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A Generalization Of The Lorentz Ether Interpretation To The Einstein Equations Of Gr

Lorentz ether general relativity

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#1 Schmelzer

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Posted 13 October 2019 - 01:22 AM

While special relativity has to different interpretations - the original one by Lorentz and Poincare known as the "Lorentz ether" and the "spacetime interpretation" proposed by Minkowski - for GR, only one interpretation is widely known, the spacetime interpretation.  

 

The non-existence of a generalization of the Lorentz ether interpretation to gravity is certainly a decisive argument against the Lorentz ether.  In such a situation, one should not wonder that the mainstream follows the spacetime interpretation and rejects the Lorentz ether. 

 

But this argument no longer holds.  There exists a surprisingly simple and beautiful Lorentz ether interpretation of the Einstein equations of GR in harmonic coordinates.  Let's see.  What is the most popular coordinate condition used in GR?  It is the harmonic condition.  It simplifies the Einstein equations in an essential way.  What are these conditions? They look like conservation laws, or, alternatively, like a wave equation for the preferred coordinates [math]X^{\nu}[/math]:

 

[math]\partial_\mu (g^{\mu\nu} \sqrt{-g} ) = 0  \text{ resp. } \square X^{\nu} = 0 [/math]

 

What are the most important classical equations for condensed matter?  They are the continuity and the Euler equations:

 

[math]\partial_t \rho + \partial_i (\rho v^i) = 0.[/math]

[math]\partial_t (\rho v^j) + \partial_i(\rho v^i v^j - \sigma^{ij}) = 0.[/math]

 

Compare them and there will be a straightforward Lorentz ether fulfilling continuity and Euler equations as reasonable for an ether:

 

[math] \rho = g^{00}\sqrt{-g}, \quad \rho v^i = g^{0i}\sqrt{-g},\quad \rho v^i v^j - \sigma^{ij} = g^{ij}\sqrt{-g}.[/math]

 

Let's note an especially interesting property of this interpretation:  The condition [math]\rho>0[/math] translates into the preferred time coordinate [math]T=X^0[/math] being really a time-like coordinate. What does this mean for solutions of the Einstein equations with causal loops? It means that they don't allow for such an ether interpretation. The Einstein equations interpreted as equations for the Lorentz ether would, of course, become invalid and meaningless if the ether density becomes zero.  This would be the boundary of the ether, the boundary conditions have not been defined, so, the boundary is simply not covered by the Einstein equations.

Solutions of the Einstein equations which are also valid solutions of the Lorentz ether have an ether density greater zero everywhere, thus, they have a global time-like coordinate as the preferred time coordinate. 

 

For more details see https:ilja-schmelzer.de/ether



#2 Dubbelosix

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Posted 31 October 2019 - 09:40 AM

OK so I have been reading this, can you explain the property of this aether? You seem to be working with terms that describe the dynamics of a fluid, the continuity is a conservation of a given fluid equation, what is the nature of the aether, it certainly isn't made of stuff moving around given we take relativity seriously since there cannot be a motion associated to it. You speak of a gravitational aether, but this too needs some defining.

Edited by Dubbelosix, 31 October 2019 - 09:56 AM.


#3 Schmelzer

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Posted 01 November 2019 - 01:09 AM

OK so I have been reading this, can you explain the property of this aether? You seem to be working with terms that describe the dynamics of a fluid, the continuity is a conservation of a given fluid equation, what is the nature of the aether, it certainly isn't made of stuff moving around given we take relativity seriously since there cannot be a motion associated to it. You speak of a gravitational aether, but this too needs some defining.

The ether is moving around, but slowly.  Only in the special-relativistic limit its velocity will be zero.  

 

For a microscopic model of the ether giving the Standard Model fields, see https:ilja-schmelzer.de/matter/.                                                                                            

For more details about the gravitational ether see https:ilja-schmelzer.de/gravity/.

