So I was curious and googled and found:
> the value of a wave function of a physical system at one point in time should determine its value at any other time
Is there a layman's explanation about what this ... is?
1. That quantum mechanics is deterministic (as far as wavefunctions go) and time-reversible. Knowing the state of a system at any given point, you can use the differential equation (Schrodinger's equation) that determines the evolution of the system, to find the state any other time.
2. The should in the statement is referring to the philosphical idea that we expect that the true laws of physics will always be deterministic and time-reversible.
Matter goes into black hole. Black hole destroys everything because too much gravity and spacetime itself might or might not literally have a break in it. Eventually the remnants of said matter radiates out as random particles.
That seems totally logical and not paradoxical at all to me. My uneducated mental models of black holes and information theory are so crude that I can't even see what the problem with this is. All I can figure is that the conclusions of a theorem in Research Area A turn out to violate an axiom that is used and dependend-on in Research Area B.
I did however find this very interesting document that seems to cover some of what I'm missing: https://plato.stanford.edu/entries/spacetime-singularities/. I'll have to make my way through it over the next few days, maybe it will benefit other people, too.
Basically, does this imply the universe is deterministic, or that we're living in a simulation?
There’s remains indexical uncertainty, as we can’t predict which timelines we’ll see. The answer is of course all of them.
Also, has been argued philosophically for thousands of years https://plato.stanford.edu/entries/freewill/
The laws of physics are mostly fully deterministic, even quantum laws.