4.-GRAVITATIONAL WAVES

The particles can be described by a wave whose wavelength is worth λ = h / m v, where m is the relativity mass m = m₀ / (1 - v²/c²)^1/2. We can express this wavelength in function of the Compton wavelength λ_c:

λ = λ_c (c² / v² -1 )^1/2    (4.1)

λ  =  λ_c (c / v ) ( 1 -  v²/c² )^1/2    (4.1)

This speed that it appears in (4.1) can be identified with the speed indicated in (2.6.1) and we can substitute it for its value, we obtain:

λ = λ_c [ (c² / (v₂² + v₁²) ) -1 ]^1/2    (4.2)

Elevating to the square the previous expression, operating and calling γ to (1 - v₂² /c² - v₁² /c²)^1/2 it is obtained:

1 / λ² = (1 / λ_c²) (v₂² / c² γ²) + (1 / λ_c²) (v₁² / c² γ²)    (4.3)

In the expression (4.3) two wavelengths similar to (4.1) can be identified. The first one, could be identified with the classic wave of De Broglie about the t₂ time and the second could be identified with a gravitational wave about the t₁ time:

λ₂  =  λ_c (c / v₂ ) ( 1 -  v₁²/c² -  v₂²/c² )^1/2    (4.4)

And

λ₁  =  λ_c (c / v₁ ) ( 1 -  v₁²/c² -  v₂²/c² )^1/2    (4.4)

This new defined function of wave of Schrödinger for the wavelength (4.3) could allow including the gravitation in the formalism of the quantum mechanics. The gravitation could be effect of the collapse of this wave function on the time t₁ produced by the interaction with the mother universe, the particles would tend to move to closer places of more probability (bigger density energy). The General Theory of Relativity would be the phenomenological description of this collapse.

_{© Jorge Ales, 2002. http://www.livinguniverseweb.com}