Experiment from Einstein Bohr debate

[atyy]

I actually agree with what I understand to be the conclusions of what you are saying. If you take "Copenhagen Interpretation" to mean "that which matches known experimental results," then the CI is the only reasonable interpretation. And if you then allow for the CI to be "agnostic about the reality of the wave function," and even agnostic about the possibility of hidden variables --then that seems very close to the view that makes the most sense to me in my current limited state of knowledge

Yes that is close to what I mean by CI. It is true that CI is not a well-defined term, and different people use it differently. I mean CI as a sort of minimal interpretation that should be consistent with most or all other possible interpretations. To be specific, I am thinking of something like the interpretation given at the start of Landau and Lifshitz's textbook on quantum mechanics.

But in a previous thread you said, "It is impossible to know both the position and momentum of a quantum particle, because it does not and cannot have both position and momentum simultaneously." My understanding was that some non-CI interpretations would not necessarily agree with that--or at least that it would be possible to believe that the particles DID have a momentum and position without contradicting any known experimental results. Einstein was at least reasonable familiar with most of the relevant theoretical results, and my understanding was that he did not agree with that. Moreover, it seems to be actually impossible to design an experiment that PROVES that particles don't have a momentum or velocity, even if it IS possible to prove that it's impossible to MEASURE both a particle's momentum and velocity.

Yes, this is technically tricky, but it is consistent with the meaning of CI I have just outlined. The main problem causing the confusion is that there are several different definitions of position and momentum. A particle may not have a certain type of position and momentum, but it can of course have another type of position and momentum. In quantum mechanics, the most usual definition of position and momentum are the non-commuting canonically conjugate position and momentum. It can be shown that in general and for all hidden variable interpretations, including any of the many possible variants of the Bohmian interpretation, that a particle cannot have simultaneously well-defined non-commuting canonically conjugate position and momentum. In Bohmian mechanics, it is possible for a particle to have a different sort of position and momentum, defined using the Hamilton-Jacobi formalism.

 

[jbmolineux]

It can be shown that in general and for all hidden variable interpretations, including any of the many possible variants of the Bohmian interpretation, that a particle cannot have simultaneously well-defined non-commuting canonically conjugate position and momentum. In Bohmian mechanics, it is possible for a particle to have a different sort of position and momentum, defined using the Hamilton-Jacobi formalism.

This is over my head at the moment, but let me try to understand. You're saying that which of my two options (a or b) is the case depends on how you define position and momentum, right?

But in the case of "well-defined non-commuting canonically conjugate position and momentum," it literally does not have both, correct? Does the concept of "well-defined non-commuting canonically conjugate position and momentum" involve defining position and momentum by measurability?

 

[atyy]

This is over my head at the moment, but let me try to understand. You're saying that which of my two options (a or b) is the case depends on how you define position and momentum, right?

Yes.

But in the case of "well-defined non-commuting canonically conjugate position and momentum," it literally does not have both, correct?

Yes, in Copenhagen, and in any hidden variable interpretation.

Does the concept of "well-defined non-commuting canonically conjugate position and momentum" involve defining position and momentum by measurability?

Something like that. Here by position and momentum I mean non-commuting canonically conjugate position and momentum. Let X stand for a quantum observable, say position or momentum. In quantum mechanics, an accurate measurement of X is a procedure that yields a certain distribution of outcomes for a given wave function. An inaccurate measurement of X is a procedure that yields a slightly different distribution of outcomes on the same given wave function. Position and momentum cannot be simultaneously accurately measured, because their respective measurement procedures require different setups which cannot be put in the same location. In addition it can be shown that position and momentum cannot be simultaneously well-defined properties of a particle in any hidden variable interpretation (there are a couple of additional assumptions needed, which are usually fulfilled). Quantum position and momentum are defined in this way because in the classical limit of quantum mechanics these become the position and momentum of the classical Hamiltonian formalism.

 

[vanhees71]

Yes that is close to what I mean by CI. It is true that CI is not a well-defined term, and different people use it differently. I mean CI as a sort of minimal interpretation that should be consistent with most or all other possible interpretations. To be specific, I am thinking of something like the interpretation given at the start of Landau and Lifshitz's textbook on quantum mechanics.

If you understand this as "Copenhagen Interpretation", I'm also a follower of CI, but as you said, CI is not a clearly defined interpretation, because there are already profound differences between Heisenberg's and Bohr's point of view which where closely collaborating in the early years of QT. I prefer to call, what I think is the only scientifically founded interpretation, the "Minimal Statistical Interpretation", which can also be subsumed under the various flavors of CI.

