Roots of Zitterbewegung and the DeBroglie Wavelength in a 2x2 Matrix Approach to the Relativistic Momentum Energy Equation
| Main Author: | Ruggeri, Francesco R. |
|---|---|
| Format: | info publication-preprint eJournal |
| Terbitan: |
, 2018
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| Subjects: | |
| Online Access: |
https://zenodo.org/record/1211698 |
Daftar Isi:
- A 2x2 matrix model of Einstein ́s relativistic momentum energy equation seems to be entirely based on the notion of light bouncing back and forth as described by the +E eigenvector (sqrt(1+v), sqrt(1-v)) which is proportional to (cos(a/2), sin(a/2)). The velocity matrix V appears to specifically pertain to this picture as well. It was also seen that there is an acceleration matrix dV/dt related to rotations of the vector (cos(a/2), sin(a/2)) which represent accelerations to new velocities. The velocity matrix dV/dt is proportional to [H,V] which is consistent with exp(-iHt) being an evolution operator just as in quantum mechanics. In earlier notes, it was argued in a loose fashion that exp(-iHt) was an evolution operator without explicitly noting that [H,V]=adV/dt (where a is a constant) can lead to this result. The operator exp(-iHt) is the ̈driver ̈ of zitterbewegung calculations as it is the source of the ̈frequency ̈ in these calculations. It seems, however, that it has deeper roots linked to a scenario of a photon bouncing back and forth. This appears to be the basis of the 2x2 matrix approach and of the resulting velocity and acceleration matrices. It also appears that the zitterbewegung approach allows for a physical picture of frequency as related to energy. If momentum is considered as an energy flux, then this may describe momentum as being proportional to 1/wavelength. In addition, zitterbewegung calculations show physical periodic motion in space which may physically represent the ̈wavelength ̈.