GEM from stochastic QM
Kh. Namsrai's paper ""xxxx describes a method of deriving the properties of an apparent classical field theory that could be considered as underlying quantum mechanics.
If we consider a simple particle, the uncertainty principle says that if we probe the region of space that includes the particle by firing photons or other particles into the region, then the particle's apparent position will be somewhat "fuzzy". When we repeat the same experiment over and over, aiming away form the particle will sometimes still register a "hit" due to the inherent uncertainty of its position.
|“||For the time being we have to admit that we do not possess any general theoretical basis for physics, which can be regarded as its logical foundation. The field theory, so far, has failed in the molecular sphere. It is agreed on all hands that the only principle which could serve as the baisis of quantum theory would be one that constituted a translation of the field theory into the scheme of quantum statistics.||”|
|— Albert Einstein, "The Fundaments of Theoretical Physics", Science, 1940|
If we plot the probability of getting a hit at any given position, we obtain, with arbitrarily-many plotted points, an increasingly smooth description of what appears to be the particle's mass, spread out into space. Since the field carries the property of mass, it would seem to be indistinguishable form a gravitational or inertial field. , suggesting that he shape of the probability distribution, interpreted as an underlying classical field viewed though the quantised measurement process, actually describes something akin to a gravity-well.
If the particle is moving, it's field carries not just mass, but also momentum - another particle passing through the region has a finite chance of undergoing a form on momentum exchange, that, in a larger-scale classical description of an astronomical problem, would look very like a form of gravitoelectromagnetic coupling.
Namsrai's accompanying diagram shows the effective field of a moving particle as a sort of tilted hat, similar to a gravity-well whose that has been tilted to point in the direction fo motion.
This is, as a sketch, indistinguishable form the representation that we get in a gravitoelectromagnetic general theory of relativity, in which the throat of a moving gravity-well shows a title to align the throat with the direction of the body's worldline through spacetime. The tilt means that the field is asymmetrical, with fieldlines splayed at one side and pulled together at the other, which then suggests the shift equivalence principle. In the gravitational case, the tilted throat represents a field asymmetry that can apply a dragging effect on nearby matter or light, but whose strength diminishes with distance.
Nasrai's diagram anticipates a non-SR acoustic physics, his accompanying text also coincides with the idea that we can shunt information from the time-domain and gravitational-domain descriptions - Namsrai says that in the model, the shape of the field lets us reconstruct the mass and state of motions of the particle, and the mass and state of motion lets us reconstruct the field - a view of the moving particle lets us derive the shape of the field at any given moment, but a single snapshot of the field at one moment allows us to reconstruct how and where it is moving, from the shape of the field.
- While work on acoustic metrics argues that classical acoustic behaviours seem indistinguishable from the statistical effects of QM, it could be argued that this is merely a useful coincidence. However, Namsrai's argument can be used to say that acouctic physics can actually be derived form quantum mechanics, as a hypothetical underlying behaviour. If QM lets us generate a classical theory, and that theory is acoustic, then this may mean that perhaps a classical theory has to be an acoustic model in order to be compatible with QM. This in turn would suggest that the chances of getting our existing classical theory of gravity – SR-based GR1960 – to work with QM may be zero. Reconciling QM with classical gravitational theory would be possible, but the reason why we had been unable to reconcile QM with GR for the past half century would not be because be because of any fundamental incompatibility between classical and quantum physics, but because we were using an incorrect classical theory.