If fundamental constants could change, this would violate energy conservation, and the second law of thermodynamics. Someone once said, if your pet theory violates the second law, there is no hope. Or am I missing something?
And in fact, energy is not conserved (and cannot even be defined) globally in General Relativity. There is a different conservation law, called the conservation of stress-energy.
The second law is not a law in the same way like the law of gravity is, it’s more a statistical statement. It simply states that more probable things will happen more often. How do we know what’s more probable? It’s what happens more often. It’s only inviolable insofar as we presume we know all the laws of nature.
Also, the second law is only applicable to closed systems. The universe may not be a closed system in the way we normally think of it.
The second law may be in a way we must evolve to conceive it, or may be in a way that we may never conceive it, or we are acting in ideas that are as distant as friction creating fire. We crawled, the we walked, then we ran, rode, motored, flew, rocketed, got stuck in orbit...
My college physics professor once said, "if in order to make progress we must leave reality, by all means let's leave reality." He also pointed to three red volumes on his shelf, and said those may interest you, and they did. (Richard Feynman)
Thermodynamics by definition only studies equilibrium processes. Applying thermodynamics laws too broadly is a common misconception, even among those who study physics at university, because not many people get far enough to study physical kinetics (like Landau vol 10).
Violating energy conservation (the first law of thermodynamics) does not inherently violate the second law of thermodynamics. It's not hard to imagine a situation where the energy of a closed system changes but not enough to decrease the total entropy of the system, for example if the energy of the closed system decreased.
My best guess at this moment is that all the fields can or may influence each other, resulting in relative changes.
Some things may seem incredibly constant, but have to be measured in such a ridiculous small or big (time) frame, that it's barely not measurable at all.
