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

Lorentz ether general relativity

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### #35 Dubbelosix

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Posted 04 November 2019 - 08:25 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 $X^{\nu}$:

$\partial_\mu (g^{\mu\nu} \sqrt{-g} ) = 0 \text{ resp. } \square X^{\nu} = 0$

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

$\partial_t \rho + \partial_i (\rho v^i) = 0.$
$\partial_t (\rho v^j) + \partial_i(\rho v^i v^j - \sigma^{ij}) = 0.$

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

$\rho = g^{00}\sqrt{-g}, \quad \rho v^i = g^{0i}\sqrt{-g},\quad \rho v^i v^j - \sigma^{ij} = g^{ij}\sqrt{-g}.$

Let's note an especially interesting property of this interpretation: The condition $\rho>0$ translates into the preferred time coordinate $T=X^0$ 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

Can I tempt you at all to revise this velocity dispute? You can preserve a type of motion to the metric as

$\partial_t g_{ij}= - 2R_{ij}$

In this, geometry can flow but we haven't assigned a velocity because motion in the aether is forbidden from first principles.

Edited by Dubbelosix, 04 November 2019 - 08:37 AM.

### #36 Dubbelosix

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Posted 04 November 2019 - 08:44 AM

I think this, not so minor difference, can be implemented into your approach in possibly an even nicer way. The issue of quantum mechanics and whether we exist in a Newtonian vacuum is also crucial which you may want to extend ideas on. Flummoxed mentioned the background density, yours is similar as you would have to calculate not only the flat approximation but also a curved correction case, in which curvature contributes to fluctuations. Even in your model, you have to calculate the nodes of density for instance

ħc ∫ k dk^3

And on the curvature of background space, it gets even more interesting. Especially when we quantize the Newtonian potential.

### #37 Dubbelosix

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Posted 04 November 2019 - 08:57 AM

Also consider another important set of identities linked to the aether as possible vanues to investigate

$\frac{\partial \sqrt{- g}}{\partial g^{\mu \nu}}$

In which

$g = \text{det} g_{\mu \nu}$

We have

$\frac{\partial \sqrt{- g}}{\partial g^{\mu \nu}} = - \frac{1}{2 \sqrt{-g}}\frac{\partial g}{\partial g^{\mu \nu}}$

### #38 Dubbelosix

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Posted 04 November 2019 - 11:20 AM

Just throwing relevant additions;

$\frac{\partial_t g^{\mu \nu}}{ \partial \sqrt{- g}} = - 2 \sqrt{-g} \frac{\partial_t g^{\mu \nu}} { \partial g}$

Since the geometric time evolution is related to the curvature tensor via,

$\partial_t g_{\mu \nu}= - 2R_{\mu \nu}$

$\frac{\partial_t g^{\mu \nu}}{ \partial \sqrt{- g}} = - 2 \sqrt{-g} \frac{\partial_t g^{\mu \nu}} { \partial g} = 4 \sqrt{-g} \frac{R_{\mu \nu}} { \partial g}$

The Geometric Ricci flow is the heat equation for a Reimannian manifold. The connections related to the curvature share the following equivelances, in which the $R_{\mu \nu} \phi$ is a type of continuity of mass flow:

$g^{\mu \nu} R_{\mu \nu} \phi = g^{\mu \nu} \nabla_{\mu} \nabla_{\nu} \phi = g^{\mu \nu} \nabla_{\mu} (\partial_{\nu} \phi) = (g^{\mu \nu} \partial_{\mu}\partial_{\nu} \phi + g^{\mu \nu} \Gamma^{\sigma}_{\mu \nu}\partial_{\sigma}\phi) = \frac{-1}{\sqrt{-g}}\partial_{\mu}(g^{\mu \nu} \sqrt{-g} \partial_{\nu} \phi)$

Edited by Dubbelosix, 04 November 2019 - 11:27 AM.

### #39 Flummoxed

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Posted 04 November 2019 - 12:58 PM

Flummox invited me to share my insights so it's really not attention seeking.

I incorrectly responded to your post thinking it was Schmelzers post re his paper being discussed by Mordred on scienceforums.net not yours. If you check the link I posted you will see it is one of Schmelzers papers being commented on by Mordred, that I linked to not yours.

The thing that interested me was Mordred didnt find anything wrong with Schmelzers earlier paper.

### #40 OverUnityDeviceUAP

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Posted 04 November 2019 - 03:13 PM

I incorrectly responded to your post thinking it was Schmelzers post re his paper being discussed by Mordred on scienceforums.net not yours. If you check the link I posted you will see it is one of Schmelzers papers being commented on by Mordred, that I linked to not yours.

The thing that interested me was Mordred didnt find anything wrong with Schmelzers earlier paper.

