Quantum interference and Zitterbewegung?
| Main Author: | Francesco R. Ruggeri |
|---|---|
| Format: | info publication-preprint |
| Terbitan: |
, 2018
|
| Subjects: | |
| Online Access: |
https://zenodo.org/record/1458269 |
Daftar Isi:
- In earlier notes, Einstein ́s 1905 energy momentum equation E2 = p2 + m2 has been converted into a linear 2x2 matrix equation (linear in E). The eigenvector (sqrt(1+v), sqrt(1-v)) found is related to forward and backward motion as a particle moves with an overall velocity v in the forward direction. It has been shown that this equation leads to the Schrodinger zitterbewegung of the Dirac equation and that even setting v=0 yields zitterbewegung in the remaining energy matrix. In this note, we consider a particle moving backwards and forwards in a box with velocity v. In such a case, one needs two linear matrix equations, one for the forward motion and one for the backward. Similarly, one obtains two Schrodinger zitterbewegung results which on average cancel in some places. It is suggested that this cancellation may be related to quantum interference. As a check, the system of a particle bouncing backwards and fowards in a box can be thought of as a new particle with a mass M. Such a particle should itself satisfy the momentum energy equation if it is moving, say with velocity w, and one could apply the 2x2 matrix approach to it. There would be a new zitterbwegung and also a zitterbewegung for w=0. The zitterbwegung for w=0 should match that of the average of the zitterbewegungs for the particle moving to the right and to the left. We find that it has the same form, but not the same coefficients. For the average of the zitterbewegungs, there are coefficients depending on m/E while for the M approach, the coefficients are 1. A coefficient proportional to m/E suggests that for small m relative to p, there are very small zitterbewegung effects for this combined approach. In realistic systems with v= 107 m/s or so as in some quantum systems, m/E will be close to one and the two approaches will have almost the same coefficients. In classical mechanics, one may have a particle bounce back and forth in a box and can also consider the box to be a new system with a new mass, but there is no ̈cancellation ̈ occurring.