Undergrad Quantum physics vs Probability theory

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SUMMARY

The discussion centers on the incompatibility between quantum physics (QP) and classical probability theory (PT), specifically Kolmogorov's framework. Participants highlight that QP employs a distinct concept of probability, termed quantum probability, which cannot be reconciled with classical models. Key points include the failure of joint probability distributions in QP due to the nature of quantum measurements, as well as the introduction of quantum logic as a framework that addresses these discrepancies. The conversation also references foundational works, such as Birkhoff and von Neumann's proposal of quantum logic, which provides insights into the unique characteristics of quantum probabilities.

PREREQUISITES
  • Understanding of quantum mechanics principles
  • Familiarity with Kolmogorov's probability theory
  • Knowledge of probability amplitudes and wave functions in quantum physics
  • Basic concepts of quantum logic and its differences from classical logic
NEXT STEPS
  • Research "quantum probability" and its formulations
  • Study Birkhoff and von Neumann's paper on quantum logic
  • Explore Bell's theorem and its implications for classical probability theory
  • Analyze the double-slit experiment from both quantum and classical probability perspectives
USEFUL FOR

Students and professionals in physics, mathematicians interested in probability theory, and researchers exploring the foundations of quantum mechanics and its philosophical implications.

  • #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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