Bohmian Mechanics

Originally posted by Soothfast
The Standard Model, quantum theory, relativity theory -- as I understand it, all are essentially mathematical constructs independent of any particular interpretation. That is, they all largely speak to "how," and not to "why." At least, not "why" at too deep a level. So, all these theories work within their appointed spheres of influence, with the Stand ...[text shortened]... lly altered interpretation of the current body of theory. That's pretty much my point, I guess.

The Standard Model has two major components, the electro-weak theory and the Strong force. They co-exist perfectly. In relativistic quantum theory there's a problem with negative energies (actually that is present in the classical theory as E² = p² + m² has two solutions for the energy) and negative probability densities. Quantum theory on a curved background is difficult as the number of particles is different in different (accelerated) reference frames. Quantum Gravity is inconsistent.

Relativity is a classical theory in the sense that particles have definite positions and momenta which are in principle exactly knowable. Making observations won't affect the motion of the body under observation in a drastic way, so there isn't really an interpretational problem. Providing an interpretation for Quantum Theory is much harder as one doesn't have any epistemological basis for making any claims about what the particle is doing between observations. In classical physics one can show that the predicted outcomes are not changed by observation by repeating experiments with and without intermediate observation. In quantum theory the outcomes are changed and so one has no basis for the claim that we could know what the particle is actually doing between observations. The Copenhagen interpretation denies claims of reality of the components of the theory, which isn't quite the same thing as denying the reality of the actual particles.

The mathematical structure of the theory rules out some interpretations. S-matrix theory was developed by Heisenberg to be theory independent. My feeling is that physics theory beyond the Standard Model will be driven by experiment rather than theory or by a reinterpretation of the theory. The reinterpretation will happen after that, not before.

Originally posted by black beetle
Edit: The problem with the de Broglie-Bohm theory is that if it makes the same predictions as traditional quantum mechanics then it has this pointless extra metaphysical entity in it and if it does make different predictions then it's ruled out by experiment (but see below). As I understand dBB theory the pilot wave is identical to the wavefunction in ...[text shortened]... whatever is meant from an orthodox point of view as “w/f of a subsystem” obscure it remains
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What neither you, nor anything I've ever read about this, has done is told me how the particle is ever detected. There is no back reaction on the pilot wave and all the properties of the particle other than position (mass, charge, spin and so on) are associated with the pilot wave. All that is detected is the pilot wave that is what does all the interacting in dBB. So it's quantum mechanics with an extra object, that doesn't appear to do anything.

Originally posted by DeepThought
What neither you, nor anything I've ever read about this, has done is told me how the particle is ever detected. There is no back reaction on the pilot wave and all the properties of the particle other than position (mass, charge, spin and so on) are associated with the pilot wave. All that is detected is the pilot wave that is what does all the intera ...[text shortened]... dBB. So it's quantum mechanics with an extra object, that doesn't appear to do anything.

At the Two Slits Experiment the w/f takes both slits into account and defines the usual probability spread on the screen. The actual photon only goes through one of the slits; but because its behavior is determined by the w/f, it hits the screen at a point determined by the w/f’s interference pattern.
That being said, since a measuring apparatus is a physical system whose dynamics is described by the laws of QM, in Bohmian Mechanics a measurement is considered to be a described by QM interaction between the observed system and the apparatus😵

Originally posted by black beetle
At the Two Slits Experiment the w/f takes both slits into account and defines the usual probability spread on the screen. The actual photon only goes through one of the slits; but because its behavior is determined by the w/f, it hits the screen at a point determined by the w/f’s interference pattern.
That being said, since a measuring apparatus is a p ...[text shortened]... s considered to be a described by QM interaction between the observed system and the apparatus😵

That being said, since a measuring apparatus is a physical system whose dynamics is described by the laws of QM, in Bohmian Mechanics a measurement is considered to be a described by QM interaction between the observed system and the apparatus

Yes, this is what I'm getting at - the dBB particle never interacts with anything, so how can its position be measured?

Originally posted by DeepThought

That being said, since a measuring apparatus is a physical system whose dynamics is described by the laws of QM, in Bohmian Mechanics a measurement is considered to be a described by QM interaction between the observed system and the apparatus

Yes, this is what I'm getting at - the dBB particle never interacts with anything, so how can its position be measured?