In any case I stand by my arithmetic's relevancy here, at least what I wrote in this thread, this length contracting phonon ether. Look at it in terms of efficiency, not Mordred's style to do so, you can't take what my graphing paper diagrams look like and assume it is not applicable exclusively multidimensional vector arrays as Mordred did in the thread I reference. I don't know latex or lorentz ciphers but I do know how to show it in matrix arrays and I did so and Mordred just ignored it.

Edited by OverUnityDeviceUAP, 04 November 2019 - 05:57 PM.

### #41 Schmelzer

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Posted 05 November 2019 - 04:26 AM

Can I tempt you at all to revise this velocity dispute? You can preserve a type of motion to the metric as

$\partial_t g_{ij}= - 2R_{ij}$

In this, geometry can flow but we haven't assigned a velocity because motion in the aether is forbidden from first principles.

No you cannot.  This is a finished theory, it is published, and a moving ether has much advantages in comparison with an ether in rest.  Last but not least, what are sound waves of the ether if not a microscopic movement of the ether?

If in some particular ether theory which you prefer for unknown reasons motion in the ether is forbidden, this is irrelevant for me.  In my ether theory the ether has a velocity, which is usually non-zero.  It is my theory which gives, in a quite natural limit $\Xi,\Upsilon\to 0$, the Einstein equations of GR, which have a lot of support by various mainstream experiments testing GR.  Changing the equation for velocity would almost certainly destroy this limit, and lead to predictions which have been already falsified by known experiments.  I see no base for doing such things.

Space is the ether.

I took a look at your front page, Schmelzer. I concur with the frozen-star black hole and early universe. However I couldn't see a variable c. I searched your 35-page pdf and didn't see it. Did I miss it?

John Duffield

The coordinate velocity of light is variable.  It is variable in GR too, but given that its role is reduced to complete physical irrelevance, it plays no role there.  But, given that in the Lorentz ether we have absolute Newtonian space and absolute time,  the coordinate velocity in these background coordinates is physically important.  And the velocity of light is, in these preferred coordinates, variable.

For the popular presentation I use my homepage, the ether theory of gravity is there at https://ilja-schmelzer.de/gravity/.  If you think that something should be explained in more detail for laymen, I will do this on my homepage.

### #42 Farsight

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Posted 05 November 2019 - 07:10 AM

The coordinate velocity of light is variable.  It is variable in GR too, but given that its role is reduced to complete physical irrelevance, it plays no role there.  But, given that in the Lorentz ether we have absolute Newtonian space and absolute time,  the coordinate velocity in these background coordinates is physically important.  And the velocity of light is, in these preferred coordinates, variable.

For the popular presentation I use my homepage, the ether theory of gravity is there at https://ilja-schmelzer.de/gravity/.  If you think that something should be explained in more detail for laymen, I will do this on my homepage.

I read your gravity page. Sorry, I didn't recognize it as part of a TOE. In fact, I was somewhat alarmed to see this:

"Now we can name the energy-momentum tensor Tμv(x) "gravitational field", and all the other, remaining fields "matter fields"".

That's because the gravitational field has a secret electromagnetic nature. Because c = 1/√(ε0μ0), and because c varies. It's a weak-field distortion of the lattice like this:

#### Attached Thumbnails

Edited by Farsight, 05 November 2019 - 07:15 AM.

### #43 Farsight

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Posted 05 November 2019 - 07:34 AM

The Einstein equivalence principle isn't Einstein's equivalence principle. It says "the outcome of any local non-gravitational experiment in a freely falling laboratory is independent of the velocity of the laboratory and its location in spacetime". But it isn't absolutely correct. You will be able to measure a change in the fine-structure constant. Solar Probe Plus was going to do this, but that experiment got canned.

Remember what I said here: https://ilja-schmelz...read.php?tid=27. When you drop a laboratory into a black hole, it falls down because there's a local gradient in the speed of light. Not for any other reason. Note that falling bodies never slow down. The laboratory falls faster and faster and faster and the local speed of light is getting slower and slower and slower. This cannot continue ad infinitum. That laboratory cannot fall faster than the local speed of light, So it turns into a gamma-ray burst.

We should talk, Schmelzer. You might like to read this: the speed of light is not constant

Edited by Farsight, 05 November 2019 - 07:35 AM.

### #44 Dubbelosix

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Posted 05 November 2019 - 09:40 AM

No you cannot.  This is a finished theory, it is published,

Yes... And you came here regardless. You do realise a good investigator truly covers all aspects of avenues not to live by a single sword because you may die for it.

### #45 VictorMedvil

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Posted 05 November 2019 - 08:27 PM

Yes... And you came here regardless. You do realise a good investigator truly covers all aspects of avenues not to live by a single sword because you may die for it.

