Theoria Motus Gravitatis Finalem

[Dubbelosix]

Summary and Abstract

 

 

1. We know from deBroglies relationships, that the particle has a dual property, it also generates a wave function. 

 

2. People have speculated on the nature of the wave function but in the direction I find more promising is that they are miniscule gravitational waves, generated from the curved paths of velocity particles. 

 

3. The gravitational wave function then makes better sense to find a guiding wave equation that would essentially be geometric and/or quantum to boot. So we did this. 

 

4. It has also been shown through the equations that a temperature can be approximated to the curved trajectory (or simply motion) of the constituent sum of the particles ~ the small acceleration would contribute to heat released from Larmor radiation. 

 

5. Back to wave particle duality, the gravitational wave only guides the particle, so while connected they are still separate phenomenon, so it cannot be a true duality in the sense the particle is a gravitational ripple itself. It's like while the particle still causes the curvature we cannot just presume the curvature causes the particle. It would seem premature to think that way when there are possibly interesting reasons why, such as a motion of a particle in an aether. 

 

6. There is no such thing as ''empty'' space so there will always be extremely small disturbances from fluctuations in the form of gravitational waves all over space, just at different magnitudes, all very small though. 

 

7. Wheeler took a different approach, unifying gravity geometrically to show it ''get's very significant at the Planck scale''. In our model, the waves generated are far too small to be ''called significant.'' If though a system was bound by a very small curvature of radius, then then relativity strictly sates in this case it would produce a very strong gravitational field. Such a particle could become entrapped within it's own gravitational field, an object Wheeler called a ''Geon.'' But if the gravitational field has entrapped the particle, it could have no where to go.

 

8. Gravity can exist in a ''phase space'' but it need not mean it should follow non-commutative laws - in fact the geodesic equation I derived uses a classical commutation defining the curve. In other words, gravity can be predicted classically in the quantum phase space; this should not to be much of a surprise, when we learn that quantum mechanics is just a special case of classical physics. 

 

9. The final result is simple enough: We went from a Hilbert space, geometrized it using curves under general relativity and in doing so we found some interesting results that has a certain... ''beauty'' to it, but beauty to me is simplicity, but really beauty is in the eye of the beholder... though saying that there was at least one great man in history who did think that the ''equations that can be considered most true'' have to be elegant and beautiful, so sayeth the late Dirac. 

 

KEY EQUATION TIME

 

 

1).  [math]\nabla_{\gamma(t)} \dot{\gamma}(t) \equiv\ min\ g^{ij}\sqrt{<\dot{\psi}|[\nabla_i,\nabla_j]|\dot{\psi}>} = 0[/math]

 

This equation was derived to define a curve in such a way that it would form the minimum of the geodesic, in this case, the covariant derivatives do not commute.

 

2).  [math]R_{ij} = [\nabla_i,\nabla_j] = [\nabla_i \nabla_j - \nabla_j \nabla_i] \geq g_{ij}^{-}\ (\frac{1}{\ell^2})[/math]

 

Any non-commutation in any derivatives of spacetime most likely looks like: A result in fact that was predicted by both loop quantum gravity and string theory, so while neither of those theories are correct, it may hint as a non-trivial relationship; certainly scattering experiments seem to support the spacetime uncertainty hypothesis.  The last equation is basically and anti-symmetric curvature tensor. 

 

3. The commutation of two connections of the gravitational field is again simply the Riemann curvature tensor:

 

[math][\nabla_i, \nabla_j] = (\partial_i + \Gamma_i)(\partial_j + \Gamma_j) - (\partial_j + \Gamma_j)(\partial_i + \Gamma_i)[/math]

 

[math]= (\partial_i \partial_j + \Gamma_i \partial_j + \partial_i \Gamma_j + \Gamma_i\Gamma_j) - (\partial_j \partial_i + \partial_j\Gamma_i + \Gamma_j \partial_i + \Gamma_j \Gamma_i)[/math]

 

[math]= -(\partial_i, \Gamma_j) + (\partial_j, \Gamma_i) + (\Gamma_i, \Gamma_j)[/math]

 

Also with, I found a non-trivial inequality bound identical in form to the quantum bound:

 

[math]<\psi|[\nabla_i, \nabla_j] |\psi>\ =\ <\psi| R_{ij}| \psi>\ \leq 2 \sqrt{|<\nabla^2_i><\nabla^2_j>|}[/math]

 

Concerning the curve equation [math]\nabla_{\gamma(t)}\dot{\gamma} = 0[/math] the product of the wave functions which have lengths of velocity in the Hilbert space is given by:

 

[math]2K_BT = m(\frac{dx^{\mu}}{d\tau} \cdot \frac{dx^{\mu}}{d\tau}) \equiv\ <\dot{\psi}|M|\dot{\psi}>[/math]

 

Which introduces temperature in a very natural non-ad hoc way from the Maupertuis's principle.

 

4. Before the idea of those bounds I came across the useful Wigner inequality, which I replace the Hamiltonian with the stress energy tensor:

 

[math]\sqrt{<\dot{\psi}|\dot{\psi}>}\ = \int \int\ |W(q,p)^2| \sqrt{<\psi|\Gamma^2|\psi>}\ dqdp \geq \frac{1}{\hbar}\sqrt{<\psi|\mathbf{T}^2|\psi>}[/math]

 

This helped me realize I could form a gravitational Schrodinger equation:

 

[math]\nabla_n|\dot{\psi}>\ =  \frac{c^4}{8 \pi G} \int \int\ |W(q,p)^2|\ (\frac{d}{dx^n}\Gamma^{ij} + \Gamma^{i}_{n\rho} \Gamma^{\rho j} + \Gamma^{j}_{n \rho}\Gamma^{\rho}_{i})|\psi>\ dqdp \geq \int\  \frac{1}{\hbar}(\frac{d}{dx^n}T^{ij} + \Gamma^{i}_{n\rho} T^{\rho j} + \Gamma^{j}_{n \rho}T^{\rho}_{i})dV|\psi>[/math] 

 

In which the velocity guidance in curved space is

 

[math] v^2 =  \frac{\hbar^2}{2m^2}\ [ \frac{d}{dx^n}\Gamma^{ij} + \Gamma^{i}_{n\rho} \Gamma^{\rho j} + \Gamma^{j}_{n \rho}\Gamma^{\rho}_{i}][/math]

 

 

This is in fact, totally analogous to an acceleration/curve in the general theory of relativity, except this time, it satisfies an equality bound and it also satisfies the wave dynamics of a Schrodinger equation

 

5. The geometric bounds holds importance for our equation which satisfied the geodesic equation

 