“Particles” over here are to be understood literally; they have positions, and follow trajectories governed by Bohm’s law of motion, which evolves a w/f that shows how the matter moves. The theory is not formulated in terms of what observers see but in terms of events, regardless of whether or not they are observed😵

Originally posted by black beetle
“Particles” over here are to be understood literally; they have positions, and follow trajectories governed by Bohm’s law of motion, which evolves a w/f that shows how the matter moves. The theory is not formulated in terms of what observers see but in terms of events, regardless of whether or not they are observed😵

But there is no event in which the dBB particle interacts with anything so it has no point.

Originally posted by DeepThought
But there is no event in which the dBB particle interacts with anything so it has no point.

But what about the experiment the fluid dynamicists are doing with oil droplets over a liquid?* The events being seen are the waves in the liquid. As I understand it, conventional quantum mechanics, as applied to this experiment, would identify the ripples in the liquid with the oil droplet itself -- which in this context I think most would agree is a weird interpretation. The double-slit experiment is, analogously, an observation of the ripples, and not the particles themselves. So wave-particle duality is just a simple outcome of observing two different things: sometimes the particle, and sometimes the pilot wave. Your objection to there being an extra moving part in dBB is seemingly to be answered with pointing out that wave-particle duality in the conventional interpretation is also an extra component -- and a far less intuitive one, though perhaps mathematically expedient.

* Referencing the article http://www.wired.com/2014/06/the-new-quantum-reality

Originally posted by DeepThought
But there is no event in which the dBB particle interacts with anything so it has no point.

No;
According to the dBB approach for many-particle systems (non-relativistic many-particle quantum systems), we describe the stats of a single-particle quantum system with an infinite ensemble of trajectories M → ∞. All these different trajectories refer to different dynamical realizations of the same single-particle quantum system;
In a quantum system with N degrees of freedom we will use a particular variable xk for each degree of freedom k = 1, . . . , N, so the w/f will be a function of all x1, . . . , xN variables; a many-particle Bohmian trajectory will involve N interacting particles x1[t], . . . , xN [t]. The N particles interact between them -in other words, the interacting potential depends on all possible particle positions V (x1, . . . , xN ) in a non-trivial way
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Originally posted by Soothfast
But what about the experiment the fluid dynamicists are doing with oil droplets over a liquid?* The events being seen are the waves in the liquid. As I understand it, conventional quantum mechanics, as applied to this experiment, would identify the ripples in the liquid with the oil droplet itself -- which in this context I think most would agree is a we ...[text shortened]... lly expedient.

* Referencing the article http://www.wired.com/2014/06/the-new-quantum-reality

I'm not a fan of the Copenhagen Interpretation, it's just I don't believe the pilot wave theory. I'm stuck with two words for slightly different concepts, where I write particle I mean the physical thing, if I'm referring to the particle in dBB I'll prefix it with dBB. So in dBB a particle consists of a pilot wave and a dBB particle, in Everett's MWI (many worlds interpretation) particles consist only of a wavefunction. The Copenhagen Interpretation is weird about this, it denies the reality of the wavefunction and talks about the outcomes of measurements - so it's not clear if there is a CI particle or not - it could be seen as a stochastic version of dBB and it could be treated as wavefunction only. Since an idealised position measurement turns the wavefunction into a delta function one can regard the particle aspect as just being a consequence of the wavefunction being highly localised.

I don't like MWI because you need measure over a space of universes but it has the nice feature that wavefunction collapse is explained in a natural way. In the Copenhagen interpretation the equipment is assumed to be classical and measurements are privileged in that ordinary interactions don't cause wavefunction collapse.

In dBB the particle does not produce a back-reaction on the pilot-wave. So it doesn't affect it's own pilot wave. All the interactions between particles are between the pilot waves. This means that either position observations are privileged and allow access to to the dBB particle or that the dBB particle is this extra thing that does nothing in the theory.

CI insists that the equipment is classical and wavefunction collapse isn't explained. I don't regard CI as complete. My feeling is that an interpretation needs to start with Quantum Field Theory rather than at the level of Quantum Mechanics, as the natural objects are fields - and a particle is just an excitation of the field.