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Most so called fundamental constants appear in the relationships between physical quantities only as a consequence of choosing arbitrary units. It is possible

Most so called fundamental constants appear in the relationships between physical quantities only as a consequence of choosing arbitrary units. It is possible to eliminate almost all fundamental constants by choosing so-called natural units for the base physical quantities, for instance the elementary charge as the unit of electric charge. For all fundamental constants that can be eliminated by choosing natural units it makes no sense to discuss about changes of them. Nevertheless, even when a natural system of units is used, there remain 2 fundamental constants (plus a few other fundamental constants that are used only in certain parts of quantum field theory). The 2 important fundamental constants that cannot be eliminated are the Newtonian constant of gravitation, which is a measure of the intensity of the gravitational interaction, and a second fundamental constant that is a measure of the intensity of the electromagnetic interaction, which is frequently expressed as the so-called constant of the fine structure. The meaning of the constant of the fine structure is that it is the ratio between the speed of light in vacuum and the speed of a charged particle with unit charge, like an electron, that rotates around another charged particle with unit charge, which is much heavier, like a nucleus, in the state with the lowest possible energy, i.e. like the ground state of a hydrogen atom, but where the nucleus would have infinite mass. The speed of the rotating particle is a measure of the strength of the electromagnetic interaction between two elementary charges. So the only fundamental constants for which there could be a evolution in time are those that characterize the strengths of the electromagnetic interaction and of the gravitational interaction (and also the fundamental constants that characterize the strengths of the nuclear strong interactions and nuclear weak interactions). The values of these fundamental constants that characterize the strengths of the different kinds of interactions determine the structure of the Universe, where the quarks are bound into nucleons, the nucleons are bound into nuclei, the nuclei are bound into atoms, the atoms are bound into molecules, the molecules are bound into solid or fluid bodies, which are bound by gravitation into big celestial bodies, then into stellar systems, then into galaxies, then into groups of galaxies. Any changes in the strengths of the fundamental interactions would lead to dramatic changes in the structure of matter, which are not seen even in the distant galaxies. So any changes in time of the true fundamental constants are very unlikely, while changes in the constants that appear as a consequence of choosing arbitrary units are not possible (because such fundamental constants are fixed by conventions, e.g. by saying that the speed of light in vacuum is 299,792,458 m/s).

addaon 2y ago
What about the constants that describe the (relative) rest masses of elementary particles? Since we don’t know the order of magnitude of neutrino masses, it seems improbable that even an order of magnitude change of those masses over time would lead to “dramatic changes in the structure of matter.”
- adrian_b 2y ago
  The masses of the particles and other specific properties, like magnetic moments, are not fundamental constants. They are the properties of those particles. There are such properties for leptons, for hadrons, for nuclei, for atoms, for molecules, for chemical substances, for humans and so on. Any object, either as small as an electron or as big as the Sun is characterized by various numeric properties, such as mass. The fundamental constants are not specific to any particular object. As I have said, after eliminating the fundamental constants that are determined by conventional choices of the system of units, the only fundamental constants that remain are those that characterize the strength of each fundamental interaction, as expressed in a natural system of units. Because most objects are composed of smaller subobjects, it should have been possible to compute their properties from the properties of their components. Starting from the properties of leptons and quarks, it should have been possible to compute the properties of hadrons, nuclei, atoms, molecules and so on. Unfortunately we do not have any theory that can compute the desired properties with enough precision and in most cases even approximate values are impossible to compute. So almost all properties of particles, nuclei, atoms or molecules must be measured experimentally. Besides the question whether the fundamental constants can change in time, one can put a separate question whether the properties of leptons and quarks can vary in time. Some of the properties of leptons and quarks are constrained by symmetry rules, but there remain a few that could vary, for instance the mass ratio between muon and electron. It is likely that a future theory might discover that this mass ratio is not an arbitrary parameter, but the muon is a kind of excited state of the electron, in which case this mass ratio could be computed as a function of the fundamental constants, so the question whether it can vary would be reduced to the question about the variation of the fundamental constants.
  - 2y ago

addaon 2y ago

What about the constants that describe the (relative) rest masses of elementary particles? Since we don’t know the order of magnitude of neutrino masses, it seems improbable that even an order of magnitude change of those masses over time would lead to “dramatic changes in the structure of matter.”

adrian_b 2y ago
The masses of the particles and other specific properties, like magnetic moments, are not fundamental constants. They are the properties of those particles. There are such properties for leptons, for hadrons, for nuclei, for atoms, for molecules, for chemical substances, for humans and so on. Any object, either as small as an electron or as big as the Sun is characterized by various numeric properties, such as mass. The fundamental constants are not specific to any particular object. As I have said, after eliminating the fundamental constants that are determined by conventional choices of the system of units, the only fundamental constants that remain are those that characterize the strength of each fundamental interaction, as expressed in a natural system of units. Because most objects are composed of smaller subobjects, it should have been possible to compute their properties from the properties of their components. Starting from the properties of leptons and quarks, it should have been possible to compute the properties of hadrons, nuclei, atoms, molecules and so on. Unfortunately we do not have any theory that can compute the desired properties with enough precision and in most cases even approximate values are impossible to compute. So almost all properties of particles, nuclei, atoms or molecules must be measured experimentally. Besides the question whether the fundamental constants can change in time, one can put a separate question whether the properties of leptons and quarks can vary in time. Some of the properties of leptons and quarks are constrained by symmetry rules, but there remain a few that could vary, for instance the mass ratio between muon and electron. It is likely that a future theory might discover that this mass ratio is not an arbitrary parameter, but the muon is a kind of excited state of the electron, in which case this mass ratio could be computed as a function of the fundamental constants, so the question whether it can vary would be reduced to the question about the variation of the fundamental constants.
- 2y ago