[math]\nabla_n \dot{\gamma}(t) = \nabla_n\frac{dx^{\mu}}{d\tau} \equiv\ min\ \sqrt{<\dot{\psi}|[\nabla_j,\nabla_j]|\dot{\psi}>} = 0[/math]

 

The product of [math]\ <\dot{\phi}|\dot{\psi}>[/math] has a length in the Hilbert space... and with second derivatives in those lengths, comes velocity and with it a definition of acceleration:

 

[math]\frac{\partial v}{\partial \tau}  \cdot \frac{\partial v}{\partial \tau} = \frac{\hbar^2}{2m^2}[\nabla \Gamma] =\ <\dot{\psi}|\dot{\psi}>[/math]

 

with 

 

[math]v^2 \equiv |U|^2 = U^{\mu}U_{\mu}[/math] 

 

Most surprisingly also it could unify the concept of phases of particles;

 

Which can have a Berry curve definition ~

 

[math]\gamma = i \oint <n(\mathbf{R})[\Gamma_{\mathbf{R}}\Gamma^{\mathbf{R}}]{\mathbf{R}}|n(\mathbf{R})>\ d\mathbf{R}[/math]

 

Obtained from a second quantization on momentum operator, while replacing the d,Alambertian for its gravitational connections and involves phase changes of particles. 

 

6.[math]\nabla_{\gamma(t)}\ \dot{\gamma}(t) \equiv\ |min| g^{\mu \nu} \sqrt{<\dot{\psi}|\dot{\psi}>}[/math]

 

From kinetic quantizaion of momentum operator with two connections of the gravitational force.

 

[math]<E_k>\ = \frac{\hbar^2}{2m}\Gamma^2 =  \frac{\hbar^2}{2m}[\Gamma, \Gamma][/math]

 

It's an operator in form because connections of the gravtational field do not generally commute. From the Virial theorem and equipartiction we find the relationship

 

[math]\phi \approx \frac{3}{5}\ g_{00} \approx  \frac{3}{2} k_BT  = \frac{1}{2} mv^2[/math]

 

scalar field defined through ideal gas law and virial theorm:

 

[math]\phi = \frac{3}{5} \frac{Gm}{r}[/math] 

 

[math]=  \frac{3}{2}   m(\frac{\partial x^{\mu}}{\partial \tau} \cdot \frac{\partial x_{\mu}}{\partial \tau})[/math]

 

[math]= \frac{\hbar^2}{2m^2}\Gamma^2 [/math]

 

These equations are so generic in set-up for linear gravitational fields, it would also be later difficult not to see this in a modified approach using the Sciama definition of the gravielectromagnetic field. 

 

Some notes...

 

 A linear wave  equation is akin to a classical formulation of wave mechanics in special relativity, it is simply not general while it may not possess curvature. The addition of Einstein's stress energy showed (maybe not so easily) that you cannot have a surface geometry without a notion of curvature, gravity and an extra temporal degree of freedom. 

 

The first equation could also be theorized as:

 

[math]<E_k>\ = \frac{\hbar^2}{2m}[\nabla_{\mu}, \Gamma^{\mu}][/math]

 

or even as

 

[math]<KE_{\mu \nu}>\ = \frac{\hbar^2}{2m}[\nabla_{\mu}, \nabla_{\nu}] = \frac{\hbar^2}{2m^2}\ <R_{\mu \nu}>[/math]

 

 Now introduce wavefunctions, revealing different relationships of kinetic energy with the geometry of spacetime. 

 

[math]<\psi|KE_{\mu \nu}|\psi> =  \frac{\hbar^2}{2m}\ <\psi|R_{\mu \nu}|\psi>[/math]

 

7. So let’s get into the subject of Pilot waves and what it has to do with what we have talked about. Let's begin talking about the guiding equation for deterministic quantum mechanics. That equation takes the form:

 

[math]\frac{dQ}{dt} = \frac{\hbar}{m}\ \mathbf{Im} \frac{\psi* \partial_k \psi}{\psi^{*} \psi}(Q_1... Q_N)[/math]

 

Where Q(t) is the first order evolution for the position of the particles. The distribution can be understood through the Born law, [math]\int |\psi|^2 = \psi^{*}\psi [/math]  in which case the ratio can be understood in terms of their respective probability density distributions in which case, you can form a time dependent Schrodinger equation taking into respect a guiding wave function:

 

[math]i \hbar \frac{\partial \psi}{\partial t} = (-\frac{h^2}{2m}\nabla^2 + V + \frac{\hbar^2}{2m}\frac{\nabla^2 \sqrt{\rho}}{\sqrt{\rho}})\psi[/math]

 

Notice, the statistical dependence is removed (or normalized) from the guidance equation

 

Under Bohmian Pilot waves, the equaion of interest is:

 

[math]\frac{\partial s}{\partial t} = \frac{S^2}{2m}\nabla^2[/math]

 

the metric is: [math]s = ct[/math]

 

Since the geodesic of the main quantification;

 

[math]\nabla^{\mu \nu}\nabla_{\sigma \lambda}\ (\frac{ds^{\sigma}}{dt} \cdot \frac{ds^{\lambda}}{dt})  \equiv |min| g^{\mu \nu} <\dot{\psi}|\dot{\psi}>[/math]

 

After squaring solves for two solutions those for conjugate ket's and bra (ie. [math]|\dot{\psi}>[/math]\ and [math]<\dot{\psi}|[/math] ) solutions. The simplest solution I found trying to model this did come from a second quantization on the momentum operator defined specially for curvilinear coordinates. The next section will describe a gravitational guiding wave function,

 

8. Curve, temperature and geometry was found as:

 

[math]K_BT = \frac{\hbar^2}{2m}[\Gamma, \Gamma] =\ \frac{1}{2} <\dot{\psi}|m|\dot{\psi}>[/math]

 

This equation in my eyes, established all the dynamics but first some hard premises I came to:

 

Though the Bohmian wave is indeed determinstic, this written in spacetime requires that the wave functions are in fact very small gravitational perturbance, known as gravitational waves. So in other words, particles create ripples in space as gravitational waves - in fact, it is under current research to see if the detector can from subatomic gravitational waves, since the detector and detected are coupled in such ways. 

 

The reason why I came to this conclusion, are for a number of things, but the real main reason, is just like the full curved Schrodinger equation I derived it has two solutions of the form (if you consider spacetime itself as an observable, as I do follow for good reasons):
 

[math]\frac{\hbar^2}{2m}[\Gamma, \Gamma] =\ \frac{1}{2} <\dot{\psi}|m|\dot{\psi}>[/math]

 

decomposing into bra-ket notation we get:

 

[math]|\dot{\psi}_{\mu}>\ = \frac{\hbar}{\sqrt{m}}\Gamma_{\mu}[/math]

 

and it's conjugate

 

[math]<\dot{\psi}^{\mu}|\ = \frac{\hbar}{\sqrt{m}}\Gamma^{\mu}[/math]

 

. The unifying idea here is that as the mass moves through spacetime, it inexorably causes the waves, and on and on the cycle goes.

