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.

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.