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In natural units, the Newton gravitational constant can be set to 1 as well. You do still need a term to characterize the strength of gravity. They sometimes u

In natural units, the Newton gravitational constant can be set to 1 as well. You do still need a term to characterize the strength of gravity. They sometimes use η, which can be defined in terms of G, c, Planck's constant, and a fundamental mass like the electron. The result is a truly fundamental unitless constant. The Standard Model has a dozen or so other fundamental constants, describing various mixing angles and fundamental masses (as ratios).

adrian_b 2y ago
Nope. While the Newton gravitational constant can be set in theory as 1, it cannot be set in practice. The so-called Planck system of units where Newton's constant is set to 1 is an interesting mathematical curiosity, because in it all the physical quantities become dimensionless. Nevertheless, when Newton's constant is set to 1, the number of fundamental constants is not reduced, but another constant that was 1 in other systems of natural units becomes a fundamental constant that must be measured experimentally, for instance the elementary charge. Besides not having any advantage, because the number of fundamental constants in non-nuclear physics remains 2, the system where Newton's constant is set to 1 cannot be used in practice. The reason is that the experimental measurement of Newton's constant has huge uncertainties. If its value is forced to be the exact "1", then those uncertainties are transferred to the absolute values of all other physical quantities. In such a system of units the only values that would be known precisely would be the ratios of two quantities of the same kind, e.g. the ratios of 2 lengths or of 2 masses. Any absolute value, such as the value of a length or the value of a mass, would be affected by huge uncertainties. So the use of such a system of units is completely impossible, even if it is mentioned from time to time by naive people who know nothing about metrology. The choice of units for the physical quantities cannot be completely arbitrary, only units that ensure very low uncertainties for the experimental measurements are eligible. Currently and in the foreseeable future, that means that one of the units that are chosen must be a frequency. For now that is the frequency corresponding to a transition in the spectrum of the cesium atom, which is likely to be changed in a few years to a frequency in the visible range or perhaps in the ultraviolet range. In a more distant future it might be changed to a frequency in a nuclear spectrum, like this frequency that has just been measured for Th229, if it would become possible to make better nuclear clocks than the current optical atomic clocks, which use either trapped ions or lattices of neutral atoms. Some of the parameters of the "standard model" are fundamental constants associated to the strong and weak interactions. It is debatable whether it makes sense to call as fundamental constants the rest of the parameters, which are specific properties of certain objects, i.e. leptons and quarks.

adrian_b 2y ago

Nope. While the Newton gravitational constant can be set in theory as 1, it cannot be set in practice. The so-called Planck system of units where Newton's constant is set to 1 is an interesting mathematical curiosity, because in it all the physical quantities become dimensionless. Nevertheless, when Newton's constant is set to 1, the number of fundamental constants is not reduced, but another constant that was 1 in other systems of natural units becomes a fundamental constant that must be measured experimentally, for instance the elementary charge. Besides not having any advantage, because the number of fundamental constants in non-nuclear physics remains 2, the system where Newton's constant is set to 1 cannot be used in practice. The reason is that the experimental measurement of Newton's constant has huge uncertainties. If its value is forced to be the exact "1", then those uncertainties are transferred to the absolute values of all other physical quantities. In such a system of units the only values that would be known precisely would be the ratios of two quantities of the same kind, e.g. the ratios of 2 lengths or of 2 masses. Any absolute value, such as the value of a length or the value of a mass, would be affected by huge uncertainties. So the use of such a system of units is completely impossible, even if it is mentioned from time to time by naive people who know nothing about metrology. The choice of units for the physical quantities cannot be completely arbitrary, only units that ensure very low uncertainties for the experimental measurements are eligible. Currently and in the foreseeable future, that means that one of the units that are chosen must be a frequency. For now that is the frequency corresponding to a transition in the spectrum of the cesium atom, which is likely to be changed in a few years to a frequency in the visible range or perhaps in the ultraviolet range. In a more distant future it might be changed to a frequency in a nuclear spectrum, like this frequency that has just been measured for Th229, if it would become possible to make better nuclear clocks than the current optical atomic clocks, which use either trapped ions or lattices of neutral atoms. Some of the parameters of the "standard model" are fundamental constants associated to the strong and weak interactions. It is debatable whether it makes sense to call as fundamental constants the rest of the parameters, which are specific properties of certain objects, i.e. leptons and quarks.