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We know that the light we measure from distant galaxies is red-shifted; the red-shift is proportional to distance; we attribute this to the expansion of space at the rate of the Hubble constant/parameter over time.

Hypothetically, if space was not expanding, would the wavelength of emitted light be constant for all distances away from the source?

What experiments have been performed to test this?

Update

After doing some more research, my question is related to the nature of the "redshift-distance relationship". Clearly, this relationship exists because we can measure it using standard candles etc. Expanding space is the generally accepted explanation, of course; however, there are alternate theories such as, Tired Light, one of which suggests light changes wavelength over distance via some yet unknown mechanism, and Chronometric cosmology where redshift is a side effect of permeating 3-sphere space.

My question can then be rephrased:

Is the redshift of light from galaxies 100% correlated to the expansion of space, or is there the possibility that other factors and mechanisms also influencing the redshift of light en-route from a distant source to us?

E.g. Is it possible that the wavelength of light can change as it permeates through space, in addition to the effects of the expansion of space?

What experiments have been performed to confirm one way or the other?

I ask because I have never heard of such experiments. If no experiments have been performed to test this, it suggests it is only an assumption that the redshift of light from galaxies is 100% correlated to the expansion of space.

One experiment that comes to mind would be to measure the apparent 'tightness' of galaxy clusters by redshift. The apparent 'tightness' of galaxy clusters should be different based on expanding space, vs tired light.

The Tolman surface brightness test is referenced as a reason to discount "tired light", but from what I understand of the test, it oddly assumes a constant wavelength and energy for the tired light scenario, and therefore it doesn't discount a tired light mechanism.

According to this wiki article there were 6 tests "that were conceived in the 1930s to check the viability of and compare new cosmological models". Unfortunately, there is no mention of what the other tests are. It would be nice to know.

br3nt
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    It would be hard to test experimentally since we don't have spare universes to experiment with. We only have the one universe and we were not consulted about whether it would be expanding or not. – John Rennie Jul 25 '21 at 06:18
  • I think this is an equivalent rephrasing of the question: From the perspective of a photon, is its wavelength constant for the duration of its lifetime? What experiments have been performed to test this? – br3nt Jul 25 '21 at 06:25
  • Surely, it should be possible to perform such an experiment within our universe to answer that question by adjusting for the Hubble constant. – br3nt Jul 25 '21 at 06:27
  • A photon just has energy =hnu, no wavelength. electromagnetic waves have wavelength acquired by the quantum mechanical superposition of the zillions of photons with energy=hnu where nu is the frequency of the light. see this single photon at a time interference experiment to see the complication. https://www.sps.ch/artikel/progresses/wave-particle-duality-of-light-for-the-classroom-13/ – anna v Jul 25 '21 at 11:22
  • @annav ok thanks. I’ll remove the word photon from my question. – br3nt Jul 25 '21 at 11:28
  • wavelength of light changes when going from one medium to another see this https://www.bbc.co.uk/bitesize/guides/z9bwpbk/revision/2 and this https://physics.stackexchange.com/questions/22385/why-does-wavelength-change-as-light-enters-a-different-medium – anna v Jul 25 '21 at 13:10
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    see https://physics.stackexchange.com/questions/156618/tired-light-red-shift-hypothesis https://physics.stackexchange.com/questions/300365/time-dilation-of-distant-cosmic-events-what-is-it – ProfRob Jul 25 '21 at 13:34
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    and https://physics.stackexchange.com/questions/412426/tired-light-frequency-damping – ProfRob Jul 25 '21 at 13:39
  • Thanks @ProfRob for the links. The linked papers on time dilation of distant supernovae is quite interesting. – br3nt Jul 25 '21 at 14:29

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There are many tests for cosmological models, classical tests and more modern 'precision cosmology' tests.

Here are some that you might want to look into:

Tolman surface brightness test

Angular diameter distance

Luminosity distance

(the two above lead to the Distance Duality test)

Number counts

Black body CMBR

Time dilation of supernovae

Hubble parameter measurements

Measurements of the Matter Density

Computer simulations of the Large Scale Structure

and the Abundancies of elements.

One of your questions was

"...is there the possibility that other factors and mechanisms also influencing the redshift of light en-route from a distant source to us?"

There have been many alternative proposals and these are discussed here

https://arxiv.org/abs/1801.07582

"On the Interpretation of Spectral Red-Shift in Astrophysics: A Survey of Red-Shift Mechanisms."

The author compiled a list of about 60 alternatives and discusses them.

John Hunter
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  • Thank you for the linked paper! It’s going to take some time to read. – br3nt Jul 25 '21 at 14:33
  • Yes, it's quite long, if you are interested in tired light theories section 6 is most relevant, pages 15-25. The Tolman test, as you mentioned, is said to rule out the usual tired light hypothesis, and maybe time dilation of supernovae http://www.astro.ucla.edu/~wright/tiredlit.htm – John Hunter Jul 25 '21 at 14:41