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.
 A: 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.
A: 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.
