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We know the universe expands with the space expansion. This follows from the FLRW solution that nicely explains the observed Hubble flow. (Since any existing acceleration is extremely small, let's assume for simplicity it is zero.)

A uniform expansion of space does not apply any forces on bodies, so they move exactly the same way as they would in a non-expanding space. For example, if two bodies are at rest relative to each other, but space between them expands, then they would remain at rest relative to each other the same way as they would in a non-expanding space. In other words, the expansion of space cannot be detected by observing the motion of massive bodies (as long as they don't cross the cosmic horizon).

The expansion does affect the speed of light, as observed remotely. The expansion also creates a cosmic horizon, beyond which nothing can be detected. Have these effects ben observed? Are there any experimental results showing that space actually expands as opposed to the galaxies simply flying apart on inertia?

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    $\begingroup$ You second paragraph seems unconvincing to me. Are you saying that the whole Hubble thingy cannot exist? $\endgroup$ – lalala Aug 19 '18 at 8:40
  • $\begingroup$ @lalala No, I don't. All that the Hubble flow shows is that the galaxies are flying apart. It does not explain why. It could be because space between them expands or because they were initially pushed apart and still keep going on inertia. (Ultimately there is not even a big difference between these two views.) $\endgroup$ – safesphere Aug 19 '18 at 8:48
  • $\begingroup$ "A uniform expansion of space does not apply any forces on bodies, so they move exactly the same way as they would in a non-expanding space. " - this is not true. The distance between the bodies grows. If they are connected by a rope, the rope would experience force. $\endgroup$ – Anixx Jan 4 at 18:12
  • $\begingroup$ @Anixx There some tidal forces in certain cases (and depending on the model), but in general no, if you tie two objects with a rope and bring them to the zero initial speed relative to each other, then the rope would not experience any force due to the space expansion, unless the expansion accelerates. You cannot tell a uniform expansion from simply moving on inertia. There is no experimental proof that space actually expands as opposed to the galaxies simply flying apart on inertia of the initial momentum. The only relevant evidence is acceleration of the expansion. $\endgroup$ – safesphere Jan 4 at 18:32
  • $\begingroup$ No, you are wrong. The rope would go tightened. $\endgroup$ – Anixx Jan 4 at 18:37
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You are not going to get an experimental proof of space expansion, because space expansion is just an interpretation, not an observable fact. If you want to describe cosmological expansion in terms of motion rather than expansion of space, you can. There is a fundamental ambiguity in the informal verbal interpretation of these cosmological metrics, because we want to visualize expansion using mental images of the Hubble flow, but those mental images implicitly assume that there is some way to define the velocity of galaxy A relative to distant galaxy B. GR does not offer any such definition. When we talk about distances between galaxies, or about recession velocities, people who understand GR realize that this is shorthand for a more complicated set of definitions that are to some extent arbitrary, and are not generically built in to GR. E.g., to talk about the "distance" between A and B, we have to define a 3-surface orthogonal to the Hubble flow, and then measure the metric distance along a spacelike geodesic inside that surface.

In other words, the expansion of space cannot be detected by observing the motion of massive bodies (as long as they don't cross the cosmic horizon).

Detecting a cosmic horizon doesn't have any special logical status here. There are all kinds of other observables, such as Doppler shifts, that rule out any attempt to interpret cosmological observations in terms of the motion of matter on a background of flat spacetime. You seem to be trying to make a dichotomy between spatial expansion and Newtonian gravity, but the observationally verifiable dichotomy is between GR and Newtonian gravity. Spatial expansion is just one way of talking about GR, and it's an optional way of talking about it, just as the Copenhagen interpretation is just one optional way of talking about quantum mechanics.

