Abstract
Quantum mechanics was developed at the beginning of the 20th century almost in parallel with relativity. It requires a high degree of abstraction and, usually, sophisticated mathematical tools. Reducing all formalism as much as possible, the accent is placed both on the counterintuitive and the novel concepts implied by the theory. The chapter starts again with Einstein’s intuition applied to the explanation of the photoelectric effect. Then the quantum behaviour of subatomic particles is introduced. Further generalizing the analysis, quantum fields are touched upon and the open problem of the conflict between general relativity and quantum mechanics is considered.
God does not play dice with the universe.
Albert Einstein, The Born-Einstein Letters 1916–55
Not only does God play dice but… he sometimes throws them where they cannot be seen.
Stephen Hawking , The Nature of Space and Time (1996) by Stephen Hawking and Roger Penrose, p. 121
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Notes
- 1.
Robert Gilmore in his beautiful (and highly recommended) book “Alice in Quantumland” makes an allegory of QM as an “extended analogy” between the realm of QM and the nonsensical world encountered by the Alice of Lewis Carroll.
- 2.
Einstein’s Nobel Prize was not related to his work on Relativity, contrary to popular misconception.
- 3.
Strictly speaking, the idea of light as a flux of particles is much more ancient than Newton’s time, going back to antiquity.
- 4.
We refer to ‘long-lasting’ oscillations. They are called the harmonics of the oscillating string.
- 5.
The frequencies, in first approximation, are inversely proportional to the wavelengths and depend on the nature and the tension of the string.
- 6.
In the real experiments made by George P. Thomson and, independently, by Davison and Germer , in 1927, a crystalline lattice was used. The diffracting openings were the regular gaps between the atoms of the lattice.
- 7.
This is the name jointly given to the particles in the nucleus of an atom, i.e. protons and neutrons. See Chap. 9.
- 8.
The analogy should not be taken too literally. A top is an extended object and the proper rotation happens in three-dimensional space; the spin of an electron is an intrinsic parameter which goes to zero when we let h → 0, i.e. when the quantum behaviour is negligible.
- 9.
Eigen comes from the German word meaning “own”. An eigenvalue is the discrete quantized value of some property (in this case the spin angular momentum) of a quantum mechanical system.
- 10.
See citation at the head of this Chapter.
- 11.
Of course these ‘colours’ and ‘flavours’ have nothing to do with the usual human perceptions, but are just conventional names for properties associated with subnuclear interactions. Their meanings and relevance will be explained in Chap. 10.
- 12.
We will discuss these somewhat esoteric particles in Chap. 10.
- 13.
Not entirely, as we shall see ahead.
- 14.
Actually this is not entirely true as we shall see when discussing the mass of neutrinos.
- 15.
We have commented already on the accuracy of QED in Chap. 3.
- 16.
We have discussed this type of experimental error in Chap. 3.
- 17.
As an example, the multiplication operation in ordinary algebra commutes because a × b = b × a. However, if a and b are non-symmetric matrices and not ordinary numbers, the products a × b and b × a are different and the matrix multiplication operator is said to be non-commutative. For a simpler example √logx is different from log√x.
- 18.
In the example the problem is related to the fact that the different harmonic waves, which superpose to form the propagating perturbation, travel with different velocities depending on each one’s frequency: we say that the medium (the sea water surface, in this case) is dispersive.
- 19.
This is the theme of the novel Fatherland by Robert Harris (Hutchinson, 1992).
- 20.
Yea, all which it inherit—shall dissolve, And like this insubstantial pageant faded, Leave not a rack behind. We are such stuff, As dreams are made on. William Shakespeare: The Tempest, Act 4, Scene 1.
- 21.
One needs to be cautious with the term ‘information’, which is used somewhat differently in QM to ordinary usage.
- 22.
We hasten to emphasise that this is a thought experiment. No real cat, living or dead, or any other animal for that matter, needs to be involved in carrying out this exercise.
References
R. Feynman, Probability and Uncertainty—the Quantum Mechanical View of Nature, chapter 6, p. 129
A. Dante, The Divine Comedy (Book I, Hell, Canto 3), translated by Clive James, Picador
R. Feynman, QED: The Strange Theory of Light and Matter. (Princeton University, 1965) p. 128
R. Penrose, The Road to Reality. (Jonathan Cape, 2004) p. 578
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Barrett, R., Delsanto, P.P., Tartaglia, A. (2016). Quantum Mechanics. In: Physics: The Ultimate Adventure. Undergraduate Lecture Notes in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-31691-8_8
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