Abstract
Quantum mechanics refers to quantum systems and their environment. The theory does not include consciousness, human subjects, or detectors. The interaction of quantum systems with detectors is the subject of a different theory: quantum theory of measurement. Quantum systems have properties that are not classical. Sometimes they behave in a similar way to classical systems such as particles or waves, but they are neither of them. Other properties, such as spin, lepton number, or color, have no classical analogous. Entanglement is a property of quantum systems that are prepared in a certain state; this property holds as far as the system does not interact with other systems exchanging energy. Quantum mechanics is a realistic, non-local, deterministic, and probabilistic theory of microphysical objects. Its dynamical equations are lineal, and hence the state functions of quantum objects obey the Principle of Superposition. This results in a phenomenology that sometimes strongly differs from what we know from classical physics and common sense.
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Notes
- 1.
A Hilbert space is an abstract vector space possessing the structure of an inner product that allows lengths and angles to be measured. Hilbert spaces are complete in the sense that there are enough limits in the space to allow the techniques of calculus to be used.
- 2.
In this definition the symbol ∗ designates the conjugate-complex of the wave function.
- 3.
I use an informal notation (with the risk of committing language abuses) instead of exact logical notation that would obscure the physics of the problem. Some unusual symbols and their meaning: \(\hat {=}\) (“…represents…”), ∕ (“…such that…”), \(\tilde {=}\) (“…isomorphic to…”).
- 4.
For the sake of simplicity I am ignoring here space and time. I will discuss in detail the ontological status of space and time, and spacetime, in the next chapter.
- 5.
In particular, \(\overline {{\sigma }}_{0}\) denotes the empty environment, \(<\sigma ,\overline {\sigma }_{0}>\) denotes a free q-system, and \(<\sigma _{0},\overline {\sigma } _{0}>\) denotes the vacuum.
- 6.
Non-Local causation is discussed, for instance, by Romero and Pérez (2012).
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Romero, G.E. (2018). Philosophical Problems of Quantum Mechanics. In: Scientific Philosophy. Springer, Cham. https://doi.org/10.1007/978-3-319-97631-0_8
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