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Suppose you are standing 5 feet (1.5 m) away from me. Then I move 10 feet (3.0 m) further away. Now you are at 15 feet (4.5 m) distance from me.

You say I moved. I say no; the space between us has expanded. You can point me to other things around you that are still at same distance from you. You say if the space has expanded then those things must have also moved away from you.

You are right of course.

If somebody say that there isn't any expansion of space. It's just objects, heavenly bodies whatever that move away from each other. Like when a bomb explode fragments of its shell move away from the center. That’s what’s going on since the Big Bang. What’s wrong in that explanation?

It does go against the well-established claim that nothing that has mass can reach the speed of light. Heavenly bodies—stars, planets, etc.—have mass, so they cannot reach the speed of light given that they start from a lower than light speed.

How can we distinguish the eexpansion of space from objects just moving away from each other? If we plot the expansion backward in time, we see all the objects getting closer to each other and also to a center point so much so that at the very start, the Big Bang, they all converge to a point.

What’s wrong in saying that the Big Bang is an explosion that’s still happening, the heavenly bodies are moving away from the center and therefore also moving away from each other, and that since we see them moving away faster and faster till they reach speed of light and thus we stop seeing them, we can safely deduce that they have reached speed of light and may have gone even beyond?

Why would we say, opposite of what we deduce on basis of observation, and nothing that we observe go against the deduction, that it’s the space that expands, not the object reaching lightspeed and then become even faster?

Is there something in observation that can be pointed out to distinguish between space expansion and heavenly bodies moving away from each other and a center point? If there is nothing in observation to distinguish that then is there something in deduction about it? Like in the thought experiment at the top of this question where you pointed other objects to proof your point that the space didn't expand between us, its I who moved?

Qmechanic
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    Expansion of space is not distinguishable from objects moving away. It is only a common misconception that there is a distinction. See https://physics.stackexchange.com/a/505727/180843 – Sten Jul 06 '23 at 08:09
  • The speed of light isn't exceeded, either. See for example https://physics.stackexchange.com/a/504948/180843 – Sten Jul 06 '23 at 08:15
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    @Sten You are saying that no galaxy is receding away from us at speed of light or exceed that speed? – Atif Jul 06 '23 at 08:17
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    @Atif There are galaxies that are inferred to recede faster than light. But cosmological recession rates are not velocities in any relativistically meaningful sense, so there's no reason to compare them to the speed of light. (See the answer I linked!) – Sten Jul 06 '23 at 08:19
  • @Sten I understand where you're coming from, and while nailing down the way this is talked about is very important for practicing physicists, for someone, like the OP, who is trying to gain some understanding of the material and doesn't have the appropriate scientific training, this is little more than opaque academic pedantry that does nothing to shed light on the subject, and may even be just as misleading, because they lack the context to understand what you're trying to say. – Filip Milovanović Jul 06 '23 at 21:56
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    @FilipMilovanović How would you propose addressing the question, then? I would contend that any answer to "how is true?" that doesn't involve " is false" is misleading. If your only objection is to the comment (and not the answer, with its added context), then I'll note that the the purpose of a comment is not to answer the question. The main reason I started with that comment was to inform potential answerers. – Sten Jul 06 '23 at 22:09
  • Two objects, A + B, are moving in opposite directions with A travelling at 45% the speed of light and B travelling at 50%. A receives a boost and accelerates to 55%. They are then moving apart faster than light can travel. Is there more to this question? – Wookie Jul 07 '23 at 11:50
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    @Sten You said "Cosmological recession rates are not velocities in any relativistically meaningful sense" then theory of relativity do not explain the data and therefore is incomplete / wrong. Our observation tells us that certain galaxies keep accelerating away from us till they reach speed of light and we infer from the available data - no deceleration - that they continue with superluminal speed. This data should be explained. Instead, to justify a theory that don't explain data definition of movement and velocity is changed. You know you can always "win" by redefining what win means. – Atif Jul 07 '23 at 20:59
  • @Atif That reasoning is backwards. We chose to define the cosmological recession rate in a particular way because it is useful in some contexts. According to the definition we chose, it is possible for objects to recede faster than the speed of light. Observations don't play a role here because we only observe redshifts. We use the established definition of the recession rate, which we already know can be superluminal, to calculate the recession rate from the redshift. There is no sense in which these observations tell us anything that is difficult to explain in the context of relativity. – Sten Jul 07 '23 at 21:10
  • @Atif Saying that superluminal recession rates require a concept of expanding space is equivalent to saying that the possibility of two particles moving at >50% the speed of light in opposite directions requires a concept of expanding/contracting/shearing (or whatever) space, lest they exceed the speed of light relative to each other. The issue is the same in both cases: relativistic velocity addition has been ignored. – Sten Jul 07 '23 at 21:15
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    @Sten We can choose any definition ofcourse, we just have to be consistent AND explain the observation. There are these two unmovable mountains on which we build theories, or we are supposed to build on that. Ofcourse we can change definitions as we know more (by observation) but then we have to go back and change all theories that use old definitions. You will agree upto this point. Its all about observations. The redshift deduction about its link with acceleration away from us is built on observation. – Atif Jul 07 '23 at 21:32
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    @Sten You have to get away from your mathematical mindset of defining your way out of problems. It works only in maths, not in physics. In physics you have to reconcile with observation. Telling fairytale equations don't work. Neither do being inconsistent work. We know by observation that mass accelerating away from us radiate photons that when reach us are redshifted. We observe that even on nearer objects accelerating away from us that nobody claim is moving away from us because of claimed expansion of space. The concept of expansion of space is built upon observing redshifted photons. – Atif Jul 07 '23 at 21:44
  • @Atif Observations just say that light from galaxies is reduced in frequency by factors up to around 10. Explain why you think that implies things are moving faster than light or space is expanding. – Sten Jul 07 '23 at 21:46
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    @Sten Good questions. I already answered them in my comments to your answer below. – Atif Jul 07 '23 at 22:17