 

The gravitational ether has a velocity defined by the gravitational field by [math]v^i = \frac{g^{0i}}{g^{00}}[/math] in the preferred coordinates, and relativity is taken into account (the Einstein equations appear in a natural limit).



#4 Dubbelosix

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Posted 01 November 2019 - 06:25 AM

The ether is moving around, but slowly.  Only in the special-relativistic limit its velocity will be zero.  
 
For a microscopic model of the ether giving the Standard Model fields, see https:ilja-schmelzer.de/matter/.                                                                                            
For more details about the gravitational ether see https:ilja-schmelzer.de/gravity/.
 
The gravitational ether has a velocity defined by the gravitational field by [math]v^i = \frac{g^{0i}}{g^{00}}[/math] in the preferred coordinates, and relativity is taken into account (the Einstein equations appear in a natural limit).


Moving around, are we talking about a Ricci Flow?

#5 Dubbelosix

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Posted 01 November 2019 - 06:27 AM

You see, aside from the Ricci flow, which doesn't use a mediator per se, the flow of space is probably well known but you cannot speak of fundamental fields when discussing an aether. There can be no motion associated to particles from first principles of relativity.

#6 Dubbelosix

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Posted 01 November 2019 - 06:47 AM

From wiki, this realization for Lorentz is a conclusion I conceded except for a special case of Ricci flow, with no gravitons,

"Also Lorentz argued during his lifetime that in all frames of reference this one has to be preferred, in which the aether is at rest. Clocks in this frame are showing the "real“ time and simultaneity is not relative. However, if the correctness of the relativity principle is accepted, it is impossible to find this system by experiment.[A 21]"

#7 Flummoxed

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Posted 01 November 2019 - 07:50 AM

I dont want to interrupt your conversation.

 

But

 

Zero point energy exists only momentarily, it is not a solid thing, it does however have a density related to planks constant. The zero point energy density is I understand from Stochaistic Electrodynamics Lorentz invariant?

 

Is this sort of where you maybe headed >

 

https://www.research..._Quantum_Theory



#8 Dubbelosix

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Posted 01 November 2019 - 08:09 AM

It's possible under a field theory model, problem is this idea never took off, and motion through the fields will still detect no motion associated to it. It seems a metric model of an aether based on gravitation will be viable in the end. We have even detected evidence for this aether, from the Sagnac effect (which led to my own model as inertia from gravitational drag) and radiation and gravitational waves travel at different speeds as detected in strong gravitational fields suggesting a type of aether.

#9 Dubbelosix

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Posted 01 November 2019 - 08:22 AM

I like the idea of approaching the harmonic condition as we remind ourselves of the covariant derivative of the density of the reciprocal of the metric tensor:

[math]
{\displaystyle 0=\left(g^{\mu \nu }{\sqrt {-g}}\right)_{;\rho }=\left(g^{\mu \nu }{\sqrt {-g}}\right)_{,\rho }+g^{\sigma \nu }\Gamma _{\sigma \rho }^{\mu }{\sqrt {-g}}+g^{\mu \sigma }\Gamma _{\sigma \rho }^{\nu }{\sqrt {-g}}-g^{\mu \nu }\Gamma _{\sigma \rho }^{\sigma }{\sqrt {-g}}\,.}{\displaystyle 0=\left(g^{\mu \nu }{\sqrt {-g}}\right)_{;\rho }=\left(g^{\mu \nu }{\sqrt {-g}}\right)_{,\rho }+g^{\sigma \nu }\Gamma _{\sigma \rho }^{\mu }{\sqrt {-g}}+g^{\mu \sigma }\Gamma _{\sigma \rho }^{\nu }{\sqrt {-g}}-g^{\mu \nu }\Gamma _{\sigma \rho }^{\sigma }{\sqrt {-g}}\,.} [/math]

Edited by Dubbelosix, 01 November 2019 - 08:30 AM.