*watches Dubbel get eaten by cranks*

*plays EVE: Online*

Now Smoking Cohiba, Cuban Cigars!

Edited by VictorMedvil, 06 November 2019 - 03:04 PM.

### #46 Schmelzer

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Posted 07 November 2019 - 06:31 AM

That's because the gravitational field has a secret electromagnetic nature. Because c = 1/√(ε0μ0), and because c varies.

This would be another theory of gravity.  My ether theory gives in the limit quite standard mainstream physics, namely the Einstein equations of GR as well as the fermions and gauge fields of the Standard Model.

I would not completely exclude that a more detailed consideration of the interactions between gravity and the matter fields (essentially I have up to now considered only the special-relativistic limit for the SM ether model) will show some non-trivial connections between the electroweak fields (which describe lattice distortions) and gravity.  But this will hardly change the number of degrees of freedom.  So, both have a common "ether nature", but there will be no hidden EM nature of gravity.

The Einstein equivalence principle isn't Einstein's equivalence principle. It says "the outcome of any local non-gravitational experiment in a freely falling laboratory is independent of the velocity of the laboratory and its location in spacetime". But it isn't absolutely correct. You will be able to measure a change in the fine-structure constant.

We should talk, Schmelzer. You might like to read this: the speed of light is not constant

What I name the Einstein Equivalence Principle is what is named by the mainstream in this way, from a mathematical point of view it means simply that the equations for the matter fields do not depend on the preferred coordinates, only the gravitational field is influenced by them.  History is not important at that point.  If some observations will show some variation of the fundamental constants, I will have to think about how to deal with this, but not now.

The linked article has only one problem:  It is not understood that in GR the coordinate speed of light is variable, even according to the mainstream interpretation.  And what one assumes to be the velocity with common sense is the distance travelled in absolute space divided by absolute time, the velocity in the preferred coordinates.

There are no preferred coordinates in GR, but there are coordinates, so, common sense velocity is simply a coordinate velocity. Often the coordinates used are the simplest ones and reasonably can be assumed to be close to the preferred ones  in a theory which has preferred coordinates. So, to get a common sense compatible picture, one has to use coordinate speed of light, and it is variable in GR.

What is constant is the speed of light as measured with the most accurate clocks and rulers, and given that the most accurate distance measurement is the measurement of time for light going forth and back the distance, the constancy of c becomes a triviality.

Yes... And you came here regardless. You do realise a good investigator truly covers all aspects of avenues not to live by a single sword because you may die for it.

But once one has found a rich gold vein, does it make sense to try other places where other people have already tried something but not found anything comparable?

### #47 Farsight

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Posted 07 November 2019 - 07:45 AM

This would be another theory of gravity. My ether theory gives in the limit quite standard mainstream physics, namely the Einstein equations of GR as well as the fermions and gauge fields of the Standard Model.

It's not another theory of gravity. Einstein made it quite clear: “the curvature of light rays occurs only in spaces where the speed of light is spatially variable”. What you think of as mainstream GR is not in accord with Einstein. As for the fermions and gauge fields of the Standard Model, they're all wrong. You cannot have a TOE with 24 fundamental fields.

I would not completely exclude that a more detailed consideration of the interactions between gravity and the matter fields (essentially I have up to now considered only the special-relativistic limit for the SM ether model) will show some non-trivial connections between the electroweak fields (which describe lattice distortions) and gravity.  But this will hardly change the number of degrees of freedom.  So, both have a common "ether nature", but there will be no hidden EM nature of gravity.

You need to consider in detail how gravity works. Einstein explained most of it in his 1920 Leyden Address. A concentration of energy in the guise of a massive star conditions the surrounding space, making it “neither homogeneous nor isotropic”, this effect diminishing with distance. As a result the speed of light varies. So light curves downwards like sonar waves curve downwards in the sea, because there’s a vertical gradient in wave speed. Then matter falls down because of the wave nature of matter. Note Louis de Broglie’s 1923 letter to Nature on waves and quanta, where he said “the wave is tuned with the length of the closed path”. Just think of the electron as light going round a closed path. The horizontal component bends downwards, so the electron’s position changes. In other words, it falls down.

What I name the Einstein Equivalence Principle is what is named by the mainstream in this way, from a mathematical point of view it means simply that the equations for the matter fields do not depend on the preferred coordinates, only the gravitational field is influenced by them.  History is not important at that point.  If some observations will show some variation of the fundamental constants, I will have to think about how to deal with this, but not now.

The linked article has only one problem:  It is not understood that in GR the coordinate speed of light is variable, even according to the mainstream interpretation.

The mainstream is wrong. That's why the mainstream doesn't have a TOE. Forget the mainstream.

