Abstract
Every course on quantum mechanics will at some point engage with the notion of “hidden variables”. The terminology is connected with the infamous no hidden variables theorems of von Neumann, Gleason, Kochen and Specker, and Bell, which assert that quantum mechanics does not allow for hidden variables.
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Notes
- 1.
J.S. Bell, Speakable and Unspeakable in Quantum Mechanics, 2nd edn, Cambridge University Press, Cambridge, 2004, p. 166.
- 2.
Springer, 1932.
- 3.
For instance, if \(\hat A = \hat H\)—the “energy operator”—and \(\hat B = \hat L\)—the “angular momentum operator”—we have, in general, different energy levels for every value of \(\hat L\) (and vice versa). A joint measurement then leads to channelling into common eigenspaces.
- 4.
Eugene Wigner (1902–1995).
- 5.
The formula also served as the starting point for the so-called decoherent (or consistent) history approaches to quantum physics.
- 6.
The four-dimensional Hilbert space is the tensor product of two two-dimensional ones, one per particle. Then to be mathematically rigorous, \(\sigma ^1_a \) should be thought of as, e.g., \(\sigma ^1_a \otimes \mathbf {1} \), and \(\sigma ^2_b\) would then be \(\mathbf {1}\otimes \sigma ^2_b\), where 1 is the two-by-two unit matrix.
- 7.
D. Bohm, A suggested interpretation of the quantum theory in terms of ‘hidden’ variables I and II. Physical Review 85, 166, 180 (1952).
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Dürr, D., Lazarovici, D. (2020). Hidden Variables. In: Understanding Quantum Mechanics . Springer, Cham. https://doi.org/10.1007/978-3-030-40068-2_9
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DOI: https://doi.org/10.1007/978-3-030-40068-2_9
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