The author proved in 1923 [1] that Einstein's 1905 theory of special relativity is nothing other than the universal Lorentz law of physics in x-t space.
Once again, Einstein's 1915 theory of general relativity is nothing other than the universal Lorentz law of physics in the four-dimensional unitary space x, y, z-t [2].
Both theories are simply expressions of the conservation or constancy of spacetime in free fall (zero Dirichlet boundary conditions).
Any energy density in infinite free space is accompanied by a curvature of space, where the energy density is the cause and the curvature of space the effect. It is noteworthy that Einstein reversed this fact in the gravitational field near the Sun and considered curvature as the cause, neglecting the force of gravity as nonexistent.
General relativity or the relationship between energy density and the curvature of space is expressed in physics in matrix/tensor form: as,
1-∇2xx ∇2xy ∇2xz ∇2xt
∇2yx ∇2yy ∇2yz ∇2yt
∇2zx ∇2zy ∇2zz ∇2zt
∇2tx ∇2ty ∇2tz ∇2tt
x
Cxx Cxy Cxz Czt
Cyx Cyy Cyz C yt
Czx Czy Czz C zt
Ctx Cty Ctz C tt
= I(unit matrix)
Where ∇2zx U= Fxy=d2/dzdx)partial , ∇2ty U=Fty = d2/dtdy)partial , ∇2tt= Ftt =d2/dtdt)partial and ∇2zz = Fzz=d2/dzdz) partial . . . . etc
It's a great start.
2- Given the symmetry of the curvature tensor and the fact that the shear curvature terms are negligible in free space, we obtain:
∇2tt U = constant . Ctt . . . .(1)
3- The author showed that [3],
U*(t)= constant . Exp -[log(1+RO)/(1-RO)]
where RO is the entry element of the main diagonal of the transition matrix B.
In vacuum, RO=0 and -[log(1+RO)/(1-RO)] = log 2. =0.693
4- Substituting into equation 1:
The mass of the Sun is 1.989 × 10^30 kg and its radius is 696.340 km. In equation 12 we get the curvature Utt = 1E-9 m^-1, which is the same conclusion as Einstein in 1916.
TO BE CONTINUED
Yes we can. But somehow different as you are expecting.
The linked article below shows how an elementary and universally valid definition of force drastically changes the conceptual world of standard physics in many respects including general relativity and how it avoids many of the dead ends into which standard physics has run precisely because of the inconsistent definition of force.
But to be clear, Einstein is only using the beautiful math from Bernhard Riemann. The article shows that we do not need that math for the description of the gravitational force.
Preprint On fundamental problems and their solution in the structure ...
Beauty is in the eye of the beholder, it's a subjective notion, mathematics and physics are impersonal constructions. The point of mathematics and physics isn't personal, it's impersonal. So Einstein did invent general relativity, but, once he invented it, what it means becomes independent of him. Anyone can understand it and use it and go further.
Its mathematical structure is invariance of the equations that describe the spacetime geometry, in the presence of matter, under diffeomorphisms and that they not contain terms with more than two derivatives. These two assumptions are necessary and sufficient to imply the form of the equations. One can argue about whether these two propositions are beautiful or not, the only thing that matters is whether alternative propositions are mathematically equivalent to these-in which case the description is equivalent to general relativity, or not. And, if not, in what way does the alternative differ.
This is a brief response aimed, on the one hand, at shedding more light on the question and its answer and, on the other hand, at thanking our distinguished contributors and readers for their helpful responses.
I was determined to continue on the subject of Einstein's general relativity when I received the brilliant response from our French friend in Tours and felt motivated to stop and comment.
My sole and main objection is that science is not a matter of taste, but rather 1+1=2.
If you apply the expression "science is a matter of taste," you divide people and scientists into contradictory groups, more than the different religions have done.
I was a lecturer and supervisor for the Basic Sciences group (mathematics, physics, chemistry, and descriptive geometry) at Cairo University. There, we strictly apply the rule, or law, that all branches of science are nothing other than universal laws of physics.
This is perhaps the secret of the unprecedented success of the Cairo theory of techniques, in which all the universal laws of physics are grouped together in an intrinsic and elegant way.
The main error of Einstein's general relativity was that he started with Riemann space, which is an incomplete and misleading space (it is not a universal law of physics), when he should have started with the statistical theory of Cairo techniques.@ Stam Nicolis
Both SR & GR are under open challenge since 2012 which is standing till today despite a few physicists accepted the same but failed miserably. Open challenge is available in my profile on ResearchGate.
The math is beautiful and the simplest: curvature is just imaginary chromoEM field tensor you can’t get better! F^2-R^2 as Lagrangian us the buggest revelation to man and NOTHING is more beautiful! The solutions arent always beautiful
Stam Nicolis "Beauty is in the eye of the beholder, it's a subjective notion, mathematics and physics are impersonal constructions."
