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JustinLevy

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(My previous thread on Bohm Interpretation quickly became 4 pages of mostly unrelated discussion. So I'm restarting here with more precise questions.)

Okay, I've read some references on the Bohm Interpretation and I am still confused. As one paper mentioned, some extensions have stochastic elements, so the main purpose of these lines of interpretation seem to be to remove the "classical measurement" from the standard interpretation. Yet even that aspect seems unclear to me.

The fact that it hasn't been soundly refuted in 50 years suggests that I am still misunderstanding it. Continuing with that assumption, please, help me understand why it hasn't been refuted.

All measurements are supposed to boil down to a measurement of position in the Bohmian interpretation.

discussion:

comment A - In BM, the configuration and evolution of a system is specified

comment B - In BM, the wavefunction is not a function of the particle position, but the possible particle positions (the position configuration space). Given N particles in D dimensions, the wavefunction maps points in the space Reals^(ND) to a complex number. The actual positions of the particles evolves according to a functional of the wavefunction. Note: the particle position evolution depends on the wavefunction but not the other way around.

comment C - Since the wavefunction evolution does not depend on the particle positions, the portion of the wavefunction corresponding to the measurement device cannot depend on the particle positions.

comment D - this leaves us in the same situation as standard quantum mechanics. A measurement just entangles you with what you are measuring. Nothing explains how you get a discrete answer instead of a superposition ... since the result up to this point should be a superposition.

The particle position is updated according to only the phase of the wavefunction, so BM uses a different definition of momentum than the standard quantum mechanics. This appears to make BM

discussion:

comment E - Since the ground state wavefunction of a bound system can often (always?) be written as a real valued function * exp(-i E hbar / t), the velocity of any particle in the system is exactly zero. The average velocity squared of a particle is therefore zero.

comment F - This alone appears to refute the BM theory. But also consider momentum conservation. Since the two theories differ, it is unclear to me how momentum can possibly be conserved in BM (especially when considering collisions of particles that can result in bound states).

comment G - Similarly, it is unclear how energy is conserved with this change in p^2 (proportional to kinetic energy). Regardless on whether they use the correct definition of KE, it is also unclear to me on general grounds if a conserved energy can be defined at all. While possibly a solved question, I'm unclear on whether the hamiltonian can be converted to a lagrangian which can be used with Noether's theorem if the number of variables are infinite (fields) AND the configuration has non-local interactions.

In standard quantum mechanics, spin is an internal degree of freedom of a particle. In BM, this degree of freedom is included in the wavefunction by borrowing from derivations in standard quantum mechanics. BM however does not give it a definitive value like it does position. Notice however, that since the wavefunction has two components for each spin (1/2) particle now, to consider evolution of the position, we MUST consider the position to have two components as well (which need not evolve similarly, so even the "real" particle positions are superpositions now!). And you cannot consider these as two individual particles, since they are not conserved (only by considering them together is particle number conserved). So in BM, while <Sx,Sy,Sz> can have any value, a system

discussion:

comment H - Since momentum is defined differently, again we have the same issue as before that it is unclear how angular momentum is conserved. However it now has the additional hurdle due to the true "unknowingness" of spin while the orbital trajectory is definite.

comment I - Because the L=1,m=0 state of the hydrogen atom can be written as a real valued wavefunction, again we have the issue that the particles are stationary. But now,

comment J - A change in basis can change the wavefunction from real valued to complex (consider using the Lz basis, or the Lx basis). So the evolution of the position states seems to depend on the choice of basis. BM can't even seem to say definitively whether their hidden particles are moving or not.

comment K - Every derivation I've seen of the spin statistics theorem relied on locality. Is there a way to get this in Bohmian mechanics as well, or does it just borrow this verbatum from standard QM as well.

Any help in answering (please, not speculating, nor hand-waving, as the theory seems vague enough to me currently as it is) these questions would be greatly appreciated.

Okay, I've read some references on the Bohm Interpretation and I am still confused. As one paper mentioned, some extensions have stochastic elements, so the main purpose of these lines of interpretation seem to be to remove the "classical measurement" from the standard interpretation. Yet even that aspect seems unclear to me.

The fact that it hasn't been soundly refuted in 50 years suggests that I am still misunderstanding it. Continuing with that assumption, please, help me understand why it hasn't been refuted.

