Популяризация науки среди студентов

«Интеграл без дифференциала — как женщина без груди: не за что ухватиться».

Лев Ландау, известный физик-теоретик

Popularization of science among students

"An integral without a differential is like a woman without breasts - nothing to hold on to."

Lev Landau, a famous theoretical physicist

Listen, if you understand the phenomenon of free fall, you wouldn't ask such questions.

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.

And what does reality say about this?

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

If this is a fundamental thesis of these theories, then there is a big problem. Because that Russian saying is true:

'«Интеграл без дифференциала — как женщина без груди: не за что ухватиться».

Лев Ландау, известный физик-теоретик'

"An integral without a differential is like a woman without breasts - nothing to hold on to."

Have you ever caught a woman's breasts without a woman?

This is a preliminary response, first to clarify the question and its answer, and second to thank our distinguished contributors and readers for their valuable contributions.

I had planned to pursue this line of thought when I received the brilliant response from our friend, Hungarian Professor László Horváth.

"Listen, if you understood the phenomenon of free fall, you wouldn't ask such questions."

It is true that Einstein's giant theory of general relativity concerns the free fall of a mass in the gravitational energy density field, but it can be generalized to the free fall of any object in any physical energy density field.

This point escaped our idol, Professor A. Einstein, when he limited his general relativity to the gravitational field alone.

This is our intention, because general relativity belongs to the statistical theory of Cairo techniques when applied to the special case of zero boundary conditions.

Dear Prof Ismail Abbas M. Abbas ,

First of all, I'm not a professor. I could be a professor, but the current political elite does not allow talented individuals who think in terms of science to become professors unless they propagate and perfect theories that are increasingly far removed from reality. We have a beautiful example of this, if we consider the valuable work of Nikola Tesla. Since then, how many professors have there been who can say that they have surpassed Tesla in terms of true scientific creation? Well, that's not the point. Let's get back to your question.

Here is a clear answer to your question:

Article The existence of the graviton can be proven physically and m...

(pg. 13 - pg. 17)

Soon, if the weather is more favorable, there will be, and may be, a situation where the temperature outside is similar to that inside the building. We will make simple measurements: several times in several places and under the same conditions. In principle, the gravitational effect outside should be smaller in most cases than inside the building... My experiments in China suggest this.

This can be a good explanation for why a ball lightning formed outdoors penetrates the building through an open door:

Preprint A villámok anyaga és a Föld térfázisának hiánya mint kulcsté...

The next prediction can be easily tested:

Research Proposal Addendum to 'A Simple Experiment to Support an EM Gravity Theory'

https://www.youtube.com/watch?v=Gp0jPTsZ4Bc

Regards,

Laszlo

The question is

“Is gravity a force or not?”

- the answer is: completely for sure Gravity is nothing else than one of the four fundamental Nature forces [3 others are Weak, Electric, and Nuclear/Strong, Forces], which,

- as that rigorously scientifically proven in the Shevchenko-Tokarevsky’s Planck scale informational physical model, in this case it is enough to read

https://www.researchgate.net/publication/367397025_The_Informational_Physical_Model_and_Fundamental_Problems_in_Physics, section 6. “Mediation of the fundamental forces in complex systems”, though, of course, to more understand what is in the section is necessary to read at least first 6 paper’s sections,

- as all other Forces, acts in the Matter’s spacetime fundamentally absolute, fundamentally flat, fundamentally continuous, and fundamentally “Cartesian”, spacetime that has metrics (at least) [4+4+1]4D (cτ,X,Y,Z, g,w,e,s,ct).

At that fundamentally nothing in Matter can impact, including to curve, on the spacetime, and fundamentally by no means the spacetime can impact on anything in Matter.

In the model it is rigorously scientifically rationally shown also that on Planck scale at least Gravity, Electric, and Nuclear/Strong, Forces act by one scheme, making Matter to be as it is,

- however all Forces are functionally fundamentally different, so there cannot be some “unification” of Forces.

More see the link, to read series of SS posts in https://www.researchgate.net/post/NO47What_is_Force_a_Field_Where_is_the_Force_Field_How_does_it_appear_Is_the_Force_Field_a_Regulating_Effect_of_the_Energy-Momentum_Field/2, pages 1,2, it is useful as well.

Cheers

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.

-----

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

xThe generalization of Lorentz universal law in unitary 4D xt space yields another universal law,The following matrix multiplication is the equivalence of Einstein stress strain tensor which is the matrix multiplication,∇^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

------------------------------------------------------Cxx Cxy Cxz CxtCyx Cyy Cyz CytCzx Czy Czz C ztC tx C ty C tz C tt

=                I

I is the unit matrix.

-------------------------------

∇^2 xx . Cxx + ∇^2 yx . Cxy + ∇^2 zx . Cxy + ∇^2 tx . Cxt  = 1

And the shear stess tensor is negligebly zero in infinte free space.

∇^2 yx . Cxy = ∇^2 zx . Cxy = ∇^2 tx . Cxt =0.

Then,

∇^2 xx . Cxx  =1.

Similarly,

∇^2 xx . Cxx  =∇^2 yy . Cyy  =∇^2 tt . Ctt  = 1.

