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The light from the galaxy GN-z11 took 13.4 billion years to arrive, but its distance from the earth is 32 billion lightyears. This is commonly explained as a result of cosmological expansion, i.e. during the photons' travel to us, space expanded, which caused its red-shift on the one hand, and its apparently greater travel distance on the other hand.

Isn't this equivalent to the assumption that space has not expanded since the big bang, but instead the speed of light has been smaller (whatever the specific relation may be) during some significant period of time in the cosmological past, and what we see as 32 billion lightyears is actually a lot smaller?

But maybe I have a wrong understanding of what cosmological expansion actually means.

Just to make sure: I know very well that the speed of light is considered constant which is the basis of all of physics, beginning with special relativity, quantum field theory and so on.

But I also think that I know that if I transform space and leave time as it is, velocity changes. And if the result of this transformation is constant speed of light, it is also possible to view space as static, and speed of light as variable over time, no? And what about transforming time instead of space?

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    $\begingroup$ Calling such a calculated quantity "distance" is common but a bit far fetched. In reality that galaxy is already far beyond the Hubble horizon, i.e. it can not be reached by us with any means in any amount of time. It is therefor now causally disconnected from us. All we are seeing now is an afterimage. $\endgroup$ May 7, 2023 at 16:31
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    $\begingroup$ Hmm, if at any one short period of time c is approximately constant (like today, when we test atomic, nuclear and solid state physics), why should there be a catrastrophic failure of any of those theories? For example, the energy levels of the hydrogen atom will be scaled by $c^2$. If c slowed down since the big bang, there is a corresponding red-shift of the spectra we observe from the past. Or is there a more subtle problem? $\endgroup$
    – oliver
    May 7, 2023 at 17:00
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    $\begingroup$ Let us restart a new conversation. Part of the problem with any analysis with a variable $c$ is that it is unit-ful, and is thus physically meaningless what particular number it is. Instead, the physically sensible thing to do is to always set it to be the speed of light (actually, rather, the spacetime conversion factor) and then we can sensibly speak of. $\endgroup$ May 8, 2023 at 4:28
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    $\begingroup$ Now, once you see that the spacetime conversion factor is set to 1, then you should be immediately able to deduce that any discrepancy to the propagation of light cannot then be explained by altering the speed of light any more, because by definition this speed of light is already set to 1. i.e. this is really new physics and cannot be explained by any variation in the speed of light. Because, even if $c$ is changing, it would already be factored into the evolution of everything, everywhere in the universe, and thus there is no way for the observed differences to be due to such changes. $\endgroup$ May 8, 2023 at 4:31
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    $\begingroup$ Light moves with the speed of time, so transforming time is the same as changing the speed of light. You can change local time relatively via time dilation, but the cosmological time is an independent variable, changing it has no physical or mathematical meaning: “time moving faster today than yesterday” is a meaningless statement, same as $x$ between $1$ and $2$ is “moving faster” than between $0$ and $1$ in $y=f(x)$. Also, changing the speed of light without changing the scale of things would break up matter. Electrons would fly away from atoms and so on. Clearly not what you mean. $\endgroup$
    – safesphere
    May 14, 2023 at 19:35

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Prof. Dan Hooper, in his popular-science book "At the Edge of Time", has a pargraph that appears to have been written to answer your quest :-)

"If you find yourself struggling with the concept of expanding space, I have a mental trick to suggest: instead of space expanding, imagine a universe in which all objects are shrinking. To understand what I mean, consider any two points in space. If you measure the distance between them and find that it is increasing with time, you would conclude that this is because the amount of space between them is increasing - space is expanding. But how do you actually go about measuring a distance between two points in space? You need some kind of measuring standard - the equivalent of a ruler or a yardstick. ... As a consequence, we have at least two very different ways that we can choose to think about expanding space. The first, and more conventional, of these is to think of the amount of space in our universe as increasing. But alternatively, we could instead imagine that everything within space is shrinking, while space itself remains unchanged. Both ways of thinking about this are completely equivalent and indistinguishable from each other. ... one can feel free to think of our universe as expanding or, instead, of everything in our universe as shrinking. When I say everything, however, I mean everything. For example. For example, we often use the time that it takes for light to travel between two points in space as a measurement of the distance between them. So, in order for all of our measuring standards to be shrinking, even the speed of light would have to be slowing down with time. Similarly, the distances between protons, neutrons, and electrons within atoms would have to be shrinking, as well as the distance between the Sun and the Earth and, well... everything. As you can imagine, it would be very challenging to find an explanation for why all these properties of nature would be changing at the same rate.

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  • $\begingroup$ I found this explanation very enlightening. Especially because I think it points to the differentiation between the metric of the universe as a whole and the metric of the local objects (galaxies, rulers, Michelson interferometers,...). As far as I have understood it, expansion of the universe means, that the metric of the universe is that of expansion, while the metric of the local objects ("their size") stays the same. And that immediately rasises another related question: $\endgroup$
    – oliver
    May 8, 2023 at 17:07
  • $\begingroup$ If the expansion of the universe leads to the somewhat "difficult" fact, that the farthest-away galaxies move faster (per retrograde observation) than the speed of light relative to us, isn't it more practical (or better: reconcilable with our terrestrial/galactic physics) to say that the speed of light for them is/was not c=2.99e+8 m/s, but some greater value, which is not exceeded by their observed motion? Is it more painful to give up relativitic speed limit (related to causality), or to give up invariable size of distant/past objects? Has cosmological standard model ruled out this view? $\endgroup$
    – oliver
    May 8, 2023 at 18:28
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You can redefine the time parameter so that the scale factor $a(t)$ in the FRLW metric becomes unity. It does not change anything physically.

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    $\begingroup$ Your answer is incorrect. Redefining the time parameter alone has no meaning, because cosmological time is an independent variable. See my comments above for details. You can however divide the Friedman metric by $a(t)$ to keep space from expanding. This would be equivalent to matter shrinking and yes, it would not change anything physically of course. The details of this procedure have been published here: vixra.org/pdf/1107.0016v1.pdf $\endgroup$
    – safesphere
    May 14, 2023 at 20:10

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