In generalization does the neighborhood refer to nearby states in wavefunction or different possible future/past wavefunctions (i.e. distributions of complex numbers over space)?
Both.Mδ is a neighborhood of spacetime.
If first, how does it work with the whole (region of) wavefunction evolving simultaneously?
The analogy to the experiment with you and the ball is recursive. You can divide the ball in half over and over again like Zeno.
…like does it actually checks out that past and future are always in the neighborhood in relative configuration space?
It is best to think first of configuration space as constrained by the laws of physics. Take it as a prior. Then proceed to the following paragraph.
Subjectively, the immediate past and the immediate future are slightly different version of your brain’s macrostate B0 because otherwise you wouldn’t feel like the same person. The highest entropy slightly different version Bf is the future macrostate and the lowest entropy slightly different version Bp is the past macrostate. (I am ignoring decoherence where “highest entropy macrostate” becomes ambiguous.)
Bf,Bp are in a neighborhood of B0 in relative configuration space because they are in a neighborhood of B0 and configuration space is continuous.
Or how do you normalize amplitude over expanding space?
I’m guessing you’re referring to normalization of the wavefunction here? This is related to subjective experience in a multiverse and does not depend on this post’s novel theory.
If second, don’t we have only one possible future because evolution of wavefunction is deterministic?
No. Is there a way you could rephrase this question without using the word “deterministic”? “Deterministic” implies causality and the original post describes a timeless multiverse.
Both.Mδ is a neighborhood of spacetime.
The analogy to the experiment with you and the ball is recursive. You can divide the ball in half over and over again like Zeno.
It is best to think first of configuration space as constrained by the laws of physics. Take it as a prior. Then proceed to the following paragraph.
Subjectively, the immediate past and the immediate future are slightly different version of your brain’s macrostate B0 because otherwise you wouldn’t feel like the same person. The highest entropy slightly different version Bf is the future macrostate and the lowest entropy slightly different version Bp is the past macrostate. (I am ignoring decoherence where “highest entropy macrostate” becomes ambiguous.)
Bf,Bp are in a neighborhood of B0 in relative configuration space because they are in a neighborhood of B0 and configuration space is continuous.
I’m guessing you’re referring to normalization of the wavefunction here? This is related to subjective experience in a multiverse and does not depend on this post’s novel theory.
No. Is there a way you could rephrase this question without using the word “deterministic”? “Deterministic” implies causality and the original post describes a timeless multiverse.