The poll by Schlosshauer et al is for sure not representative, because it was taken among "33 paticipants of a conference on the foundations of quantum mechanics". I think this is a very small subject of specialist thinking (not to say speculating ;-)) about the "foundations of quantum mechanics". In my experience these specialists tend to be quite far from the main-stream use of QT in the larger scientific community which is more interested in the physics than the metaphysics of the subject (particle and nuclear physicists like myself or the condensed matter physicists). I'd guess, without having made a poll among my colleagues, most of them follow the Minimal Interpretation or more something like the "shut up and calculate/measure" interpretation. They just use quantum mechanics as a theory to predict probabilities like cross sections of reactions occurring in particle/nuclear collisions or the properties of quantum many-body systems (usually in or close to thermal equilibrium) and then check these predictions by experiment. I'd count this vast majority of quantum practitioners as Copenhagenians in the broad sense as atyy put it above.

 

[Ilja]

Compared to this Bohmian mechanics is just a dead end, because it does not provide any new insight into quantum theory. The predictions of Bohmian mechanics are the same as those of non-relativistic quantum theory, and the extension to relativistic quantum field theory is, to my knowledge, not yet achieved at all. Also Bohm's "orbits" are not observed in nature. There is even an experiment by Scully et al which disproves orbits, predicted by Bohmian ideas, but that's for photons, and indeed for massless spin-1 particles the idea of orbits in position space do indeed make the least sense of all examples. So perhaps, this "disproof" is a bit unjust towards Bohmian mechanics, but I've never understood what the advantage of BM might be, except to provide some puzzling exercises for higher mathematics to find Bohm's orbits on top of the solutions of Schrödinger's wave equation.

Regarding relativistic QFT, you are wrong, the first example of a relativistic field theory in the Bohmian approach can be found already at the original paper (for the EM field). Essentially one can consider Bohmian versions in a straightforward way whenever the Hamiltonian is quadratic in the momentum variables. Which is not a problem in QFT where the Hamiltonian of a field is usually a variant of $\pi^2+\partial_i\phi^2+V(\phi)$.

"Disproofs" of de Broglie-Bohm theory are usually the consequences of incorrect understanding of what the theory tells. The proponents of this theory are sometimes not innocent in this connection. The greatest error is IMHO the focus on many particle theory (one should start with the general variant of a general configuration space, and not a special choice of the configuration space).

The advantages of BM are quite obvious. It is realistic (in the precise meaning used by Bell in his theorem), deterministic and causal. Different from many words and inconsistent histories (SCNR) it makes sense. Different from Copenhagen, it has no distinction between classical and quantum domain, but covers above domains. It does not have to focus on the uncertain notion of measurement, because measurements are described by the same math as usual evolution. And it has no measurement problem, because the collapse appears as a natural consequence of the general formula for definition of an effective wave function for a subsystem.

Then, it allows to derive (via Valentinis subquantum H-theorem) the quantum equilibrium, and, thus, the Born rule.

And, no, you cannot eliminate the Bohmian trajectories - because everything you see are trajectories. And you, yourself, are also described by some trajectory. All you can, is to eliminate it quite inconsistently from some artificially subdivided part of the universe named "quantum part". This would introduce an additional artificial subdivision (quantum vs. classical parts of the world) with unclear connections and different equations, and, even worse, unclear boundaries between them. So, removing the trajectories from dBB gives horrible results - the only point in favour of this horror is that we are already used to this horror, have even a name for it (Copenhagen interpretation) and are used to "shut up and calculate".

 

[Ilja]

Well, sex is not always necessarily good, and Bohmian mechanics is bad sex ;-).

Couldn't resist to consider the question which interpretation can be associated with which type of sexual behaviour:

Many worlds: Total promiscuity, you cannot resist even sex with the ugliest person you can imagine, every imaginable perversion really happens.
Consistent histories: Many different sex with different persons at the same time, telling everybody a consistent history about fidelity.
Copenhagen: Man and women live separately, sometimes they meet, have short sex, nobody really knows what the other thinks about this.
Bohm: Back to classical laws - sex as part of the marriage, with love, fidelity and all this. But, let's not forget, in some quantum corners some sex happens which is not classical at all, and seems to be against the law of the majority.
Transactional interpretation: The name tells it - prostitution.
Bayesian interpretation: All what counts are the subjective expectations - no real sex, only nice dreams alone at home.
Ithaca: All what counts is information - no real sex, but a lot of pornography.

So, your choice ;-)

 

[Dale]

I think this thread has run its course.