quite right. If anything the math doesn't work out because there is no way to transform a normal trajectory into a superluminal one.
Sure you can just define a line through space-time that is superluminal. That's basically equivalent to just defining a singular moment in time, the same way that an (inertial) trajectory defines a constant position.
Particles that travel faster than light have been theorized about for a long time. However, if something was traveling faster than light speed it apparently could never slow down to light speed.
I'm not too sure this question is well-posed, there simply isn't an isometry of space that would take a trajectory traveling faster than the speed of light and make it inertial. As such we have no description of the laws of physics that someone would experience on such a trajectory. So how things like red/blue-shifting etc. would work out is simply not knowable.
Now if you were just wondering what you'd see if you simply changed position really quickly then you can just imagine putting lots of cameras in a long straight line and triggering them in turn to simulate a superluminal speed then you basically would just see the stars move more quickly than possible. You'd also see time progressing backwards on the stars that you are 'moving' away from and more quickly on the stars that you are 'approaching'.
So the stripy stars bit is not really that far off.
> Now if you were just wondering what you'd see if you simply changed position really quickly then you can just imagine putting lots of cameras in a long straight line and triggering them in turn to simulate a superluminal speed then you basically would just see the stars move more quickly than possible.
Or just watch Star Trek, as the iconic “moving through stars” happens throughout the series (mostly TOS, as others added different effects)
Assuming N<1, you see a scrunched up, blue-shifted version of the night sky in the forward direction and very little in the aft direction... this is a combination of the fact that the stars at the various grid points where the stars are now are truly Lorentz-transformed to be more numerous in the forward direction + the usual "aberration" effect accounting for the fact that you are seeing the stars at the retarded time where they were when their light was emitted, not right now. See: https://math.ucr.edu/home/baez/physics/Relativity/SR/Spacesh...
One thing I don't understand about what this page seems to suggest: shouldn't there be a bright ring of starlight at some non-zero angle away from dead ahead?
Given a finite collection of objects out to a certain radius (stars), relativistic length contraction will compress it along the direction of travel, so an observer looking out from the centre should see the density increase to a maximum when perpendicular to the contracted direction (in a way that's sort of the opposite of synchrotron radiation ending up tightly directed forward and backward). I guess the aberration described in your link will bend this fore-wards from the perpendicular, but it seems like it should still be visible.
If you travel through a localized clump of stars then yes, as you describe, the clump would be pancake-shaped. However, the Lorentz transform of an infinite lattice is another infinite lattice, just one in which the spacing between stars in one of the three directions is smaller. So, in particular, the average density everywhere remains uniform (no matter where you are situated within the lattice).
The reason you don’t see an isotropic distribution of light from this uniform density is the distortion due to aberration + the synchrotron effect you mention (which makes the stars in the forward direction brighter).
So, in conclusion no “critical angle” but the dots of light appear more densely concentrated toward front and they are brighter, bluer.
The question likely makes no sense, you can't travel at N-times the speed of light for N >= 1. If we're wrong and you can, we probably have no idea what it'd look like.
You could kind of guess by trying to extend our models out to those speeds, but I think you're going to just find random guesses and formulas that no longer make any sense because you've exceeded the range of values they're defined over.
That's a good question, I am naive to this as well. However my guess is that if you looked forward you would see a dilation effect. Looking backward, you would see the same, just reversed. If you could go faster than light then looking behind you would be darkness (since light can't catch you). However looking forward, could it be that normal light is dilated to such a degree that we change perspective and can see things normally not in our visual range (like Infrared)?
Looking forward, you will see light with wave length contracted or frequency multiplied by factor N+1, e.g. at N=1 front light will have wave length reduced/ frequency increased by 2x.
Looking backward or left/right, you will see nothing (darkness), because these photons have no chance to hit you. It will be more like a Pac-Man game: chose a photon, hit it, consume it, then move forward to a next photon.
IIRC the light coming from in front of you gets blue shifted, each photon increasing in energy, and the count increases because of the geometric changes you see in the video (the angles in front seem to shrink).
Light from the rear red shifts (each photon has less energy), and there are fewer as some of the (formerly incident) photons "rotated" to the front.
(edit: typo)
(edit: didn't read the question closely, this is about approaching c, not exceeding it)
i cloned the repo earlier to see what would happen. difference between .95c and .999c is unremarkable. equal to and above 1 results in all of the geometry disappearing, just shows black.
You find a number of ships fleeing from a small space station. You hail them, asking what's wrong: "Help! We're being overrun by some sort of giant alien spiders!"
Only at c. Once you are beyond it (even though you can’t pass it), you’ll get squared imaginary numbers, however, which I’m sure would not be healthy for human passengers.
https://en.wikipedia.org/wiki/Terrell_rotation
It’s based entirely on special relativity—not to be confused with general relativity, which deals with curved spacetime in the presence of gravitational fields.