Don’t think of it in terms of interaction. Think of it as relationships within a static network. The laws of physics constrain the network into a quasicrystalline structure.
Some nodes in this network are self-aware. The self-aware nodes tend to form channels which we call “people”. When the channels fork we call it “decoherence”.
Suppose you run a temporally causal experiment at macrostate M0. For example, you drop a ball and want to see if it falls down to the ground. The results of your experiment cannot be located in the multiverse at M0 because M0 is where you released the ball. The ball has not moved nor has the clock ticked inside your head. Neither can the results of your experiment be located far away from M0 because the initial experimental macrostate M0 is self-locating information[1]. If such a state existed anywhere in the multiverse then it would be located at M0 by definition.
In a neighborhood of M0, there are many slightly different versions of you and many slightly different versions of the ball. The results (possible futures) of your experiment is Omδ where mδ is the set of all elements in m such that 0<min|mδ−O−1M0|<ϵ i.e.mδ is the set of all microstates in a neighborhood of the inverse image O−1M0, excluding O−1M0 itself.
The entropy of the macrostates where the clock in your head and the ball have both ticked forward in time vastly outnumber the entropy of all alternative macrostates within Omδ. To a self-aware macrostate inside the multiverse, time is experimentally equivalent to a random walk along microstates—and is easily mistaken for causality—but time is fundamentally just the inside macrostatic view of a timeless quasicrystalline structure.
In a neighborhood of M0, there are many slightly different versions of you and many slightly different versions of the ball.
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)?
If first, how does it work with the whole (region of) wavefunction evolving simultaneously? I guess I just have unresolved doubts about timeless distribution of amplitude, like does it actually checks out that past and future are always in the neighborhood in relative configuration space? Or how do you normalize amplitude over expanding space? And in that picture without interaction it’s harder for me to, well, justify laws that generate amplitudes for neighboring states.
If second, don’t we have only one possible future because evolution of wavefunction is deterministic?
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.
Yes, it does generalize.
Don’t think of it in terms of interaction. Think of it as relationships within a static network. The laws of physics constrain the network into a quasicrystalline structure.
Some nodes in this network are self-aware. The self-aware nodes tend to form channels which we call “people”. When the channels fork we call it “decoherence”.
Suppose you run a temporally causal experiment at macrostate M0. For example, you drop a ball and want to see if it falls down to the ground. The results of your experiment cannot be located in the multiverse at M0 because M0 is where you released the ball. The ball has not moved nor has the clock ticked inside your head. Neither can the results of your experiment be located far away from M0 because the initial experimental macrostate M0 is self-locating information[1]. If such a state existed anywhere in the multiverse then it would be located at M0 by definition.
In a neighborhood of M0, there are many slightly different versions of you and many slightly different versions of the ball. The results (possible futures) of your experiment is Omδ where mδ is the set of all elements in m such that 0<min|mδ−O−1M0|<ϵ i.e.mδ is the set of all microstates in a neighborhood of the inverse image O−1M0, excluding O−1M0 itself.
The entropy of the macrostates where the clock in your head and the ball have both ticked forward in time vastly outnumber the entropy of all alternative macrostates within Omδ. To a self-aware macrostate inside the multiverse, time is experimentally equivalent to a random walk along microstates—and is easily mistaken for causality—but time is fundamentally just the inside macrostatic view of a timeless quasicrystalline structure.
Also, the laws of physics constrain a relationship between you and the ball.
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)?
If first, how does it work with the whole (region of) wavefunction evolving simultaneously? I guess I just have unresolved doubts about timeless distribution of amplitude, like does it actually checks out that past and future are always in the neighborhood in relative configuration space? Or how do you normalize amplitude over expanding space? And in that picture without interaction it’s harder for me to, well, justify laws that generate amplitudes for neighboring states.
If second, don’t we have only one possible future because evolution of wavefunction is deterministic?
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.