Here's a question:
What makes causality so sacrosanct?
The fact that every time we think we have found an instance in which it is violated, we turn out to have missed something important. It's kind of like the conservation laws in that respect. In fact, the conservation laws are based on causality- without causality, none of the conservation laws make any sense.
The neutrino is pretty much the poster child for the conservation laws.
What happened was, physicists made observations and measurements of beta decay, a type of radioactive decay in which a neutron within a nucleus turns to a proton, and an electron is emitted from the nucleus. They did calculations of the residual energy, and figured out how much energy the electrons should have. And they measured the energy of the electrons. And what they found was, the energy they calculated was a
maximum- and a value they almost never saw. They always saw something less than the maximum.
Wolfgang Pauli theorized that there had to be some other particle emerging from this interaction- a particle that didn't have an electric charge, didn't have much mass, and didn't interact with matter much (otherwise we'd detect it as easily as we did the electrons). Most physicists said, "well, that's nice, but show us one."
Pretty soon, physicists found that
spin angular momentum was also conserved- and that this conservation law was also present in the macro world, as the conservation of angular momentum. And when they went and looked at beta decay, they had a problem: the spin of the proton and neutron were equal, so
where did the spin of the electron come from? So now there were
two conservation laws that the neutrino could save, assuming that it could have an equal and opposite spin to the electron.
So some theoretical physicists worked out what the properties of the neutrino had to be. And what they came up with was a particle that would be very hard to detect. For quite a long time, decades in fact, there was debate about the existence of the neutrino. But finally, someone came up with a way to detect them: they theorized that although there was a
very small chance of seeing an interaction involving a neutrino, it was not
zero, and if they could get enough mass together and watch for an interaction that without the neutrino would violate the conservation laws, then they could take a source of putative neutrinos and see whether they could establish that the occurrence of this interaction would be more common with a source of neutrinos than not. They did this experiment, showed that the interaction occurred far more often under circumstances where neutrinos would be expected, and won a Nobel Prize for the discovery of the neutrino.
All that from just the conservation laws.
So when we talk about causality, you have to keep in mind that the conservation laws are all based on causality; and the neutrino is hardly the only thing to have been discovered by looking into an apparent violation of these laws. It's to the point now where if someone sees what appears to be a violation of a conservation law, they don't even question the law; they go looking for the cause, because everyone who has explained such a thing has gotten famous.
So it's not that causality is
sacrosanct; it's that we've never observed it to be violated. Just like conservation of mass/energy. Just like conservation of momentum or angular momentum. Just like conservation of parity.
The first order answer would have to be something to the effect of: without an assumption of the inviolability of causality, nothing would make sense!
As a matter of fact, that's very nearly it, from a non-technical point of view. Newton's Laws, for example, are dependent upon causality.
However, in terms of physical quantities, is entropy a stand-in for causality?
Not really. Entropy is more a
consequence of causality, or more properly, without causality, entropy is not definable.