I downvoted because your answer presupposes tharmt space can expand globally. Only mass can stretch space locally. It is assumed that dark energy is responsible but that energy is just a way of hiding ohr ignorance towards what we think to be expansion of space. But when asked about the Nature of this energy then nobody knows. Dark energy and space expansion are misleading.

@DescheleSchilder This is a site for mainstream physics. Downvoting because you have a hypothesis that goes against my mainstream answer is not fair. Moreover, while you’re of course free to think what you wish, the fact that you vigorously and without listening to reason try to promote a hypothesis that thousands upon thousands of physicists worldwide disagree with, on the basis of countless experiments and calculations, is downright pretentious, I think. By the way, I did not downvote your answer, despite disagreeing with it.

I know. But mainstream can be wrong.

Indeed, but again, this site is not the place for you to promote your ideas. This site is made for mainstream physics. If you have a non-mainstream conjecture, then conceive a falsifiable experiment, test your hypothesis, and publish it. That's how science works.

I dont promote my own ideas. These are well known ideas. I just cant stand it if untrue things, even if mainstream, are trusted to the chips, so to speak.

@pela It does contract by the same factor it was expanded by: if the photon is emitted at a scale factor a=1, then expands to a scale factor say a=2, it contracts back to a scale factor a=1 again if it enters a region of space that did not take part in the expansion.

@Thomas If you place two particles in intergalactic space they will move away from each other. But what if these particles are placed in the interstellar space of the Milky Way? Will they move towards one another again, returning to the state when they were releasd in intergalactic space (or another interstellar space of another galaxy)?

Hi @Thomas I think I see what you mean now. But the point is that, while the MW (and surroundings) does not expand, it also doesn’t contract. Space expanded for (say) 10 billion years while the photon was traveling, causing it to redshift. Every time the photon enters a region that doesn’t expand, it doesn’t redshift, e.g. when it enters the MW. If at some point it enters a region that contracts, it will blueshift. The MW is not such a region.

@Thomas In other words, if what you say was to happen, it would mean that the observed wavelength depend on the current, local scale of the Universe, implying an absolute scale. But there’s no absolute scale, only a relative scale. The total redshift is the sum of an infinite number of infinitesimally small redshifts, happening along the photon’s path. I added a paragraph in the last section to clarify this.

+1 for the comprehensive answer and responses.

@pela There is no absolute scale involved with my argument, only the relative local scale factors at the moment of emission of the photon and some moment whilst in the Hubble flow on the one hand, and the relative scale factors between the Hubble flow and when it has entered our galaxy/ solar system on the other. The photon would effectively see space contracting when making the latter transition.

@pela Note also the quote from Steven Weinberg (taken from the Wikpedia redshift article): "The increase of wavelength from emission to absorption of light does not depend on the rate of change of a(t) at the times of emission or absorption, but on the increase of a(t) in the whole period from emission to absorption". In other words, the redshift should only be determined by the ratio of the local scale factors at the locations/moments of emission and absorption. If these are equal (in case space did locally not expand) there should not be any redshift (the period in between is irrelevant).

@Thomas Yes, I think I phrased myself badly, or wrongly, at first. The total redshift only depending on initial and final value of $a$, is only correct if you take $a$ to mean the global scale factor. And the global scale factor today is 1, even though locally space has not expanded since MW’s collapse. The correct way to calculate the total redshift is through an integral. When you leave a region that has expanded, and enter a region that has not, space doesn’t start shrinking, it just stops expanding, and hence stops adding to the redshift.

@Thomas If MW had expanded along with the rest of the Universe, but then contracted just as the photon made its last part of its journey, then it would be blueshifted back to its initial value.

@pela The interstellar space does contract. Just as intergalactic space expands. How else does a photon experience blueshift?

@Thomas Regarding Weinberg’s word, note that he (correctly) says that the redshift doesn’t depend on $da/dt$, but on $a = a(t)$.

The other reason for my downvote is that you say the interstellar space does not contract. This is obviously false. If a mass falls to Earth, doesnt space between the mass and Earth contract?

@pela Obviously, if you assume a global expansion, then the photon will never see the scale factor a(t) getting smaller again, unless the expansion turns into a contraction. However, if you have regions of the universe that don't take part in the global expansion, then the photon will see the scale factor getting smaller as soon as it enters such a region. The metric in this region will be the same metric as the one when the photon was emitted.

@Thomas But you don't "see" the scale factor. There is no underlying coordinate system where you can check the absolute size of space. If one part of the Universe expanded by some factor, and another part didn't, and the Universe then became globally static, then you wouldn't know which part had expanded and which one had not (except for the fact that particles in the expanded part would be more diluted).

@Thomas What is important for the redshift is the relative scale of space, locally in infinitesimal steps, from the point $r_1$ at the time $t_1$ where the scale factor is $a_1$, to the point $r_2 = r_1 + dr$ at the time $t_2 = t_1 + dt$ where the scale factor is $a_2 = a_1 + da$. What happens to the scale at $r_1$ when the photon has proceeded to $r_3$ doesn't matter, and likewise, what happens to $r_3$ before the photon arrives there doesn't matter.