 

We came from a totally logical, not add-hoc but some assumptions thrown in. The second quantization of a momentum operator with derivatives related to the gravitational field, is at least a tantalizing approach. It has been openened up for discussion that you could theoretically complexify these last two equation, in objection to the Wheeler de Witt equation which treats gravity as a ''real'' field (without complexification) making it it at odds with the rest of the ''fundamental'' forces of nature.

 

After my assumption of the wave function being gravitational wave ripples in spacetime, came to a surprising shock to find the following article too see if anyone was mad enough as me to think this way:

 

 

https://readingfeynman.org/2017/09/30/wavefunctions-as-gravitational-waves/

 

The velocity equation as well

 

[math]\frac{\hbar^2}{2m^2}[\Gamma, \Gamma] =\ \frac{1}{2} <\dot{\psi}|\dot{\psi}>[/math]

 

Is really similar in structure to the accelertion/curve equation, save for the fact it features the Riemann curvature tensor. 

 

[math]\nabla_n \dot{\gamma}(t) = \nabla_n \frac{dx}{d\tau} \equiv\ min\ \sqrt{<\dot{\psi}|[\nabla_j,\nabla_j]|\dot{\psi}>} = 0[/math]

 

9.You will recall that we obtained the velocity squared formula. It might interest you to know that this formula is a covariant derivative away from  curve equation: It not only guides the particle using gravitational waves but it seems to contribute to the four velocity or more accurately, a four-acceleration 

 

[math](\frac{S(r,t)}{m})^2[\Gamma_{\mu}, \Gamma^{\mu}] = \mathbf{U}_{\mu}\mathbf{U}^{\mu} [/math]

 

And that four-acceleration is in fact implemented like: 

 

[math]\frac{\mathbf{D}\mathbf{U}^{\lambda}}{\partial \tau} = \frac{\partial \mathbf{U}^{\lambda}}{\partial \tau} + \Gamma^{\lambda}_{\mu \nu}\mathbf{U}^{\mu}\mathbf{U}^{\nu}[/math]

Edited December 6, 2018 by Dubbelosix

[Dubbelosix]

particle production in gravitational fields solves our chicken-egg problem, curvature came first, then came particles generated from it. 

 

Origin or source of this large curvature could be seen as a condensed multi-gravitational system. Since there are no (or very little) thermal degrees of freedom in the pre big bang state, this condensate will have little to no temperature freedom to it; what we can imagine though is a pre-big bang state which I have wrote about a few times. In those model we suggested a degenerate gas of particles contributing no thermal out-put - our theory would have to accommodate a different view of the phyics , say if we want the gravitational aether to be part of the pre-bang phase, then there cannot be any particles associated to it, because this is forbidden by the laws of motion within relativity.

 

My gravitational aether is made from permittivity and permeability variables, which solves a lot of problems, such as the information paradox - in the model, the speed of light cannot by principle reach zero so radiation can escape black holes.

 

There is no motion from particles from first principles of relativity, but is a ''substance'' that we are yet to properly understand. I beleive the statement there is no such thing as a 'free'' space is an indication to a vacuum made of something at the very least, albeit, it points out the obvious, does not solve the problem. 

 

If my theory is right, then spacetime is made of at least four ingredients: fluctuations and a wave function gravitational in nature. It was never explained why a moving particle would generate a wave as it moved space other than it moving through some type of aether, but it is answered here as a phenomenon of gravitational waves themselves. The last two ingredients may be even more fundamental, it is about the thickness of spacetime due to variable permittivity and permeability. 

 

Particle production exponentially drops off proportional to density, this involves non-trivial matters such as volume and scale factor since gravity gets weaker in a universe whee volume increases. But what heated a cold universe up? It was suggested to me by Matti that he would look for instabilities in the metric and that sounded very appealing... and still does. 

 

When talking about phases, we are in what is called a matter dominated phase, before that early on the universe was hot and dense, a radiation dominated phase (we think black holes cannot form in but this will be something I will contest in a later essay). A pre big bang state is also a Helmholtz problem. Our pre big bang phase was in fact a liquid stage: For the gravitational waves to be in a liquid form, is something I need to investigate!  

 

There is even a chemical state below this, called a crystalized state... so maybe the universe has undergone more phases than we could have possibly imagine, from crystal, to fluid, then to gas and then to a new type of cold dominated and condensed matter physics. 

Edited November 6, 2018 by Dubbelosix

[Dubbelosix]

https://prebigbang.quora.com/

[Dubbelosix]

 

Summary and Abstract

 

 

1. We know from deBroglies relationships, that the particle has a dual property, it also generates a wave function. 

 

2. People have speculated on the nature of the wave function but in the direction I find more promising is that they are miniscule gravitational waves, generated from the curved paths of velocity particles. 

 

3. The gravitational wave function then makes better sense to find a guiding wave equation that would essentially be geometric and/or quantum to boot. So we did this. 

 

4. It has also been shown through the equations that a temperature can be approximated to the curved trajectory (or simply motion) of the constituent sum of the particles ~ the small acceleration would contribute to heat released from Larmor radiation. 

 

5. Back to wave particle duality, the gravitational wave only guides the particle, so while connected they are still separate phenomenon, so it cannot be a true duality in the sense the particle is a gravitational ripple itself. It's like while the particle still causes the curvature we cannot just presume the curvature causes the particle. It would seem premature to think that way when there are possibly interesting reasons why, such as a motion of a particle in an aether. 

 

6. There is no such thing as ''empty'' space so there will always be extremely small disturbances from fluctuations in the form of gravitational waves all over space, just at different magnitudes, all very small though. 

 

7. Wheeler took a different approach, unifying gravity geometrically to show it ''get's very significant at the Planck scale''. In our model, the waves generated are far too small to be ''called significant.'' If though a system was bound by a very small curvature of radius, then then relativity strictly sates in this case it would produce a very strong gravitational field. Such a particle could become entrapped within it's own gravitational field, an object Wheeler called a ''Geon.'' But if the gravitational field has entrapped the particle, it could have no where to go.

 

8. Gravity can exist in a ''phase space'' but it need not mean it should follow non-commutative laws - in fact the geodesic equation I derived uses a classical commutation defining the curve. In other words, gravity can be predicted classically in the quantum phase space; this should not to be much of a surprise, when we learn that quantum mechanics is just a special case of classical physics. 

