No, none whatsoever, beyond the fact that PDEs appear in both cases. However knowing how to solve Schrödinger's equation doesn't provide any insight into how to solve Einstein's equations and vice versa. The fact that Planck's constant appears in one and not the other is one crucial difference: Schrödinger's equation provides a way for describing quantum fluctuations, Einstein's equations do not.

(The square of the Schrödinger equation doesn't make any sense, incidentally; the Schrödinger equation, already, describes energy, since the spatial part is the Hamiltonian.)

This is a preliminary answer intended to shed light on the question and its answer.

Our French friend from Tours' understanding of physics and mathematics is completely flawed and dates back to the Middle Ages.

Like many other physicists and mathematicians, he adopts the language of PDEs as Nil Bohr understood them a century ago.

This is a disaster in itself, holding back progress in theoretical physics over the past century.

It is the main reason why the West is losing the battle of quantum mechanics.

Our language is not that of time-dependent PDEs, but that of B-matrix chains (proposed by the author), which completely ignores PDEs as if they had never existed.

When we formulate the square of the Schrödinger PDE as a matrix in the 4D unit x-t space and reformulate the cosmic energy elements of the Einstein cosmic space as matrices in the 4D unit x-t space, a striking similarity appears in the description of the energy density by the two matrices and thus the sought-after connection between the Schrödinger PDE and the Einstein General Relativity is discovered.

Ismail Abbas M. Abbas

The typical scheme of your "questions" always follows the same path:

First, a title that poses a question which is simple to answer for anyone with a decent Bachelor's degree in physics.

Then you put out a text with several trivially false claims ranging from inaccuracy to lie, mostly with respect to the historic opinions of Schrödinger or Einstein, or more recently about a fictional person named "Nil Bohr" who is a mashup of incorrectly retold stories about Niels Bohr and Max Born (plus Mermin in your last one). Sometimes more sophisticated inaccuracies are added, occasionally salted with references to publications with predatory publishers.

If somebody competent like in this case Stam Nicolis answers the trivial question and points out the trivial errors, you never address these but instead just declare everybody else incompetent.

Do you really hope that a motivation of your theory by false claims and calling everybody who notices it stupid will get you respect?

I don't have hope that this results in you stopping this, I just wanted to let you know that we see what you are doing.

One might wonder how two seemingly different subjects or theories, one Eastern (quantum mechanics) and the other Western (general relativity), can fit together.

The answer is that they have more common properties than differences.

1- Both live and operate in an infinite free space bounded by Dirichlet boundary conditions.

2- Both can be studied by matrix mechanics in a 4D unit xt space, inside a closed volume delimited by a closed area, presented by the author as a control volume.

3- Most importantly, the geometry of both theories in x-y-z space follows the sawtooth shape, whether in 1D, 2D or 3D.

We therefore assume that the foundations of quantum mechanics and general relativity should be related in some way, since they both constitute a special case of studying the vacuum energy density within the same statistical theory of Cairo techniques.

In previous answers, we have stated that:

Cairo Intelligence Techniques = Natural Intelligence = Artificial Intelligence in the strict sense = Unified Field Theory

is a universal law of physics in the 4D unitary x-t space.

This outstanding Q/A reformulates the foundations of quantum physics and classical general relativity to fit the predefined control volume in the four-dimensional unitary x-t space and explains in more detail what the principles of quantum mechanics and general relativity are.

The current description of quantum physics and the theory of gravity is incomplete, even misleading.

General relativity and quantum mechanics are the newest sciences and should therefore be the most accurate, but unfortunately, the opposite is true.

The field of cosmic science, or the nature of the universe, as well as the subject of quantum physics, is so vast and confusing that its theoretical practitioners will always have to adopt new explanations from their own context to conform to the facts of recent discoveries.

Foundations of Quantum Mechanics and GeneralRelativity – Theory and Practice

One might wonder how two seemingly different subjects or theories, one Eastern (quantum mechanics) and the other Western (general relativity), can fit together.

The answer is that they have more common properties than differences.

1- Both live and operate in an infinite free space bounded by Dirichlet boundary conditions.

2- Both can be studied by matrix mechanics in a 4D unit x-t space, inside a closed volume delimited by a closed area, proposed by the author as a control volume.

3- Most importantly, the geometry of both theories in x-y-z space follows the sawtooth shape, whether in 1D, 2D or 3D.We therefore assume that the foundations of quantum mechanics and general relativity should be related in some way, since they both constitute a special case of studying the vacuum energy density within the same statistical theory of Cairo techniques.

Einstein's classical general relativity established the tensor equation for the gravity field in 1915:

G_μν = (8πG/C²) T_μν.. . . . (1)

where G_μν is the Einstein tensor, T_μν the stress-energy tensor, G the gravitational constant, and C the speed of light.

On the other hand, there is another technique for deriving equation 1 from the Cairo technique theory and its B-matrix chains when applied to volume control in infinite free space subject to zero Dirichlet boundary conditions (sometimes called free fall).

In the statistical theory of Cairo techniques, the matrix equivalent to the Einstein stress tensor in a 4D unitary x-t space is expressed as follows:

Fxx Fxy Fxz Fxt

Fyx Fyy Fyz Fyt

Fzx Fzy Fzz Fzt

Ftx  Fty Ftz F tt

Where Fii is the stress force and Fij is the shear force, considered negligible in vacuum.