__For currently, the theories do not appear equivalent to me.__I will try to be as clear as possible with my questions, so please try to be as clear as possible with your answers. In particular, please clearly define any terms you use that I appear to be misunderstanding, as I am probably unaware that I am misunderstanding them.**Question 1:**All measurements are supposed to boil down to a measurement of position in the Bohmian interpretation.

**What IS a position measurement in the Bohmian interpretation?**discussion:

comment A - In BM, the configuration and evolution of a system is specified

*in totality*by the wavefunction, Hamiltonian, and particle positions.comment B - In BM, the wavefunction is not a function of the particle position, but the possible particle positions (the position configuration space). Given N particles in D dimensions, the wavefunction maps points in the space Reals^(ND) to a complex number. The actual positions of the particles evolves according to a functional of the wavefunction. Note: the particle position evolution depends on the wavefunction but not the other way around.

comment C - Since the wavefunction evolution does not depend on the particle positions, the portion of the wavefunction corresponding to the measurement device cannot depend on the particle positions.

comment D - this leaves us in the same situation as standard quantum mechanics. A measurement just entangles you with what you are measuring. Nothing explains how you get a discrete answer instead of a superposition ... since the result up to this point should be a superposition.

*The very thing BM was supposed to supply, it appears to fail to accomplish. You need to rely on decoherence, or many minds, etc. other interpretations to get anything out despite adding additional information in.***Question 2:**The particle position is updated according to only the phase of the wavefunction, so BM uses a different definition of momentum than the standard quantum mechanics. This appears to make BM

*quantifiably falsifiable*(ie. it is a different theory, not a different interpretation of the underlying math).**What IS a momentum or momentum^2 measurement in the Bohmian interpretation?**discussion:

comment E - Since the ground state wavefunction of a bound system can often (always?) be written as a real valued function * exp(-i E hbar / t), the velocity of any particle in the system is exactly zero. The average velocity squared of a particle is therefore zero.

comment F - This alone appears to refute the BM theory. But also consider momentum conservation. Since the two theories differ, it is unclear to me how momentum can possibly be conserved in BM (especially when considering collisions of particles that can result in bound states).

comment G - Similarly, it is unclear how energy is conserved with this change in p^2 (proportional to kinetic energy). Regardless on whether they use the correct definition of KE, it is also unclear to me on general grounds if a conserved energy can be defined at all. While possibly a solved question, I'm unclear on whether the hamiltonian can be converted to a lagrangian which can be used with Noether's theorem if the number of variables are infinite (fields) AND the configuration has non-local interactions.

**Question 3:**In standard quantum mechanics, spin is an internal degree of freedom of a particle. In BM, this degree of freedom is included in the wavefunction by borrowing from derivations in standard quantum mechanics. BM however does not give it a definitive value like it does position. Notice however, that since the wavefunction has two components for each spin (1/2) particle now, to consider evolution of the position, we MUST consider the position to have two components as well (which need not evolve similarly, so even the "real" particle positions are superpositions now!). And you cannot consider these as two individual particles, since they are not conserved (only by considering them together is particle number conserved). So in BM, while <Sx,Sy,Sz> can have any value, a system

*really truely*does not have a known spin direction which seems contrary to a hidden variable theory and also which is distinct to orbital angular momentum due to real trajectories of particles.**So what IS angular momentum and spin in the Bohmian interpretation?**discussion:

comment H - Since momentum is defined differently, again we have the same issue as before that it is unclear how angular momentum is conserved. However it now has the additional hurdle due to the true "unknowingness" of spin while the orbital trajectory is definite.

comment I - Because the L=1,m=0 state of the hydrogen atom can be written as a real valued wavefunction, again we have the issue that the particles are stationary. But now,

*the particles are stationary even though there is*. So not only does it seem to contradict experiment, but it seems internally inconsistent.__orbital__angular momentumcomment J - A change in basis can change the wavefunction from real valued to complex (consider using the Lz basis, or the Lx basis). So the evolution of the position states seems to depend on the choice of basis. BM can't even seem to say definitively whether their hidden particles are moving or not.

comment K - Every derivation I've seen of the spin statistics theorem relied on locality. Is there a way to get this in Bohmian mechanics as well, or does it just borrow this verbatum from standard QM as well.

Any help in answering (please, not speculating, nor hand-waving, as the theory seems vague enough to me currently as it is) these questions would be greatly appreciated.

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