Einstein was not unfamiliar with mathematical difficulties. He found it difficult to define energy in a manner that respected both the rule of energy conservation and covariance, which is a key aspect of general relativity that states that physical laws apply to all observers equally.

A research team at Kyoto University’s Yukawa Institute for Theoretical Physics has now proposed a novel approach to this longstanding problem by defining energy to incorporate the concept of entropy. Although a great deal of effort has gone into reconciling the elegance of general relativity with quantum mechanics, team member Shuichi Yokoyama says, “The solution is shockingly intuitive.”

Einstein’s field equations describe how matter and energy shape spacetime and how in turn the structure of spacetime moves matter and energy. Solving this set of equations, however, is notoriously difficult, such as with pinning down the behavior of a charge associated with an energy-momentum tensor, the troublesome factor that describes mass and energy.

The research team has observed that the conservation of charge resembles entropy, which can be described as a measure of the number of different ways of arranging parts of a system.

And there’s the rub: conserved entropy defies this standard definition.

The existence of this conserved quantity contradicts a principle in basic physics known as Noether’s theorem, in which the conservation of any quantity generally arises because of some kind of symmetry in a system.

Surprised that other researchers have not already applied this new definition of the energy-momentum tensor, another team member, Shinya Aoki, adds that he is “also intrigued that in general curved spacetime, a conserved quantity can be defined even without symmetry.”

In fact, the team has also applied this novel approach to observe a variety of cosmic phenomena, such as the expansion of the universe and black holes. While the calculations correspond well with the currently accepted behavior of entropy for a Schwarzschild black hole, the equations show that entropy density is concentrated at the singularity in the center of the black hole, a region where spacetime becomes poorly defined.

The authors hope that their research will spur deeper discussion among many scientists not only in gravity theory but also in basic physics.

Reference: “Charge conservation, entropy current and gravitation” by Sinya Aoki, Tetsuya Onogi and Shuichi Yokoyama, 2 November 2021, *International Journal of Modern Physics A*.

DOI: 10.1142/S0217751X21502018

This fact is free of doubt that charge and entropy are similar in a black hole.As a consequence both are equal.So nothung is new to add in astrophysics,but entropy is a different branch and is isolatedhas nothing to mention that has no practical application.But thanksto the author for dealing basic theoritical equal entropy part of black hole.Charge and magnetism of super massive black holes are established independently as entropy and charge(magnetism) generate simultaneously and not different in vale of energy.

How entropy can be measuted??

This is from velocity(accelerated and nonaccelerated as derived from the Hubble’s law) and charge(or resulting magnetism) in a time interval,òf a super massive black hole(in the host galaxy).

When no one remain on the earth to observe this phenomena then everything will be gone.Seer and seen are dependable to each other .

What Albert really know I what kind of Measuremet he had In thouse Agent times?!

You people realize that Einstein has been dead since 1955, right? How is it that he’s “warming up” to anything??

Entropy is a count – the “different ways of arranging parts” – so it is discrete, quantized. Coupling it to the smooth, continuous measures of energy, time and space may be the hook needed to finally join general relativity with quantum physics. It would give the macro measures their fuzzy, quantum interface.

Ridiculous article apparently written to impress slack-jawed yokels.

… “as a measure of the number of different ways of arranging parts of a system”

this is kind of introduction to a probability, and it kicks in…

Really not seeing the link between symmetry, entropy, space-time and conservation. Also, more importantly how it would have anything to do with QM/CM.

I thought Noether’s theorem was already proven. Has it just been unproven or is it just a matter of fact that you really can’t apply math to physics meaning physics is totally emperical not logical. Which means then that it will never be more than an approximation so don’t bother to try to unify it.

The idea of a conservative without symmetry is curious and interesting as symmetry and mathematical beauty have dominated physics last 75 years or so. Think there is something in thinking more about the subtleties of entrophy mathematically it’s relationship to asymmetry and some underlying dynamic process that manifests/functions as symmetry resulting in apparent conservation.

I love learning about our Universe! 💕

I think this really important. Once you fix the information entropy of a binary vector, actions on it necessarily become nonlocal, things get entangled. The set of matrices that transform it become permutation matrices, part of special unitary group that holds DFT, (takes fourier transform). But this magic is from fixed information entropy only.

If you look at physical system in these terms, same behavior emerges. Planets don’t copy and erase themselves all over universe, their count remains constant, so with numbered cells of positions, they permute positions. Macro property count is conserved.

So look at universe as information system, conserved information entropy is *defining* trait of many features, not jibing with physics entropy always increasing. Need a richer picture of it all.

What you have here is the process of dark matter electrical-magnically

changing solid matter back to it’s

original atomic elements, this process creates gravity.

Quote: You people realize that Einstein has been dead since 1955, right? How is it that he’s “warming up” to anything??

Um… Quantum smelling salts and an atomic particle heater?

The quantum gravity theory for single particles I have it ,it explains why the universe is speeding up also does the cosmological constant have to do with momentum cause I found momentum in space time