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https://physics.stackexchange.com/questions/400457/what-does-general-relativity-say-about-the-relative-velocities-of-objects-that-a

"we can actually observe galaxies that are moving away from us at >c"

Um, I think I missed the groundbreaking headline that said scientists have directly measured a galaxy moving away from us at speeds faster than light.

So the first answer seems to contradict this other answer

https://physics.stackexchange.com/questions/107748/how-are-galaxies-receding-faster-than-light-visible-to-observers

"If recession velocity at the location of a traveling photon were greater than the speed of light the entire time the photon from a distance galaxy were traveling, we would never observe the photon."

It seems like common sense that at a certain distance, space is expanding faster than light, thus preventing light beyond a certain distance from reaching Earth which means we can't directly measure galaxies traveling faster than light, but we can imply that they do by projecting their velocity beyond the observable universe. But who's right?

If a galaxy used to be within the observable universe, we can measure photons from that galaxy reaching Earth despite that that galaxy may be currently outside the observable radius of the universe. Galaxies can be projected as travelling faster than light due to the expansion of space, but I haven't seen that we can directly measure them as doing such since the redshift of photons is proportional do the amount of space that is expanding between us and a certain distance.

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    $\begingroup$ Both are, though the second could be clearer. Read Davis & Lineweaver arxiv.org/abs/astro-ph/0310808 $\endgroup$ – Rob Jeffries Apr 18 '18 at 6:35
  • $\begingroup$ Consider the standard Physics 101 example of a "value" greater than the speed of light: take a flashlight and rotate it. The beam spot at a distance of, say, 1LY, is perceived to be moving at $2\pi * c$ , but no actual energy or information is travelling at that speed. $\endgroup$ – Carl Witthoft Apr 18 '18 at 15:22
  • $\begingroup$ The photons emitted from the source are still traveling at c, rotation does not change that. However, the actual pillar/cone shape of the light beam can, at a certain distance, be projected to angular velocities faster than c. $\endgroup$ – John Joe Apr 19 '18 at 0:38
  • $\begingroup$ "recession velocity at the location of a traveling photon were greater than the speed of light the entire time the photon from a distance galaxy were traveling, we would never observe the photon." is not correct. If necessary I could look for the extreme of a reference. Answering your question requires an account on the whole cosmology, I am afraid. .. $\endgroup$ – Alchimista Apr 23 '18 at 8:27
  • $\begingroup$ PS: Actually the ref. is given in the answer by @John Duffield $\endgroup$ – Alchimista Apr 23 '18 at 8:30
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So where are these measurements of galaxies moving faster than light?

They're redshift measurements. Check out the Wikipedia redshift article. It's good stuff.

"we can actually observe galaxies that are moving away from us at >c"

It's true. You might think it cannot be, but it can.

Um, I think I missed the groundbreaking headline that said scientists have measured a galaxy moving away from us at speeds faster than light.

It's not groundbreaking at all. It's simpler than you think.

So the first answer seems to contradict this other answer https://physics.stackexchange.com/questions/107748/how-are-galaxies-receding-faster-than-light-visible-to-observers "If recession velocity at the location of a traveling photon were greater than the speed of light the entire time the photon from a distance galaxy were traveling, we would never observe the photon".

Yes, that's a bit unfortunate, because he also says this: "galaxies with red shifts greater than ~3 were and are receding from us faster than light".

It seems like common sense that at a certain distance, space is expanding faster than light, thus preventing light beyond a certain distance from reaching Earth which means we can't directly measure galaxies traveling faster than light. But who's right?

The guy who says we can see galaxies that were and are receding from us faster than light. As per Rob's comment, see Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the Universe by Tamara Davis and Charles Lineweaver. Note this: "We show that we can observe galaxies that have, and always have had, recession velocities greater than the speed of light." See page 8: "Amongst those who acknowledge that recession velocities can exceed the speed of light, the claim is sometimes made that objects with recession velocities faster than the speed of light are not observable [App. B: 9–13]."

Also have a read of the Wikipedia ant on a rubber rope article. The rubber rope is being stretched as the ant walks along it: "At first consideration it seems that the ant will never reach the end of the rope, but in fact it does (although in the form stated above the time taken is colossal). Whatever the length of the rope and the relative speeds of the ant and the stretching, providing the ant's speed and the stretching remain steady the ant will always be able to reach the end given sufficient time. Once the ant has begun moving, the rubber rope is stretching both in front of and behind the ant, conserving the proportion of the rope already walked by the ant and enabling the ant to make continual progress".

