- #1

Killtech

- 344

- 35

- TL;DR Summary
- Looking for a interpretation that is consistent with classic probability

So back in the other thread I asked about compatibility of classical probability theory (PT) and QM – and it turns out there is no inherent reason why they need to be incompatible. Therefore I was looking for something that makes them compatible, which wasn’t easy to search for. But there seems to be a few – though not under that ‘search keyword’.

Anyhow, in terms of PT we have all we need: we have the time evolution of the system and how to extract probabilities from it. So starting at Schrödinger all we need to do is to formulate it into the PT framework by for example finding a stochastic process (SP) for that (I found many attempts in this direction but none doing the thing I would consider canonical). Looking at the time evolution of the probability density - Madelung equations in particular - it becomes directly clear that those are not linear. Therefore they are not suited to form the stochastic kernel (I.e. the PTs equivalent of a Hamilton operator) as its linearity is nonnegotiable. That simply means that the phase space of a point like particle is not viable for the classical PT state space ##\Omega##. The problem seems to be that the wave function just stores too much information (way more than the 6 DoF of a particle) that is crucial for the time evolution that cannot be reduced without breaking predictions (well, no surprise there, since that is the premise of quantum information I suppose).

But with so much irreducible degrees of freedom the smallest state space i could find to fit the information in was that of a field. That would allow to make the stochastic kernel linear but make the corresponding stochastic process mostly a deterministic one leaving mainly the initial distribution and measurements to the domain of stochastics. Anyhow this is the type of interpretations i am looking for.

Trying to give this field any physical interpretation then lead me straight to a hydrodynamic interpretation which I didn’t know before. Now why is this interpretation actually so less popular compared to the others that it’s quite hard find much about it?

I have given it a bit of thought and it appears to me that this yields a very intuitive interpretation for a lot of quantum behavior. But admittedly it comes with a long rattail of consequences from dragging classical physics into quantum territory which undoubtedly causes some conflicts. Interestingly however I haven’t found where this leads to any serious contradictions that cannot be resolved by accepting that Schrödinger is just a situational proxy for QED.

So obviously I want to read more into this and thus am looking for openly available material on this topic. In particular how the aspects of classical field interactions implied by classical physics are handled/interpreted vs how QM does it. But also why do we try to interpret QM with point particles if they don’t even carry nearly enough information to properly describe the time evolution of the system? Shouldn’t we be discourage enough from knowing how much trouble the very idea of a point like charge already causes in classical physics?

Anyhow, in terms of PT we have all we need: we have the time evolution of the system and how to extract probabilities from it. So starting at Schrödinger all we need to do is to formulate it into the PT framework by for example finding a stochastic process (SP) for that (I found many attempts in this direction but none doing the thing I would consider canonical). Looking at the time evolution of the probability density - Madelung equations in particular - it becomes directly clear that those are not linear. Therefore they are not suited to form the stochastic kernel (I.e. the PTs equivalent of a Hamilton operator) as its linearity is nonnegotiable. That simply means that the phase space of a point like particle is not viable for the classical PT state space ##\Omega##. The problem seems to be that the wave function just stores too much information (way more than the 6 DoF of a particle) that is crucial for the time evolution that cannot be reduced without breaking predictions (well, no surprise there, since that is the premise of quantum information I suppose).

But with so much irreducible degrees of freedom the smallest state space i could find to fit the information in was that of a field. That would allow to make the stochastic kernel linear but make the corresponding stochastic process mostly a deterministic one leaving mainly the initial distribution and measurements to the domain of stochastics. Anyhow this is the type of interpretations i am looking for.

Trying to give this field any physical interpretation then lead me straight to a hydrodynamic interpretation which I didn’t know before. Now why is this interpretation actually so less popular compared to the others that it’s quite hard find much about it?

I have given it a bit of thought and it appears to me that this yields a very intuitive interpretation for a lot of quantum behavior. But admittedly it comes with a long rattail of consequences from dragging classical physics into quantum territory which undoubtedly causes some conflicts. Interestingly however I haven’t found where this leads to any serious contradictions that cannot be resolved by accepting that Schrödinger is just a situational proxy for QED.

So obviously I want to read more into this and thus am looking for openly available material on this topic. In particular how the aspects of classical field interactions implied by classical physics are handled/interpreted vs how QM does it. But also why do we try to interpret QM with point particles if they don’t even carry nearly enough information to properly describe the time evolution of the system? Shouldn’t we be discourage enough from knowing how much trouble the very idea of a point like charge already causes in classical physics?