Hi guys. I have something stuck in my head since a few days and I'd like to have your opinion about that. I don't know if I am missing something in my assumptions so please feel free to enlighten me.(adsbygoogle = window.adsbygoogle || []).push({});

Here's the thing: considering two protons (or electrons), one fixed at the origin of the frame of reference and the second lying on the X axis fixed at a distance L. As we well know, the electric repulsive force is stronger than the gravitational pull between them and they will experience a repulsive resultant force in their frame of reference (they are at rest relative to each other but moving in relation to our frame of reference with a speed V).

In their frame of reference the charge/mass ratio is equal to e/mp where "e" is the charge of the proton and mp its mass. However in our frame of reference this ratio will be different because of the relativistic mass. The charge is invariable with the speed but the mass increases.

Consider what I will call "Planck's particle". This particle has the Planck mass and the Planck charge thus the square of the ratio charge/mass is equal to 4∏εG. If you calculate the interaction between two such particles you will find that the electric repulsive force equals the gravitational pull between them and they won't interact at all. If they are at rest they will keep at rest no matter how close or far they are from each other. So, let's go back to the protons. If their frame of reference is moving with such a speed V that the square of the charge/mass ratio will be equal to 4∏εG, these two protons will not interact with each other (in our frame of reference). So if we measure the resultant force of these two moving protons it will be zero. I've calculated that speed (it's quite high) and its value is:

v = c.[1-(mp^2/α.M^2)]^0,5 where "c" is the speed of light, mp is the mass of the proton (or electron), alpha is the fine-structure constant and M is the Planck mass. Also we would see them (if we'd be able to see them) closer than they really are since the distance L would be contracted from our point of view by the Lorentz factor.

Is that possible that we measure no resultant force at all while in their frame of reference they are experiencing a resultant force?

Thanks in advance for any help.

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# Charge/mass ratio of moving particles (SR)

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