Resurrection of the Lorentzian Aether

[profloater]

Interesting. I would have to dig up a citation for you, but in this theory when I state "perfect fluid" it doesn't necessarily mean it actually flows like water. It could also be considered a perfectly elastic medium, something akin to what Faraday had in mind.

Well fluids flow within boundaries and whilst perfect elasticity must be also assumed, especially if the aether contributes inertia as a fundamental property. Movement within a perfectly elastic medium has no limits or losses associated with strain. However the aether would have to be also an extracordinary fluid as to be only defined by itself and its properties, so I guess the term aether can not be generalised with other states of matter or energy.

The spinning points in space time (PISTs (?)) would be capable of carrying the alternating ES EM waves including polarisation. I apologise that I cannot resist imagining the aether as a physical model before considering its mathematical analysis, it probably limits my understanding. I can imagine stable complex spinning knots of this stuff looking like particles and having natural frequencies and energy bands too like "orbiting" electrons and so on.

[Tensor]

This is what I think of when I state Mach's principle, from The Collected Papers of Albert Einstein Vol. 6 (emphasis mine)

Well, that's the point of the paper. Everyone has their own interpretation of exactly what "Mach's Principle" is exactly. So, it's rather useless to try to invoke it, as your interpretation is more than likely not anywhere near what anyone else's is.

[JMessenger]

Well fluids flow within boundaries and whilst perfect elasticity must be also assumed, especially if the aether contributes inertia as a fundamental property. Movement within a perfectly elastic medium has no limits or losses associated with strain. However the aether would have to be also an extracordinary fluid as to be only defined by itself and its properties, so I guess the term aether can not be generalised with other states of matter or energy.

The spinning points in space time (PISTs (?)) would be capable of carrying the alternating ES EM waves including polarisation. I apologise that I cannot resist imagining the aether as a physical model before considering its mathematical analysis, it probably limits my understanding. I can imagine stable complex spinning knots of this stuff looking like particles and having natural frequencies and energy bands too like "orbiting" electrons and so on.

PISTS... I also resort to physical models at times, but try to keep an open mind that some physical models are going to be difficult to understand in four dimensions
http://en.wikipedia.org/wiki/Four-dimensional_space
What would your spinning knots look like in 4 dimensions?

[JMessenger]

Well, that's the point of the paper. Everyone has their own interpretation of exactly what "Mach's Principle" is exactly. So, it's rather useless to try to invoke it, as your interpretation is more than likely not anywhere near what anyone else's is.

While the point of the paper is to compare different views on Mach's principle, I doubt the authors would have agreed that it is pointless. Whether it is pointless for me to explain my version, it does not matter in the slightest whether it is anywhere close to other's, only that it is related to what I am espousing in the thread.

[JMessenger]

Tensor,
While Mach's principle is all well and good (and easy to argue with), I noticed that you haven't yet proffered a statement on whether Einstein's curvature tensor can be negative.

[profloater]

PISTS... I also resort to physical models at times, but try to keep an open mind that some physical models are going to be difficult to understand in four dimensions
http://en.wikipedia.org/wiki/Four-dimensional_space
What would your spinning knots look like in 4 dimensions?

Well I did not want to expand too much since this is your thread and I am using my questions to understand more but my PISTs are individually points on a Minkowski diagram since obviously the Lorentz transformation is required and individually the points are moving in space and time and since I imagine the spin as related to c the "view" of each PIST is a rotating light cone. The relation of a spinning (and writhing) knot to its neighbours is also a complex ever changing light cone giving directional properties since unless trapped inside atoms, these things are also moving around at high speed. Like complex molecules, these knots will have preferred attachment locations which are changing in space and time. Charge is my problem.

[JMessenger]

Well I did not want to expand too much since this is your thread and I am using my questions to understand more but my PISTs are individually points on a Minkowski diagram since obviously the Lorentz transformation is required and individually the points are moving in space and time and since I imagine the spin as related to c the "view" of each PIST is a rotating light cone. The relation of a spinning (and writhing) knot to its neighbours is also a complex ever changing light cone giving directional properties since unless trapped inside atoms, these things are also moving around at high speed. Like complex molecules, these knots will have preferred attachment locations which are changing in space and time. Charge is my problem.

Interesting. But you are right, we should keep this stuff to PM from now on.

[JMessenger]

If you do a search for "aether" on Bautforum, you will run into quite a few other threads. One of these has to do with why does the aether seem to have such an almost fanatical hold on some adherents. This is a good question, and there were some good responses pro and con.

In addition in post #11, John M. stated

Then, of course, you can demonstrate and have observations to support that gravitational binding effectively prevents expansion out to the size of galaxy clusters? (You have to take all of the mainstream into account.)

Another post (of which I can't find the source now) stated (paraphrasing) that the person never saw an aether theory that didn't introduce more problems than it solved.

