This page is under construction by Hartwig Poth, firstname.lastname@example.org
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 . 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.
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
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 .
↑'Massless particles and the Neutrino', from Hartwig Poth, published on 11.01.2022 under ISBN9783844243321
↑'Four Potential Gravitation and its Quantization', from Hartwig Poth, published on 05.04.2014 under ISBN978-3-8442-9165-0
↑'Four Potential Gravitation and its Quantization', chapter 13 on page 29 equation (191), from Hartwig Poth, published on 05.04.2014 under ISBN978-3-8442-9165-0