So where are these measurements of galaxies moving faster than light?

Question

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.

Answer 1

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".

Answer 2

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.

Answer 3

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.

Answer 4

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.