The statistical theory of Cairo techniques allows us to explain this complex situation in more detail:

The time-dependent diffusion equation (like the Laplacian operator equation) represents or models the natural binary collision relaxation process in a closed-surface control volume subject to Dirichlet boundary conditions.

1- In both time-dependent and time-independent processes, the information waves are always contained within the same control volume.

2- This means that the diffusion process is associated with and controlled by the information waves filling the control volume, both in macroscopic classical physics, such as the macroscopic heat diffusion equation, and in microscopic subatomic quantum physics.

Information waves are the driving force: no diffusion without permission.

3- This means that the Schrödinger partial differential equation is not a pure wave equation, but a partially diffusion and partially wave equation. 4- When we attempt to extract information from a quantum system through measurement, the information wave diminishes and the system transforms into a pure scattering system, a system of colliding particles.

This is sometimes called quantum wave collapse.

TO BE CONTINUED.

What is the second theory for you?

It has only vague diffusíon similarty. A probability density wave.

Here's a brief comment on our Argentinian friend's important response: "What does the second theory represent to you?

It has only a vague similarity in terms of diffusion. A probability density wave."

Let's simply recall the following three concepts, never known or defined before 2020, the year the statistical theory of Cairo techniques was born [1]:

1- The control volume V contained within the closed surface Area A (in 1D, 2D, 3D), replaces infinite real space or phase space before 2020.

2- This control volume is delimited by Dirichlet boundary conditions (the total probability of the row of matrix B = the total probability of the column of matrix B = the total probability of the entire space = 1).

3- The theory of Cairo techniques in 4D unitary x-t space redefines almost everything that was expressed before 2020 in the R^4 space (3D and real-time as an external controller) of 4D unitary x-t space.

Such as entanglement, superposition, etc.

Note that Einstein's special and general theories of relativity live and operate in 4-dimensional unitary x-t space, which perhaps explains why they are still so powerful.

1- I. Abbas, A Numerical Statistical Solution to EDPLs and EDPPs, Journal of the IJISRT, 2020.

Earthquake seismology (the propagation, reflection, and refraction of Earth's seismic waves) is the best tool for understanding the Earth's interior.

It also allows us to understand the Earth's interior.

It also explains the techniques of Cairo's statistical theory, combined with the theory of information propagation (the propagation, reflection, and refraction of information waves).

During an earthquake, the released energy takes the form of elastic waves transmitted by diffusion through the Earth.

However, this diffusion (propagating at a speed of a few kilometers per minute) is guided or controlled by the much faster information sphere, which propagates at the speed of light C.

Seismic wave propagation is ground movement, including compressional and shear waves, radially from the source of seismic energy (source center S) to the surrounding rock and soil. Seismic wave fields propagate through the Earth in two ways: body waves and surface waves. Body waves propagate within the Earth (body) and illuminate deep geological targets. It is noteworthy that seismic wave propagation follows the shortest path theory, with refractions predetermined by the information sphere's exploration command, similar to the refraction of light and electromagnetic waves between two media.

SIMPLE CHALLENGE

The simple challenge to our distinguished contributors and readers is the statistical transition matrix B for a closed control volume of surface A subject to Dirichlet boundary conditions,

U(x,y,z,t+dt)=B. U(x,y,z,t) . . . (1)

Equation 1 is not only universal, but it also describes and solves all time-dependent phenomena in the entire universe (partial differential equations of classical physics in its most general form, quantum physics, statistical distributions, integration and differentiation, etc.).

The challenge is as follows:

Name a single physical phenomenon from the four above that does not belong to Equation 1.

Thank you.

What I can contribute is that if we are referring to the squared form of the Schrödinger equation, then there's an interesting connection to entangled states particularly Bell states of two qubits which inherently involve the square root of two in their normalization. These mathematical structures may interact conceptually with tensor formulations of quantum mechanics, especially when considering composite systems and spin representations.

The 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 ∇^2tz  ∇^2 tt

x

Cxx Cxy Cxz Cx

tCyx Cyy Cyz Cyt

Czx Czy Czz C zt

C tx C ty C tz C tt

=                I

I is the unit matrix.

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

The result of multiplication for the first raw is,

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

And the shear stress tensor is negligibly zero in an infinite 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

Therefore,

-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.