In 1915, Einstein abandoned the energy-momentum tensor of the gravitational field in the theory of gravity. This ensured the general covariance of the gravitational field equation (Einstein's equation).
Dear Stefan Rüster
I talk a lot about it for a long time. Therefore, I will facilitate our conversation and limit myself to short remarks.
The story is like that. Einstein in 1913 put forward the postulate that the energy of the gravitational field should create a gravitational field. He suggested that the energy of the gravitational field should enter the right side of the equation of the gravitational field. To do this, he tried to replace the energy tensor of the gravitational field with a pseudo-tensor, which was calculated from the law of conservation of energy. But this violated the covariance of the equation. After two years of doubt and enumeration of options, Einstein was forced to abandon the energy of the gravitational field in his equation. Landau and Lifshitz justify this by the smallness of the gravitational constant.
To some extent, this justifies the fact that I decided to abandon the Einstein equation. At first I found the metric of a uniform gravitational field, without using the Einstein equation. Then he found the equation of the gravitational field.
Sincerely, Valery
Dear both, isn't it the Gravity that we know, still a theory? We do not know the origin of gravity yet!
We know that gravity is one of the four forces, but how could a force be depend on mass to create force of gravity? it is like I be father of my father!
Dear Javad,
Theories find a relationship between phenomena, describe the laws of nature. Theories are not called to answer questions of the universe. The theory of everything is a myth, the limit to which is most likely unattainable. Nobody promised us that the laws of nature are described exhaustively by modern theories. The more tasks we solve, the more new problems arise.
Regards, Valery
In 1918, Einstein introduced the Levi-Civita energy conservation equation
Tim + Fim = 0
This is the sum of the energy-momentum tensors of matter and the gravitational field. Einstein could not object to this and did not object.
It is pretty simple. The sum of the energy of matter and the negative energy of the field is constant. The substance may occur due to the gravitational field. In the same way and vice versa. The process is reversible.
I got the gravitational field equalization. This equation has two solutions for concentrated masses. One is ordinary with a center of gravity, the other is an ejection solution. One of them reduces the energy of matter, the other increases it.
In nature, both processes are observed - collapse and explosions.
This ensures balance.
If we believe building block of universe is a quantum mechanics, then we have to look for origin of gravity inside of atom. any chemical element in space of universe create spherical https://www.youtube.com/watch?v=L9xdiDOeXvE for more detail read this as well. we all are entitle to think out the boxArticle Quantum Mechanics Gravity, Mechanical Gravity of Newton is Myth
best to all
Correct words. But I am sure that the path to this ultimate goal is not close. I think you understand that the phenomenological theory of gravity has already done a lot and you can’t ignore the finished results. The combination of general relativity with quantum mechanics is inevitable and it is necessary to find the right path. I have a feeling that while people working in this direction have not found the right unjust. What is now called "quantum gravity" is the mechanical union of two dissimilar theories. It was not for nothing that R. Feynman, after reading his lectures on quantum gravity, never returned to this topic.
Need a new series of ideas. But for now, I see flaws in classical general relativity and try to fix them. Only a good understanding of general relativity can one get enough of success in quantum gravity. I see most working in this area hopes to do without this knowledge.
In order to sculpt the theory of gravity from quantum mechanics, it is necessary to know what exactly needs to be sculpted.
Dear Valery, our science is coming from universe, and based on our conscious we creating "Question" under some evidence. on these stage we call it "Theory" i.e. Quantum Mechanics was a theory, but few decades it became reality. I believe "Gravity" is another form of theory that we should solve it. My believe, we all forgot that universe has function to hold all these massive of galaxies weightless and rotate them by its power, we forgot that "Space" of universe must have character to show each atom differently, we all forgot that universe is a quantum mechanics, not Einstein's mechanical GTR,STR or mechanical gravity. It is very easy to reject all these mechanical theory for universe, and think out the box, and realize that universe is a complete entity that does most the work for us. A good scientist should not be follower, Like Einstein, Newton and many millions of them. best regard Javad
The Einstein example has the exact opposite meaning. Einstein worked simultaneously on quantum mechanics and on general relativity. In both cases, he went the unexpected way, found a connection to honey with gravity and inertial properties and the geometry of the space of time, and those who followed the traditional path Abraham and Nordstrom did not come anywhere. No less unexpected was the train of thought in quantum mechanics from the Planck hypothesis; he developed the principles of theory. No less unusual than GR. For which he received the Nobel Prize.
I agree that an unexpected step is needed. And if the direction in which it is necessary to move were known, we would have long had a quantum theory of gravity.
Regards, Valery
One of the strange force is Gravity. At first it show itself quantum mechanics form in atom (primordial) or, one of the four forces to create universe (Mass, space) and then it become dependent on mass mechanically to be created. I do not think the gravity is working this way. If earth had gravity, we would not have rain!
"One of the strange force is Gravity."