 

9. The final result is simple enough: We went from a Hilbert space, geometrized it using curves under general relativity and in doing so we found some interesting results that has a certain... ''beauty'' to it, but beauty to me is simplicity, but really beauty is in the eye of the beholder... though saying that there was at least one great man in history who did think that the ''equations that can be considered most true'' have to be elegant and beautiful, so sayeth the late Dirac. 

 

KEY EQUATION TIME

 

 

1).  [math]\nabla_{\gamma(t)} \dot{\gamma}(t) \equiv\ min\ g^{ij}\sqrt{<\dot{\psi}|[\nabla_i,\nabla_j]|\dot{\psi}>} = 0[/math]

 

This equation was derived to define a curve in such a way that it would form the minimum of the geodesic, in this case, the covariant derivatives do not commute.

 

2).  [math]R_{ij} = [\nabla_i,\nabla_j] = [\nabla_i \nabla_j - \nabla_j \nabla_i] \geq g_{ij}^{-}\ (\frac{1}{\ell^2})[/math]

 

Any non-commutation in any derivatives of spacetime most likely looks like: A result in fact that was predicted by both loop quantum gravity and string theory, so while neither of those theories are correct, it may hint as a non-trivial relationship; certainly scattering experiments seem to support the spacetime uncertainty hypothesis.  The last equation is basically and anti-symmetric curvature tensor. 

 

3. The commutation of two connections of the gravitational field is again simply the Riemann curvature tensor:

 

[math][\nabla_i, \nabla_j] = (\partial_i + \Gamma_i)(\partial_j + \Gamma_j) - (\partial_j + \Gamma_j)(\partial_i + \Gamma_i)[/math]

 

[math]= (\partial_i \partial_j + \Gamma_i \partial_j + \partial_i \Gamma_j + \Gamma_i\Gamma_j) - (\partial_j \partial_i + \partial_j\Gamma_i + \Gamma_j \partial_i + \Gamma_j \Gamma_i)[/math]

 

[math]= -(\partial_i, \Gamma_j) + (\partial_j, \Gamma_i) + (\Gamma_i, \Gamma_j)[/math]

 

Also with, I found a non-trivial inequality bound identical in form to the quantum bound:

 

[math]<\psi|[\nabla_i, \nabla_j] |\psi>\ =\ <\psi| R_{ij}| \psi>\ \leq 2 \sqrt{|<\nabla^2_i><\nabla^2_j>|}[/math]

 

Concerning the curve equation [math]\nabla_{\gamma(t)}\dot{\gamma} = 0[/math] the product of the wave functions which have lengths of velocity in the Hilbert space is given by:

 

[math]2K_BT = m(\frac{dx^{\mu}}{d\tau} \cdot \frac{dx^{\mu}}{d\tau}) \equiv\ <\dot{\psi}|M|\dot{\psi}>[/math]

 

Which introduces temperature in a very natural non-ad hoc way from the Maupertuis's principle.

 

4. Before the idea of those bounds I came across the useful Wigner inequality, which I replace the Hamiltonian with the stress energy tensor:

 

[math]\sqrt{<\dot{\psi}|\dot{\psi}>}\ = \int \int\ |W(q,p)^2| \sqrt{<\psi|\Gamma^2|\psi>}\ dqdp \geq \frac{1}{\hbar}\sqrt{<\psi|\mathbf{T}^2|\psi>}[/math]

 

This helped me realize I could form a gravitational Schrodinger equation:

 

[math]\nabla_n|\dot{\psi}>\ =  \frac{c^4}{8 \pi G} \int \int\ |W(q,p)^2|\ (\frac{d}{dx^n}\Gamma^{ij} + \Gamma^{i}_{n\rho} \Gamma^{\rho j} + \Gamma^{j}_{n \rho}\Gamma^{\rho}_{i})|\psi>\ dqdp \geq \int\  \frac{1}{\hbar}(\frac{d}{dx^n}T^{ij} + \Gamma^{i}_{n\rho} T^{\rho j} + \Gamma^{j}_{n \rho}T^{\rho}_{i})dV|\psi>[/math] 

 

In which the velocity guidance in curved space is

 

[math] v^2 =  \frac{\hbar^2}{2m^2}\ [ \frac{d}{dx^n}\Gamma^{ij} + \Gamma^{i}_{n\rho} \Gamma^{\rho j} + \Gamma^{j}_{n \rho}\Gamma^{\rho}_{i}][/math]

 

 

This is in fact, totally analogous to an acceleration/curve in the general theory of relativity, except this time, it satisfies an equality bound and it also satisfies the wave dynamics of a Schrodinger equation

 

5. The geometric bounds holds importance for our equation which satisfied the geodesic equation

 

[math]\nabla_n \dot{\gamma}(t) = \nabla_n\frac{dx^{\mu}}{d\tau} \equiv\ min\ \sqrt{<\dot{\psi}|[\nabla_j,\nabla_j]|\dot{\psi}>} = 0[/math]

 

The product of [math]\ <\dot{\phi}|\dot{\psi}>[/math] has a length in the Hilbert space... and with second derivatives in those lengths, comes velocity and with it a definition of acceleration:

 

[math]\frac{\partial v}{\partial \tau}  \cdot \frac{\partial v}{\partial \tau} = \frac{\hbar^2}{2m^2}[\nabla \Gamma] =\ <\dot{\psi}|\dot{\psi}>[/math]

 

with 

 

[math]v^2 \equiv |U|^2 = U^{\mu}U_{\mu}[/math] 

 

Most surprisingly also it could unify the concept of phases of particles;

 

Which can have a Berry curve definition ~

 

[math]\gamma = i \oint <n(\mathbf{R})[\Gamma_{\mathbf{R}}\Gamma^{\mathbf{R}}]{\mathbf{R}}|n(\mathbf{R})>\ d\mathbf{R}[/math]

 

Obtained from a second quantization on momentum operator, while replacing the d,Alambertian for its gravitational connections and involves phase changes of particles. 

 

6.[math]\nabla_{\gamma(t)}\ \dot{\gamma}(t) \equiv\ |min| g^{\mu \nu} \sqrt{<\dot{\psi}|\dot{\psi}>}[/math]

 

From kinetic quantizaion of momentum operator with two connections of the gravitational force.

 

[math]<E_k>\ = \frac{\hbar^2}{2m}\Gamma^2 =  \frac{\hbar^2}{2m}[\Gamma, \Gamma][/math]

 

It's an operator in form because connections of the gravtational field do not generally commute. From the Virial theorem and equipartiction we find the relationsip

 

[math]\phi \approx \frac{3}{5}\ g_{00} \approx  \frac{3}{2} k_BT  = \frac{1}{2} mv^2[/math]

 

scalar field defined through ideal gas law and virial theorm:

 

[math]\phi = \frac{3}{5} \frac{Gm}{r}[/math] 

 

[math]=  \frac{3}{2}   m(\frac{\partial x^{\mu}}{\partial \tau} \cdot \frac{\partial x_{\mu}}{\partial \tau})[/math]

 

[math]= \frac{\hbar^2}{2m^2}\Gamma^2 [/math]

 

These equations are so generic in set-up for linear gravitational fields, it would also be later difficult not to see this in a modified approach using the Sciama definition of the gravielectromagnetic field. 

