Abstract
I first start by reminders of classical mechanics, probabilities and quantum mechanics, in their usual formulations in theoretical physics. This is mostly very standard material. The last section on reversibility and probabilities in quantum mechanics is a slightly more original presentation of these questions.
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Notes
- 1.
Probability theory appeared and developed in parallel with classical physics, with important contributors in both fields, from Pascal, Bernoulli, and Laplace to Poincaré and Kolmogorov.
- 2.
Looking for efficiency and operability does not mean adopting the (in)famous “shut up and calculate” stance, an advice often but falsely attributed to R. Feynman.
- 3.
At least for finite dimensional and simple cases of infinite dimensional Hilbert spaces, see the discussion on superselection sectors.
- 4.
In a Bayesian sense.
- 5.
This question makes sense if for instance, Alice has made a bet with Bob. Again, and especially for this protocol, the probability has to be taken in a Bayesian sense.
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David, F. (2015). The Standard Formulations of Classical and Quantum Mechanics. In: The Formalisms of Quantum Mechanics. Lecture Notes in Physics, vol 893. Springer, Cham. https://doi.org/10.1007/978-3-319-10539-0_2
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