Mar 29 2010

## CERN LHC

According to what one reads, the CERN LHC is set to start colliding 3.5 TeV proton beams tomorrow, if they can get the beams, running for days now, lined up by then.  The LHC will obtain a variety of downscattered energies, however photons of the same energy and phase can add together in the same measurement.  In terms of discrete photons, it should be a continuous spectrum with a peak near the highest energy that the instrument can effectively measure.

With particle masses on the other hand, nobody knows for sure.  It could be an extension upon the “zoo of elementary particles that the experimentalists were discovering in their particle accelerators” * prior to the development of the Standard Model of particle physics.

In some ways it would appear easier to work with one elementary particle instead of sixteen or more.

* Smolin, Lee, The Trouble with Physics, Houghton Mifflin Company, c. 2006, p. 54

(The Standard Model of particle physics was not the main focus of Smolin’s book.)

Mar 17 2010

## Magnetic Moment of the Electron

Using Tipler’s notation starting on page 917, we begin with a particle of charge q and mass M, in a circular Bohr orbit of radius r.  Never mind that there is no such thing as a circular electron atomic orbit; the results are valid.

Particle velocity, v, and orbital period, T, are related by:

vT = 2πr

The charge traveling in a circle produces a current of:

I = q/T = qv/2πr

Multiplying this current by the enclosed area, the magnetic moment is obtained:

m = (qv/2πr) πr2 = (qvr)/2                    , 39-16, pg 918

Angular momentum for the mass is:

L = Mvr = M (2m/q)

Rearranging and writing magnetic moment and angular momentum vectors in bold type:

m = (q/2M) L                                        , 39-17, pg 918

Having used a circular orbit of a particle with charge and mass to obtain this formula, it can also be used when spin angular momentum is inserted for L.  For the electron, the spin angular momentum is known to be ћ/2.  Also, still following Tipler, we can now insert e for the charge of the electron in place of q, and me for the mass of the electron in place of the general mass M.  There is just one problem when doing this however.  “For electron spin, the magnetic moment is twice that predicted by this equation.  This extra factor of 2 is a quantum-mechanical result which has no analog in classical mechanics.” (, pg 918)

The extra factor of 2 is the electron spin g factor, and is more precisely found to be:

ge = -2.002 319 304 3622        

The magnetic moment of an electron can then be written as:

m = ge (e/2me) (ћ/2),

or equivalently:

μS = geμB(S/ћ)         

This extra factor of 2.002 319 304 3622 shows that the gravitons which pass through electrons, and are not absorbed, serve as conjugate wave functions that double the expected magnetic moment of the electron.

 Tipler, Paul A., Physics, Worth Publishers, Inc., 1976