Probabilistics of Quantum Physics

[Svensken]

Hey Guys and Gals!

This is my first post ever!

I would like to discuss something i have recently thought about.

If classical physics is deterministic and allows us to create laws, since quantum physics is probabilistic can we ever create any quantum physics laws? (i don't think there are any - i may be wrong?)

 

[jambaugh]

Hey Svensken, Welcome to Physics Forum!
I think the appropriate answer to your question is that the classical laws are deterministic laws while the quantum laws are probabilistic laws. We i.e. express the probabilities for sequences of observations.

Think of this as a generalization of the classical case where we also express probabilities but they are restricted to boolean values 1 or 0 for determined vs forbidden cases.

With that in mind also note that in the classical case since one is restricting to 1 vs 0 predictions of observable values, one can paint below the directly observable a "reality model" i.e. an ontological description of "what is". In the quantum case without that restriction to certainty one should acknowledge that one is abstracted one level from "reality" and are describing only probabilities of actualized observations. It's more phenomenological, describing "what happens" you can distinguish as "actuality" vs "reality".

With that said, one must then be more careful about the meaning of "deterministic". Without that underlying classical reality model one can't speak of a one-to-one deterministic dynamic evolution of states. The quantum "state vector" is something quite different from the classical objective state, it is a state of knowledge about the system and not a state of reality of the system.

In short the term "deterministic" is not opposite the term "probabilistic". In a probabilistic language you can still have deterministic dynamics. Indeed the dynamic evolution of quantum systems still have deterministic evolution of expectation values, as well as the ability to assure or forbid particular outcomes by controlling initial conditions and dynamics sufficiently.

Finally when one considers e.g. the dynamic evolution of a pair of entangled particles, the preservation of that entanglement (strong correlation between observables) indicates locally deterministic evolution of each half of the pair while at the same time requiring a probabilistic description of outcomes and thus no underlying "reality model" description. You'll see many debates and favored interpretations (I've painted here a bit of my own) trying to make sense of this.

 

[Svensken]

Well, thank you for your quick response!
This was a lot to comprehend, i shall be thinking about what you've said and comment when i have gained further insight.
Thanks again!

 

[Tao-Fu]

By my understanding, a law isn't specifically something that you derive from a theory. Laws describe empirical relationships. Determinism is a feature of a theory, not of a law. Laws just relate measurable quantities without regard to particular mechanisms for explaining the relationship. So, there's nothing preventing physical laws from applying to observables that are describable by a quantum theory.

 

[Matterwave]

The dBB (de-Broglie-Bohm) pilot wave interpretation of QM is deterministic (it is a non-local hidden variable theory), rather than probabilistic. In non-relativistic QM, it is equivalent to standard QM AFAIK. So, I don't think QM is 100% for sure probabilistic, although, it quite probably is.

 

[Frame Dragger]

The dBB (de-Broglie-Bohm) pilot wave interpretation of QM is deterministic (it is a non-local hidden variable theory), rather than probabilistic. In non-relativistic QM, it is equivalent to standard QM AFAIK. So, I don't think QM is 100% for sure probabilistic, although, it quite probably is.

SQM is 100% probablistic. dBB would be except that you separate the wave and particle components so that wave behaviour appears on detectors while ensembles of particles follow classical trajectories.

dBB = Deterministic
QM = Probabilstic

Svensken I would just throw out there that Laplace's Demon is a good thought experiement to ponder. QM does away with that possiblity, but beyond that it doesn't eliminate predictions (especially on a macroscopic scale).