Quantum Indeterminacy is Key to the Arrow of Time
There is no machinery to explain the randomness (as Mr. <PERSON> answered from <PERSON>), but maybe a connection to other phenomena can help.
I'm going to go out on a limb here, because answers in this forum are supposed to be from established science. But I think I can make a case for an important explanation that I think follows logically, even if I haven't seen in the literature.
I think we can make the case that there is a fundamental connection between quantum randomness and the arrow of time. Here are the parts of that idea:
Special Relativity and Time Reversal
We know from Special Relativity that all inertial frames are equally valid, that the laws of physics in one (non-accelerating) frame are exactly the same as in any other. This principle also applies to frames of reference where time is reversed. 562
In fact the <PERSON>-Stueckelberg interpretation of antimatter is the idea that antimatter is matter going backwards in time.
Time Reversal and Entropy
But we know from the second law of thermodynamics that entropy either increases or stays the same, but it doesn't decrease (at least not on the macro scale). So one principle says that the laws of physics are the same under time reversal (actually something called CPT) but another says that entropy increases are irreversible.
This contradiction is called Loschmidt's Paradox.
Time Reversal and Quantum Choices
Now here's the idea that I came up with. It's probably already out there somewhere, I've looked and haven't seen it though. If someone knows where this has been developed (if it has) I would very much like a reference.
If a sequence of events is deterministic (one with no random quantum choices) then the time reversal of that sequence must also be deterministic, and the reversal of that sequence would always return the system to its original state.
But if a sequence of events involves random quantum choices, then the reversal of that sequence also involves random quantum choices, and those choices don't have to return the system to its original state when time is rolled back to the original time.
Example:
A photon goes towards an atom, its absorbed by that atom, the atom waits a random amount of time, then it emits a photon in a random direction, and the photon moves away from that atom.
If we could start with the end of this sequence and reverse time, then we get the same kind of sequence, but the time the atom exists in an excited state doesn't depend on the original time and so is probably not going to be the same amount of time, and the direction the photon is emitted is also random, so is probably not going to be in the original direction.
So we can have both the rules of physics be the same between a frame going forwards in time and backwards in time, and still have the forwards and reversed sequences be different, as long as there are random quantum choices in that sequence.
So I think the resolution to Loschmidt's Paradox is this: If entropy increases in a process and so the process is irreversible, it must involve random quantum choices. If a process is deterministic, and doesn't involve random quantum choices, then it must also be reversible and so the entropy in that system will stay the same. 795