Apr 09 2010

## Origin of Mass

In the complex number system (a – bi) is the conjugate of (a + bi). For a wave function, e^{-ikx} is the conjugate of e^{ikx}, where:

e^{ikx} = cos kx + i sin kx, and

e^{-ikx} = cos kx – i sin kx

Gravitons passing through an electron, proton, or neutron create potential wells for the standing waves inside these particles, which internal waves are in bound states. To borrow from Kronig-Penny Hamiltonian math, in the “well domain of the potential array” ([1], pg 295) we may have:

φ_{I} = Ae^ik_{1}x + Be^-ik_{1}x,

and in the “barrier domain”:

φ_{II} = Ce^ik_{2}x + De^-ik_{2}x, ([1], (8.65), pg 307)

The speed of a conjugate wave graviton slows to less than the speed of light in a vacuum as it passes through an electron or a nucleus. Its frequency stays the same while its amplitude increases. Coming free out the other side, the graviton resumes the speed of light in a vacuum and returns to lower amplitude. Gravitons arriving isotropically, with the exception of those absorbed and becoming mass, help cradle the particle mass and, in summation, gravitational pressure at the boundary between the well and barrier domains holds particle mass together and keeps it from flying apart.

The letter k is used for wave number, which is in units of radians per meter. Since k_{1} > k_{2}, the full wavelength is shorter in distance for φ_{I} compared to φ_{II}, the conjugate wave graviton then being compacted within a subatomic particle. The conjugate graviton would also have a rotational component in phase with a corresponding rotational component constituent to the mass and earlier written [2], in the well domain.

In terms of a Fourier transform of dimension inside the particle mass we have:

d(x-x_{0}) = (1/(2πћ)) ∫_{-¥}^{+¥} dp e^{ip(x-x}^{0}^{)/ћ} = (1/(2π)) ∫_{-¥}^{+¥} dk e^{ik(x-x}^{0}^{)} ([3], (34), pg 1473)

where x_{0} is the position of the particle, k is k_{1} from above, and p is the momentum of a graviton otherwise known as p_{g} [2].

As some gravitons escape into deep space, entropy in the universe is always increasing from a state of original creation, – no “big bang”. The force we have all been aware of our entire lives may be associated with the single source of all energy and mass.

[1] Liboff, Richard L., Introductory Quantum Mechanics, Fourth Edition, Addison Wesley, 2003

[2] https://www.fruechtetheory.com/blog/2008/04/01/wave-function-transfer-2-2/

[3] Cohen-Tannoudji, Dui, Laloë, Quantum Mechanics, Hermann, 1977, Paris, France, Appendix II

PS: The Dirac delta symbol and plus and minus infinity limits of integration in the Cohen-Tannoudji, Dui, Laloë equation do not transfer into this blog properly. Go to reference [3] if you want more clarity.