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

[Schmelzer]

Essentially, there is no modern understanding of ether theory.  There is the classical Lorentz ether, where the metric is only the Minkowski metric.  Here the [math]\eta^{0i}=0[/math] so that the velocity is zero and the density [math]\rho=g^{00}\sqrt{-g}[/math] is constant.  And there is the Leyden lecture, which is nothing than a popular lecture, which has been essentially ignored by the mainstream which made "ether" a bad word.  All this essentially a century old. There are ether freaks who don't even understand SR, unpublishable for good reasons. There is Jacobson's "Einstein ether" which is based on completely different concepts. What else?

 

Just a small question how are the dimensions being constructed on the right hand side here;

v_i(x, t) = g_[oi](x, t) / g_[oo](x, t)

I know the definition 9f the metric terms, so this is just a general question about the dimensions alone. Thanks in advance.

Usually I follow the c=1 convention, so that a velocity becomes a dimensionless number (simply v/c).  If one would have to handle it with c, then one would have to include the appropriate factors of c to everything.  In order to avoid giving the different components of [math]g^{\mu\nu}[/math] different dimensions, the appropriate choice would be to use the [math]x^0 = ct[/math]  so that all the coordinates [math]x^\mu[/math] have the same dimension of length. Then [math]v_i(x, t)/c = g^{0i}(x, t) / g^{oo}(x, t)[/math] would be the correct dimensionless  expression.  

 

BTW, the components are the ones with upper indices, the coefficients used in the wave equation [math]\square = \partial_\mu g^{\mu\nu}\sqrt{-g} \partial_\nu[/math] and the harmonic condition [math]\square x^\nu = \partial_\mu g^{\mu\nu}\sqrt{-g} = 0[/math].  These have to be identified with the continuity and Euler equations of condensed matter theory, applied to the ether:

[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]

in such a way as to get the appropriate factors of c into it. 

Edited November 12, 2019 by Schmelzer

[Dubbelosix]

Essentially, there is no modern understanding of ether theory.  There is the classical Lorentz ether, where the metric is only the Minkowski metric.  Here the [math]\eta^{0i}=0[/math] so that the velocity is zero and the density [math]\rho=g^{00}\sqrt{-g}[/math] is constant.  And there is the Leyden lecture, which is nothing than a popular lecture, which has been essentially ignored by the mainstream which made "ether" a bad word.  All this essentially a century old. There are ether freaks who don't even understand SR, unpublishable for good reasons. There is Jacobson's "Einstein ether" which is based on completely different concepts. What else?

 

 

Usually I follow the c=1 convention, so that a velocity becomes a dimensionless number (simply v/c).  If one would have to handle it with c, then one would have to include the appropriate factors of c to everything.  In order to avoid giving the different components of [math]g^{\mu\nu}[/math] different dimensions, the appropriate choice would be to use the [math]x^0 = ct[/math]  so that all the coordinates [math]x^\mu[/math] have the same dimension of length. Then [math]v_i(x, t)/c = g^{0i}(x, t) / g^{oo}(x, t)[/math] would be the correct dimensionless  expression.  

 

 

OK, this looks good.

[Dubbelosix]

Just a bit of advice then for now, if you do come to use natural units, try and explain this in your paper as it can make the understanding a bit clearer. Authors do tend to do this, from time to time to help the reader keep track more efficiently.

[Dubbelosix]

I would like to extend the model. I'll call it the Schmelzer model. You won't like it, but I will give credit to aspects of the aether you have created from the basis of your argument. Any deviations I make from your model, will be explained. Consider this, a compliment.

[Dubbelosix]

Probably take a while though.

[Dubbelosix]

A new question, since you clarified something a few posts back, are you aware that the choices of gauge depends on a gravitational aether with an assigned Doppler shift term;

 

v/c = g^(i0) /g^(00) = (1 - 1/γ)

 

In which γ goes under standard Lorentz convention.

 

And obviously

 

(v/c)^2 = (g^(i0) /g^(00)) ^2 = (1 - 1/γ^2)

[Schmelzer]

A new question, since you clarified something a few posts back, are you aware that the choices of gauge depends on a gravitational aether with an assigned Doppler shift term;

 

v/c = g^(i0) /g^(00) = (1 - 1/γ)

 

In which γ goes under standard Lorentz convention.

 

And obviously

 

(v/c)^2 = (g^(i0) /g^(00)) ^2 = (1 - 1/γ^2)

 

You combine here terms from different theories and different contexts.  