#10 Flummoxed

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Posted 02 November 2019 - 04:27 AM

It's possible under a field theory model, problem is this idea never took off, and motion through the fields will still detect no motion associated to it. It seems a metric model of an aether based on gravitation will be viable in the end. We have even detected evidence for this aether, from the Sagnac effect (which led to my own model as inertia from gravitational drag) and radiation and gravitational waves travel at different speeds as detected in strong gravitational fields suggesting a type of aether.

 

Quantum field theory is quite successful :) SED is still a toy, but interesting.

 

Absorption and emission in a actual substance of varying densities could be viewed as a drag and would be measurable in something like the  michelson morley setup

 

The zero point field is not an actual substance, and is not considered in some field theories, it is however a possible candidate for dark energy etc.

 

 

I like the idea of approaching the harmonic condition as we remind ourselves of the covariant derivative of the density of the reciprocal of the metric tensor:

[math]
{\displaystyle 0=\left(g^{\mu \nu }{\sqrt {-g}}\right)_{;\rho }=\left(g^{\mu \nu }{\sqrt {-g}}\right)_{,\rho }+g^{\sigma \nu }\Gamma _{\sigma \rho }^{\mu }{\sqrt {-g}}+g^{\mu \sigma }\Gamma _{\sigma \rho }^{\nu }{\sqrt {-g}}-g^{\mu \nu }\Gamma _{\sigma \rho }^{\sigma }{\sqrt {-g}}\,.}{\displaystyle 0=\left(g^{\mu \nu }{\sqrt {-g}}\right)_{;\rho }=\left(g^{\mu \nu }{\sqrt {-g}}\right)_{,\rho }+g^{\sigma \nu }\Gamma _{\sigma \rho }^{\mu }{\sqrt {-g}}+g^{\mu \sigma }\Gamma _{\sigma \rho }^{\nu }{\sqrt {-g}}-g^{\mu \nu }\Gamma _{\sigma \rho }^{\sigma }{\sqrt {-g}}\,.} [/math]

 

What ! I think I will step out. 



#11 Schmelzer

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Posted 02 November 2019 - 05:51 AM

This thread is not about Stochastics Electrodynamics.   

Moving around, are we talking about a Ricci Flow?

No.  The formula for the velocity of the ether, [math]v^i = g^{0i}/g^{00}[/math], has nothing to do with Ricci flow. 

 

You see, aside from the Ricci flow, which doesn't use a mediator per se, the flow of space is probably well known but you cannot speak of fundamental fields when discussing an aether. There can be no motion associated to particles from first principles of relativity.

I don't understand this.  The Lorentz ether has, of course, waves, in particular light waves have always been ether waves, and light waves obviously move. Particles are interpreted as pseudoparticles, similar to phonons in condensed matter, so they can also move even if the average velocity of the ether is zero.  

From wiki, this realization for Lorentz is a conclusion I conceded except for a special case of Ricci flow, with no gravitons,

"Also Lorentz argued during his lifetime that in all frames of reference this one has to be preferred, in which the aether is at rest. Clocks in this frame are showing the "real“ time and simultaneity is not relative. However, if the correctness of the relativity principle is accepted, it is impossible to find this system by experiment.[A 21]"

This holds in special relativity, where we have such a preferred frame where the ether velocity is zero.  In the generalization, the preferred frame simply defined Newtonian absolute space and time, but the ether moves relative to absolute space.  The impossible to identify that rest frame remains because the Einstein Equivalence Principle can be derived (it follows from the action equals reaction symmetry). 

 

We have even detected evidence for this aether, from the Sagnac effect (which led to my own model as inertia from gravitational drag) and radiation and gravitational waves travel at different speeds as detected in strong gravitational fields suggesting a type of aether.

I don't think Sagnac gives anything, and the claim that the speed of gravitational waves differs from c sounds quite non-mainstream too. 


Edited by Schmelzer, 02 November 2019 - 05:52 AM.