In terms of matrix B notation, the stress matrix will be,

∇^2 xx ∇^2 xy ∇^2xz  ∇^2 xt

∇^2 yx ∇^2 yy ∇^2 yz ∇^2 yt

∇^2 zx ∇^2 zy ∇^2zz  ∇^2 zt

∇^2 tx  ∇^2 ty  ∇^2 tz  ∇^2t

It is clear that ∇^2 yy, ∇^2 yz, ∇^2 yt, etc., applied to an energy density force field such as gravity, constitute a stress or a force per unit area.

Where ∇^2 ty = d^2/dt^2)partial, ∇^2 tt = d^2/dt^2)partial and ∇^2 zz = d2/d^z) partial, etc.

The strain tensor, or space curvature C, is expressed in terms of the space curvature resulting from the energy density constraint:

Cxx Cxy Cxz Cxt

Cyx Cyy Cyz Cyt

Czx Czy Czz C zt

C tx C ty C tz C tt

We call it the C-curvature matrix.

To convert the dark energy field tensor to mass curvature, the energy density field must be multiplied by a factor of C², in accordance with the mass-energy transformation law E=mc².

Conversely, to convert the gravity energy field tensor to mass curvature, the energy density field must be multiplied by a factor of 1/C².

It is straightforward to demonstrate that a correction factor of(8πG/C²) must be multiplied by the above energy density matrix/tensor.

The final result is is obtained from the matrix expression,

B . C = I . . . (2)

Gravity is not a virtual force induced by the curvature of space, but a real force causing this curvature.

Contrary to Einstein's conclusion, gravity is a real force that induces curvature in space, not the other way around.

This suggests that the graviton should theoretically exist, but in cosmic space, not on Earth.

(PDF) Foundations of Quantum Mechanics and General Relativity -Theory and Practice. Available ResearchGate. Jul 2025.

The objective of this answer is to calculate the curvature of spacetime around the Sun, deduced from the statistical theory of Cairo techniques in 2020, and not from Einstein's theory of general relativity in 1915.

Einstein calculated the curvature of spacetime C around the Sun as follows:

C=1.E-9 m^-1. . . . .(1)

Therefore, there are currently two theories of general relativity:1- Einstein's general theory of 1915;

2- the statistical theory of Cairo techniques in 2020. The second theory of general relativity is not very complicated, but quite long.

To master the statistical theory of Cairo techniques, you must master the following three prerequisites:

1- Calculations and multiplications of second-order matrices and tensors;

2- Construction of arithmetic programming algorithms in C++ and Fortran;

3- Perfect knowledge of the universal laws of physics.

We assert our power as follows:

The Einstein field equations are expressed as follows:

G_μν = (8πG/c^4) T_μν . . .(2)

where G_μν is the Einstein tensor, T_μν is the stress-energy tensor, G is the gravitational constant, and c is the speed of light.

I-The tensor/matrix equivalence in Cairo statistical theory in the 4D unitary xt space is:

Fxx Fxy Fxz Fxt

Fyx Fyy Fyz Fyt

Fzx Fzy Fzz Fzt

Ftx Fty Ftz Ftt

It can be expressed as a Laplacian matrix:

∇^2xx ∇^2xy ∇^2xz ∇^2xt

∇^2yx ∇^2yx ∇^2yz ∇^2yt

∇^2zx ∇^2zy ∇^2zz ∇^2zt

∇^2tx ∇^2ty ∇^2tz ∇^2tt

We call this matrix B.

It is obvious that ∇^2yx=d^2/dxdy)partial, ∇^2yx =d^2/dydx)partial and ∇^2tt=d^2/d^2t)partial . . etc.

II-Similarly, the curvature matrix C is expressed as follows:

Cxx Cxy Cxz Cxt

Cyx Cyy Cyz Cyt

Czx Czy Czz Czt

Ctx Cty Ctz Ctt

We call this matrix the curvature matrix C.

III - In his special theory of 1905, Einstein omitted the physical law of constancy of the 4-dimensional unitary space x-t [1] written as follows:

x t = x^ t^ . .. . (3)

Sometimes called Lorentz transformations.

The universal law of special relativity 3 should be generalized to general relativity in matrix form:

B . C = I . . . . (4)

where I is the unitary matrix.

IV-The matrix multiplication,

∇^2xx ∇^2xy ∇^2xz ∇^2xt

∇^2yx ∇^2yx ∇^2yz ∇^2yt

∇^2zx ∇^2zy ∇^2zz ∇^2zt

∇^2tx ∇^2ty ∇^2tz ∇^2tt

x

Cxx Cxy Cxz Cxt

Cyx Cyy Cyz Cyt

Czx Czy Czz Czt

Ctx Cty Ctz Ctt

=I

is greatly simplified by the symmetry of the B matrix.

Moreover, only the stress in the main diagonal remains, the off-diagonal stresses being called negligible shear stresses.

Finally, if we stick to,

G is approximately: 6.674 × 10⁻¹¹ N⋅m²/kg².

Sun › Mass: 1.989 × 10^30 kg

Sun › Radius: 696,340 km

We obtain C=1E-9m^-1, which corresponds to Einstein's calculation in equation 1.

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1- I. Abbas, A Rigorous Reformulation of Einstein's Derivation of Special Relativity.