Ismail's point is not replacing ugly math by beautiful math. It is replacing ugly math by beautiful physics. The abstraction here, which I fully share, is that a far fetched purely mathematical explanation is something which is questionable by principle. In terms of logics, this is indeed "ugly". If this could be replaced by a pure physical comprehensible explanation, again in terms of logic, this would be a beautiful solution. This is completely without any subjective notion.
There doesn't exist a ``physical" explanation, that's different from a ``mathematical" explanation, that's a common mistake. There do exist mathematical structures that are not relevant for describing natural phenomena; there don't exist natural phenomena that don't have, or can't have a mathematical description, which, in effect, means an impersonal description.
Another angry response from our French friend from Tours. But this time, it's clear that this answer is completely wrong.
He may be a good mathematician, but he knows nothing about physics.
Which means he'll never understand a word of Cairo's theory of technology.
The author wants to replace the catastrophic mathematics of Einstein's 1915 general relativity with the beautiful physics of 2020.
Furthermore, we propose a new general relativity different from Einstein's.
The proposed modern theory of general relativity predicts a quantization of the curvature of space around the Sun, unlike Einstein's general theory.
This test can be carried out experimentally using spacecraft and space laboratories measuring the curvature of space around the Sun.
Stam Nicolis "There doesn't exist a ``physical" explanation, that's different from a ``mathematical" explanation, that's a common mistake."
No, there is a really beautiful simple and comprehensible physical explanation for the gravitational force.
The gravitational force F on an object which contributes with its own gravitational field to the earth field is caused by the dependency of the energy content W in the common field on the position s (the height) of the object. F=dW/ds. The common field g is given as g=g(object)+g(Earth). The energy density E of the common field is proportional to g². The height dependend energy W is given as W=∫EdV. V is the volume mainly filled with the combined field g.
Wouldn't you admit that this explanation of the gravitational force is rather a physical explanation then a mathematical one? Only very basic mathematical expressions appear here. But using elementary math is unavoidable as soon as quantitative statements must be made.
First, we need to correct the error in STR -- return the scale (Doppler) factor to the Lorentz transformation formulas. The consequences of this for the theory of gravity and cosmology will be truly grandiose.
The recession of galaxies (Hubble's law) is cancelled, because with an increase in the speed of the object's removal, the Doppler effect increases (the wavelength increases). This leads to an increase in the length scale. Accordingly, the distance to the object decreases. (It is possible that there will be a stationary Universe.)
This is a great example:
Can you derive and explain Einstein's general relativity in one page?
Yes.
1- The deformation is not scalar (only one component).
The deformation has 16 components.
The deformation in a 4D unit x-t space is composed of 16 components called curvature.
Cxy Cxy Cxz Cxt
Cyx Cyy Cyz Cyt
Czx Czy Czz Czt
Ctx Cty Ctz Ctt . . . . . . . (1)
It is called the deformation or curvature matrix/tensor C.
Stress is not a force/area scalar (a single component).
Stress tensor has 16 components.
Stress in a 4D unit x-t space is composed of 16 components, called stress tensors.
∇2xx ∇2xy ∇2xz ∇2xt U(x,y,z,t)
∇2yx ∇2yy ∇2yz ∇2yt U(x,y,z,t)
∇2zx ∇2zy ∇2zz ∇ zt U(x,y,z,t)
∇2tx ∇2ty ∇ 2tz ∇2tt U(x,y,z,t)
. . . . (2)
Where ∇2 xx= ,d^2U/d^2x )partial and ∇2 xy=d^2U/dxdy)partial , .........etc
This is called the stress matrix/tensor B.
The Lorentz law in x,y,z,t which is a universal law of physicst meaning the unitary 4D xt space is conserved,implies,
B . A = I . . . . . (3)
Equation 3 is equivalent to Einstein's stress-strain tensor, and even more precise!
Contrary to Einstein,
Contrary to Einstein, stress or energy density, like gravity, causes space to curve, not the other way around.
How to find a simple solution to equation 3?
1- It is clear that the curvature components are symmetric (Cij = Cji) and the shear components are zero in free space.
2- It is also clear that the stress tensor components are symmetric (∇2 xy = ∇2 yx, etc.).
3- The principal components of the diagonal entries are equal.
We then obtain the resulting equation:
Ctt = constant .G /C^2. . ∇2tt near the surface of the Sun. (4)
where G is the universal gravitational constant and C is the speed of light.
Replacing the mass of the Sun with the correct value in kg, and its radius with its proper value in meters, we obtain
Ctt = 1 E-9 m^-1,
the same value concluded by Einstein in 1915.
