Quantum physics vs Probability theory

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Discussion Overview

The discussion centers on the relationship between quantum physics (QP) and classical probability theory (PT), specifically exploring why quantum phenomena cannot be adequately modeled using Kolmogorov's framework of probability. Participants share their experiences and challenges in reconciling the two fields, raising questions about the foundational aspects of probability in the context of quantum mechanics.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Exploratory

Main Points Raised

  • Some participants express difficulty in understanding quantum physics due to its probabilistic nature, which seems incompatible with classical probability theory.
  • One participant notes that while classical probability can model random variables with specific values, quantum mechanics involves pairs of quantities that do not have simultaneous specific values, complicating the application of classical models.
  • Another participant suggests that the wave function in quantum mechanics represents a complex probability amplitude rather than a direct probability, with its modulus squared giving the probability density function.
  • Some argue that the classical approach to probability can still be applied abstractly to quantum experiments by focusing on input-output relationships, although this perspective is contested.
  • There is a contention regarding whether the limitations of classical probability in modeling quantum phenomena stem from the nature of quantum mechanics itself or from the frameworks we use to describe it.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether quantum physics can be modeled using classical probability theory. Multiple competing views remain, with some asserting that classical models fail due to the inherent nature of quantum mechanics, while others believe that a different modeling approach could be viable.

Contextual Notes

Participants highlight the need for specific underlying sample spaces in probability theory to model quantum experiments, indicating that classical probability may not accommodate the unique characteristics of quantum systems. There are unresolved questions regarding the foundational aspects of probability theory as applied to quantum mechanics.

  • #121
vanhees71 said:
Of course, QT-time evolution is not equivalent to a stochastic Markov process. Why should it be?

The question of whether a phenomena is or isn't a Markov process isn't well posed until we specify the definition of "state". One thought is that the claim that QM predictions can't be modeled by a Markov process means that they cannot be modeled a Markov process using the QM definition of state. (Given absolute freedom to define "state" as one wishes, how could we show that no Markov model of a phenomena exists?)

However, if the state of a physical system evolves deterministically, there there is no probability involved in the model unless we regard it as a trivial Markov process where the state at time t transitions to the state at time t + dt with probability 1. However, isn't the claim that the QM model is not a Markov process more than an objection to such triviality?

What definition of "state of a process" is being used when we say that the results of QM cannot be modeled by a Markov process?
 
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