This is not a force at all. The fall of bodies does not depend on the mass of bodies. Therefore, in the equation of motion of GR there is no mass. Moreover, this equation correctly describes the motion of bodies in Newtonian mechanics. With its help, you can find centripetal acceleration and Coriolis acceleration. Which also do not depend on mass.
Schrödinger (1916) showed that nothing is clear with the energy of the gravitational field. Einstein agreed with him. Some are trying to pretend that everything is in order.
But Einstein (1915) proposed an equation for the empty space G_ {im} = 0. Which means - the energy-momentum tensor of the gravitational field is zero. The pseudo-tensor does not allow one to calculate the field energy, only to ensure the conservation of energy in a closed system.
The Einstein tensor G_ {im} is proportional to the momentum energy tensor; therefore, Einstein almost equalized the energy of the gravitational field to zero. In weak fields, the field energy does not play a special role. Therefore, the Einstein equation showed itself well ...
But is this true when describing black holes?
Dear Stefan,
Thank you, this is interesting enough. I devoted several articles to something similar. I set other tasks, but got interesting results. Perhaps it will be interesting to you.
This is not the real law of gravity, but a demonstration of the need to take into account the density of the gravitational field.
Article The new gravity law almost entirely congruent with the Schwa...
Sincerely, Valery
Dear Stefan,
I think I found the reason why the field energy density (energy-momentum-tension tensor) disappeared from GR. And to some extent it was possible to solve this problem. Preprint On Einstein equation and energy of gravity field
Sincerely, Valery
The metric in the paper cited above has a nonzero Einstein tensor. Since the Einstein tensor is proportional to the energy-momentum tensor, we can assume that this is the energy-momentum tensor of the gravitational field, and the time component of this tensor is the field energy density. But in an empty homogeneous space, the field is zero. But the energy is not zero. The energy density of the homogeneous space turned out to be equal to the critical Friedmann density. This allows us to consider this energy as dark energy ...
As in the case of an electromagnetic field, the energy density is proportional to the square of the energy, but there is no such connection with the potential. The truth for this metric should not be a solution to the Einstein equation. Because Einstein proposed to consider the energy-momentum tensor zero. Otherwise, Einstein's equation became non-covariant. Einstein is forced to do this so that the equation gives plausible results. It is possible to restore the field energy-momentum tensor in GR, if we abandon the Einstein equation. I did it.
Preprint The General Theory of Relativity, a New Iteration
It all changed. A nonzero field-energy-momentum tensor appeared and the GR singularities disappeared.
"The scenario would be more complicated, if the test mass in the small space-time region possesses a non-negligible mass/mass density. Then, not only its mass/mass density, but also its gravitational potential energy density has to be incorporated together with the outside mass/mass density somehow ...
Is such a scenario considered in Einstein's GR?"
In general, when considering the long time of gravitational interaction in large regions, significant changes in the energy and momentum of the gravitational field occur and this field begins to interact with matter in a new way. The field accelerates matter and accelerates itself. There is a semblance of a shock wave.
Article Extreme Gravity Fields and Equation of Gravity Field. Astrop...
Einstein extended this equation and obtained the tensor equation of Einstein. But the difficulty arose according to Einstein, the gravitational field is the source of the gravitational field. But the inclusion of field energy in the left side of the equation led to the non-covariance of the equation. Therefore, Einstein compromised and removed the field energy from the equation. Despite this, the equation satisfactorily describes weak fields.
it is necessary to abandon the Einstein equation.
Landau and Lifshitz in the book Field Theory. (§ 95. The Einstein equations) noticed …
The new gravitational field equation is derived from simple and clear assumption
Article The General Theory of Relativity, a New Iteration
One of the strange force is Gravity. At first it show itself quantum mechanics form in atom (primordial) or, one of the four forces to create universe (Mass, space) and then it become dependent on mass mechanically to be created. I do not think the gravity is working this way. If earth had gravity, we would not have rain, we wouldn't be here. The earth would not have hurricane, trees never grow tall, the root would aimed to the center, and airplane could not fly.
https://www.researchgate.net/publication/333855510_Quantum_Mechanics_Gravity_Mechanical_Gravity_of_Newton_is_Myth?_
The result of replacing the Einstein equation for the Schwarzschild problem
How to find the equation of the gravitational field, bypassing the analogy with the Newtonian Laplace equation for the potential?
It is necessary to recall the almost obvious statement - a continuous field and the limit of a small scale is homogeneous. This follows from the definition of continuity. Further, the metric of a continuous field in the same limit should be the metric of a homogeneous field. If we know the metric of a homogeneous field, we can write a general view of the metric of a continuous gravitational field. It remains to find an equation whose solution is a general metric.
Article The General Theory of Relativity, a New Iteration
Trying to separate the energy of the field from that of the mass, in my opinion, is a bit like going against Einstein's unified idea and against his efforts to see mass and field as one. His idea, I think, was that there is no source of the gravitational field, meaning that every point of the field is source and not.