And what one assumes to be the velocity with common sense is the distance travelled in absolute space divided by absolute time, the velocity in the preferred coordinates.

There are no preferred coordinates in GR, but there are coordinates, so, common sense velocity is simply a coordinate velocity. Often the coordinates used are the simplest ones and reasonably can be assumed to be close to the preferred ones  in a theory which has preferred coordinates. So, to get a common sense compatible picture, one has to use coordinate speed of light, and it is variable in GR.

Yes, the common sense speed is the coordinate speed of light. Only Einstein didn't call it the coordinate speed of light. He called it the speed of light. It varies in the room you're in. If it didn't, light wouldn't curve and your pencil wouldn't fall down.

What is constant is the speed of light as measured with the most accurate clocks and rulers, and given that the most accurate distance measurement is the measurement of time for light going forth and back the distance, the constancy of c becomes a triviality.

It isn't a triviality, it's an idiocy. See Comments on “Note on varying speed of light theories” where John Moffat and João Magueijo talk about the tautology. People use the local motion of light to define the second and the metre, and they they use the second and the metre to measure the local motion of light. It doesn't matter how fast the light is moving, they will always end up saying the speed of light is 299,792,458 m/s. Because of this they can't tell you how gravity works, so they tell you nonsense like "light follows the curvature of spacetime". They can't tell you how electromagnetism works either.  Or how the nuclear force works.

Nuclear force plot from the Dux college HSC physics course, neutron charge distribution image by Dru Renner, inverted by me

Edited by Farsight, 07 November 2019 - 07:48 AM.

### #48 Dubbelosix

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Posted 07 November 2019 - 07:54 AM

But once one has found a rich gold vein, does it make sense to try other places where other people have already tried something but not found anything comparable?

Well, yes it would if your model proposes dynamics which is at odds with experimentation. It's not enough to predict Einsteins Equations, the model itself needs to agree with what we already understand of such an aether...

### #49 Schmelzer

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Posted 08 November 2019 - 03:34 AM

Well, yes it would if your model proposes dynamics which is at odds with experimentation. It's not enough to predict Einsteins Equations, the model itself needs to agree with what we already understand of such an aether...

The agreement with observation is sufficiently fine, as for GR (with $\Lambda CDM$ cosmology) as well as for the SM. About the ether we know nothing. There is the Lorentz ether, which is SR with a preferred frame, and that's all. Everything else is either old ether on the dustbin of history or not even a theory. Except Jacobson's Einstein aether, which is conceptually very different (it has no background)

Einstein made it quite clear: “the curvature of light rays occurs only in spaces where the speed of light is spatially variable”. What you think of as mainstream GR is not in accord with Einstein.

Yes, the common sense speed is the coordinate speed of light. Only Einstein didn't call it the coordinate speed of light. He called it the speed of light. It varies in the room you're in. If it didn't, light wouldn't curve and your pencil wouldn't fall down.

To repeat myself: This is not an issue. First, there is no such difference, second, it would not matter if there would be one. Names are nothing but conventions. If modern textbooks name "speed of light" the constant c and what Einstein has named "speed of light" is named "coordinate speed of light" I do not care about this, but accept the modern language.

As for the fermions and gauge fields of the Standard Model, they're all wrong. You cannot have a TOE with 24 fundamental fields.

The mainstream is wrong. That's why the mainstream doesn't have a TOE. Forget the mainstream.

I follow a different strategy. I accept all that the mainstream claims about observations as well as the mathematics of the mainstream theories but doubt the interpretations, the metaphysics.

You need to consider in detail how gravity works. Einstein explained most of it in his 1920 Leyden Address

It isn't a triviality, it's an idiocy. See Comments on “Note on varying speed of light theories” where John Moffat and João Magueijo talk about the tautology. People use the local motion of light to define the second and the metre, and they they use the second and the metre to measure the local motion of light. It doesn't matter how fast the light is moving, they will always end up saying the speed of light is 299,792,458 m/s. Because of this they can't tell you how gravity works, so they tell you nonsense like "light follows the curvature of spacetime". They can't tell you how electromagnetism works either.  Or how the nuclear force works.

The Leyden lecture was nothing but a popular lecture, and of course I know it. I also know GR on the level of mathematics in a quite good way.  The notes are acceptable, but irrelevant, because they are about different theories.

### #50 Dubbelosix

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Posted 08 November 2019 - 06:45 AM

Why are you so happy about this model when it cannot agree with the deduction, that an aether has no particle associated with it? Your model is at odds with everything I know about the aether.

### #51 Dubbelosix

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Posted 08 November 2019 - 06:47 AM

You assigned a velocity for instance, no where have you addressed the stationary aether problem, which has been addressed fully by GR but which lacks dynamic purpose in your theory because surely such a motion cannot be detected.