Classical and Quantum probabilities

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Discussion Overview

The discussion revolves around the differences and similarities between classical probabilities, as defined by Kolmogorov's axiomatization, and quantum probabilities, particularly in the context of statistical results and experimental outcomes. Participants explore whether these two frameworks can be distinguished based solely on statistical results, such as the frequency of events, and the implications of these differences for understanding probability in classical and quantum systems.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants propose that classical probabilities arise from a lack of information about individual particles, while quantum probabilities are seen as fundamental characteristics of nature.
  • Others argue that the mathematical rules of classical probability, such as the sum rule for mutually exclusive events, still hold in quantum mechanics, but the interpretation of events may differ.
  • A participant mentions Bell's inequalities as a notable difference between classical and quantum probabilities.
  • There is a discussion about the two-slit experiment, where participants analyze the implications of detecting an electron and how classical assumptions may lead to incorrect interpretations of quantum events.
  • Some participants express uncertainty about whether classical and quantum probabilities can be clearly distinguished, suggesting that both frameworks may be applicable under different conditions.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether classical and quantum probabilities can be distinctly categorized based on statistical results. Multiple competing views remain regarding the interpretation and implications of these probabilities in different contexts.

Contextual Notes

Participants highlight the importance of physical assumptions in interpreting probabilities, particularly in quantum mechanics, and note that classical probability does not inherently forbid changes in probability laws due to measurements.

  • #31
slyboy said:
Bohmian mechanics is a good example of the kind of thing I am talking about. There your ontic state (state of reality) is just the particle positions and the quantum state vector. You just have an ordinary Kolmogorv distribution over particle positions.

Yes, this is the part of Bohmian mechanics that is sufficient to show that you do not NEED any "quantum probability rules" that go beyond Kolmogorov probability ; the very fact that it is possible to construct a model that gives you the same predictions as QM using Kolmogorov probability is sufficient to show that. Don't understand me wrong: I didn't want to say that Bohmian mechanics must therefore be "right" or whatever ; it is just that the very existence of that model, giving QM probabilities, and obeying Kolmogorov probabilities, disproves the statement that you cannot have QM probabilities satisfying Kolmogorov's axioms.

However, there are perfectly good Kolmogorov distributions over position that are not allowed in this theory, since they have to obey the ``equilibrium hypothesis'' in order to agree with the predictions of QM, i.e. the prob. distribution must be the one coming from the Born rule applied to the state vector.

Yes, this is correct ; however, it doesn't invalidate the claim that QM probabities CAN be generated by a system obeying Kolmogorov's axioms. If that system can also generate other probabilities (not those of QM) doesn't matter. The very fact that with the right distributions, you DO get out the QM predictions, is enough.

Just as a side note: this doesn't mean I endorse Bohmian mechanics. I have mixed feelings towards it, my main complaint being that the guiding equations do not obey the imposed symmetries on the wave dynamics (like Lorentz invariance). But I do think that it is very useful to study Bohmian mechanics because it is a model that disproves a lot of claims about QM, like the one we're discussing here, namely that "quantum probabilities" are somehow not "normal probabilities as we know them" (Kolmogorov axioms).

cheers,
Patrick.
 

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