#12 Dubbelosix

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Posted 02 November 2019 - 12:02 PM

This thread is not about Stochastics Electrodynamics.   

No.  The formula for the velocity of the ether, [math]v^i = g^{0i}/g^{00}[/math], has nothing to do with Ricci flow. 
 

I don't understand this.  The Lorentz ether has, of course, waves, in particular light waves have always been ether waves, and light waves obviously move. Particles are interpreted as pseudoparticles, similar to phonons in condensed matter, so they can also move even if the average velocity of the ether is zero.  

This holds in special relativity, where we have such a preferred frame where the ether velocity is zero.  In the generalization, the preferred frame simply defined Newtonian absolute space and time, but the ether moves relative to absolute space.  The impossible to identify that rest frame remains because the Einstein Equivalence Principle can be derived (it follows from the action equals reaction symmetry). 
 

I don't think Sagnac gives anything, and the claim that the speed of gravitational waves differs from c sounds quite non-mainstream too.


I might need to step out because what you call a gravitational aether, you attach to light. This is not how I understand it.

#13 Dubbelosix

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Posted 02 November 2019 - 12:03 PM

 

I don't think Sagnac gives anything, and the claim that the speed of gravitational waves differs from c sounds quite non-mainstream too.


The results are documented, check wiki.

#14 Dubbelosix

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Posted 02 November 2019 - 12:09 PM

Sorry, you need to checkout Shapiro effect specifically, though Sagnac believed his results due to an aether.

#15 Dubbelosix

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Posted 02 November 2019 - 12:12 PM

Excerpt
Shapiro delay of neutrinos and gravitational waves

From the nearly simultaneous observations of neutrinos and photons from SN 1987A, the Shapiro delay for high-energy neutrinos must be the same as that for photons to within 10%, consistent with recent estimates of the neutrino mass, which imply that those neutrinos were moving at very close to the speed of light. After the direct detection of gravitational waves in 2016, the one-way Shapiro delay was calculated by two groups and is about 1800 days. In general relativity and other metric theories of gravity, though, the Shapiro delay for gravitational waves is expected to be the same as that for light and neutrinos. However, in theories such as tensor-vector-scalar gravity and other modified GR theories, which reproduce Milgrom's law and avoid the need for dark matter, the Shapiro delay for gravitational waves is much smaller than that for neutrinos or photons. The observed 1.7-second difference in arrival times seen between gravitational wave and gamma ray arrivals from neutron star merger GW170817 was far less than the estimated Shapiro delay of about 1000 days. This rules out a class of modified models of gravity that dispense with the need for dark matter.[5]

#16 OverUnityDeviceUAP

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Posted 02 November 2019 - 02:06 PM

My model agrees with both Schmelzer's "phonon"-lorentz ether and the Shapiro effect because it states matter is trapped or "tired light" as Mordred called it, both energy and matter as fluctuations in a vacuum with a Planck geodesic that slows as they propagate due to length contraction but are continously generated as approx c phonons in the same locations within a particle horizon (cmbr).

#17 Schmelzer

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Posted 03 November 2019 - 03:33 AM

I might need to step out because what you call a gravitational aether, you attach to light. This is not how I understand it.

The ether theory which is proposed is universal.  All waves which have the same characteristic speed c, known as the speed of light, are waves of the ether.  

 

The theory consists of two parts, a theory of gravity which does not specify the other fields, but identifies the gravitational field with density, velocity and stress tensor of the ether, and a particular model for the matter fields of the Standard Model of particle physics.

 

So, with the old ether it shares the interpretation of light waves as waves of the ether.  But the waves which are usually identified with sound waves (the acoustic phonons) are degrees of freedom of the gravitational field, moreover, they are those additional fields which appear in the theory only after the preferred frame has been accepted.

 

The extracts about the use of the Shapiro delay are fine, but afaiu are nothing but a confirmation of standard GR, and in these questions there will be no difference between the General Lorentz Ether and GR, so, fine but not really a surprise. 





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