 

Some notes...

 

 A linear wave  equation is akin to a classical formulation of wave mechanics in special relativity, it is simply not general while it may not possess curvature. The addition of Einstein's stress energy showed (maybe not so easily) that you cannot have a surface geometry without a notion of curvature, gravity and an extra temporal degree of freedom. 

 

The first equation could also be theorized as:

 

[math]<E_k>\ = \frac{\hbar^2}{2m}[\nabla_{\mu}, \Gamma^{\mu}][/math]

 

or even as

 

[math]<KE_{\mu \nu}>\ = \frac{\hbar^2}{2m}[\nabla_{\mu}, \nabla_{\nu}] = \frac{\hbar^2}{2m^2}\ <R_{\mu \nu}>[/math]

 

 Now introduce wavefunctions, revealing different relationships of kinetic energy with the geometry of spacetime. 

 

[math]<\psi|KE_{\mu \nu}|\psi> =  \frac{\hbar^2}{2m}\ <\psi|R_{\mu \nu}|\psi>[/math]

 

7. So let’s get into the subject of Pilot waves and what it has to do with what we have talked about. Let's begin talking about the guiding equation for deterministic quantum mechanics. That equation takes the form:

 

[math]\frac{dQ}{dt} = \frac{\hbar}{m}\ \mathbf{Im} \frac{\psi* \partial_k \psi}{\psi^{*} \psi}(Q_1... Q_N)[/math]

 

Where Q(t) is the first order evolution for the position of the particles. The distribution can be understood through the Born law, [math]\int |\psi|^2 = \psi^{*}\psi [/math]  in which case the ratio can be understood in terms of their respective probability density distributions in which case, you can form a time dependent Schrodinger equation taking into respect a guiding wave function:

 

[math]i \hbar \frac{\partial \psi}{\partial t} = (-\frac{h^2}{2m}\nabla^2 + V + \frac{\hbar^2}{2m}\frac{\nabla^2 \sqrt{\rho}}{\sqrt{\rho}})\psi[/math]

 

Notice, the statistical dependence is removed (or normalized) from the guidance equation

 

Under Bohmian Pilot waves, the equaion of interest is:

 

[math]\frac{\partial s}{\partial t} = \frac{s^2}{2m}\nabla^2[/math]

 

the metric is: [math]s = ct[/math]

 

Since the geodesic of the main quantification;

 

[math]\nabla^{\mu \nu}\nabla_{\sigma \lambda}\ (\frac{ds^{\sigma}}{dt} \cdot \frac{ds^{\lambda}}{dt})  \equiv |min| g^{\mu \nu} <\dot{\psi}|\dot{\psi}>[/math]

 

After squaring solves for two solutions those for conjugate ket's and bra (ie. [math]|\dot{\psi}>[/math]\ and [math]<\dot{\psi}|[/math] ) solutions. The simplest solution I found trying to model this did come from a second quantization on the momentum operator defined specially for curvilinear coordinates. The next section will describe a gravitational guiding wave function,

 

8. Curve, temperature and geometry was found as:

 

[math]K_BT = \frac{\hbar^2}{2m}[\Gamma, \Gamma] =\ \frac{1}{2} <\dot{\psi}|m|\dot{\psi}>[/math]

 

This equation in my eyes, established all the dynamics but first some hard premises I came to:

 

Though the Bohmian wave is indeed determinstic, this written in spacetime requires that the wave functions are in fact very small gravitational perturbance, known as gravitational waves. So in other words, particles create ripples in space as gravitational waves - in fact, it is under current research to see if the detector can from subatomic gravitational waves, since the detector and detected are coupled in such ways. 

 

The reason why I came to this conclusion, are for a number of things, but the real main reason, is just like the full curved Schrodinger equation I derived it has two solutions of the form (if you consider spacetime itself as an observable, as I do follow for good reasons):

 

[math]\frac{\hbar^2}{2m}[\Gamma, \Gamma] =\ \frac{1}{2} <\dot{\psi}|m|\dot{\psi}>[/math]

 

decomposing into bra-ket notation we get:

 

[math]|\dot{\psi}_{\mu}>\ = \frac{\hbar}{\sqrt{m}}\Gamma_{\mu}[/math]

 

and it's conjugate

 

[math]<\dot{\psi}^{\mu}|\ = \frac{\hbar}{\sqrt{m}}\Gamma^{\mu}[/math]

 

. The unifying idea here is that as the mass moves through spacetime, it inexorably causes the waves, and on and on the cycle goes.

 

We came from a totally logical, not add-hoc but some assumptions thrown in. The second quantization of a momentum operator with derivatives related to the gravitational field, is at least a tantalizing approach. It has been openened up for discussion that you could theoretically complexify these last two equation, in objection to the Wheeler de Witt equation which treats gravity as a ''real'' field (without complexification) making it it at odds with the rest of the ''fundamental'' forces of nature.

 

After my assumption of the wave function being gravitational wave ripples in spacetime, came to a surprising shock to find the following article too see if anyone was mad enough as me to think this way:

 

 

https://readingfeynman.org/2017/09/30/wavefunctions-as-gravitational-waves/

 

The velocity equation as well

 

[math]\frac{\hbar^2}{2m^2}[\Gamma, \Gamma] =\ \frac{1}{2} <\dot{\psi}|\dot{\psi}>[/math]

 

Is really similar in structure to the accelertion/curve equation, save for the fact it features the Riemann curvature tensor. 

