# Galaxies traveling faster than c away from each other

## Main Question or Discussion Point

It is known that, by the expansion of the universe, galaxies that are roughly 4200 megaparsecs away travel away from each other faster than c.

A little thought experiment on this;

1- The equation for relativity suggests that results become unphysical.
2- Time would be stopping or going backwards.
3- Effects can be before the cause.
4- Mass of an object would become infinite

Now, this would be disproving everything we know so far. And assuming we know things right, we can conclude;

1- When two galaxies move away from each other faster than c, they can no longer communicate with each other. Therefore this solves the arising problem that effect can be before cause.

2- For them to be unable to communicate with each other, even if an object travels back faster than c from one galaxy by any means, it can not reach the other galaxy. This would mean that once two galaxies are past the threshold they no longer are part of the same universe. (To explain simply)

3- Beyond the threshold the galaxy slowly becomes stationary and redshift and disappear from the other galaxies universe.

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Now after reading these points, i have one question. Since the galaxy is becoming stationary and redshifting from the other galaxies point of view. How does relativity explain what happens after enough time passes and a galaxy reaches to the coordinates that another galaxy has redshifted from its universe?

Normally the galaxy A is no longer there, and no effect would be expected. But from galaxy Bs point of view that coordinate is the exit point of the galaxy A. And relativity suggests its mass would be infinite, its time would have stopped.

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PeterDonis
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It is known that, by the expansion of the universe, galaxies that are roughly 4200 megaparsecs away travel away from each other faster than c.
That's not quite what "is known". What is known is that a certain quantity that appears in the math has a value greater than 1 (or $c$ if you use conventional units where the speed of light is not 1). But you can't interpret that quantity as a "speed" in the usual sense, because it isn't. In general relativity, "speed" (in the usual special relativistic sense, where nothing can go faster than light), or more precisely "relative speed", can only be defined for objects that are co-located in space; there is no invariant way to define "relative speed" between objects that are spatially separated, because of spacetime curvature; the way "relative speed" is defined in special relativity for spatially separated objects only works if spacetime is flat (i.e,. no gravity).

A little thought experiment on this
Your thought experiment doesn't work, because it's based on an incorrect interpretation of the quantity in the math that you are calling the "speed of recession" of the galaxy.

Orodruin
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Your thoughts are based on assuming special relativity and that expansion is due to relative motion. This is not true, expansion is an expansion of space itself and must be treated with general relativity.

A.T.
When two galaxies move away from each other faster than c, they can no longer communicate with each other.
They don't move away in the sense of relative movement, so they can communicate:

A.T. you can recieve the ancient light from such galaxies.

The distance from such galaxy is shown as the orange line while the light you are recieving is shown as red. That doesn't mean you can communicate with them.

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So special relativity doesn't work for my examples. These objects must be co-located, i get that. But in the end, every galaxy was co-located at the point of Big Bang, or were they not?

When exactly Special Relativity stopped working for these co-located objects?

And one last question about gravity.. How come we can talk about gravity and general relativity between these Galaxy A and Galaxy B, if there were some kind of gravitational force in the area between them, then space wouldn't be expanding. Isn't that so?

PeterDonis
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every galaxy was co-located at the point of Big Bang, or were they not?
Well, there weren't any galaxies when the Big Bang took place; galaxies didn't form until a long time after the Big Bang. But we can rephrase your question to be "all worldlines in the universe, when extended back into the past, meet up with each other and were therefore co-located at the Big Bang, or were they not?" The answer is, yes, in principle, they were.

When exactly Special Relativity stopped working for these co-located objects?
When the combination of spacetime curvature and separation of the objects by expansion of the universe meant that they could no longer be included in the same local inertial frame. This would have happened very quickly, within about $10^{-35}$ second after the Big Bang, because the universe was undergoing inflation then.

if there were some kind of gravitational force in the area between them, then space wouldn't be expanding. Isn't that so?
No. The effect of the gravity of the various galaxies is to slow down the expansion, which is just what you would expect: objects are flying apart, but there is an attraction between them that slows down the flying apart.

It's true that, for the last few billion years, the expansion of the universe has been speeding up, not slowing down. But that's because a few billion years ago, the effect of dark energy became stronger than the effect of the gravity of the galaxies and other matter in the universe. So before a few billion years ago, when the effect of the gravity of the matter was stronger, the expansion was indeed slowing down.

A.T.
A.T. you can recieve the ancient light from such galaxies.
Our signals send out now can reach a galaxy that is already receding from us faster than c.

When exactly Special Relativity stopped working for these co-located objects?
Special Relativity works only in flat space-time, which doesn't exist. It is just an approximation. When approximations stop working depends on how accurate the results must be.

phinds
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... we can rephrase your question to be "all worldlines in the universe, when extended back into the past, meet up with each other and were therefore co-located at the Big Bang, or were they not?" The answer is, yes, in principle, they were.
How does that work if it does turn out that the universe is (and was) infinite in extent?

