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The question Are photons aged? and answers therein have got me thinking:

I vaguely remember hearing something about experiments where "old photons" were collected by large telescopes from very distant objects, and either their energies or their frequencies were compared to their wavelengths to check the (linear or inverse) some fundamental constants, perhaps those used in:

$$E = hf = h \frac{c}{\lambda}$$

Questions:

  1. Am I misremembering, or has this been done?
  2. What were the results and to what level of precision was non-variation constrained?
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  • $\begingroup$ Plus one but shouldn't be h a property of the space in which the electromagnetic wave propagates? Here and now? $\endgroup$
    – Alchimista
    Feb 26, 2020 at 9:48
  • $\begingroup$ @Alchimista If one (or more) fundamental constants can vary over time and/or space, then a situation could arise when nature (or the photo) has to choose between conserving momentum and conserving energy. Presumably if an experiment like one described was done or even proposed hopefully we can read about the motivations or justifications for it. $\endgroup$
    – uhoh
    Feb 26, 2020 at 10:07
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    $\begingroup$ I see and therefore it is somehow intriguing. But what I wanted to say is that what we observe in term of E=hf must be here and now. It would be the same measuring c. I guess only complicated analysis could in principle show a varyng c. $\endgroup$
    – Alchimista
    Feb 26, 2020 at 10:23
  • $\begingroup$ @Alchimista it's all above my head, but $E=hf$ has generally been checked only for fresh photons, how do we even know it holds for old photons? I think that $E/f$ being constant is certainly assumed in our use of Physics, but how to we know it really is constant? To me it seems to be simply an assumption. Then again isn't that what a lot of science is? We observe something that continues to be true over and over, then call it a "law" but rarely is it proven that it must always be true in all cases. Don't we assume conservation of energy only because we've never seen it not conserved? $\endgroup$
    – uhoh
    Feb 27, 2020 at 1:32

1 Answer 1

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You can not check if a dimensional constant has changed because you can always reverse that change by a smart change of coordinates (system of units). Despite that, since the current Physics assumes the immutability of certain constants, you can verify this assumption by testing the change of an adimensional constant.

One of the most common adimensional constants that is used to search for constant variability if the fine-structure constant (a fundamental physical constant characterizing the strength of the electromagnetic interaction between elementary charged particles) $$\alpha=\dfrac{1}{4\pi\epsilon_0}\dfrac{e^2}{\hbar c}\,.$$

The Wikipedia pages about Time-variation of fundamental constants and fine-structure constant have nice explanations about this.

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  • $\begingroup$ Thank you for your answer and +1 because this certainly sounds right though I can't yet understand what a "smart change of coordinates (system of units)" might be. Perhaps I'll ask for clarification on that in Physics SE. If so I'll ping you here in case you'd like to join and answer there. Sometimes I don't understand answers to my question there and sometimes I have to post answers to my own questions. In the mean time I'll check out these links. $\endgroup$
    – uhoh
    Feb 26, 2020 at 21:48
  • $\begingroup$ but as far as an actual answer to this particular question, I wonder if something in arxiv.org/abs/astro-ph/0012539v3 applies? (found by searching for the string "astr" here) fyi I've relaxed the constraints of the question somewhat to allow for instructive answers. $\endgroup$
    – uhoh
    Feb 26, 2020 at 23:54
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    $\begingroup$ @uhoh, that is a good and important paper in this area. Additionally, more instruments are currently improving our constrain on $\alpha$ variation, for example [EXPRESSO][1]. From my experience, not many people believe the constants vary but nevertheless, it is important to test it. In Physics you can never prove anything, you can only disprove. [1]: eso.org/sci/facilities/paranal/instruments/espresso/… $\endgroup$
    – Catarina Alves
    Mar 2, 2020 at 12:52

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