 

[math]\nabla_n \dot{\gamma}(t) = \nabla_n \frac{dx}{d\tau} \equiv\ min\ \sqrt{<\dot{\psi}|[\nabla_j,\nabla_j]|\dot{\psi}>} = 0[/math]

 

9.You will recall that we obtained the velocity squared formula. It might interest you to know that this formula is a covariant derivative away from  curve equation: It not only guides the particle using gravitational waves but it seems to contribute to the four velocity or more accurately, a four-acceleration 

 

[math] (\frac{S(r,t)}{m})^2[\Gamma_{\mu}, \Gamma^{\mu}] = \mathbf{U}_{\mu}\mathbf{U}^{\mu} [/math]

 

And that four-acceleration is in fact implemented like: 

 

[math]\frac{\mathbf{D}\mathbf{U}^{\lambda}}{\partial \tau} = \frac{\partial \mathbf{U}^{\lambda}}{\partial \tau} + \Gamma^{\lambda}_{\mu \nu}\mathbf{U}^{\mu}\mathbf{U}^{\nu}[/math]

 

 

 

I had to edit because of errors with latex, I really am rubbish and careless. While I have been away I have been considering the theory more deeply, though I wrote a lot to go with it, I'll just keep to equations for now. . The kinetic energy associated to the mass tensor in the Hilbert space is

 

 

[math]2KE_{\mu \nu} =\ <\dot{\psi}|M_{\mu \nu}|\dot{\psi}>[/math]

 

Since the mass tensor  is related to stress energy tensor then it is also true:

 

[math]T_{\mu \nu} =\ <\dot{\psi}|M_{\mu \nu}|\dot{\psi}>[/math]

 

with stress energy as

 

[math]T_{\mu \nu} = M_{\mu \nu}c^2[/math]

 

And it's not hard to understand why we end up with the relationship since we consider the right hand side a matter of curvilinear trajectories as a curved interval. Solving for the spacetime tension (using the Estakhr tensor which is the inverse of the Einstein tensor) we have

 

[math]\frac{c^4}{8 \pi G} = A^{\mu \nu} T_{\mu \nu} =\ A^{\mu \nu} <\dot{\psi}|M_{\mu \nu}|\dot{\psi}>[/math]

 

While it is true that this appears to suggest that there is a spacetime ''constant'' this is only one such interpretation, but its very likely the realistic outcome will favor a dynamic tension, just as we have Einstein's dynamic stress. This is of course, an issue of the physics we consider, especially the units we work in. One formulation of the Planck force, does have literature for a formula in which the force will vary with the mass of a particle,

 

[math]F = \frac{mc^2}{(\frac{\hbar}{mc})} = \frac{m^2c^3}{\hbar}[/math]

 

Under the new parameters we would obtain:

 

[math]m_{\mu}m^{\mu}\ \frac{c^3}{\hbar} = A^{\mu \nu} T_{\mu \nu} =\ A^{\mu \nu} <\dot{\psi}|M_{\mu \nu}|\dot{\psi}>[/math]

 

might be more realistic in terms of the tension caused by a particle moving in spacetime? Certainly for me at least, I didn't like the idea of a constant spacetime tension, so I have tried to look at it from a different perspective. The approach though looks a bit iffy... we have a mass on the left hand side and a mass tensor on the right hand side, maybe instead of being directly equivalent, we can see as all the terms describing similar if not identical physics but in different ways. The difference is now the left is able to vary in terms of the mass being used, suggesting that tension is a variable dynamic of spacetime.

 

as wiki states:

 

'' Here the force is different for every mass (for the electron, for example, the force is responsible for the Schwinger effect; see page 3 here [1]). It is Planck force only for the Planck mass (approximately 2.18 × 10⁻⁸ kg). This follows from the fact that the Planck length is a reduced Compton wavelength equal to half the Schwarzschild radius of the Planck mass: ''

 

[math]\frac{c^4}{8 \pi G} = A^{\mu \nu} T_{\mu \nu} =\ [\mathbf{G}^{\mu \nu}]^{-1} <\dot{\psi}|M_{\mu \nu}|\dot{\psi}>[/math]

 

[math]\mathbf{G}_{\mu \nu} = \mathbf{R}_{\mu \nu} - \frac{1}{2}g_{\mu \nu}R =  \frac{8 \pi G}{c^4}<\dot{\psi}|M_{\mu \nu}|\dot{\psi}>[/math]

 

The main point with explaining gravity in the way of commutators is to see whether gravity as understood within this model, requires quantization at all. It seems for instance, a guiding velocity is described by commutating operators:

 

[math]v^2 = (\frac{ds}{dt})^2 = \frac{(\nabla S)^2}{m^2} = \frac{S^2}{m^2}[\Gamma_0,\Gamma_0][/math]

 

This is a completely classical view of the velocity guidance, but in curved space. The gravity acts classically as does the action [math]S[/math]. Obtaining the solution for the energy translates also as

 

[math]mc^2\ g_{00} = \int\ T_{00}\ dV  = \frac{S^2}{m}[\Gamma_0,\Gamma_0][/math]

 

Perfectly classical but I expect it to be more an approximation. The physics isn't simple and it isn't easy getting a foot on the correct ground as there is little to obtain in the way of literature for such a direction for gravity. We are not saying that ''quantum things'' don't happen at the scale of particles, but this is what a phase space is for, especially for anti-commuting operators which are required to smear the classical into the quantum. Instead we ask whether gravity is classical all the way down? Calculating [math]T_{00}[/math] tends to be a representation of a flat spacetime, high energy scales for [math]T_{00}[/math] are unknown in the context for a 'quantum gravity.' But since recent experiments seem to show gravity acts the same way for all kinds of particles in different energy scales, it looks like gravity could be manifestly classical.

Edited December 6, 2018 by Dubbelosix

[Dubbelosix]

I had to edit because of errors with latex, I really am rubbish and careless. While I have been away I have been considering the theory more deeply, though I wrote a lot to go with it, I'll just keep to equations for now. . The kinetic energy associated to the mass tensor in the Hilbert space is

 

 

[math]2KE_{\mu \nu} =\ <\dot{\psi}|M_{\mu \nu}|\dot{\psi}>[/math]

 

Since the mass tensor  is related to stress energy tensor then it is also true:

 

[math]T_{\mu \nu} =\ <\dot{\psi}|M_{\mu \nu}|\dot{\psi}>[/math]

 

with stress energy as

 

[math]T_{\mu \nu} = M_{\mu \nu}c^2[/math]

 

And it's not hard to understand why we end up with the relationship since we consider the right hand side a matter of curvilinear trajectories as a curved interval. Solving for the spacetime tension (using the Estakhr tensor which is the inverse of the Einstein tensor) we have

 

[math]\frac{c^4}{8 \pi G} = A^{\mu \nu} T_{\mu \nu} =\ A^{\mu \nu} <\dot{\psi}|M_{\mu \nu}|\dot{\psi}>[/math]

 

While it is true that this appears to suggest that there is a spacetime ''constant'' this is only one such interpretation, but its very likely the realistic outcome will favor a dynamic tension, just as we have Einstein's dynamic stress. This is of course, an issue of the physics we consider, especially the units we work in. One formulation of the Planck force, does have literature for a formula in which the force will vary with the mass of a particle,

 

[math]F = \frac{mc^2}{(\frac{\hbar}{mc})} = \frac{m^2c^3}{\hbar}[/math]

 

Under the new parameters we would obtain:

 

[math]m_{\mu}m^{\mu}\ \frac{c^3}{\hbar} = A^{\mu \nu} T_{\mu \nu} =\ A^{\mu \nu} <\dot{\psi}|M_{\mu \nu}|\dot{\psi}>[/math]

 

might be more realistic in terms of the tension caused by a particle moving in spacetime? Certainly for me at least, I didn't like the idea of a constant spacetime tension, so I have tried to look at it from a different perspective. The approach though looks a bit iffy... we have a mass on the left hand side and a mass tensor on the right hand side, maybe instead of being directly equivalent, we can see as all the terms describing similar if not identical physics but in different ways. The difference is now the left is able to vary in terms of the mass being used, suggesting that tension is a variable dynamic of spacetime.

