Saturday, March 11, 2017

More extensions to my paper on ArXiv

This version (v5) obtains that the modulating factor on the inverse-square radial magnetic force between equal mass and parallel-spin zitter particles satisfies the three-dimensional time-dependent Schroedinger equation, except that hbar multiplying the partial derivative with respect to time is replaced by hbar/2.  This equation implies an angular momentum spectrum in terms of integer multiples of hbar, but an energy spectrum in terms of integer multiples of hbar/2.  This is consistent both with the energy per photon as derived in the same paper for a composite photon to be h/2 times the photon frequency, and so that the accepted value of Planck's constant (h) is only half the correct value.  This also implies that the electron g-factor is approximately unity, rather than approximately 2 as currently thought.

Spin-Spin Interaction as Quantum Phase Measurement and the Mechanism of Atom Formation

Next I will go over everything in it again and try to shorten it, and then submit it to a journal.  Since Foundations of Physics published my earlier paper from which this one derives, I plan to submit there.

There is much more I would like to do on it, in particular to try to derive the same result using Hamilton-Jacobi theory, but I have no idea if I can succeed at that or how long it might take, so I think it is a good enough time to submit.  I hope at least they will review it.    

Thursday, January 12, 2017

Why the electron g-factor is 2

It's because the generally accepted value of Planck's constant is only half the correct value.

The quantity h-bar in the Schroedinger equation is actually h-bar/2.  That's because it represents the spin of the electron, not of the photon, as implicitly assumed by de Broglie and carried forward by Schroedinger, and everyone else.

This fact has been overlooked because it was not recognized that the photon frequency is related to its energy not as E = h nu, but as E = h nu /(1 + v_l/c), where c is the limiting velocity of relativity theory, and v_l is the velocity of the photon, which is only very slightly less than c.

Although I derived that the energy of a composite photon is half the accepted value several months ago, and posted it about here previously, I didn't realize the implications until a few days ago, when I realized that the modulating factor on the Coulomb-like magnetic force between zitter particles satisfies the Schroedinger equation for a free particle in one spatial dimension.  Except, the hbar must be replaced by hbar/2.  This makes the energy difference between atomic energy levels half as large as previously thought, consistent with the photon energy being half the accepted value.  However, simply replacing the hbar in the SE by hbar/2 leads obviously also to an angular momentum spectrum in multiples of hbar/2 rather than hbar.  This cannot be, and the photon energy being hbar/2 can only be correct if, in addition to hbar being twice the currently-accepted value, hbar remains the quantum unit of angular momentum.  So, the form of the SE has to change from its current form.

The modulation factor that I derived is equivalent to the Schroedinger wavefunction in one dimension, but not in three dimensions.  There is a preferred dimension defined by the null four-displacement between the zitter particles.  It is essentially the relativistic Doppler effect along the radial direction that gives rise to the modulating factor that can be equated with the de Broglie wave if hbar is replaced by hbar/2.  (De Broglie was reasoning by analogy with the photon without knowing of the intrinsic angular momentum difference of the electron.  Had he known of the difference, he would have expected the hbar/2.)   In the cross-radial direction, though, the modulation goes over to a de Broglie wavelength (rather than half it for radial motion), as I showed in my FOOP paper.  So it seems plausible that the Schroedinger-like equation based on the magnetic force modulation could lead to an ebergy spectrum in terms of multiples of hbar/2 but an angular momentum spectrum, but that is work to do at the moment.

Sorry there are some typos I'll fix in the next revision.  Current is v4: https://arxiv.org/abs/1609.04446