I very much agree with both, so why the confidence in this theory? Because I am not arguing that I would change any of the magnitudes put into the equations which predicts these effects (which I am not aware require ). The critical thinking part deals with the papers that not only include this prediction of gravitational binding, but also already place back into them the cosmological constant in order to account for a linear repulsion at large radii. The papers are unwittingly making my argument for me, in that while the data certainly suggests that the extra term is needed, it does not seem to be mathematically sensible to do so except by subtracting the curvature tensor from the cosmological constant and according the model of a perfect fluid. These aren't my equations nor did I come up with the perfect fluid tensor. I am not the one who stated that the cosmological constant problem was the "worst prediction in physics". Albert Einstein died over a decade before anyone suggested anything about the quantum vacuum levels. No one predicted an accelerating expansion.

While I have always been a skeptic about non mainstream claims, I now just cannot bring myself to believe that we can magically attribute a repulsive energy to a constant of integration. Taking in all the evidence, and every issue, from the beginning of the study of gravity to where we are today, it seems overwhelmingly one sided. My skepticism has flipped sides.

[Reality Check]

I noticed that you haven't yet proffered a statement on whether Einstein's curvature tensor can be negative.

FYI, JMessenger, is a rank 2 tensor and thus by definition can never be negative or positive since that is the property of a number.
It is also not called a "curvature" tensor .
If you are thinking of spacetime curvature then that can be negative.

[JMessenger]

It is also not called a "curvature" tensor .

Ouch! Correct you are sir, I had somehow gotten into the habit of that. Gravitation by MWT refer to it simply as the Einstein tensor.

FYI, JMessenger, is a rank 2 tensor and thus by definition can never be negative or positive since that is the property of a number.

If you are thinking of spacetime curvature then that can be negative.

Perhaps it would be more correct to state there needs to be a difference taken between the cosmological constant and the Einstein tensor?

[caveman1917]

Perhaps it would be more correct to state there needs to be a difference taken between the cosmological constant and the Einstein tensor?

What does that statement mean? The Einstein tensor describes the spacetime curvature while the cosmological constant term (though it can be moved to either side of the EFE) seems more in place as a curvature source with the stress-energy tensor. What do you mean by "a difference needs to be taken"?

[caveman1917]

I now just cannot bring myself to believe that we can magically attribute a repulsive energy to a constant of integration.

What constant of integration?
How are we "magically attributing a repulsive energy to a constant of integration"?

[JMessenger]

What constant of integration?
How are we "magically attributing a repulsive energy to a constant of integration"?

A bit late to the party. Dark Energy, cosmological constant magnitude problem, etc etc.
Did you read the thread?

[JMessenger]

Perhaps it would be more correct to state there needs to be a difference taken between the cosmological constant and the Einstein tensor?

Yes, that would seem a more correct statement. We are taking the difference of the components of the tensors instead of the sum of the components.

[caveman1917]

Did you read the thread?

Well, considering that the first equation in your OP, under the header "Einstein Field Equations" isn't the Einstein field equations, and the second equation, under "fundamental theorem of calculus", isn't the fundamental theorem of calculus, i suppose you could forgive me for skipping a bit ahead to find out what it is exactly that you are talking about. I did skim through it though and didn't find any direct explanation of my question.

If you have already answered the question i asked, could you please refer me to the post in which you did?

Dark Energy, cosmological constant magnitude problem, etc etc.

What cosmological constant magnitude problem?

[JMessenger]

What cosmological constant magnitude problem?

From General Relativity: An Introduction for Physcists by Hobson et al.

How can we calculate the energy density of the vacuum? This is one of the
major unsolved problems in physics. The simplest calculation involves summing
the quantum mechanical zero-point energies of all the fields known in Nature.
This gives an answer about 120 orders of magnitude higher than the upper limits
on set by cosmological observations. This is probably the worst theoretical
prediction in the history of physics! Nobody knows how to make sense of this
result. Some physical mechanism must exist that makes the cosmological constant
very small.

[JMessenger]

What constant of integration?

The cosmological constant is a constant of integration. See for example http://arxiv.org/abs/gr-qc/0411093

[JMessenger]

What constant of integration?
How are we "magically attributing a repulsive energy to a constant of integration"?

See the DETF paper: http://arxiv.org/abs/astroph/0609591

[JMessenger]

How are we "magically attributing a repulsive energy to a constant of integration"?

Here is a paper giving the reason for why a cosmological constant is a leading candidate for dark energy:http://arxiv.org/pdf/1201.3608v1.pdf .

Our main finding is that the expansion history is consistent with that predicted by a flat potential. The data do not require extra parameters beyond a constant term in the Lagrangian to explain the current accelerated expansion. Further, we have shown that the potential deviations from a constant are constrained to be below 6%. Observational constraints allow the parameters describing the Lagrangian to vary only within certain limits; the relative range of the allowed variation of the parameters confirms a well defined hierarchy where the linear and quadratic terms dominate over higher-order terms, justifying the basic assumption of the effective theory approach. Observational constraints also give some indications of the relevant energy scales involved. Because a direct determination of a Lagrangian allows us to determine the underlying symmetries in the theory, our results
can be used to shed light on this as well.

Thus, according to the theory in this thread, the problem with the Lagrangians on Wikipedia's page http://en.wikipedia.org/wiki/Lagrang..._test_particle is that the "m" in the equations is directly derived from the change in density of a perfect fluid within a volume from . Instead of ad-hoc throwing the cosmological constant into the equation to account for dark energy, it should come naturally from the fundamental theorem of calculus so that (I am removing the other terms that are with the cc in order to make it more illustrative on what the paper is stating) .