 

as wiki states:

 

'' Here the force is different for every mass (for the electron, for example, the force is responsible for the Schwinger effect; see page 3 here [1]). It is Planck force only for the Planck mass (approximately 2.18 × 10⁻⁸ kg). This follows from the fact that the Planck length is a reduced Compton wavelength equal to half the Schwarzschild radius of the Planck mass: ''

 

[math]\frac{c^4}{8 \pi G} = A^{\mu \nu} T_{\mu \nu} =\ A^{\mu \nu} <\dot{\psi}|M_{\mu \nu}|\dot{\psi}>[/math]

 

The main point with explaining gravity in the way of commutators is to see whether gravity as understood within this model, requires quantization at all. It seems for instance, a guiding velocity is described by commutating operators:

 

[math]v^2 = (\frac{ds}{dt})^2 = \frac{(\nabla S)^2}{m^2} = \frac{S^2}{m^2}[\Gamma_0,\Gamma_0][/math]

 

This is a completely classical view of the velocity guidance, but in curved space. The gravity acts classically as does the action [math]S[/math]. Obtaining the solution for the energy translates also as

 

[math]mc^2\ g_{00} = \int\ T_{00}\ dV  = \frac{S^2}{m}[\Gamma_0,\Gamma_0][/math]

 

Perfectly classical but I expect it to be more an approximation. The physics isn't simple and it isn't easy getting a foot on the correct ground as there is little to obtain in the way of literature for such a direction for gravity. We are not saying that ''quantum things'' don't happen at the scale of particles, but this is what a phase space is for, especially for anti-commuting operators which are required to smear the classical into the quantum. Instead we ask whether gravity is classical all the way down? Calculating [math]T_{00}[/math] tends to be a representation of a flat spacetime, high energy scales for [math]T_{00}[/math] are unknown in the context for a 'quantum gravity.' But since recent experiments seem to show gravity acts the same way for all kinds of particles in different energy scales, it looks like gravity could be manifestly classical.

 

 

There was some curiosity also from myself concerning the curvature tensor

 

 

 

[math]<KE_{\mu \nu}>\ = \frac{\hbar^2}{2m}[\nabla_{\mu}, \nabla_{\nu}] = \frac{\hbar^2}{2m}\ <R_{\mu \nu}>[/math]

 

 

with [math]\mu = (x + y + z)\ and\ \nu = 0\ (time)[/math] then this appears like a more expected form for the description of geometry with the presence of the Riemann curvature tensor on the far right. If however gravity is completely classical in the usual range of [math]T_{00}[/math] for Einstein's theory then there are no quantum corrections as far as the phenomenon is understood. That places the restriction on terms concerning the curvature as related to the stress energy. And knowing the difference between these formula just comes down to indices. The above equation is ok for anti-commutating systems, just as space does not commute with time generally-speaking.

Edited December 6, 2018 by Dubbelosix

[Dubbelosix]

https://readingfeynman.org/2017/09/30/wavefunctions-as-gravitational-waves/

 

The velocity equation as well

 

[math]\frac{\hbar^2}{2m^2}[\Gamma, \Gamma] =\ \frac{1}{2} <\dot{\psi}|\dot{\psi}>[/math]

 

Is really similar in structure to the accelertion/curve equation, save for the fact it features the Riemann curvature tensor. 

 

[math]\nabla_n \dot{\gamma}(t) = \nabla_n \frac{dx}{d\tau} \equiv\ min\ \sqrt{<\dot{\psi}|[\nabla_j,\nabla_j]|\dot{\psi}>} = 0[/math]

 

9.You will recall that we obtained the velocity squared formula. It might interest you to know that this formula is a covariant derivative away from  curve equation: It not only guides the particle using gravitational waves but it seems to contribute to the four velocity or more accurately, a four-acceleration 

 

[math](\frac{S(r,t)}{m})^2[\Gamma_{\mu}, \Gamma^{\mu}] = \mathbf{U}_{\mu}\mathbf{U}^{\mu} [/math]

 

And that four-acceleration is in fact implemented like: 

 

[math]\frac{\mathbf{D}\mathbf{U}^{\lambda}}{\partial \tau} = \frac{\partial \mathbf{U}^{\lambda}}{\partial \tau} + \Gamma^{\lambda}_{\mu \nu}\mathbf{U}^{\mu}\mathbf{U}^{\nu}[/math]

 

 

 

To understand this last equation, it is best to view this part [math]\frac{\partial \mathbf{U}^{\lambda}}{\partial \tau}[/math] denoting flat space, and the second term is the correction, with [math]\Gamma^{\lambda}_{\mu \nu}\mathbf{U}^{\mu}[/math] yielding what is known as the time operator:

 

[math]\frac{\mathbf{D}}{\mathbf{D}\tau} = \mathbf{U}^{\mu} \nabla_{\mu}[/math]

 

As always, the space derivatives are conventionally replaced by their connections. It can also be noticed from this equation:

 

[math](\frac{S(r,t)}{m})^2[\Gamma_{\mu}, \Gamma^{\mu}] = \mathbf{U}_{\mu}\mathbf{U}^{\mu} [/math]

 

That it can be separated to find a single solution for the velocity

 

[math]\frac{S(r,t)}{m}\Gamma_{\mu} = \mathbf{U}_{\mu}[/math]

 

Using

 

[math]\frac{\mathbf{D}}{\mathbf{D}\tau} = \mathbf{U}^{\mu} \nabla_{\mu}[/math]

 

we find

 

[math]\frac{S(r,t)}{m}[\nabla^{\mu},\Gamma_{\mu}] = \mathbf{U}_{\mu}\nabla^{\mu} =\frac{\mathbf{D}}{\mathbf{D}\tau} [/math]

 

The four acceleration is found as

 

[math]\frac{S(r,t)\mathbf{U}^{\lambda}}{m}[\nabla^{\mu},\Gamma_{\mu}] = \mathbf{U}^{\lambda}\mathbf{U}_{\mu}\nabla^{\mu} =\frac{\mathbf{D}\mathbf{U}^{\lambda}}{\mathbf{D}\tau } = \frac{\partial \mathbf{U}^{\lambda}}{\partial \tau} + \Gamma^{\lambda}_{\mu \nu}\mathbf{U}^{\mu}\mathbf{U}^{\nu}[/math]