PeterDonis
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How does that work if it does turn out that the universe is (and was) infinite in extent?
Good point; a more precise rephrasing would, instead of "all worldlines", say something like "all worldlines which are within our observable universe (or some other finite region, such as within 4200 megaparsecs) at the present time".

If the universe is (as our current best-fit model says) infinite in extent, then things get very counterintuitive as we approach the Big Bang: the scale factor approaches zero, so the proper distance between any two given worldlines approaches zero; but since the universe is still infinite in extent, one can always find *some* worldline at any instant of time after the Big Bang that is farther away from a given worldline than any chosen distance, however large.

We should also note that the "Big Bang" singularity itself, which is often talked about as being a "single point" even if the universe is infinite in extent, is not actually part of spacetime; it can only be approached as a limit.

phinds
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Thanks. I thought that was what it should be.

Well, by all this information at hand. How can anybody say that objects can't travel faster than c because the results of the special relativity equation becomes unphysical.

While we also know that Special Relativity doesn't work in the universe when you can't talk about locality for any two frames in the universe?

By the effort Peter showing it seems like, its quite hard to explain what the math says in English. Is that the problem here?

A good way to overcoming this kind of confusion about relative velocities is to realize that the only restriction relativity poses on the motion of massive particles is that their four-velocities be time-like.
I dont see how relative spatial velocities have much meaning if at all, in special relativity the statement that nothing can go faster than light has a defined meaning, but even there i'd not think it's very useful.

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A.T.
By the effort Peter showing it seems like, its quite hard to explain what the math says in English. Is that the problem here?
Yes. Pop-sci explanations always leave out many caveats that constrain the area of their validity.

pervect
Staff Emeritus
Well, by all this information at hand. How can anybody say that objects can't travel faster than c because the results of the special relativity equation becomes unphysical.

While we also know that Special Relativity doesn't work in the universe when you can't talk about locality for any two frames in the universe?

By the effort Peter showing it seems like, its quite hard to explain what the math says in English. Is that the problem here?
It's not really that hard to explain, but the explanation turns out to be very abstract. My impression is that people wind up not understanding it due to a combination of the abstractness of the explanation, and the fact that they have a lot of pre-existing ideas, so that understanding the abstract issues here aren't possible in a specific manner until one has understood SR. Unfortunately people who are asking the question ask it in a effort to understand SR :(.

The mathematicians tell us that velocity can only be precisely defined for two objects at the same location.

See for instance http://math.ucr.edu/home/baez/einstein/einstein.pdf

Before stating Einstein's equation, we need a little preparation. We assume the reader is somewhat familiar with special relativity -- otherwise general relativity will be too hard. But there are some big differences between special and general relativity, which can cause immense confusion if neglected.

In special relativity, we cannot talk about absolute velocities, but only relative velocities. For example, we cannot sensibly ask if a particle is at rest, only whether it is at rest relative to another. The reason is that in this theory, velocities are described as vectors in 4-dimensional spacetime. Switching to a different inertial coordinate system can change which way these vectors point relative to our coordinate axes, but not whether two of them point the same way.

In general relativity, we cannot even talk about relative velocities, except for two particles at the same point of spacetime -- that is, at the same place at the same instant. The reason is that in general relativity, we take very seriously the notion that a vector is a little arrow sitting at a particular point in spacetime. To compare vectors at different points of spacetime, we must carry one over to the other. The process of carrying a vector along a path without turning or stretching it is called `parallel transport'. When spacetime is curved, the result of parallel transport from one point to another depends on the path taken! In fact, this is the very definition of what it means for spacetime to be curved. Thus it is ambiguous to ask whether two particles have the same velocity vector unless they are at the same point of spacetime.
For sensibility, I would add that when Baez says "we can't even talk about relative velocities", it's implied that he means "we can't talk about relative velocities in a coordinate and observer independent manner".

So the situation is that in the flat space-time of SR we can definitely say that objects can't go faster than "c", but there does exist a coordinate independent way of comparing velocities to get a relative velocity. In GR we can only compare velocities in a coordinate independent manner when they are at the same point, or at least so very close that curvature effects due to GR can be avoided.

So how do people talk about "recession velocities" if we can't compare relative velocities? This is an example of a coordinate-dependent method of comparison, where one assumes what is called "cosmological coordinates", loosely speaking these are the coordinates of observers moving so that the universe as a whole (and the cosmic microwave background in particular) appears to be the same in all directions (i.e. isotropic).

Difficulties arise when we "forget" that this widely used method of comparing velocities in cosmology depends on the choice of a particular observer and a particular coordinate system unique to our universe, especially since GR avoids doing this in other contexts.

Drakkith
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