1 Answers1

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In general relativity, expansion of space is not distinguishable from objects moving away.

It is only a common misconception that there is a distinction. This point has been addressed in a number of other answers on this site, by myself and others. Rather than argue it again, I will link a few of my favorites:

However, most readers won't have the general relativity background to assess these arguments on their merits. If you are not sure, then, whether to believe random people on Stack Exchange, take it from eminent cosmologists instead:

The idea of an expanding universe can easily lead to confusion, and this note tries to counter some of the more tenacious misconceptions. The worst of these is the ‘expanding space’ fallacy.

One of the key ideas of general relativity is the importance of distinguishing between coordinate-independent and coordinate-dependent statements. Another is the idea that spacetime is always locally indistinguishable from Minkowski spacetime. Cosmology instructors, books (especially at the introductory level), and students often fall into the fallacy of reifying the rubber sheet; that is, treating the expanding-rubber-sheet model of space as if it were a real substance. This error leads people away from both of these key ideas and causes mistaken intuitions such as that the Milky Way Galaxy must constantly “resist the temptation” to expand with the expanding universe or that the “tethered galaxy” described in Sec. I moves away after the tether is cut.

The answer is: space does not expand. Cosmologists sometimes talk about expanding space – but they should know better.

Expanding space is a very unhelpful concept. Think of the Universe in a Newtonian way – that is simply, in terms of galaxies exploding away from each other.

are not arguments about the theory — everyone agrees on what GR predicts for observables in cosmology. These are only arguments about an analogy, i.e. the translation into English words.

By the way, the last point is why you won't find much discussion of whether space is expanding in academic circles. It's just not a scientific question. That's why the only academic article on this list is an article about pedagogy.

What about faster-than-light recession rates?

There is no need to invoke expansion of space to explain galaxies receding faster than light. Nor do such recession rates violate relativity. This is because the cosmological recession rate is not a relative velocity.

