The ratio of strength between electro magnetic and gravitational force

[bobsmith76]

In stenger's book he claims that the ratio between gravity and the electro magnetic is not 10³⁹

Let me know if you think he's right

Note that N1 (ratio of EM force to gravity) is not a universal number; it depends on the charges and masses of the bodies you use in the calculation. For an electron and proton the ratio is the famous 10³⁹ that I will continue to call N1. But why assume these two particles in defining N1? The proton is not even fundamental. It is made of quarks. For two electrons, the ratio is 10⁴⁷. If we have two unit-charged particles of equal mass 1.85 x 10^-9 kilograms, N1 = 1 and the two forces would be equal!
If we were to ask what mass is the most fundamental, it would be the Planck mass, which is formed from the fundamental constants and equals 2.18 x 10^-8 kg. The gravitational force between two particles, each with the Planck mass and unit electric charge, is 137 times stronger than the electric force!

 

[torquil]

Defining the ratio for the electron is only one possible choice, as you have understood. I do think that when this ratio is discussed, it is in the context of forces acting on fundamental particles, and the electron is simply taken as an example. Of course, the statement that the electric force is 10^39 stronger than the gravity can easily be misunderstood. That said, for any electrically charged particle in the standard model particle table, the electric force is significantly stronger than gravity. I think this is the main point, not that it is exactly 10^39. I think that the electron is just the most popular example to illustrate the large difference between electric and gravitational forces on fundamental particles.

Btw, I would not say that the Planck mass is the "most fundamental" mass, since it is not (yet) related to current real-world physics, even though it is a value that can be formed from fundamental physical constants. The Planck mass it so far above the highest experimentally probed energies. Nobody knows what will be discovered between LHC and Planck energies. I.e. nobody knows of the Planck is related to any real physics because of this.

Since the mass is the "gravitational coupling constant" and electrical charge is the "electric coupling constant", it is possible to imagine a particle for which this ratio is any arbitrary value. But this doesn't mean that such a fundamental particle exists.