Edited December 6, 2018 by Dubbelosix

[Dubbelosix]

''WHY Gravitational waves operate in all directions, where in nature are they guided. perhaps I am misunderstanding you. ''

 

 

Gravitational waves are transverse waves - they are not dipole like electromagnetic waves, they are quadrupole waves. This even makes my head hurt. Basically, a transverse was has oscillations which are perpendicular to the direction of motion. Wave functions can also be described in a transverse way. If we want a theory of gravity, I asked the question why a wave is guided, assuming it is? A particle with a self energy would warp spacetime around it, in this sense geometry could form the path the particle takes, from it's own self field. The only issue here is that self-fields are often treated as divergent - but these issues I feel are more deeper related to the way we treat our theories. In absence of any external force, it is therefore proposed the wave function guides the particles as a gravitational wave. It could be a reason for instance why there are no particles truly at rest, simply because the curvature they produce would also produce an acceleration in the direction of the bending of spacetime. So its not so much gravitational waves are guided, but particles could be guided by gravitational waves if they are interpreted on subatomic scales as the wave function itself. It could answer why we can't see a wave function, but we can detect a particle whenever we come to measure it (Copenhagen issue).

 

''You are on dodgy ground with Lamor his equation incorrectly predicts that an electron in a hydrogen atom will quickly radiate away all its kinetic energy and fal into the nucleus, also it is non relativistic.''

 

 

There is technically nothing wrong with Larmor's equation and even though it is true classical physics predicts atoms are unstable, the wave functions of electrons removes classical acceleration. The Larmor equation also can be expressed relativistically, such approaches have been investigated quite well.

 

''I thought classical physics was a simplification of quantum physics''

 

 

Certainly a simplification, but I said it was a special case, it is true to say that classical physics is a special case of quantum mechanics, (in the simplified limit of low energy physics).

 

 

''QUESTION what predictions does your final result achieve, apart from making my head hurt''

 

 

In the case of the Hilbert space, I have found that gravity appears to act classically, this may not always be true, but for the case of the geodesic equation, it was shown that the covariant derivatives commute making it possibly manifestly classical in nature. The idea gravity acts classically at the quantum level is at least in agreement with experiment. As for seeing the wave function as gravitational disturbances (waves) in spacetime, is something I am still working on. It could have implication for entanglement; especially entanglement between space and matter.

[Dubbelosix]

Just how it goes, while the gravitational wave function maybe was an attractive idea, I have no idea how it explains the wave function in the case of observing the system. For instance, measuring the particle in a double slit experiment makes a two-band interference. I wouldn't understand how gravitational waves would come to explain these things.

[Dubbelosix]

I haven't disregarded so far the gravitational aether.

[Dubbelosix]

I was hoping the gravitational wave explanation could explain a number of phenomenon and may even explain a small disturbance as affected the orbits of electrons inside atoms. I was also hoping they could form what is known as the empty wave:

 

https://sci-hub.tw/https://doi.org/10.1016/0375-9601(92)90618-V

 

Just as with an aether, there cannot be any particles associated to it, this is about as empty as I can imagine.

[Dubbelosix]

I also believe the laws of thermodynamics are preserved before the big bang: I have interpreted a cold big bang as making more sense with the laws of thermodynamics.

[Dubbelosix]

The link goes to a none english language website that needs a login key. Is this what you are referring to https://arxiv.org/ftp/arxiv/papers/1008/1008.4849.pdf .

 

I find the micro black hole theory a little intriguing when thinking of particles and gravity in a zero energy universe. I have come to view the micro black holes as wormholes, or pin pricks in the membrane of space time. When one thinks of entanglement effects between particles, having fields of various shapes around worm holes all connecting etc. One can build an entire universe. If gravity is connected to entanglement as has been suggested in a number of recent theories it makes sense to have wormholes connecting particles to another dimension. 

 

As for an empty ether: Viewing it as a smooth field is OK when zoomed out, but zooming in to the quantum level it has properties and is full of virtual particles, as demonstrated by the Casimir effect and the HUP.

 

Speculation:- A rough idea of what I am thinking is as follows. I think taking a wormhole in a 5 dimensional space, (pin pricks in space time), ie borrowing a few ideas of the micro black hole theory and most of Verlindes ideas on entanglement, I have a Laymans theory of everything coming together. The HUP would need a temperature term that would allow stable particle creation at absolute zero, to become a certainty over time at some pre big bang era. The low temperature would allow particle condensates to form like huge particles full of matter and anti matter, until a time when they could collide, explode, and heat up space time, preventing further particle formation. Hoyle has matter formation pretty well covered after this with super novae producing all the heavier elements etc etc  :)  

 

That paper is significantly more difficult to read than the one I intended to post: Hardy, L. (1992). "On the existence of empty waves in quantum theory". Physics Letters A. 167 (1): 11–16. Bibcode:1992PhLA..167...11H. doi:10.1016/0375-9601(92)90618-V.

[Dubbelosix]

As for what the '''aether looks like quantum mechanically'' may not be so easy to apply concepts like discrete fluctuations. Attempts to measure the discreteness of the vacuum has failed, so either this quantum world hardly ever couples to real matter, or... the situation is even more complicated. It would have been nice to find evidence of the discreteness outside conjecture. 

[Dubbelosix]

In the model I chose, the gravitational aether is not exactly ''nothing'' but is in fact a dynamic thickness that varies through space, due to gravitational density - this thickness of space and time is measured by what the aether is ''made of'' which is permeability and permittvity, two variables (not constants) which affect the speed in which light can travel. One consequence is that light can escape black holes, and this is important. 

[Dubbelosix]

When I talk about empty waves, this does not technically mean nothing, but instead, means absence of quantization ie. graviton or absence of test particle. 

Edited December 10, 2018 by Dubbelosix

[Dubbelosix]

The wave function as a gravitational wave was intuitive, because it allowed the idea of empty waves in my model because the gravitational wave ''is not nothing.'' There are some issues though when I studied this idea next to the double slit experiment, namely that the empty wave should move faster than the test particle: This is a problem because how can a tardyon be directed by a gravitational wave which is expected to move at light speed. It did however offer a nice explanation to the quantum leap, a small gravitational disturbance in either way could cause an electron to either fall or increase an energy level, which would appear to an observer as pretty much instantaneous. Maybe to explain a wave function as a gravitational pilot wave requires that the gravitational wave does not always move at light speed but can be in phase with matter, is a radical idea, but so wild it could be true, 

[Dubbelosix]

On what it means for waves to be in phases:

 

https://www.quora.com/What-exactly-are-in-phase-and-out-of-phase-in-terms-of-waves