Conceptually, imagine a chain of galaxies that leads to your target galaxy. Each galaxy along the chain has some small velocity relative to the galaxy before it. If you add all of those relative velocities together, that should give you the velocity of the target galaxy, right? However, velocities in relativity add in a special way; see the relativistic velocity addition formula. The cosmological recession rate is computed by instead just adding the relative velocities naively, without properly using relativistic velocity addition. That's why we should not be concerned that it can exceed the speed of light.

Other good explanations as to why faster-than-light cosmological recession is not concerning include:

Also, note that there is not a unique way to define the relative velocity between cosmologically distant objects; see this question for more detail. This is part of why we are fine with talking about recession rates instead of actual relative velocities. There is no unique "actual" relative velocity to even talk about.

Sten
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    Theory of Relativity has assumption that nothing that has mass can travel faster than speed of light. The theory is built upon that. If anything massive can be shown to move faster than speed of light then the theory just become a fairytale, may be symmetric and beautiful, even logical but dont explain anything about this universe. We have data that show galaxies - that are obviously massive - moving away from each other at speed of light and since we observe them still accelerating - photons from them continue to come redshifted - AND we stop seeing them after that we can deduce they go ... – Atif Jul 07 '23 at 22:02
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    ... superluminal. This is observation. It goes against the speed of light assumption in theory of relativity. It makes the theory a fairytale. The theory do not explain this universe even in approximation because the base of theory is gone. Theories are based on assumptions. Its a matter of fundamentals. The theory now explain a fictional universe. So please don't keep bringing it up. Try to think outside that theory and give an explanation. I don't downvote your answer because its clear and logical. It just don't explain anything outside an anti-observation theory. – Atif Jul 07 '23 at 22:11
  • @Atif We don't have data showing that things move faster than light. The recession rate is inferred theoretically, and we already know it can be faster than light even without observations. Again, it's not a relative velocity. (See the linked answers explaining what the recession rate means!) Also, we don't "stop seeing" galaxies, nor do we expect to. Neither the "expanding space" nor the "galaxies moving apart" conventions (which are again equivalent) predict that. – Sten Jul 07 '23 at 22:17
  • @Atif To clarify that last point, since I've seen misconception about it elsewhere too: there are galaxies that "leave our horizon" at some point in their history. We won't see the future of those galaxies beyond some point. But they never disappear from our view -- we just continue to see them in the past. This is similar to a black hole's event horizon, if you've heard of what happens there. – Sten Jul 07 '23 at 22:23
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    Agreed that galaxies moving at superluminal speeds away from us is a deduction, not an observation, but its a deduction based on data and there is no data that go against this deduction. "Again, its not a relative velocity" If you mean relative as a term in theory of relativity then don't keep bringing theory of relativity up because it dont agree with data. Its like being a witness in your own case. Theory of relativity cannot prove itself, duh. If you mean relative in normal sense then how? If a thing move away from me then it moved away relative to me, had a velocity relative to me. – Atif Jul 07 '23 at 22:29
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    @Atif Does the fact that two particles can move in opposite directions each at more than half the speed of light disprove relativity? – Sten Jul 07 '23 at 22:30
  • @Atif As explained in one of the linked answers, the cosmological recession rate is what you get if consider a sequence of galaxies leading to your target object and add the relative velocities between all of the galaxies without using the relativistic velocity addition formula. So we should no more worry about the result being superluminal here than we should worry about the two oppositely moving particles having a superluminal relative velocity. – Sten Jul 07 '23 at 22:37
