In my last post I proposed a structure for a proton just before it splits into quarks.
This structure is topologically reasonable, but it has gaping hole relating to its mass. The sum of the masses of two up quarks and one down quark that make up a proton is 9.1 MeV/c². What these units mean is irrelevant for now. What is important is that a proton has a mass of about 938 MeV/c². This means that about 99 % of the mass of protons isn’t in the quarks. Or more probably is present as relativistic mass, as the increase of speed in an object increases its mass. If I’m not completely mistaken, the increase of mass from 9.1 to 938 (i.e. a 103-fold increase) means that the particles moves at 99.995 % of the speed of light. That is, assuming that both types of quarks are sped up to the same speed.
But what does this mean in terms of structure? If mass, be it rest mass or relativistic mass, is always physical elementary particles of energy, (dots) this extra mass must be present in the structure at the point of quark detachment. And the only way you can increase the mass of a sting of dots, is to increase the length of this string. If the number of turns in a helix is fixed, the only way to have more length is to increase the height of a single turn. The length of a helix can be calculated. Without going into mathematical details, its length is both determined by its circumference and the height of a single turn. If the height of a turn is zero (quark at rest), we have a simple circle. Simplifying a bit, if the length of a helix is 938 times higher when the height of a turn, then the height of a turn is roughly 938 times higher than the circumference of the turn. Or the height of a turn is roughly 149 times larger than its radius.
In practice, this ratio looks like this:
Perhaps I should start using this ratio in my illustrations as well.
An interesting question is whether quarks really are ever at rest? Possibly if one devises a clever experimental setting, you can actually stop them. But from the little I’ve read of quarks, a lot of their properties are inferred indirectly.
I think I’ll leave today’s post at this. This is an incredibly simple concept. The extra mass in quarks and indirectly in protons and larger particles is just about stretching of a helical string. Nothing more complicated than that.
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