But ctt equals,

Ctt=λ*^2 Exp - λ* = 1

-2 Log λ*+ λ* =0 . . (1)

Substituting the mass and radius of the Sun into Ms (1.989 × 10^30 kg) and Rs (696,340 km) and the gravitational constant G (6.674 × 10⁻¹¹ N⋅m²/kg²), the solution to equation 1 gives the required spatial curvature, which should be equal to Einstein's, i.e., 1E-9m^-1.

Before asking if gravity is a force, you should be kind enough to tell us what you understand by a force. The concept has been much discussed without consensus.

Since the emergence of the Cairo technique theory in 4D unitary x-t space in 2020, the author adopts the definition of vector force F as the Laplacian of the energy density U,

Fxy = ∇^2 xy U,

Fxz = ∇^2 xz,

Fxt = ∇^2 xt U,

Jose Gaite etc.

Ismail Abbas M. Abbas

There are multiple issues with gravity, which is why when using present theories, gravity & quantum mechanics can't be incorporated in a common model.

Mass (particle) scales with energy, as does the Planck constant h. G has actual dimensions 1/m, and its value is only valid at the electron charge radius. (Same with charge and alpha, electric permittivity, and magnetic permeability). Relationships between multiple parameters show that gravity can not be a force because it scales incorrectly. The self-gravity of any particle is just Gm (valued for that particle only) and does not include the r term for dimensions for gravity. In my paper there is a large section on why it isn't a force. You can read it here.

DOI: 10.22541/au.175087018.88558419/v1

When gravity is shown as Gm, it is incorporated seamlessly with quantum theory in a running standard model, where special relativity is also modified (runs the wrong way, multiple issues with it due to the Lorentz factor.)

Gravity essentially is local contraction of the EM field (visualise field lines contracting) as the wave-particle duality passes through such location. This is why it is always negative (contracting). Gravity includes mass, which in turn includes the electromagnetic field component of which the elementary charge (particle specific) is a sub-part. Space does not include time - this is an anthropic construct - so there is no intrinsic 'curvature' of 'space'. 'Curvature' is simply local contraction for each passing wave-particle duality, and for macroscopic objects, a huge amount of 'space' (EM fields) has contracted, causing the attraction between masses that we observe.

Gravity is a running parameter, and is velocity and temperature dependent. This concept then removes most of the anomalies of the standard model, allows for the weak & strong interactions, and unification to be understood.

Dark matter (missing mass) is easily resolved. This modified standard model then becomes very robust, verifiable by multiple systems of analysis simultaneously. Regards

In my opinion the term “gravity” refers to the phenomenon of the gravitational interaction between material objects: two material objects anchored in an inertial reference frame are subjected to a tendency to move towards each other and if they are free to move they change each other’s linear momentum in a well-defined way. This means that each material object exerts an action on every other material object in his wide environment. That action is called the "gravitational force".

In the frame of the gravitoelectromagnetic description of the gravitational phenomena and laws it is assumed that the gravitational interaction is made possible by the mediation of the gravitational field: a dual entity always having a field and an induction component.

Reference: The Gravitational Interaction between Moving Mass Particles Explained by the Theory of Informatons. (https://doi.org/10.4236/jhepgc.2024.103060)

Dear Ismail Abbas M. Abbas ,

I don't know the meaning of "Cairo technique" but what you write looks like a tidal force. It is not a proper force.

By the way, the "tidal force" is properly called tidal stress.

The answer below is only a commentary and not a rigorous answer:

1- Minkowski was one of the greatest mathematicians, but one of the least physicists.

This is why his space is catastrophic and only increases misunderstandings and confusion.

I dare say that Minkowsky and all the other great scientists of the time did not fully understand what a space is.

2- The idea of combining the space of the Schrödinger equation SE of quantum mechanics with the space of Einstein's general relativity is ridiculous, because they actually constitute a single space without any need to falsify it (if SE is replaced by its square).

Cairo's theory of techniques naturally unifies the two spaces into one, and this is why it is the only theory of everything, or unified field theory. i- Able to solve classical physics PDEs in their most general form.

ii- Able to solve quantum physics PDEs in their most general form.

iii- Able to solve integration and differentiation problems in pure mathematics and derive statistical distributions in their most general form.

Finally, when I hear the name Minkowski space, I feel depressed.

@ all our distinguished readers and contributors.

Dear Ismail Abbas M. Abbas ,

Without knowing history well, I cannot agree with demeaning Minkowski.

As to your theory, why do you call it a "statistical" theory?

I have just seen a very similar question:

An old question that is still fresh: Is gravity a Newtonian force or Einstein space-time curvature?

by Parviz Parvin

Unfortunately, it has 14629 answers so far, which is a bit too much to read

:-(

The thread question is really scientifically answered in SS post on page 1.

3 recent SS posts in https://www.researchgate.net/post/Do_Static_Gravitational_Fields_Propagate

- are relevant to this thread question as well.

Cheers

The following is a great illustration:

Can you derive and explain Einstein's general relativity in one page?

The answer is 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.

This means that contrary to Einstein, gravity exists as a force and the graviton theoretically exists but in free space and not on Earth.

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.