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    Please don't mix things up. Ofcourse photons emitted millions of years ago will continue to reach us for millions of years because then the galaxy wasn't moving away from us with speed of light or above. The discussion is about photons generated after the galaxy went superluminal. Come to think of this, if space is not expanding then even those photons will reach us and normally so. The photons always travel at speed of light ofcourse so whether or not the galaxy went superluminal do not matter. We will continue to see the galaxy. There cannot be a Hubble Sphere then. What do you think? – Atif Jul 07 '23 at 22:37
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    "Does the fact that two particles ..." How it don't? Aren't all frames-of-reference equally valid? Is there any data that show that one particle do not see the other moving away from it at superluminal speed? Even if there is it dont prove the theory of relativity. One counter example is enough to disprove a theory. It don't matter how many pro example you being then. – Atif Jul 07 '23 at 22:48
  • @Atif Regarding photons not reaching us: that's because of the gravitational influence of the dark energy. (Just like why photons can't reach us from inside a black hole's horizon.) Note that this doesn't correspond to the galaxy reaching a recession rate equal to the speed of light. As you have been arguing yourself, we already observe galaxies with recession rates greater than the speed of light. It's really just a function of how much dark energy there is and how large the distance is. – Sten Jul 07 '23 at 22:51
  • @Atif See relativistic velocity addition. If two particles are moving in opposite directions, each at 0.9 the speed of light, then they are moving at (0.9 + 0.9)/(1 + 0.9*0.9) = 0.994 the speed of light relative to each other. – Sten Jul 07 '23 at 22:55
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    Nobody knows what Dark Energy is. It just a term invented to fill hole in theory of relativity. Look at history of the term. As science advance more and more data come into observation because of more precise equipments. Theory of Relativity is unable to explain the data. Instead of correcting the theory or making another, professors went the lazy way or making up things willy nilly. They are loose variable because they aren't defined beyond "the thing I need here to plug this hole". They cannot be defined because they aren't known. – Atif Jul 07 '23 at 23:06
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    For example, what happened to "Energy can neither be created nor be destroyed but can only be converted from one form to another"? What is being converted to Dark Energy? Where do the Dark Energy come from? No where. The above theory is proved wrong by observation that galaxies are accelerating away from us. Net energy is being added to this universe. "See relativistic velocity addition" Why? Observation proved the theory wrong. Why apply it? Its very dangerous to use a wrong theory in your calculations because its not a matter of degree. Its a matter of fundamentals. You can be hit anywhere. – Atif Jul 07 '23 at 23:13
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    @Atif To be clear, I am answering (as stated at the outset) within the context of general relativity. If you wish to depart from that paradigm, I'll not stop you! – Sten Jul 07 '23 at 23:27
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    Atif, superluminous argument is completely bogus. You can't take distances from one model and compare redshifts with another model. That doesn't work. Distance is model dependant and derived variable, not an observation. Locally we do measure distances by angular velocities in the sky. However in cosmology we don't do that. What we measure is "luminosity distance" which is very different thing. For expanding space hypothesis and for objects moving away hypothesis, both theories predict the same luminosity distance - redshift relationship, and as Sten mentioned, it's indistinguishable – Gintaras Sep 06 '23 at 16:21
  • @Sten there is one way to distinguish actually, angular diameter. Expanding space expands: 1) distance 2) angular diameter. Objects moving away expands: 1) distance. In non-expanding space angular diameter doesn't change. There are observations like:"Giant young galaxies appear to be too compact", "packing as many stars as the Milky Way, but in a size 30 times smaller". It favours non-expanding space. There are not compact, object's size is model dependant. In the end, space does not expand. – Gintaras Sep 06 '23 at 16:31
  • @Gintaras In the context of general relativity, angular sizes grow at large distances due to gravitational lensing by the universe's mass distribution. It converges light from distant sources, making them appear bigger. In the standard FLRW cosmology, you can check explicitly that this effect diminishes as you bring down the density of the universe (raise $\Omega_k$). When $\Omega_k = 1$ (negligible energy density), angular sizes never grow with distance. – Sten Sep 06 '23 at 17:11
  • @Sten you didn't understand my statement. – Gintaras Sep 06 '23 at 17:25
  • @Gintaras Perhaps not! I thought you were referring to angular diameter turnover. – Sten Sep 06 '23 at 17:27