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My physics textbook includes the following table:

enter image description here

My question is about the fourth row, where it compares the relative strengths of the fundamental interactions. How are these determined? Is the ratio of electromagnetic and gravitational simply the ratio of the force between 2 1kg point masses separated by 1m, and the force between 2 1C point charges separated by 1m? (that was the explanation my teacher gave me) If so, how can this be justified, since the C and kg are just arbitrary units?

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  • $\begingroup$ If so, how can this be justified, since the C and kg are just arbitrary units? I think you mean to say the scenarios you describe seem to be arbitrary. The term "arbitrary units" has a specific meaning in science, and the kilogram and Coulomb are not arbitrary units. They are quite the opposite, actually. Also, please say which book you are using $\endgroup$ – BioPhysicist Apr 28 '19 at 11:06
  • $\begingroup$ @AaronStevens the kilogram and Coulomb are not arbitrary units. They are quite the opposite, actually. Apparently OP means these units have been fixed (historically) in a quite arbitrary way. In fact other systems of units have been in use. I fully agree with OP that a classification of fundamental interactions as given in that table is very questionable and meaningless to be given at a school level where it's impossible to offer the slightest justification. Surely it can't be what the OP believes, but it's not his fault. $\endgroup$ – Elio Fabri Apr 28 '19 at 13:59
  • $\begingroup$ @AaronStevens the book I am using is an online textbook (kognity.com). Also, by arbitrary units, I meant arbitrarily defined units. $\endgroup$ – Jorge Romeu Apr 28 '19 at 17:05
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    $\begingroup$ The ratio of the strengths of the gravitational force and the electromagnetic force is easy: just compute these two forces on two electrons, two protons, or an electron and a proton separated by any distance. These will give somewhat different ratios, but they are all in the neighborhood of $10^{-40}$. $\endgroup$ – G. Smith Apr 28 '19 at 18:39
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Here is another table of fundamntal forces as used in particle physics.

funfor

Fundamental means the basic framework, and the basic framework is quantum mechanics, from which macroscopic forces emerge which can be demonstrated mathematically. These forces exist at the particle level, and their strength relative to each other enter in the Feynman diagram description of the complicated integrals that have to be computed in order to describe data at the particle level.

The column called "strength" gives the coupling constants that have to enter in a multiplicative manner whenever a vertex in a feynman diagram involves the corresponding force. The coupling constants are measured from data. Example here for weak and here for electromagnetic. Mesurements are fitted by specific calculations, and thus the valuce of the coupling constants are defined.

The relative strength is gotten from data that need two different couplings, so the Feynman diagram calculations are fitted to the data, and the relative strength is determined.

In a hand waving way, the diagrams with the weak constant gives small crossections with respect to the ones with electromagnetic vertices, that is why the were called weak. The calculations quantify this.

Here is a link for measuring the strong force coupling.

Gravitation is still not definitively quantized, but the coupling constant is used in effective quantizations. Here is a link on how it is defined.

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Of course anna v's answer is right, here are a few things I would like to add:

  1. EM force strength is measured from experimental data

  2. weak force strength is measured from experimental data

  3. gravitational force strength is not measured, but is only theoretically predicted

  4. strong force strength is theoretically measured and in experiments too, like with the exotic atoms, like the pionic atom. The pionic atom is an atom where around the proton, the electrons are replaced by pions. Since the pions are made of quarks and antiquarks, they show bosonic characteristics, and thus the nucleus and the pions are not held together by the EM force but by the strong force. This way they can measure the strength of the strong force too.

Please see here:

https://tel.archives-ouvertes.fr/tel-01674426/document

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There is also another good answer re the strengths of the known forces in this blog

Summary:

Take two objects of some type, perhaps elementary particles, and place them a distance $r$ apart. Suppose each exerts a force $F$ on the other. Then we will say this force is weak if $F$ is much less than $ℏc\over r²$ where $\hbar$ is Planck’s reduced constant and $c$ is the speed of light.

In short, for particle physicists:

  • a weak force has $F r²$ much less than $ℏ c$
  • a strong force has $F r²$ about as big as $ℏ c$
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