B Strong nuclei force and extra dimensions

  • Thread starter GTOM
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Sorry for my speculative question, i just wondered, is there any sensible theory that thinks strong nuclei force is so weak in the distance, because it isnt three dimensional?

Again i dont intend to say my speculations are facts, but i think the above question needs a bit explanation.
I would think, since the surface of a three dimensional orb depends on square of the radius, the power of a three dimensional orb shaped field should decrease with square of the radius. But strong nuclei force is stronger than repulsive electric force at very low distance, but much weaker at larger distance, that is why heavy elements are unstable.

If this speculation is totally wrong, i would like to have a reading material about that phenonemon, since i only learned about theese things in middle school.
 
Yukawa found the right explanation in 1935, in this paper: the nuclear force between protons and neutrons decreases with the square of the radius, times an extra factor which makes it drop off exponentially. The extra factor is because the force particle is massive (whereas the photon of the electromagnetic force is massless), and Yukawa correctly estimated from the size of the nucleus, that the particle's mass is about two hundred times the electron mass. The particle is the "pion".

The form of the "Yukawa potential", with that extra exponential factor, is explained as due to the uncertainty principle, which sets a limit on how long a virtual particle with the mass of the pion can exist, and therefore a limit on how far it can travel (see "Calculating the mass of a pion").

(Today we go a little deeper and say protons, neutrons, and pions are all made of quarks bound by gluons. The gluon force is the real strong force, and the pion force is a side effect of that.)

Now, none of that involves extra dimensions in the way you suggest. And the problem with using extra dimensions to make a force drop off faster than the inverse square, is that we would somehow need matter affected by the attenuated force, to nonetheless stay within three dimensions. In braneworld models this is achieved by having matter somehow stuck on a 3d brane.

There are two well-known models which use extra dimensions to explain the weakness of gravity. One is the Randall-Sundrum braneworld. This involves a warped or stretched extra dimension, rather than the simple attenuation arising from extra dimensions, so it is not what you suggest.

However, the other is the "ADD model" of large extra dimensions (but here that just means large compared to the very shortest distances, the size of the extra dimensions is less than a millimeter, possibly much less), in which a deviation from the inverse square law for gravity, might actually be observed on scales at which the extra spatial dimensions are comparable in significance to the three dimensions that we know. I take it that this is what you are suggesting.

The ADD model of gravity seems to be regarded as all but falsified. And we have a very robust model of nuclear and subnuclear physics which doesn't use extra dimensions. (We also have string theory, which might explain some things about physics using extra dimensions, but not in the ADD way.)

So the idea of an "ADD model of the nuclear force" seems to be mainly of interest as a historical thought experiment: Suppose they had the ideas of ADD in the 1930s, how closely could they match the data, and what would eventually force them to reject it in favor of Yukawa's model? Someone might enjoy thinking about that.
 

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