# De Broglie- Bohm Quantum Theory

From what I have read the Standard Model of Particle Physics uses quantum mechanics,special relativity, along with other assorted mathematics to make predictions and provide a framework for QED, QCD, and EWT. There is not much attention given to the De Broglie - Bohm model of QM in the press. My question is this' What TYPE of quantum mechanics does the Standard Model Use? Can it be replaced with the Bohm model? Which by the way is the model apparently that Bell liked and it also explains non locality very nicely. OR is it that the quantum mechanics used in the Standard Model are just general rules which apply to ALL interpretations of quantum mechanics. The reason I ask is that since the Standard Model appears to be stuck why don't scientists replace the QM used in the model with the De Broglie - Bohm QM to see if it makes any difference? Thank you so much. Any clue would help.

• De Broglie-Bohm, when applicable, is equivalent to standard QM. As far as I know, de Broglie-Bohm cannot be self-sufficient because it doesn't deal with spin (correct me if I'm wrong). They're just interpretations. Also, you should be careful to say the Standard Model is stuck so little time after the discovery of the Higgs boson. In what sense is it stuck? – QuantumBrick Jul 1 '16 at 17:17
• The standard model was invented to explain actual experimental data, the Bohm interpretation was invented to explain philosophical misconceptions of the early founders of quantum mechanics. It became pretty clear early on that nature follows wave equations, but somehow these wave equations seemed to make particles-like tracks in detectors, which is somewhat mysterious. In 1929 Mott came up with a beautiful (and correct) explanation for how these particle tracks form. Bohm obviously never understood it... the rest is history. – CuriousOne Jul 1 '16 at 17:46
• @CuriousOne how can an interpretation be right or wrong? by definition is a philosophical choice beyond any experimental consequence. What kind of reasoning makes you believe that the interpretation of your choice is "correct" and the rest are "wrong" – Wolphram jonny Jul 1 '16 at 18:05
• @Wolphramjonny: It's not wrong, it's completely unnecessary. That's much worse. This has nothing to do with belief but anything to do with science history. Quantum mystics have stopped reading any and all physics papers except for their own since roughly 1926. They live in a time bubble in which things that have long been resolved are still on the menu. – CuriousOne Jul 1 '16 at 18:07
• @CuriousOne How can an interpretation be wrong and how you decide which one is necessary and which not? you always escape and never answer the basic questions posed to you in response to your missleading comments – Wolphram jonny Jul 1 '16 at 18:11

The de Broglie-Bohm (dBB) interpretation really only applies to nonrelativistic quantum mechanics.

It can handle spin just fine, but isn't well adapted to special relativity, quantum field theory, particle creation or destruction and so on.

For example, if you have a situation that is well described by the Schrödinger equation or the Schrödinger-Pauli equation then you can use dBB just as easily.

It doesn't give you any different predictions than the regular/common use of non relativistic wave mechanics.

But that isn't what is used in the standard model. The standard model includes particle creation and particle destruction and full use of special relativity.

• That make good sense Timaeus, it would most certainly explain why the Standard Model is not well motivated to include this model! I guess my confusion here is inherent in the history of why Bell promoted it and was in fact very sure of himself on this. He worked for CERN up to 1990 and was well aware of the Standard Model. In fact I am sure he had a part in it since he was a particle physicist at CERN during the wonder years. Maybe my confusion belongs on the history of science sections? – Sedumjoy Jul 1 '16 at 19:43
• @JuliusMazzarella One purpose of the dBB interpretation is to be a counterexample to incorrect claims about what is or is not possible in quantum mechanics. As a scientist you don't want to be unfairly constrained. But it only goes so far if you haven't figured out how to handle relativity, particle creation, particle destruction, quantum fields and so on. – Timaeus Jul 1 '16 at 19:59
• Hello. May I ask for a reference or maybe an example by you illustrating the reason for the problematic extension of the dBB model to SR or Many-Body situations? Is the reason hidden in some principle of the model forbidding SR or Many-Body considerations or is a weakness in general of the principles to be extended to such frameworks? Thank you. – Constantine Black Aug 17 '16 at 9:57
• Forgive me, what I had in mind as Many-Body was the particle creation-annihilation events through interactions with energies above a certain threshold. You are correct. – Constantine Black Aug 17 '16 at 16:24

The de Broglie-Bohm interpretation is a way of putting quantum mechanics in a classical-like format. It is somewhat contrived in a way. It starts with the wave function put in polar form $\psi~=~Re^{-iS/\hbar}$ and the Schrodinger equation for a particle moving in a potential $$i\hbar\frac{\partial\psi}{\partial t}~=~-\frac{\hbar^2}{2m}\nabla^2\psi~+~V\psi$$ This gives a pair of real and imaginary equations. The real equation is a modified Hamiltonian-Jacobi equation $$-\frac{\partial S}{\partial t}~=~\frac{1}{2m}p^2~+~V~-~\frac{\hbar}{2m}\frac{\nabla^2R}{R},$$ for $p~=~\nabla S$. The imaginary part is a continuity equation $$\frac{\partial\rho}{\partial t}~+~\nabla(\rho v)~=~0,~\rho~=~R^2$$ The first equation is interpreted as the perturbation of a classsical particle by a quantum potential $Q~=~-\frac{\hbar}{2m}\frac{\nabla^2R}{R}$. There is a bit of a problem with this, for it considers this particle as classical, but there is not the sort of correspondence one wants that is in line with the Born theorem. The second part is considered to be a continuity for a pilot wave, which is a bit like a fluid wave.

The applicability of this is limited. It is not really relativistic QM that is a problem. One can take the Klein-Gordon equation, input a polar wave and get similar equations. The problem is really with interacting QM, and that is worse with relativistic QM. Since there is no Hilbert space there is no easy way to describe the creation and absorption of particles. Things get worse with relativistic QM for the creation of an $e,~e^+$ pair has a mass-gap $2mc^2$ that Bohm QM can't work with. Supposedly Shelly Goldstein and his group at Rutgers have worked this out, which means a lot of effort has gone into figuring out something known by ordinary QM back in the 1930s.

For this reason nobody doing quantum field theory, QED, QCD and standard model EW unification has used Bohm's QM. It really would be extremely cumbersome. Bohm's QM might have some use with quantum chaos. The classical-like structure of it might have some utility with understanding quantum chaos according to the Greene methods with perturbation theory.

If one thinks of the polar wave as $\psi~=~e^{r~+~iS/\hbar}$, clearly $R~=~e^r$, then if you sum over all possible symplectic transformations something interesting happens. In the Bohm language the polar wave is associated with an active channel. The other channels are called inactive. A symplectic transformation gives another active channel. A big sum over these is then similar to a path integral. In this way Bohm's QM might construct more ordinary QM. QM is unitary and Bohm's QM might more properly be unitary-symplectic or $Usp(n)$, if one is considering something like a gauge field.