There's a section on the metric expansion of space. It says this: "By thinking of photons of light as ants crawling along the rubber rope of space between the galaxy and us, we can see that just as the ant can eventually reach the end of the rope, so light from distant galaxies, even some that appear to be receding at a speed greater than the speed of light, can eventually reach Earth, given sufficient time. However, the metric expansion of space is accelerating. An ant on a rubber rope whose expansion increases with time is not guaranteed to reach the endpoint.[3] The light from sufficiently distant galaxies may still therefore never reach Earth".

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  • $\begingroup$ Don't you remember that fiasco where an error in the LHC was reported as showing neutroinos traveling faster than light? If the media had a chance to say something was traveling faster than light, they would take it. What you're saying still seems like a strawman: I'm not doubting that there are galaxies traveling faster than light, I'm simply doubting that we can directly measure those galaxies in the act. Obviously photons from when a galaxy used to be in the observable universe are measurable, but photons from that same galaxy Currently Outside the OU should not be measurable. $\endgroup$ – John Joe Apr 18 '18 at 15:11
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    $\begingroup$ @JohnJoe no, the galaxies are not travelling faster than light. It's the expansion of the universe itself (a very confusing concept) which causes the distance between us and the galaxy to increase faster than a photon can travel. $\endgroup$ – Carl Witthoft Apr 18 '18 at 15:20
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    $\begingroup$ Yes there are 100% absolutely galaxies traveling faster than light according to the most accurate cosmological models, it is only that the means of doing so is the expansion of space rather than using kinetic energy, thus preserving locality. Whether it's by expanding space or kinetic energy, the overall distance between us and those galaxies is still increasing in either instance. $\endgroup$ – John Joe Apr 18 '18 at 15:27
  • $\begingroup$ @John Joe : there's plenty of stuff in the media about it. But it's old news. It was probably all over the front pages fifty years ago or something. Mind you, I wouldn't be surprised if something like that was all over the news at some future date. Google on neutrinos arrived first. $\endgroup$ – John Duffield Apr 18 '18 at 15:56
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Without going into the technicalities of spacetime diagrams and ants, I think the quickest way to wrap your head around this is to look at it from the distant galaxy's perspective. For instance, let's take GN-z11, which actually receded from us at $v\simeq4c$ when it emitted the light we see today:

A photon left GN-z11 at $v=c$. Space expands, so although the photon at any time travels locally at $v=c$, it increased its distance to GN-z11 at an ever-increasing speed $v>c$.

The Milky Way receded from GN-z11 at $v\simeq4c$, but locally it has $v\simeq0$, and until recently the Universe expanded slower and slower.

At some point, the photon reached a point where the Universe expanded at, say, $v=0.1c$ wrt. GN-z11, so the photon receded at $v=1.1c$. Later, it reached a point where the Universe expands at $v=c$ wrt. GN-z11, so it receded at $v=2c$ from GN-z11. And so on.

Eventually, it simply "caught up" with the Milky Way.

It is important to note, though, that this is only possible because the expansion rate didn't accelerate until recently. The acceleration puts a limit to how fast galaxies may recede and still be visible. Today, that limit happens to be roughly $v=1.2c$, corresponding to galaxies roughly 17 billion lightyears away. Photons leaving GN-z11 today will never reach us, even though it "only" recedes from us at $v=2.2c$ today.

