Whose modern understanding of MWI? Give me a mathematical formalism for “world” that allows world count to be conserved as interactions go forward (if the worlds ‘were split all along’, then something like ‘world count’ is constant).
Your understanding also seems to have implications for (“the modern understanding of”) MWI and Bell’s theorem- since you are applying if I know enough about the degrees of freedom “I don’t care about” I can track which world I am in. This should reduce to some sort of hidden variable approach, I would think.
Give me a mathematical formalism for “world” that allows world count to be conserved as interactions go forward (if the worlds ‘were split all along’, then something like ‘world count’ is constant).
As Manfred says, thinking of worlds as discrete isn’t helpful. Anyway, the time evolution dictated by Schrödinger’s equation is unitary, so if it always applies (i.e. there’s no such thing as objective collapse), the measure stays constant.
I know enough about the degrees of freedom “I don’t care about” I can track which world I am in.
If I understand decoherence well enough (probably I don’t), the answer to that is “in you could, yes, but you can’t, because thermodynamics”. The differential equations of quantum field theory are more-or-less time-symmetric (i.e. reversing time is equivalent to boring stuff such as conjugating complex phases and swapping particles with anti-particles and left with right), so the reason stuff appears to be irreversible is the boundary condition that the past had very little entropy. (And I think I’ve seen the argument that given that T-symmetry is equivalent to CP-symmetry, the fact that the past had that little entropy may (or may not) have something to do with the fact that there are so many more particles than antiparticles.)
You have to have a mechanism to separate world as discrete or you have a theory that can’t make predictions. If you want to talk about the aligned/anti-aligned beam in the Stern-Gerlach experiment you have to be able to point and say “this represents the world where observers measure aligned, and this bit over here represents the world where observers measure anti-aligned.” If you can’t do that, you have no theory.
If I understand decoherence well enough (probably I don’t), the answer to that is “in you could, yes, but you can’t, because thermodynamics”.
This has to be wrong, otherwise MWI would predict violations of Bell inequalities.
I think your ‘the world is already split’ interpretation is actually the fundamental misunderstanding- I can’t make any sense of it other than as a hidden variable theory of the type already experimentally ruled out by Aspect-like experiments.
Edit: Unrelated, but to clarify- you can show that (assuming energy is bounded below) a Lorentz invariant Hamiltonian has a combined CPT symmetry, which can mean a lot of things, depending on dimension. T has to be related to CP, but not necessarily the-same-as, unless you have a state where CP^2 = 1.
Generally, you pick up a phase factor after CP^2. The story is exactly like parity (P) if you can embed P^2 in a continuous symmetry, you can define away the phase factor, but if you can’t you are just stuck with it.
Whose modern understanding of MWI? Give me a mathematical formalism for “world” that allows world count to be conserved as interactions go forward (if the worlds ‘were split all along’, then something like ‘world count’ is constant).
Your understanding also seems to have implications for (“the modern understanding of”) MWI and Bell’s theorem- since you are applying if I know enough about the degrees of freedom “I don’t care about” I can track which world I am in. This should reduce to some sort of hidden variable approach, I would think.
As Manfred says, thinking of worlds as discrete isn’t helpful. Anyway, the time evolution dictated by Schrödinger’s equation is unitary, so if it always applies (i.e. there’s no such thing as objective collapse), the measure stays constant.
If I understand decoherence well enough (probably I don’t), the answer to that is “in you could, yes, but you can’t, because thermodynamics”. The differential equations of quantum field theory are more-or-less time-symmetric (i.e. reversing time is equivalent to boring stuff such as conjugating complex phases and swapping particles with anti-particles and left with right), so the reason stuff appears to be irreversible is the boundary condition that the past had very little entropy. (And I think I’ve seen the argument that given that T-symmetry is equivalent to CP-symmetry, the fact that the past had that little entropy may (or may not) have something to do with the fact that there are so many more particles than antiparticles.)
You have to have a mechanism to separate world as discrete or you have a theory that can’t make predictions. If you want to talk about the aligned/anti-aligned beam in the Stern-Gerlach experiment you have to be able to point and say “this represents the world where observers measure aligned, and this bit over here represents the world where observers measure anti-aligned.” If you can’t do that, you have no theory.
This has to be wrong, otherwise MWI would predict violations of Bell inequalities.
I think your ‘the world is already split’ interpretation is actually the fundamental misunderstanding- I can’t make any sense of it other than as a hidden variable theory of the type already experimentally ruled out by Aspect-like experiments.
Edit: Unrelated, but to clarify- you can show that (assuming energy is bounded below) a Lorentz invariant Hamiltonian has a combined CPT symmetry, which can mean a lot of things, depending on dimension. T has to be related to CP, but not necessarily the-same-as, unless you have a state where CP^2 = 1.
How can it be anything else? Even then, T would equal (CP)^-1.
Generally, you pick up a phase factor after CP^2. The story is exactly like parity (P) if you can embed P^2 in a continuous symmetry, you can define away the phase factor, but if you can’t you are just stuck with it.
That’s still in the reference class I called “boring stuff”, though.