Resurrection of the Lorentzian Aether

[JMessenger]

I am not certain that . I may have missed where you gave expressions for . Can you point me to where this given, or provide it in the context of a point mass a point mass?

First, in order to understand how the mainstream concept for how the "stress-energy tensor of matter" came to be defined/equated to the Einstein tensor you need an in depth understanding of the logic of how fluid density, energy density and mass density are equated in the models. Although it is hinted at in the aether debates, I haven't found this story spelled out in any historical texts, let alone modern day GR texts.
I have some speculations of how this was developed.

Easiest answer is that represents a point in a perfect fluid where all points in the immediate neighborhood have the same values of and . It does not represent matter, mass or energy and the coordinate system that it represents, if there were any matter or energy present (which there isn't) is Euclidean. The perfect fluid is empty space.
If you want to model mass, matter or energy in this perfect fluid, you need a change in the values of and at a point. This is where the stress-energy tensor of a perfect fluid comes in. What it tells you is the deviation of and from . For mainstream GR physics, this deviation (or increase) in the perfect fluid is from zero or nothing (empty vacuum), but we equate to energy density and equivalently density of both inertial and gravitational mass. If one now takes the inertial mass density located within a certain volume and calculates the effects it has across empty vacuum the same as if it were a perfect fluid, it works. Since we only need the deviation of density and pressures to account for accurate GR answers and Newtonian gravity, there was no need to keep the perfect fluid itself as long as you don't have a problem with action at a distance. The questions of what "mass" and "energy" mean fundamentally in GR is not something I have seen answered.

I am convinced that there exists a mathematically equivalent representation of GR having the density convention you are describing, and that this theory is what you intend to represent. caveman seems more qualified than I in pointing out nuances this change in convention may encounter.

I have long held the ATM idea that all of electromagnetism is flawed, because charge is defined with the wrong sign. I am pretty sure that almost everyone has considered this, since the electron's charge became standard on the quantum level anyways.

Science has a long tradition of maintaining priority of conventions until there is a compelling reason to change, occasionally even if this means adding cumbersome terms. What makes your convention more compelling than the standard density convention with a cosmological constant?

Excellent question. I don't really consider it a convention, but more of a conversion factor and the beginnings of a physical model to enable a crossover in equating energy due to gravitational effects with those of the quantum world.

Suppose I had a region of space-time filled with a uniform fluid of constant mass and charge density and a constant electric field. This will produce an electric force on the fluid. Will the fluid accelerate according to or ?

First you would need to decide either between space-time or the perfect fluid as they both represent the same thing, GR for space-time and perfect fluid for this theory. The other thing concerns the misconception that this perfect fluid is any different than an emag field. The point of this theory is to provide one perfect fluid theory that can account for all fields. A tall order perhaps but with baby steps maybe we can get there. Thus I cannot answer your question yet.

If it is the former, then the wouldn't the equivalence principle suggest that the mainstream convention is superior to your density convention?

Not sure which equivalence principle you mean again. Mainstream Newtonian physics will always have a superior place simply due to this is the way we perceive the world we live in, and for many practical aspects of our daily lives it serves well. Using this to develop a better quantum theory has many many practical applications in integrated circuits, i.e. overcoming crystal defects, heat transfer improvements...etc.

[JMessenger]

If it is the former, then the wouldn't the equivalence principle suggest that the mainstream convention is superior to your density convention?

Thinking about your question some more, I may get the gist of what you mean about the equivalence of and . I am not saying I know how to derive the ~20 parameters of the standard model, but if there were a way to approach the problem differently, I would think any difficulty of a convention change to attempt this would be insignificant.

[Reality Check]

quintessence? Really? Ever heard of Bernard Schutz? Know why he doesn't like quintessence? I am paraphrasing but it was something to the effect of "even some cosmologists have taken to a theory called quintessence, which is really depressing because this is nothing more than another name for the Aether."

Citing this quote is silly because all he is doing is pointing out that the ancient Greeks has a concept of 4 elements + aether (which they called quintessence). He just does not like the name used.
See his book: Gravity from the Ground Up

But if you want to restrict the candidates for dark energy to just a non-zero cosmological constant then go ahead!

[JMessenger]

Citing this quote is silly because all he is doing is pointing out that the ancient Greeks has a concept of 4 elements + aether (which they called quintessence). He just does not like the name used.
See his book: Gravity from the Ground Up

Actually, that is where I got the quote from...one of the margins. Perhaps I misread his intent, and it was in regards to the name only. I stopped when I wrote him about a practice question within the book. He stated that if a box has a gas inside of it, and the box is accelerated so as to experience length contractions, the pressure in the box will go up due to the decreased volume. I simply did not understand the logic behind this.

Or read his description of Fundamental physics with LISA and how it can

Can what? Have a link?

But if you want to restrict the candidates for dark energy to just a non-zero cosmological constant then go ahead!

Okeydoke. Thanks.

[Reality Check]

You are now claiming that is not the stress energy tensor for a perfect fluid with and as the diagonal components?

No one who knows about GR would claim that, JMessenger.
is the stress energy tensor and is not "for a perect fluid::

The stress–energy tensor (sometimes stress–energy–momentum tensor) is a tensor quantity in physics that describes the density and flux of energy and momentum in spacetime, generalizing the stress tensor of Newtonian physics. It is an attribute of matter, radiation, and non-gravitational force fields. The stress-energy tensor is the source of the gravitational field in the Einstein field equations of general relativity, just as mass density is the source of such a field in Newtonian gravity.

Most of the solutions of the EFE start with assuming that is a perfect fluid.

Some use imperfect fluids as the stress–energy tensor:
Viscous fluid collapse, A. A. Coley, B. O. J. Tupper. Phys. Rev. D 29, 2701–2704 (1984)

The problem of seeking solutions of Einstein's field equations that represent the collapse of realistic matter distributions is discussed. A specialized approach to this problem is taken in which the fact that a given energy-momentum tensor may formally represent different types of matter distribution is exploited. A solution is presented in which an "interior" solution consisting of a collapsing viscous fluid (i.e., a solution of the Einstein field equations for an imperfect fluid source) is matched continuously across its boundary to a Schwarzschild "exterior." In this solution the geometrical part corresponding to the interior solution is formally identical to that of a closed (i.e., k=+1) Friedmann-Robertson-Walker dust model.

[JMessenger]

No one who knows about GR would claim that, JMessenger.
is the stress energy tensor and is not "for a perect fluid::

Most of the solutions of the EFE start with assuming that is a perfect fluid.

Some use imperfect fluids as the stress–energy tensor:
Viscous fluid collapse, A. A. Coley, B. O. J. Tupper. Phys. Rev. D 29, 2701–2704 (1984)

Yes, there are many fluid theories. However, where do you think the entire concept of the stress-energy tensor originated? was adopted from hydrodynamics, not the other way around, unless you know otherwise.

[JMessenger]

No one who knows about GR would claim that, JMessenger.

I would like to point out something interesting in your quote:

The stress-energy tensor is the source of the gravitational field in the Einstein field equations of general relativity, just as mass density is the source of such a field in Newtonian gravity.

It is because of the definition in this sentence (and only because of it) that dark matter must exist as some highly specialized new type of matter (meaning the standard model does not predict these types of particles). is the only source for curvature with GR, and all the effects of Dark Matter are inferred from the gravitational effects. It doesn't make sense (as far as I have ever read) for space-time to curve without the corresponding mass present.

[tusenfem]

Time's up, thread closed.