A Does Gravity Criticism in Maxwell's Equations Apply to All Gravity-Medium Analogies?

[Jerome Wang]

I read a paper published in General Relativity and Gravitation:

On gravity as a medium property in Maxwell equations

The argument of this paper is as follows in a nutshell:

Modifying the homogeneous part by gravity is inevitable to any observer, and the result cannot be interpreted as the medium property.

For an observer, the effect of gravity can be encoded in the effective polarizations and magnetizations appearing in both the homogeneous and inhomogeneous parts, thus as the medium properties of strange sorts demanding beyond the conventional constitutive relations of the material medium.

The P and M present in the homogeneous Maxwell’s equations cannot be interpreted as a medium property.

There are currently many analog models and theories of gravity, including some based on medium analogy.

Analog models: Analogue Gravity
Condensed matter: Fermionic Quartet and Vestigial Gravity, Type-II Weyl Semimetal versus Gravastar, A Generalization of the Lorentz Ether to Gravity with General-Relativistic Limit, The superfluid as a source of all interactions
Elastic material: Mechanistic Model of Gravitation, Mechanical Model of Maxwell’s Equations and of Lorentz Transformations, Experimental tests of rotation sensitivity in Cosserat elasticity and in gravitation, Mechanical conversion of the gravitational Einstein’s constant κ
Crystallographic defect: Non-linear plane gravitational waves as space-time defects
Le Sage: Gravity from refraction of CMB photons using the optical-mechanical analogy in general relativity
Archimedes’ thrust: Gravity as Archimedes’ Thrust and a Bifurcation in that Theory
etc.

This brings up a question:
Does the criticism of gravity as a medium property in Maxwell equations apply to all gravity-medium analogy?
This issue concerns the feasibility of all gravitational theories based on medium analogy and the validity of all medium analogy models of gravity.

 

[anuttarasammyak]

EM and GR have no problems between. If medium analogy has a problem, that would mean that the analogy is inappropriate. That would apply not only EM but other subjects.

 

[Jerome Wang]

EM and GR have no problems between. If medium analogy has a problem, that would mean that the analogy is inappropriate. That would apply not only EM but other subjects.

There is certainly no problem with EM and GR, but whether the criticism in On gravity as a medium property in Maxwell equations is applicable to all medium analogies is another problem.

All of the above papers are from journals covered by Clarivate MJL, and any mathematical or physical flaws will be difficult to detect, which is why I am asking this question here.

On gravity as a medium property in Maxwell equations is from General Relativity and Gravitation (Clarivate MJL: 0001-7701 / 1572-9532).
Analogue Gravity is from Living Reviews in Relativity (Clarivate MJL: 1433-8351).
Fermionic Quartet and Vestigial Gravity is from JETP Letters (Clarivate MJL: 0021-3640 / 1090-6487).
Type-II Weyl Semimetal versus Gravastar is from JETP Letters (Clarivate MJL: 0021-3640 / 1090-6487).
A Generalization of the Lorentz Ether to Gravity with General-Relativistic Limit is from Advances in Applied Clifford Algebras (Clarivate MJL: 0188-7009 / 1661-4909).
The superfluid as a source of all interactions is from Foundations of Physics (Clarivate MJL: 0015-9018 / 1572-9516).
Mechanistic Model of Gravitation is from Lobachevskii Journal of Mathematics (Clarivate MJL: 1995-0802 / 1818-9962).
Mechanical Model of Maxwell’s Equations and of Lorentz Transformations is from Foundations of Physics (Clarivate MJL: 0015-9018 / 1572-9516).
Experimental tests of rotation sensitivity in Cosserat elasticity and in gravitation is from Zeitschrift für angewandte Mathematik und Physik (Clarivate MJL: 0044-2275 / 1420-9039).
Mechanical conversion of the gravitational Einstein’s constant κ is from Pramana (Clarivate MJL: 0304-4289 / 0973-7111).
Non-linear plane gravitational waves as space-time defects is from The European Physical Journal C (Clarivate MJL: 1434-6044 / 1434-6052).
Gravity from refraction of CMB photons using the optical-mechanical analogy in general relativity is from Astrophysics and Space Science (Clarivate MJL: 0004-640X / 1572-946X).
Gravity as Archimedes’ Thrust and a Bifurcation in that Theory is from Foundations of Physics (Clarivate MJL: 0015-9018 / 1572-9516).