Definition of the components of time and the collapse of Einstein's theories of relativity.
A correct definition of the components of time leads to the collapse of Einstein's theories of relativity.
In the three-dimensional geometric space x, y, z, and with real time t as the external controller, all of physics and mathematics are incomplete, even ill-defined.
For example, the Laplacian operator ∇2 is defined as follows:
∇2=∇2xx +∇2yy +∇2zz
which is incomplete and ill-defined.
Similarly, the (thermal) diffusivity D is defined as follows:
D=k/Roh .C in normal convention.
which is also incomplete and ill-defined.
In contrast, in the four-dimensional unitary space xyzt, ∇2 is defined as follows:
∇2 = ∇2xx + ∇2yy + ∇2zz + ∇2tt
It is this last term that determines the curvature of space in Einstein's general relativity and defines the world of quantum mechanics from that of classical physics.
For example, Einstein's general relativity is nothing other than the universal Lorentz law, that is, the conservation of four-dimensional unitary space in free fall (Dirichlet boundary conditions = 0).
The above theory induces Einstein's general relativity in a single sentence. In the matrix/tensor formulation,
∇2xx ∇2xy ∇2xz ∇2xt
∇2yx ∇2yy ∇2yz ∇2yt
∇2zx ∇2zy ∇2zz ∇2zt
∇2tx ∇2ty ∇2tz ∇2tt
x
Cxx Cxy Cxz Czt
Cyx Cyy Cyz C yt
Czx Czy Czz C zt
Ctx Cty Ctz C tt
= I(unit matrix)
where C is the curvature of geometric space.
The last equation is itself the Eistein equation of general relativity.
Note that the above discussion is completed with the information field rule:
No distribution without permission.
The theory of general relativity is essentially defined by the energy density U(x,y,z,t) and the four-dimensional unitary space xyzt, in two distinct ways:
1- The geometric space xyz is infinite, and time t is integrated into it as a continuous spatial variable.
This is Einstein's classical theory of relativity from 1915, which we consider incomplete and sometimes misleading.
2- The modern theory of general relativity proposed by the author in 2020, which is more precise and complete.
In any case, the theory of general relativity is defined by the following matrix/tensor equation:
[The proposed theory induces Einstein's general relativity in a single sentence. In the matrix/tensor formulation],
∇2xx ∇2xy ∇2xz ∇2xt
∇2yx ∇2yy ∇2yz ∇2yt
∇2zx ∇2zy ∇2zz ∇2zt
∇2tx ∇2ty ∇2tz ∇2tt
What is the energy density of space-time!
x
Cxx Cxy Cxz Czt
Cyx Cyy Cyz C yt
Czx Czy Czz C zt
Ctx Cty Ctz C tt
= I(unit matrix)
where C is the curvature of geometric spacetime.
. . . . (1)
Einstein's fatal error was to invert equation 1, a flawed process that asserts that curvature creates gravity and not the other way around.
Equation 1 shows how and why the energy field of sound waves cause space-time to bend in a similar way to general relativity.
Ismail Abbas M. Abbas "where C is the curvature of geometric spacetime."
We have the Einstein tensor Guv=Ruv-1/2guvR.
What is the curvature C in the context of Einstein's field equations? The Einstein tensor G, the Riemann curvature tensor Ruv or the scalar Ricci curvature R? Or is it something different?
Or are you not talking about Einstein's field equations?
Ismail Abbas M. Abbas,
Physically, Einstein's General Relativity reflects the beauty of God, who is a mathematician. Put another way, God is physically relativity and that relativity is mathematically Einsteinian.
The Hidden and Little-Known History of Physics and Mathematics:
1- The universal law of physics:
U(x,y,z,t+dt)=B. U(x,y,z,t) . . . . (1)
in a control volume bounded by Dirichlet boundary conditions is rarely mentioned.
where B is the well-defined transition matrix and U(x,y,z,t) the energy density vector field.
Note that the quantum theory of transition matrices Q is intrinsically included in Equation 1 by simple substitution Q=SQRT(B).
2- It can be argued that Universal Law 1 is not only extremely important, but that it is the only universal law.
In other words, any other universal law can be derived from Equation 1, or be a subset of it. 3- Consider the intensity of the sound field and its reverberation time:
TR = 4 V / 6 A S C. . . (2)
Derived experimentally by W. Sabin a hundred years ago.
No physicist or mathematician has dared to address equation 2 in the last hundred years, and will not be able to do so in the next hundred years, simply because it is a universal law of physics or a subset of equation 1.