Locally, any gravitational field disappears under certain conditions (i.e. in homogeneous field) and therefore the gravitational field is an "emerging phenomenon". In principle, one could separate, using different models, the energy part of the field from the energy part of matter but this would lose beauty and simplicity to Einstein's theory, trying to make it linear what is not.
The two sides, in fact, are closely linked, are faces of the same coin, so separating them, proposing a new theory, would mean introducing a set of terms that take into account, dynamically, the continuity between the two aspects. A bad forcing.
In general relativity, massive bodies are described as surrounded by “clouds of mass" (or "energy") of gravitational field. The exact way this gravitational field "mass" is distributed will depend on which stress-energy tensor is used for the field.
What, exactly, acts as a source of gravitation seems to depend on the way we choose to write Einstein's field equations, because there is no real source. In this case the field is much more complicated than the electromagnetic field, which does not carry charge, and which can be described by linear equations.
The nonlinearity of relativistic equations represents the effect of gravitation on itself. This makes extremely difficult to separate the two aspects and would ruin the beauty of the theory that would end up resembling the theory of epicycles (moving further and further away from a "simple" description, how Einstein would have liked). I think that this explains why Einstein didn't go in this path and took a geometric approach, with no energy density, even at the risk of being more superficial and vague.
Sergio Reina, I looked at your ideas with pleasure. Of course, everything is not so simple. Any equation of the gravitational field must be non-linear because the gravitational field must itself be a source of the field. Einstein understood this in 1913. But he was forced to abandon this principle in 1915. In return, he received a rather simple equation of the gravitational field. Unfortunately, this equation leads to singular solutions. Unfortunately, these singularities are taken seriously (black holes, big bang). This is not a consequence of the general theory of relativity, it is a flaw in the Einstein equation.
Dear Valery Borisovich Morozov
I just can not see the singularities as flaws in Einstein's theory, but just interpretations. They depend on metrics, because their only meaning (if you want, in geometrical vision) is: “points where we cannot extend geodesics”. However, you can choose non-affine parameters so that you can see, with an appropriate choice of coordinates, the singularities as corresponding to the infinite. You can, also, allow to the fabric of space-time to degenerate so that two events space-like separated by a zero distance do not necessarily coincide (singular semi-riemannian approach) or you could, also, interpret singularities as real void, where space-time and anti-space-time merge.
Dear Sergio Reina ,
The task of physics is not to interpret mathematically meaningless objects. Singularities in general relativity that are not solutions of the Einstein equation. The only way to get rid of them is to abandon the Einstein equation. Which is a compromise, because it does not contain the energy of the gravitational field as a source of the field itself. On the contrary, the field momentum energy tensor is assumed to be zero.
I managed to find a reasonable replacement for the Einstein equation. The Einstein equation is not the only covariant equation. My covariant equation is a simple wave equation that defines a single parameter of the field metric. This makes the procedure for solving the equation very simple.
Preprint New version of the general theory of relativity (Initial pri...
This is not a hypothesized product. The equation follows from the principles of general relativity. This is a complete replacement for the Einstein equation. The presented equation has a solution that practically coincides with the Schwarzschild solution when moving away from the Schwarzschild radius.
Comparison with the Schwarzschild solution. The Christoffel symbol values for the two solutions are shown. A new solution exists for everyone r > 0
After some time
Tensor introduced in my work
fμν=1/κ (Bμν-1/2 gμν B) (1)
where
Bμν= -(∂Γμαα)/(∂xν )+Γμνα Γαββ
Equation (1) gives zero for solutions to the Einstein equation. therefore, the Einstein equation is replaced by the new equation of the gravitational field
(∂Γμνα)/(∂xα )-Γμβα Γναβ=κ(Tμν-1/2 gμν T) (2)
This equation satisfies all of Einstein's principles, and these principles include the principle (Einstein failed to use it) that gravitational energy is the source of the gravitational field. Just like any other energy.
Equation (2) has an equivalent equation:
Gμν=κ(Tμν+fμν ) (3)
Which differs from the Einstein equation by the presence of the energy-momentum tensor of the gravitational field fμν.
Preprint Gravitational Field Equation and the Structure of Black Holes
Einstein did almost everything. But Einstein assumed that equation (1) is equal to zero. Therefore, the solutions of the Einstein equation do not contain the energy of the gravitational field. I assumed that (1) is the energy-momentum tensor of the gravitational field.
As a result, a full-fledged law of conservation of energy-momentum appeared in the theory. The singularity disappeared from the solutions. Now the core of the black hole is a region close to the limiting potential -c2 .
It's funny, but the new equations of the gravitational field are much simpler than Einstein's equations. Although the solution for a point source turned out to be difficult. I had to decide numerically.
Perhaps there is a simpler analytical solution.