4 ms·

One thing I've never been clear on is whether this is empirically the case, or theoretically the case. That is to say, is it theoretically possible that someday

One thing I've never been clear on is whether this is empirically the case, or theoretically the case. That is to say, is it theoretically possible that someday we may find evidence that supports Bohm's interpretation and falsifies the others? Or are they truly mathematically equivalent theories?

jldugger 10y ago
My layman's understanding of is that fundamental uncertainty can't really be distinguished from a hidden variable we cannot observe or influence.
- eru 10y ago
  Alas, it's a bit more complicated than that.
ewjordan 10y ago
If memory serves, as far as classical quantum mechanics goes, Bohm's interpretation is 100% mathematically equivalent to the standard interpretation, making it observationally impossible to distinguish the two (much like many worlds vs. Copenhagen). It would be in extensions to the theory where things might differ, though I don't know much about attempts to extend pilot wave theory to QFT.
- SEMW 10y ago
  > Bohm's interpretation is 100% mathematically equivalent to the standard interpretation, making it observationally impossible to distinguish the two This is not quite correct. It is mathematically equivalent to Copenhagen only at times of 'quantum equilibrium', which is when ρ = φ² (probability density is the square of the wavefunction). Copenhagenists call this the Born rule and treat it as axiomatic. Bohmians don't since they don't need to, since in Bohmian mechanics a system which is not in quantum equilibrium will evolve to be in quantum equilibrium in a very very short time. Which gives a way to empirically distinguish pilot-wave theory if the universe began in quantum non-equilibrium. (We have no reason to think it did, but we have no reason to think it didn't, so, shrug). If it did, the early universe would have evolved differently in the first femtosecond after the big bang, which should theoretically be detectable to us by analysis of CMB anisotropies. This has been worked on: a friend of mine did a masters project which among other things involved porting some simulation code on very-early-universe numeric simulations under quantum non-equilibrium (IIRC from fortran 77 to fortran 95, because physicists), under Mike Towler.

jldugger 10y ago

My layman's understanding of is that fundamental uncertainty can't really be distinguished from a hidden variable we cannot observe or influence.

eru 10y ago
Alas, it's a bit more complicated than that.

ewjordan 10y ago

If memory serves, as far as classical quantum mechanics goes, Bohm's interpretation is 100% mathematically equivalent to the standard interpretation, making it observationally impossible to distinguish the two (much like many worlds vs. Copenhagen). It would be in extensions to the theory where things might differ, though I don't know much about attempts to extend pilot wave theory to QFT.

SEMW 10y ago
> Bohm's interpretation is 100% mathematically equivalent to the standard interpretation, making it observationally impossible to distinguish the two This is not quite correct. It is mathematically equivalent to Copenhagen only at times of 'quantum equilibrium', which is when ρ = φ² (probability density is the square of the wavefunction). Copenhagenists call this the Born rule and treat it as axiomatic. Bohmians don't since they don't need to, since in Bohmian mechanics a system which is not in quantum equilibrium will evolve to be in quantum equilibrium in a very very short time. Which gives a way to empirically distinguish pilot-wave theory if the universe began in quantum non-equilibrium. (We have no reason to think it did, but we have no reason to think it didn't, so, shrug). If it did, the early universe would have evolved differently in the first femtosecond after the big bang, which should theoretically be detectable to us by analysis of CMB anisotropies. This has been worked on: a friend of mine did a masters project which among other things involved porting some simulation code on very-early-universe numeric simulations under quantum non-equilibrium (IIRC from fortran 77 to fortran 95, because physicists), under Mike Towler.