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  • $\begingroup$ From a distant galaxy's perspective, if space expands faster than c at its observable radius, then light from the Milky Way at the time it exceeds that galaxy's observable radius will not reach that galaxy. Prior to space expanding at the speed of light at that distance, photons from that distance will still reach that galaxy, assuming a constant rate. $\endgroup$ – John Joe Apr 19 '18 at 0:35
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    $\begingroup$ @JohnJoe Actually, that's not correct. When GN-z11 emitted the light we see today, it was some 2½ Glyr away, well outside our observable Universe at that time, which was only ~1 Glyr in radius, and at the edge of which stuff already receded from us at v ~ 2c. $\endgroup$ – pela Apr 19 '18 at 12:13
  • $\begingroup$ But if you don't just want to take my word for it (although I can assure you it's correct), I think you'll have to understand a spacetime diagrams, as well as how to calculate distances, recession speed, etc. Start by having a look at this great post from physics.SE. $\endgroup$ – pela Apr 19 '18 at 12:15
  • $\begingroup$ Again this is with an acceleration in the acceleration of space, I specifically referred to constant acceleration. I don't see evidence that a constant expansion wouldn't yield the results I described, as also described in the arXiv article. $\endgroup$ – John Joe Apr 19 '18 at 16:17
  • $\begingroup$ I don't think I understand exactly what you object to. You're right that we don't measure velocities of galaxies. We measure redshifts, and interpret them as being due to the photons having traveled through an expanding space, and then further interpret that as meaning that the expanding space carries distant galaxies away from us at an ever-increasing speed. This is general relativity. A special relativistic interpretation is in principle possible, but is ruled out at a very high significance, as explained in Davis & Lineweaver 2004. $\endgroup$ – pela Apr 19 '18 at 16:44
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The situation doesn't even require general relativity, the same thing can happen with ants crawling on a rubber picnic sheet. Imagine you are sitting in the center of a very stretchy rubber sheet, and ants are crawling toward you at ant-speed from the outer edges of the sheet. You ask some friends to keep pulling the edges of the sheet away from you at a speed somewhat faster than ants can crawl. Will that protect you from the ants? No, believe it or not, the ants will still reach you. At first they are getting farther from you, but if you mark gridlines on that sheet, you'll see the ants are still advancing across those gridlines all the same. They get to you eventually, just like the light from a galaxy whose distance from us is increasing faster than c.

Note the second quote is not about the speed at the edge of the sheet, it says the ants don't get to you if all the points on the sheet that the ants access are all moving away from you faster than ant-speed. That's a very different situation.

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    $\begingroup$ This doesn't seem to take into account accelerating expansion. In that situation, ants (or light) beyond a certain distance can never reach you. $\endgroup$ – Chappo Says Reinstate Monica Apr 18 '18 at 11:18
  • $\begingroup$ Again, I'm not doubting there are galaxies traveling faster than light, I am simply doubting we directly measure galaxies in the act of doing such. $\endgroup$ – John Joe Apr 18 '18 at 15:13
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    $\begingroup$ @JohnJoe Doubt all you like. Cosmological redshift is not a Doppler shift related to a velocity in the same way as the special relativistic Doppler effect. Objects at redshifts greater than about 1.5 are currently receding from us faster than the speed of light. $\endgroup$ – Rob Jeffries Apr 18 '18 at 18:10
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    $\begingroup$ @Chappo-- yes, the rubber sheet analogy would need to be accelerating to be a perfect analogy, but the basic idea still holds-- ants can get to you even when they start on parts of the sheet receding faster than ant-speed. But if the acceleration is fast enough, eventually they won't be able to get to you any more. $\endgroup$ – Ken G Apr 18 '18 at 20:26
  • $\begingroup$ In the arXiv document, " Light that superluminally receding objects emit propagates towards us with a local peculiar velocity of c, but since the recession velocity at that distance is greater than c, the total velocity of the light is away from us (Eq. 20)" The document appears to be saying that photons emitted from a greater distance than the radius of the observable universe will be traveling "away" from us, not towards us, so yes I will continue to doubt all I like. $\endgroup$ – John Joe Apr 19 '18 at 0:30
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If I understand the context correctly, the problem of misunderstanding here is the frame of reference. So, the answer is that both are correct because they are talking by using different frames.

The second diagram in this site might help you understand better. Y is lookback time, or age of universe. X is comoving distance. The observer is at today. Light cone is red and is not a straight line as one might expect from special relativity because of the universe expansion. However, if you take the vicinity around the observer, the light cone is still approximately the straight line.

So, if you extrapolate the straight line out of the observer, you will see stuff staying in the region where v>c (i.e., spacelike). For example, you see the object at comoving distance at 16 Gly today from its emission at about 9 Gyr in the past, and 16 Gly / 9 year is slightly greater than c, as expected.

This seems to be counter intuitive scenario is because of expressing the distance as comoving frame. Instead, the first diagrame from the site shows X as the proper distance, and now all visible locations are in the v

As depicted by the diagrams you will see that we can see only far away as about 46 Gly (comoving distance), a.k.a. horizon. This is because if we go further than that spot, regarding to the history of universe expansion, we at today will stay out of the spacelike.

Note: all the analysis here still assume speed of light as the constant c in any frame of reference. This might be another misunderstanding, but I will not go into details at this moment.

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