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Linking Curvature With Wave Mechanics


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The biggest conclusions I reached from my papers during lockdown was that the ground state hydrogen atom does not radiate, not because of a wave function per se, but because the electron is in a state of free fall and that the wave is completely analogous to de Broglie's pilot wave theory - this was motivated largely from the fact Bohrs planatary model gives all the right results. Another one was an extension from the weak equivalence principle which drew on a peculiar resemblance of Einsteins work which states,” while matter tells space how to curve and curvature tells space and matter how to move,” to de Broglies principles corresponds by saying,”the wave tells the particle how to move whereas the particle tells the wave how to spread.” The extension could be a load of rubbish, but if true, it would mean the wave function is in fact microscopic gravitational waves. I gave some examples in which the absorption or emission of a gravitational wave at microscopic scales could explain quantum jumps inside the atom, either raising the electron or lowering it between energy levels. Another implication suggested showed that de Broglies ”empty wave" would be an in-phase gravitional wave. Maybe wild enough to be true or wild enough to be rubbish. Either way, my investigation led to a thorough examination of Bohr's orbit equation, linking scattering processes with the Bragg Condition and even came to 18 final propositions in the work elucidating on the nature of black holes as a special optik theory allowing me to extend the work of Satori (where photons are not indefinitely captured by black holes) and can he regarded from my own hypothesis as a special case of a prism where Snell's law and the equations of heat engines gives rise to a transition formula for internal reflection of light. I do not rule out the particle creation at the horizon but do conclude that treating black holes as a special prism plausible. There are far too many equations to cover so in next post, we shall look at only one result derived, that being the transition formula for the black hole entropy.

Edited by Dubbelosix
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From my recent seven papers.... the main equation for the transition of a black hole is given by the entropy transition equation for discrete quantum processes

 

S(ΔT) = k(ΔT)

 

= N⋅mc²/(1 - T (2)/T (1) (tan θ)²)

 

S is the entropy given in units which k which is the Boltzmann constant. N is the number of particles emitted by the black hole and the denominator comes from the laws of heat engines but the tan angle tells us about a geometric application of the radiation when leaving the cavity. It also came from applying Snells law and the index of refraction.

Edited by Dubbelosix
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A quick set of equations that feature in my paper which requires little format goes like this; we wish to derive the motion of the electron around the nucleus and see if it obeys Kepler's third law. We start off by writing down the general force equation in electromagnetic theory

 

k [e/R]^2 = B (e Z/R^2)

 

= Ze (v^2/R) = Ze (4π^2R^2/Rt)

 

Where Ze is the nuclear charge and k = B as the Boltzmann constant. We notice the nuclear charge cancels and by rearranging we obtain

 

e = 4π^2/k [R^3/t^2]

 

And viola! Its that simple, we retrieved Kepler's third law for the planetary motion in which it's acceleration is simply

 

a = k [Ze/R^2] = v^2/R

 

In the more complicated arguments of my papers I explain that this acceleration disappears in the ground state, again due to it being in a state of free fall. There are still wave mechanics in the theory, but I'm interested only in the case where the wave pilots the electron. That requires the simple de Broglie guiding equation.

Edited by Dubbelosix
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Yes, thermodynamic equilibrium was briefly discussed from the black hole investigation. I start with only one assumption:

 

'Suppose a black hole is the most ideal black body heat engine," and then go on to say,"then it will convert heat into mechanical energy into a cooler environment. If the black hole was capable of becoming the same temperature as the background space then it would be in a state of equilibrium. The maximum fraction of heat supply that can be used is

 

(T(1) - T(2)/T(1))

 

and from algebra we learn that it is the same thing as saying

 

1 - T(2)/T(1)

 

Where T(1) is the "absolute temperature" of the cavity and T(2) is the temperature of the environment."

 

These were the first heat principles I drew on before deriving the discrete transition equation for the black hole. More or less I ended up with

 

1/3 N*mc^2/KT = (1 - T(2)/T(1))

 

There was an additional factor of index of refractions or some quantized principle numbers of n^2(2)/n^2(1) attached to the transformation from the Rydberg formula, which was the universal starting point for any transition for discrete quantum systems. I later interpreted it from Snell's law and the indices of refraction.

Edited by Dubbelosix
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The idea behind using Snell's law was really based on the Brewster angle θ which is the angle of incidence. Snell's law will obey

 

tan θ = n(2)/n(1)

 

The transition formula was once again

 

S(ΔT) = k(ΔT)

 

= N⋅mc²/(1 - T (2)/T (1) (tan θ)²)

 

Whenever you see N⋅mc² it is proportional to the pressure and from relativity, an additive correction of density associated to the system. Basically

 

PV = N⋅mc²

 

Under normal convention and from variation using calculus we have also

 

PdV + dPV = dN⋅(m(2) - m(1))c²

Edited by Dubbelosix
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Basically what it means is that any radiation leaving the cavity (black hole) does so vertically and even cuts down the glare like sunglasses do for the black hole by polarizing the radiation by a reflection from a horizontal surface (which is fine for any localised spot on a supermassive black hole). The black hole gives off an additional glow by a reflection of light.

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This is why I attended the thought of the "curious case of the black hole in the nightime" since Hawking already elucidated that black holes whoukd glow... But if the they are special cases of geometric prisms then they have additional surface glow from incident reflected radiation.

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A quick set of equations that feature in my paper which requires little format goes like this; we wish to derive the motion of the electron around the nucleus and see if it obeys Kepler's third law. We start off by writing down the general force equation in electromagnetic theory

k [e/R]^2 = B (e Z/R^2)

= Ze (v^2/R) = Ze (4π^2R^2/Rt)

Where Ze is the nuclear charge and k = B as the Boltzmann constant. We notice the nuclear charge cancels and by rearranging we obtain

e = 4π^2/k [R^3/t^2]

And viola! Its that simple, we retrieved Kepler's third law for the planetary motion in which it's acceleration is simply

a = k [Ze/R^2] = v^2/R

In the more complicated arguments of my papers I explain that this acceleration disappears in the ground state, again due to it being in a state of free fall. There are still wave mechanics in the theory, but I'm interested only in the case where the wave pilots the electron. That requires the simple de Broglie guiding equation.

I should have noted also that

 

R^3/t^2 = Gm/4π^2

 

Where Gm = R(s)c^2 as the gravitational parameter. Pulling the remaining constant to the LHS gives

 

ek/4π^2 = [R^3/t^2] => Gm/4π^2

Edited by Dubbelosix
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