“What really interests me is whether God could have created the world any differently; in other words, whether the requirement of logical simplicity admits a margin of freedom.” This is a quote from Einstein, and it has intrigued me. Is our universe the only way it could have been done. Are the forces of nature the only ones possible. Are these questions even possible to answer regardless of their answers.
I'll try to address both the OP's question and some that appear in the comments section.
A better way to think about the question of different possible universes with different fundamental constants, or constants that change with time, is the influence these effects would have on the time evolution of those universes and specifically if they would support the formation of fundamental particles, atoms, molecules, galaxies, stars, solar systems, and planets- and hence life as we know it.
This is important because if for example stars had lifetimes too short to stay lit long enough to give evolution a chance, then we wouldn't be here to make any observations.
Computers allow us to predict what the consequences would be on the development of a universe from a big bang if for example the electromagnetic force were a little stronger or weaker relative to gravity and so on. The results indicate that even very small alterations like this would furnish a universe without us in it- meaning that our existence depends on all the constants of physics being within very tightly-specified ranges. How did that happen? This is known as the anthropic problem, which does not have an accepted answer at present.
Are different fundamental forces possible? Are different formulations of gravity, with different force versus distance relationships, possible? Looking at gravity, we can model the effects of deviations from the so-called inverse square law by positing different numbers of physical dimensions and then seeing if solar systems could form. We know just from the math that four dimensions of space would yield a form of gravity in which stable orbits in space between gravitating masses would not exist- meaning that galaxy clusters, galaxies, and solar systems would be absent.
Regarding VSL models, the main reason they are not considered "mainstream" is that they do not conserve energy.
It seems to me that there is a piece missing from that quote, that either Einstein didn't include (or was assumed wen spoken), or has been lost since then.
“What really interests me is whether God could have created the world any differently; in other words, whether the requirement of logical simplicity admits a margin of freedom.” ..... Is our universe the only way it could have been done. Are the forces of nature the only ones possible.
A margin of freedom to what? The only way a universe could be done with what properties and outcomes? The only ones possible if you want what as the result? These are completely unspecified. What's missing is "... to what"? With what constraints and requirements of the outcome?
You might assume that's "obvious", but to me it is incredibly weakly defined, or not defined at all. So let's follow this a bit.
What is the actual question.....?
Let's start by anthropomorphising a bit and assume a purposeful creator, who is about to set one universe up. We want to ask if they could have done differently, or if the way the universe is, *requires the one way it was apparently done.
But what counts as the same, or different? If the universe was as we see it, but cats hadn't evolved, would that count as the same? What if the earth hadn't existed, or our home galaxy the Milky Way, but life based on earthlike chemistry instead existed on other planets?
We would probably say then, it's the same universe, for these purposes. After all, same physical laws, same life for any practical purposes, humans or humanoids looking out asking these questions.....
Now suppose the life looking out was silicon based, or something non-earthly. They'd still look out and still ask the same question. They'd assume silicon in their world view, as we assume carbon. But really, same outcome.
Now let's go radical. Suppose the entire structure of the universe was different. Gravity, other fundamental forces, don't exist, something else exists but completely alien to us, no stars, no planets, no elements as we know them, but an entire other physics. And in that unimaginable universe, some being made of fundamental structures we have no words for, asks a friend, "is this the only way God could have made it"?
Would that be "the same universe" in some sense?
..... Which suggests.....
This is the anthropomorphic principle. In asking why the universe is as it is, and how unlikely that seems, and did a notional God have a choice, we assume so much in the question itself.
If we were different (or the earth, or the entire universe fundamentally different) but there was still an entity able to ask "Could it have been done differently", then - we could be that entity. We might, right now, be the ones in that position. We could be the ones in that alternate speculative fundamentally changed universe, and we would have no way to know it.
So the question comes down to, being more specific.
If it means, "could this exact universe have been done differently" - no, by definition. To be this exact universe would need everything as we see it.
If it means "could a universe with some entity capable of asking why, exist, in some other way", then probably. But we don't have the details.
The universe we know is not the only possible universe.
When changing the values of the fundamental constants of physics within certain boundaries one gets different universes. Typical fundamental constants are
the speed of light, the fine structure constant, the value of the electron mass, the coupling constants for the different types of forces.
In our present theories these constants have the role of parameters. They cannot be derived from the theory but have to be determined by observation and measurement. It is always a challenge to reduce the number of free parameters in a physical theory.
A weak analogy: The distances of our planets does not derive from Newton’s theory but has to be measured. It seems plausible that the planets in other solar systems have different distances from their central stars.