 

The v in my formula is the velocity of the ether, in a GR context.  In the SR context, it is zero.  The factor [math]\gamma[/math] is relevant for clocks moving against the ether, and in this form makes sense only in SR. So, it makes no sense to combine them into a single formula.  

[Dubbelosix]

It still doesn't make sense to me why relativity gives up a velocity condition for the aether in GR and a static case for SR. Nevertheless, whenever you use the ratio v/c it is almost always associated to the Doppler shift. And it would not always mean it applies for clocks in the aether, the dynamic interpretation could be more deeper than that since gravitational redshift is believed to arise from a variation in the metric.

Edited November 22, 2019 by Dubbelosix

[Dubbelosix]

In fact the transformation laws may even have something to do with the dynamic properties of stretching space.

[Schmelzer]

In fact the transformation laws may even have something to do with the dynamic properties of stretching space.

In my ether interpretation, there is no stretching of space at all. The space is a classical Euclidean absolute space as used by Newton and Kant.  Everything what is dynamical is the ether.  So all the components of the gravitational field describe ether properties (density, velocity, stress tensor) instead of properties of some "spacetime".  The velocity of the ether is a velocity field, defined everywhere, [math] v^i(x,t)[/math].

 

It still doesn't make sense to me why relativity gives up a velocity condition for the aether in GR and a static case for SR. Nevertheless, whenever you use the ratio v/c it is almost always associated to the Doppler shift. And it would not always mean it applies for clocks in the aether, the dynamic interpretation could be more deeper than that since gravitational redshift is believed to arise from a variation in the metric.

The metric is completely defined by density, velocity, and stress tensor of the ether.  Of course, these are functions which vary.  And this leads, indeed, to redshift.  

 

"Proper time", as defined by the GR formula [math]c\tau = \int \sqrt{g_{\mu\nu}(x,t) \frac{dx^\mu(t)}{dt}\frac{dx^\nu(t)}{dt}} dt [/math], is always clock time of a clock following the trajectory [math]x^\mu(t)[/math] with velocity [math]v^i(t)  = \frac{dx^i}{dt}, c = \frac{dx^0}{dt}[/math].  The velocity is defined here only on a particular trajectory [math]x^\mu(t)[/math].   So, these are completely different objects. 

 

Relativity as understood by the mainstream does not have any notion of the ether, thus, cannot give up anything about any ether and its properties.

 

So, all you could mean here is a single popular lecture of Einstein in Leyden.  Where Einstein, confused  by positivistc "unobservables do not exist" ideology, made the error of claiming "impossible" where "not yet found" would have been correct.

[Dubbelosix]

I'm still working on the extension of the model, I don't think you'll like it much. But a finished theory does not mean the mind must become stale.

[Dubbelosix]

I did a write up but posted it in a new thread here, I did not want to hijack your thread.

[TonyYuan2020]

The speed of light we measure on the earth by traditional methods is always constant. Just like a car in the water, the speed of the car is calculated by the distance / round-trip time between point A and point B, which will never change.

 

 

 

We cannot conclude that the speed of light is constant in any inertial reference frame. Like a car in water, its speed relative to the water surface is different from the speed relative to the ground.

 

 

 

Without any hypothesis, we can explain why the interference fringes can not be observed in the Morey experiment by using the conventional physical theory.

 

 

 

http://www.scienceforums.com/topic/36469-why-morley-experiment-could-not-observe-the-movement-of-interference-fringe/

Edited February 22, 2020 by TonyYuan2020

[Dubbelosix]

But it's not a constant, even Einstein demonstrated this from general relativity, it is only a true constant as we understand it, in a vacuum. What Einstein didn't seem to accept was that if light was spatially variable, it is also temporally variable which is interesting he could not accept that part, because it meant even his theory was incomplete and believing it is temporally variable also meant it would cause contradictions by the principles he set in place for special relativity.

[Dubbelosix]

The temporal variation of light does naturally lead to a tired light theory, something that has attracted the attention of scientists, but because the mainstream is set in its own ways, the theory has often be classed as a nonsense.

[Dubbelosix]

What is interesting though is that some believe it will lead to a decay formalism in curved space, but this is only an assumption, for if there is no simpler particle to decay into, then it will not in principle.

[Dubbelosix]

The real question then, is whether light truly loses energy, it may just require a new updated model so that there is no true loss of energy, but only appears that way.