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Discussions in the literature (e.g. https://arxiv.org/pdf/1412.2040.pdf) say in no uncertain terms that it is meaningless to consider time variations of fundamental dimensionful parameters such as c, G, ... If one must consider this type of thing, one must use dimensionless parameters. Fine, the arguments seem reasonable.

But what if one wishes to investigate a theory where a (nearly)classical theory morphs through time continuously into a fully relativistic theory. The naive way to approach it would be to make c vary with time, starting with some very large value and decreasing. But that is not permitted.

Is this because such a theory is physically unrealizable?

Similar question: is it meaningful to say that two universes in the multiverse differ in their value of a dimensionful parameter, say, hbar, and that this difference has anthropic consequences?

Last similar question: Can a theorist predict roughly the properties of a model of the universe where hbar is replaced by hbar/2? I assume the answer to this is YES.

I do not feel that this is a duplicate. The referenced discussion (which an excellent link) is relevant (and mentions the same paper that I identify) but my problem is really - how does one interpret the paper. Can I predict different physics for separate universes, for example? Can I have a weakly relativistic universe that morphs into a strongly relativistic one? Or a completely nonrelativistic that changes into relativistic?

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    $\begingroup$ "starting with some very large value" - "very large" compared to what? $\endgroup$
    – ACuriousMind ♦
    Commented Mar 15, 2018 at 21:08
  • $\begingroup$ to be precise, let’s say we multiply the currently measured value by 1000. You could call both versions fully relativistic, of course. But I consider the modified version to be more weakly relativistic. $\endgroup$
    – abby yorker
    Commented Mar 15, 2018 at 21:10
  • $\begingroup$ Since $m_p/m_e$ is dimensionless, we know what it would mean for it to vary. If it did, one or both masses would vary despite being dimensionful. So that has to in principle be possible, whatever it might mean. $\endgroup$
    – J.G.
    Commented Mar 15, 2018 at 21:42
  • $\begingroup$ I am actually thinking of variations in fundamental constants c, G, h. But, given a change in the mass ratio, how would you know whether it is proton or electron? It could be mixed with changes in the fundamental constants. $\endgroup$
    – abby yorker
    Commented Mar 15, 2018 at 21:59
  • $\begingroup$ I don't feel that your edit really warrants reopening as it stands (v3). Asking a mildly altered version of an existing thread isn't enough; you probably have enough material to ask a distinctly different question that builds on top of the existing discussions, but you do have to edit your question into that form. As it stands, the answer to your question is the same as before: you can't have $c$ depend on time because you cannot meaningfully distinguish the cases where $c$ increases from cases where your clocks become sslower. $\endgroup$
    – Emilio Pisanty
    Commented Mar 16, 2018 at 10:44

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