Abstract
The properties of every object in the universe, from subatomic particles to giant galaxies, are determined, in the final analysis, by a set of numbers that we call “constants of nature”.
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Notes
- 1.
The values of the constants depend on the units we use to measure them. Physicists therefore focus on dimensionless combinations of the constants, like the ratios of particle masses, which do not depend on the units. The number we quote (30) is the number of independent dimensionless combinations of the constants.
- 2.
On a more fundamental level, protons and neutrons are made up of quarks, so it is more appropriate to regard the quark masses as fundamental constants of nature. But the general conclusion does not change: we are driven to either a hydrogen world or a neutron world, unless the quark masses are suitably fine-tuned.
- 3.
One of these is the Casimir effect which predicts that there will be an attractive force between two uncharged parallel conducting plates in a vacuum. The reason is that electromagnetic field fluctuations are restricted between the plates and unrestricted outside them. This results in more pressure from the outside pushing the plates towards one another. This effect has been measured. Also, the energy levels of the hydrogen atom have been measured and agree with the theory to a very high precision if we take into account the virtual particles which swarm inside the hydrogen atom.
- 4.
The reason for this difference is that fermions are mathematically described by so-called Grassmann numbers , which are rather different from ordinary numbers. When you multiply ordinary numbers, the result does not depend on the ordering of the factors; for example, 3 × 5 = 5 × 3. But for Grassmann numbers the product changes sign under factor ordering: a × b = −b × a.
- 5.
This fact was discovered by the ancient Greeks . The Platonic solids are the tetrahedron, cube, octahedron, dodecahedron and icosahedron.
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Perlov, D., Vilenkin, A. (2017). Anthropic Selection. In: Cosmology for the Curious. Springer, Cham. https://doi.org/10.1007/978-3-319-57040-2_20
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DOI: https://doi.org/10.1007/978-3-319-57040-2_20
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