From

The resulting constraints on the parameters of the Lagrangian are shown in Fig. 1, where we show the scatter plot of the models sampled by our MCMC. The results do not display any sign of the existence of discrete symmetries, as for instance , that would signal the spontaneously breaking of a gauge symmetry [21].

would seem to fit this definition.

[JMessenger]

What does that statement mean? The Einstein tensor describes the spacetime curvature while the cosmological constant term (though it can be moved to either side of the EFE) seems more in place as a curvature source with the stress-energy tensor. What do you mean by "a difference needs to be taken"?

So my main question, in order to falsify this theory, a proof should show that I cannot write:

[caveman1917]

From General Relativity: An Introduction for Physcists by Hobson et al.

You mean the problem that QFT cannot predict the observed vacuum energy density? That is indeed a problem, so i presume you have a theory that, whilst reproducing the results of QFT, does predict a reasonable value?

[caveman1917]

The cosmological constant is a constant of integration. See for example http://arxiv.org/abs/gr-qc/0411093

Which solves exactly nothing. Using a unimodular approach will either break general covariance, or you could reproduce the full EFE thinking of the cosmological constant as a constant of integration but that doesn't solve a thing since the trace of the stress-energy still contributes to it.

[JMessenger]

You mean the problem that QFT cannot predict the observed vacuum energy density? That is indeed a problem, so i presume you have a theory that, whilst reproducing the results of QFT, does predict a reasonable value?

A mechanism for the observed low value, yes. Prediction for the exact energy density, no (simply for lack of effort). At the moment only the prediction for when gravity becomes repulsive. I do not have a QFT replacement at this time. I would need to first find ensure the proof of that formula.

[JMessenger]

Which solves exactly nothing. Using a unimodular approach will either break general covariance, or you could reproduce the full EFE thinking of the cosmological constant as a constant of integration but that doesn't solve a thing since the trace of the stress-energy still contributes to it.

I believe that is what the paper is stating also, although I would have to reread it.

[JMessenger]

Which solves exactly nothing. Using a unimodular approach will either break general covariance, or you could reproduce the full EFE thinking of the cosmological constant as a constant of integration but that doesn't solve a thing since the trace of the stress-energy still contributes to it.

Hmm..you might be helping me sort through this. For my theory when there is no matter or energy present so so there is no trace, correct?

[caveman1917]

Here is a paper giving the reason for why a cosmological constant is a leading candidate for dark energy:http://arxiv.org/pdf/1201.3608v1.pdf .

There's nothing "magical" about it, incorporating the term in the stress-energy naturally gives it the interpetation of the vacuum energy.

Thus, according to the theory in this thread, the problem with the Lagrangians on Wikipedia's page http://en.wikipedia.org/wiki/Lagrang..._test_particle is that the "m" in the equations is directly derived from the change in density of a perfect fluid within a volume from .

What would the correct Lagrangian then be?

Instead of ad-hoc throwing the cosmological constant into the equation to account for dark energy, it should come naturally from the fundamental theorem of calculus so that (I am removing the other terms that are with the cc in order to make it more illustrative on what the paper is stating) .

Then please show how it comes "naturally from the fundamental theorem of calculus".
Also, would you not be getting negative mass that way?

[JMessenger]

There's nothing "magical" about it, incorporating the term in the stress-energy naturally gives it the interpetation of the vacuum energy.

What would the correct Lagrangian then be?

Then please show how it comes "naturally from the fundamental theorem of calculus".
Also, would you not be getting negative mass that way?

Getting a bit head of myself here on this explanation. Basically for the stress-energy tensor of a perfect fluid I am using density reductions instead of increases. So the is actually the residuals. It might be more clear on any mistake I am making in my derivation (old) see page 5: http://vixra.org/pdf/1203.0025v1.pdf

[caveman1917]

So my main question, in order to falsify this theory, a proof should show that I cannot write:

is defined as so i'm sure you can see the problem there.

[JMessenger]

is defined as so i'm sure you can see the problem there.

That would seem to contradict what Einstein stated in his footnote:

It must be pointed out that there is a minimum of arbitrariness in the choice of these equations. For besides  there is no tensor of second rank which is formed from the  and its derivatives, contains no derivations higher than second, and is linear in these derivatives.*
These equations, which proceed, by the method of pure mathematics, from the requirement of the general theory of relativity, give us, in combination with the equations of motion ([equation number removed]), to a first approximation Newton's law of attraction, and to a second approximation the explanation of the motion of the perihelion of the planet Mercury discovered by Leverrier (as it remains after corrections for perturbation have been made). These facts must, in my opinion, be taken as a convincing proof of the correctness of the theory."

The footnote being:

Properly speaking, this can be affirmed only of the tensor ; where  is a constant. If, however, we set this tensor = 0, we come back again to the equation  = 0."

[caveman1917]

That would seem to contradict what Einstein stated in his footnote:

I don't see how that contradicts the definition of as