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  • $\begingroup$ A defection of the particle horizon would be one proof of expansion, because motion alone cannot explain the existence of the horizon. Your answer states that the expansion cannot be proven. Just to clarify, are you saying that the horizon cannot be detected? For example, the redshift of some galaxy can be increasing until the galaxy completely disappears. The number of photons received would decrease along with the increasing redshift. A function of this number by time (interpolated) would cross zero in finite time unlike with the black hole horizon. Is there a logical flaw in this argument? $\endgroup$ – safesphere Aug 19 '18 at 15:52
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    $\begingroup$ My question is about the existence of experimental proof of the space expansion not necessarily by observing moving bodies that would be impossible as I stated in the question. In your answer you first say, "You are not going to get an experimental proof of space expansion", but later you state, "There are all kinds of other observables, such as Doppler shifts, that rule out any attempt to interpret cosmological observations in terms of the motion of matter on a background of flat spacetime." Would these observables not proove the expansion of space? Could you please clarify? $\endgroup$ – safesphere Aug 19 '18 at 16:08
  • $\begingroup$ A defection of the particle horizon would be one proof of expansion, because motion alone cannot explain the existence of the horizon. This is sloppy logic. Detection of a horizon would not be consistent with Newtonian gravity. That doesn't mean that it proves space expansion. For the reasons described in my answer and timm's, space expansion is not an empirically testable prediction of general relativity. Would these observables not proove the expansion of space? Could you please clarify? I've explained why they don't. You haven't explained why you think they do. $\endgroup$ – Ben Crowell Aug 19 '18 at 20:16
  • $\begingroup$ "the observationally verifiable dichotomy is between GR and Newtonian gravity" - Neither has anything to do with my question. The Newtonian gravity is irrelevant, because galaxies would move on inertia even without any gravity between them. And GR does not require a horizon. For example, the Milne model is GR compliant, but nothing crosses the horizon. It is widely accepted that galaxies beyond the horizon move away faster than light due to the expansion of space. This is exactly what my question is about. However, instead of answering it, you seem to fight the conventional interpretation. $\endgroup$ – safesphere Aug 20 '18 at 2:56
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The expansion also creates a cosmic horizon, beyond which nothing can be detected. Have these effects ben observed?

We see photons which have been emitted beyond the Hubble sphere. These photons have been receding from us in the early universe. If you say "cosmic horizon" you probably mean the particle horizon, which is today 46 Glyr away from us. We can't detect photons from beyond this horizon per definition, as the particle horizon limits the observable universe.

Are there any experimental results showing that space actually expands as opposed to the galaxies simply flying apart on inertia?

No, there aren't. Expansion of the universe means increasing distances between comoving objects. Whether space expands or distant galaxies are moving away from each other depends on the chosen coordinates. So neither of these views - being not invariant - may be considered as a measurable physical phenomenon. Space expands in FRW-coordinates and galaxies move away in normal-coordinates.

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  • $\begingroup$ "We see photons which have been emitted beyond the Hubble sphere." - How do you know this? If you could actually know this (the existence of the particle horizon), it would be a proof of the space expansion, but according to your own answer and others no such proof exists. $\endgroup$ – safesphere Aug 19 '18 at 15:37
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    $\begingroup$ You asked if "space actually expands" or if galaxies are "simply flying apart ". Neither of these possibilities can be verified experimentally. Instead the cosmological red-shift data tell us that the distances are increasing which is often plainly but erroneously described as expanding space. Rees&Weinberg said (1993): "... how is it possible for space, which is utterly empty, to expand? How can nothing expand? The answer is: space does not expand." $\endgroup$ – timm Aug 19 '18 at 16:13
  • $\begingroup$ Nice quote. I wish I had this book to see the full context. One example of space expansion that cannot be interpreted as a mere increase of distances due to motion is the fact that the size of a closed universe is increasing. This size can be easily measured by comparing the optical effects in a closed space against their redshift. Another example of space expansion is the existence of the particle horizon that also can be detected (as in my comment under Ben's question). So your statement that the experimental proof is not even possible would need a better support. Could you please clarify? $\endgroup$ – safesphere Aug 19 '18 at 16:26
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    $\begingroup$ Your way of thinking is quite natural, but you are missing one thing. Think of some galaxies which occupy a certain volume. As their physical distances increase (or decrease in case the universe contracts) this volume changes, corresponding to a change of the metric. The volume change doesn't imply however that space expands like material, e.g. like a rubber sheet. You can find this discussion a bit more detailed in Expanding Space: the Root of all Evil?. One can argue similarly regarding the distance to the particle horizon. ∗ $\endgroup$ – timm Aug 19 '18 at 20:11
  • $\begingroup$ Thanks for the paper. The only concept new to me is "cosmological tidal forces", which implies that my second paragraph may have been incorrect, as noted in the comments. The existence of these forces also would be a proof I am asking about. You and Ben seem to misinterpret my question and fight me on terminology. I don't care if you call it "space expansion" or "metric expansion". You are welcome to call it "a lobster", if you prefer. My question is if there is any direct evidence of it, whether the tidal forces, horizon, anything, but the galaxies just flying as pushed in a static spacetime. $\endgroup$ – safesphere Aug 20 '18 at 4:02

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