3- The solution found for the first time from equation 1 follows simply from:
∇2xx ∇2xy ∇2xz ∇2xt
∇2yx ∇2yy ∇2yz ∇2yt
∇2zx ∇2zy ∇2zz ∇2zt
∇2tx ∇2ty ∇2tz ∇2tt
x
Cxx Cxy Cxz Czt
Cyx Cyy Cyz C yt
Czx Czy Czz C zt
Ctx Cty Ctz C tt
= I(unit matrix)
where C is the curvature of geometric space.
The last equation is itself the Einstein curvature equation of general relativity.
Ismail Abbas M. Abbas,
Do you think that what you propose may lead you to win the Nobel Prize in Physics?
Ismail Abbas M. Abbas "TR = 4 V / 6 A S C. . . (2)"
Your terms are undefined.
Wolfgang Konle
A. Einstein loved the complications we call ugly mathematics.
The Einstein tensor [(Gµν) describes the curvature of spacetime in general relativity. It is a mathematical object that relates the geometry of spacetime to the distribution of matter and energy within it.]
Our goal, as the Q&A session indicates, is to find a physical description equivalent to Einstein's general relativity using cutting-edge physics.
The little-known and rarely mentioned genius Wallace Sabine was a professor of mathematical physics at Harvard and, in between, a leading consultant on sound quality in the finest concert halls.
Let's return to W. Sabine, who experimentally demonstrated his famous law of reverberation time, or the mean time between two successive reflections, TR, in regularly shaped acoustic rooms:
TR = 4 V / 6 A S C. . . (1)
where C is the speed of sound, V the volume, A the internal surface area, and S the absorptivity (corresponding to the diffusivity) of the walls.
Since then, no physicist or mathematician has dared to address equation 1 in over a hundred years, and will not be able to do so in the next hundred years, simply because it is a universal law of physics or a subset of the Cairo techniques. We can now theoretically prove Sabine's formula from the statistical theory of Cairo techniques, in the same way that we proved Einstein's classical general relativity in 1915, namely:
Note that any universal law can be deduced from the statistical theory of Cairo techniques or be a subset of it, simply because it is the theory of everything.
Ismail Abbas M. Abbas "Note that any universal law can be deduced from the statistical theory of Cairo techniques or be a subset of it, simply because it is the theory of everything."
This is an extremely general claim. Is this claim also applicable to laws close to axiomatic relations like energy modification dW equals force F times displacement ds, dW=F*ds?
Can you with your Cairo technique also deduce the following general force law of mechanics, which equally holds for all forces in our world?
"Every force F on an object is caused by the dependency of an amount W of energy on the position s of the object. F=dW/ds,
with dW/ds=(∂W/∂sx, ∂W/∂sy, ∂W/∂sz)".
Wolfgang Konle Lev Verkhovsky We demonstrate and deduce Einstein's special relativity in 1D using techniques from the Cairo language:The starting point is matrix multiplication:[1]∇2xx ∇2xy ∇2xz ∇2xt∇2yx ∇2yy ∇2yz ∇2yt∇2zx ∇2zy ∇2zz ∇2zt∇2tx ∇2ty ∇2tz ∇2ttXCxy Cxy Cxz CxtCyx Cyy Cyz CytCzx Czy Czz CztCtx Cty Ctz CttIn x-dimension, the matrix multiplication above reduces to:v^2/C^2 00 00 V^2/C^200 00 00 0000 00 00 00∇^2/C^2 00 00 V^2t/C^2XCxx 00 00 Cxt00 00 00 0000 0o0 00 00Ctx Cty Ctz Ctt
The matrix multiplication above yields two equations with three unknowns (Cxx, Cxt, Ctt).
The third equation needed to complete the above system comes from the parametric equation:
x*=γ x. . (1)
And,
t*= t /γ . . (2)
x and t represent real space and real time, respectively.
Equation 1 is called space contraction, and Equation 2 is called time dilation.
Finding a linear expression for gamma from the three equations above, we obtain:
γ=SQRT(1/(1-v^2/C^2))
Which is Einstein's theory of special relativity in 1905.
1-I. Abbas,
A rigorous reformulation of Einstein derivation of the special theory of relativity,
- February 2022,
>>>We demonstrate and deduce Einstein's special relativity in 1D using techniques from the Cairo language
--------------------------
You do not take into account the influence of the Doppler effect on the scales of length and time, that is, you repeat the mistake of Lorentz, Poincaré and Einstein.
Ismail Abbas M. Abbas "∇2xx ∇2xy ∇2xz ∇2xt∇2yx ∇2yy ∇2yz ∇2yt∇2zx ∇2zy ∇2zz ∇2zt∇2tx ∇2ty ∇2tz ∇2ttXCxy Cxy Cxz CxtCyx Cyy Cyz CytCzx Czy Czz CztCtx Cty Ctz Ctt"
Sorry, but this notation is confusing. Couldn't you use indices instead of providing linear sets of components.
What exactly is that C-matrix?
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