 

[renormalize]

On gravity as a medium property in Maxwell equations

Per the abstract:
"The effect of gravity in Maxwell’s equations is often treated as a medium property."
The authors then illustrate why this method of using an exotic dielectric medium has shortcomings that are avoided simply by using standard GR:
"For optical properties one should directly handle Maxwell’s equations in curved spacetime."
So yes, the dielectric-medium approach to gravity is flawed.

There are currently many analog models and theories of gravity, including some based on medium analogy.
Analog models: Analogue Gravity
...
This brings up a question:
Does the criticism of gravity as a medium property in Maxwell equations apply to all gravity-medium analogy?
This issue concerns the feasibility of all gravitational theories based on medium analogy and the validity of all medium analogy models of gravity.

In contrast, from the section 7.10 of Analogue Gravity:
"More generally, the phrase “emergent gravity” is now used to describe the whole class of theories in which the spacetime metric arises as a low-energy approximation, and in which the microphysical degrees of freedom might be radically different. Analogue models, and in particular analogue models based on fluid mechanics or the fluid dynamic approximation to BECs, are specific examples of “emergent physics” in which the microphysics is well understood. As such, they are useful for providing hints as to how such a procedure might work in a more fundamental theory of quantum gravity." (bolding added)
So the answer to your question is no, because the first paper involves a dielectric medium and is thus inapplicable to analog gravity that emerges from media like fluids or Bose-Einstein condensates.

 

[Yuras]

The authors then illustrate why this method of using an exotic dielectric medium has shortcomings that are avoided simply by using standard GR

Sorry if I'm misreading your comment, but it sounds like material analogy is a separate theory, not related to GR. Per my understanding it's not the case. Instead it's merely a small part of GR, and the article seem to just explore the limits of applicability of the approach. E.g. see "The classical field theory" by Landau (I don't have access to English version of this book, but in my copy it's an exercise to paragraph 90.) There e.g. the following Maxwell equation in an external gravitational field is derived:
$$\nabla\times\vec E = - \frac{1}{c \sqrt\gamma}\frac{\partial}{\partial t}(\sqrt\gamma\vec B)$$
Here $\gamma$ seems to be a determinant of the 3-dimentional metric tensor. For static gravitational field $\sqrt\gamma$ cancels, which allows to draw a formal analogy to Maxwell equations in a linear medium without gravity. If gravitation field is not static, then one can try to replace it with a nonlinear medium analogy, but, as the article supposedly shows, such attempts often fail.

 

[renormalize]

Sorry if I'm misreading your comment, but it sounds like material analogy is a separate theory, not related to GR. Per my understanding it's not the case.

No, you haven't misread me. From the first two sentences from the abstract of the paper I cited:
"The effect of gravity in Maxwell’s equations is often treated as a medium property. The commonly used formulation is based on managing Maxwell’s equations in exactly the same form as in Minkowski spacetime and expressing the effect of gravity as a set of constitutive relations." (emphasis added)
My take is that the authors are clearly describing attempts set in flat-spacetime (i.e., not GR) that try to explain gravity via dielectric properties. Do you read it differently?

 

[Yuras]

My take is that the authors are clearly describing attempts set in flat-spacetime (i.e., not GR) that try to explain gravity via dielectric properties. Do you read it differently?

That's how I read it as well. Though I don't see any contradiction. Maxwell equations without sources in presence of a static external gravitational field in GR look exactly like Maxwell equations in Minkowski spacetime in presence of linear medium - according to Landau this statement follows from GR.

I actually found the article on the arxiv: https://arxiv.org/pdf/2401.08888 I only skimmed over it, but looks like equations from 11 to 14 actually are Maxwell equations from GR. But if there are no sources, they take the form of Maxwell equations in Minkowski space with a medium with constitutive relations 19. (CORRECTION: equation 19 might actually not be directly related.) At least that's what authors seem to be claiming.