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.
Einstein is my symbol and idol. His discoveries and theories are unimaginable.
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 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.
Einstein was known for his physics skills and his vivid imagination, but his weakness lay in his limited mathematical abilities.
This statement is false because
Einstein and his followers were weak in classical universal physics and ignored the time components tx, ty, tz, tt.
In the case of special and general relativity, they were well aware of the starting point and the final result thanks to the experience gained at the time in terrestrial and space laboratories, but they did not find the right path.
The author demonstrated in 2023 that Einstein's 1905 theory of special relativity is nothing other than the universal law of the Lorentz transformation of physics in x-t space. Once again, Einstein's 1915 theory of general relativity is nothing other than the universal law of the Lorentz transformation of physics in the four-dimensional unit space x, y, z, t. Both theories are simply expressions of the conservation or constancy of spacetime in the free fall of the energy density field.
The SR and GR theories are based on a single formula, proposed by the author in 2020.
In the matrix/tensor formulation,
∇2xx ∇2xy ∇2xz ∇2xt
∇2yx ∇2yy ∇2yz ∇2yt
∇2zx ∇2zy ∇2zz ∇2zt∇2tx ∇2ty
∇2tz ∇2ttx
This is called the B matrix.
x
Cxx Cxy Cxz Czt
Cyx Cyy Cyz C yt
Czx Czy Czz C zt
Ctx Cty Ctz C tt
= I(unit matrix)
Einstein's fatal error was to invert equation 1, a flawed process that asserts that curvature creates gravity, not the other way around.
The equations above apply to general relativity. A good example is to derive SR from GR (impossible with Einstein in 1915) by writing matrix multiplication as follows:
∇2xx 00 00 ∇2xt
00 00 00 00
00 00 00 00
∇2tx 00 00 ∇2tx
x
Cxx 00 00 Cxt
00 00 00 00
00 00 00 00
Ctx 0 00 C tt
= I(unit matrix)
1-Note that The above system is composed of two equations in 3 unknowns (Cxx,Cxt,Ctt) but introducing the parameter γ=√[1/(1-v^2/c^2)]
γ . GE.1
Note also that,
∇2xx = v^2/c^2 where c has no physical meaning as the speed of light, but c^2 is defined as the mass-energy transformation constant E=mc^2[1].
Introduction:
γ=x/x*
called space contraction.
and,
γ=t*/t
called time dilation.
x, t denote real space and real time, respectively.
Suppose xt=x*t*
is the third equation completing the above system of equations.
The only linear solution for γ is: γ=1/√[(1/(1-v^2/c^2)]: WHAT IS EINSTEIN'S SPECIAL RELTIVITY
By the end of 2025, the author expects both of Einstein's theories of relativity to be a thing of the past.
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