## Saturday, October 12, 2013

### The Magnetic Force as the Ultra-Strong Force that Binds Preons to form Quarks and Leptons

I want to make the point in this post, that although one could easily dismiss my contention that existence of the Thomas precession along with electrostatic forces implies existence of an anti-centrifugal force that can overcome electrostatic repulsion as speculative and unproven (and you'd be right), it is a different matter so far as the existence of strong magnetic force that can do the same is concerned.  Anyone with an undergraduate physics student's understanding of electrodynamics can see this for their self with a half-hour's worth of derivation.

To derive the interparticle separation, between two like charges, where the magnetic force will overcome electrostatic repulsion, while not leading to a mass for the bound composite that exceeds the proton mass, one can simply evaluate the magnetic part of the Lorentz force for a first relativistic charge moving in the magnetic field of a second relativistically-moving charge, that is also accelerating due to electrostatic forces due to the presence nearby of the first charge.  Everything needed is in a standard electrodynamics textbook such as Jackson or Griffiths, and on just a couple of pages (or on wikipedia, alternatively).

First, calculate the acceleration of a charge with arbitrary rest mass in the non-radiative electric field of a second nearby charge, as a function of the separation between the charges and their velocities.  This must be done using the proper relativistic forms for both the electric field, using the electric field derived from the Lienard-Wiechert potentials, and for the resulting acceleration due to the electric force, which must be based on the relativistic equivalent of Newton's law of inertia.

Next, get the magnetic part of the radiative field due to the accelerated (second) charge, again using the Lienard-Wiechert field expressions.  Assume the second charge is moving at approximately (i.e., asymptotically close to) the speed of light perpendicularly to the direction of its acceleration.  This is consistent with

## Sunday, October 6, 2013

### The Preon Model as a Possible Application for Relativistic Kinematical Forces

A few days ago I read an article in the November 2012 Scientific American, by Don Lincoln of Fermilab, "The Inner Life of Quarks," that describes arguments that quarks and leptons are not themselves fundamental, but rather are made up of more fundamental objects named "preons."  The fact that leptons and quarks come in three known "families", with a hierarchy of increasing mass across them, and where the members of  heavier families decay rapidly into the equivalent members of the lightest family, suggests the more-massive families' members are just excited forms of the lightest. Since it is difficult to see how a truly fundamental object can have excited states, more fundamental constituents seem likely.

In the preon model described in the article, which is said to be only one of several that have been put forward, there are two different fundamental preons, termed the "plus (+)" and the "zero (0)", along with their antiparticles.  The plus and its antiparticle have electrical charge, while the zero and its antiparticle do not.
The gluons that are the carriers of the strong force are also composite objects made of the same set of preons.

Lincoln writes and illustrates that the preon model does a good job of representing the known hierarchy of the various families of quarks and leptons and their associated bosonic force particles.  But, according to the article, there is a fundamental problem with the preon model: because the masses of the leptons and quarks are already established, there is no room in it to accommodate the masses of force carrying particles needed to bind like-charged preons into the various charged quarks and leptons.  For example, gluons in the Standard Model account for most of the proton mass, while the up and down quarks are quite light comparatively.  Particles to bind preons with similar charges as quarks would need to be at least as massive as the gluons, and so would lead to larger quark masses than observed. This is where the anti-centrifugal force of the Thomas precession can help.  It provides a mechanism for overcoming electrostatic repulsion that does not require mediation by massive force-carrying particles.  It is simply a kinematical necessity of