# Massless particles and the Neutrino

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**This page is under construction** by Hartwig Poth, hupoth@gmail.com

For the four potential theory of gravitation, cf. Four potential theory of gravitation, a quantum particle, the 'gravon', can be found. It is massless and is defined by the following four vector wave function

wherein is the gravitational four potential ^{[1]}. The gravon has obviously the spin 0.

With (1) we obtain

This is a linear wave equation for the gravon and also a continuity equation; it is furthermore the third Maxwell type field equation for the four potential gravitation^{[2]}.

In analogy to (1) a photon can be defined by

wherein is the spin vector for the spin 1 of the photon; the spin vector behaves like an ordinary spatial vector and is directed along the momentum of the photon. The time like component of the complete spinor in (3) is . The linear wave equation for this photon is

That equation (4) allows for example to apply the four potential of gravitation in analogy to the influence of the common electromagnetic four potential onto the Dirac electron^{[3]}

to the propagation of the photon

When we suppose that vanishes, if the source of gravitation is virtually at rest and if we consider for simplicity a photon which propagates along the -axis with the momentum we obtain eventually

and thus for the respective energies of the photon at positions and an energy difference

This result is already known from the general theory of relativity ^{[4]}.

- ↑ 'Massless particles and the Neutrino', from Hartwig Poth, published on 11.01.2022 under ISBN 9783844243321
- ↑ 'Four Potential Gravitation and its Quantization', from Hartwig Poth, published on 05.04.2014 under ISBN 978-3-8442-9165-0
- ↑ 'Four Potential Gravitation and its Quantization', chapter 13 on page 29 equation (191), from Hartwig Poth, published on 05.04.2014 under ISBN 978-3-8442-9165-0
- ↑ Torsten Fließbach,
*Allgemeine Relativitätstheorie*(Spektrum Akademischer Verlag, Heidelberg Berlin, 4. Auflage ISBN3-8274-1356-7), 12 Photonen im Gravitationsfeld p.62