Quantized Structure of a Graviton

[Antonio Lao]

The quantum of gravity is called graviton. And using symbols for quanta of length, [itex] \psi_E[/itex] and [itex] \psi_B[/itex] and quanta of linear momentum, [itex] \phi_E[/itex] and [itex] \phi_B[/itex], the time independent structure of graviton, [itex] G^{-}[/itex] is given by

[tex]G^{-} = \psi_E \times \phi_E \cdot \psi_B \times \phi_B[/tex]

 

[Antonio Lao]

The time independent structure of antigraviton is given by

[tex]G^{+} = - \psi_E \times \phi_E \cdot \psi_B \times \phi_B[/tex]

the interactions between graviton and antigraviton follow the rules:

[tex]G^{+}G^{-} = \alpha G^{-} [/tex]

[tex]G^{-}G^{-} = \beta G^{+} [/tex]

[tex]G^{+}G^{+} = \gamma G^{+} [/tex]

 

[Janitor]

I note that your G has the unusual units of [tex]M^2 L^4 /T^2[/tex] if what you are calling a quantum of length has the anticipated unit of [tex]L[/tex] and if what you are calling a quantum of momentum has the anticipated unit of [tex]ML/T[/tex].

 

[Antonio Lao]

I note that your G has the unusual units of ...

You are correct. The unit is proportional to the square of Planck's constant of action. This is a unit of double actions.

For the case of a time dependent structure, that is to say the time derivative of the linear momentum is not zero giving the existence of a force, the quanta are squares of energy.