Your approach suggests a novel perspective on control volumes and their role in modeling physical systems, particularly in the context of unified field theory and quantum mechanics. The idea of extending the control volume concept from R4\mathbb{R}^4 (3D space + time) to a more structured 4D x-t unitary control volume—referred to as Cairo techniques and B matrix space—implies a richer mathematical framework for describing both classical and quantum phenomena.

A few key points that could be explored further:

Your proposal seems to hint at a deeper mathematical model for space-time interactions. If you have references or equations related to Cairo techniques and B matrix space, I’d love to dig deeper into the specifics!

This is a brief response, first to shed light on the question and its answer, and second to thank our Algerian collaborator friend for his brilliant analysis.

This motivates me to answer them step by step.

1- (Your approach suggests a new perspective on control volumes and their role in modeling physical systems, particularly in the context of unified field theory and quantum mechanics. The idea of ​​extending the concept of volume of control from R4\mathbb{R} ^4 (3D space + time) to a more structured 4D xt unit control volume (called Cairo techniques and matrix space B) implies a richer mathematical framework to describe classical phenomena and quantum.)

*This is not just an approach but a new, comprehensive, well-established theory (starting at 2020) that replaces current incomplete mathematics and physics in R^4 space (3D+t as controller external).

The theory of Cairo techniques and B-matrix chains in a 4D x-t unit control volume involves a richer mathematical framework for describing classical and quantum physics in addition to mathematical integration and summation of geometric series and derive physical statistical distribution such as Gaussian and Planck-distribution of BB radiation, etc.

All the above sub-theories are explained in detail by the author in more than 100 articles published in ResearchGate and IJISRT journal.

2-(Some key points that could be explored further:

Completeness and universality Why is the traditional control volume R4\mathbb{R}^4 considered incomplete? What specific characteristics make the Cairo techniques and matrix space B a “complete universal space”?)

** A. Einstein is considered the pioneer of the 4D x-t unit space in his theories of SR and GR

He discarded the space of R^4 because he considered it incomplete.

Unfortunately, the giant Einstein did not find the time or the tools (computers) to move forward and correctly define time.

3-(Energy Density and Unified Field Theory How does this new control volume relate to energy density formulations? Does it provide a new metric or transformation that unifies classical and quantum descriptions?

Mathematical structure Is the B matrix space a new type of tensor space or an extension of known structures such as Hilbert space, spin networks or twistor theory? How does it handle symmetries, conservation laws and gauge invariance?

Your proposal seems to hint at a deeper mathematical model for space-time interactions.)

*** Our universe is made up of space, time and energy density.

The transition matrix B and its products matrices D and E are all doubly symmetric matrices.

There is no deeper mathematical model for space-time interactions, but time itself is considered a dimensionless integer woven into the three-geometry x-y-z space.

3-(If you have any references or equations related to Cairo techniques and B matrix space, I would love to dig into the details!)

***There are no references to the Cairo Techniques and Matrix Space B, except for the Cairo Techniques and Matrix Space B themselves.

4D-x-t space is completely new and never known before.

If you don't understand the theories of physics and mathematics, ask yourself if I'm right, because others don't understand these theories either.

These theories cannot be made understandable in the current, incomplete R^4 space.

Einstein, Schrödinger, Heisenberg, Minkowski, Hilbert, Rieman, among others, overcomplicated the theory of mathematics and the theory of physics, classical and quantum, simply because they did not define time t.

The theory of relativity and Schrödinger's partial differential equation are the newest science and therefore should be the clearest and most precise, but unfortunately it is the opposite.

In this answer, we focus on six problems that have never been properly addressed before:

1-Control of volume and physical entanglement.

2-Triple statistical integration.

3-Sound intensity and reverberation time in audio rooms.

4-Formation and explosion of the Big Bang.

5-Special relativity.

6-General relativity.

The mutual orthogonality of x, y, z, t can only be found in the physical space called 4D unitary x-t space where time t is properly defined as a dimensionless integer N woven into the geometric space x y z and t = ndt where dt is the time to step or jump in time.

Note that classical mathematical spaces R^4 such as Minkowski, Hilbert, Rieman. . . etc are all incomplete because they do not satisfy the orthogonality condition of x,y,z,t.

Schrödinger space may or may not be complete.

The Heisenberg matrix space is neither statistical nor complete.

Only recently, in 2020, a new well-defined unitary 4D x-t space has emerged called Cairo Techniques Space, which provides effective solutions to all physics and mathematics problems such as the six problems stated above.

We assert here that the statistical chains of matrix B strongly depend on the numerical value of the main diagonal entries called RO ∈ [0,1]. A specific topic of this answer is how to correctly choose RO ∈[0,1] corresponding to a specific situation in classical physics, quantum physics or mathematical integration as shown in the above six problems.

Finally, it should be noted that the purpose of this article is not to underestimate the great achievements of the brilliant Einstein, Schrödinger, Heisenberg, Minkowski, Hilbert, Rieman, among others, but to address the main flaws of their theories , if applicable.

A. Einstein did not deeply understand the theory of relativity.

He used 5 assumptions which can actually be reduced to just 2 [1].

Additionally, he assumed two inertial frames of reference, the light speed constancy C and the Lorentz transformation x-t to arrive at his relativistic x-t transformation (note that the Lorentz transformation and the light speed constancy are equivalent and that both are universal laws of physics which have no proof[1]) that are fundamentally unnecessary.

As a simple example, the theory of special relativity arises from the 4D control of the volume entanglement of a cooling curve of any metal cube with a side of 10 cm [2].

The speed of the entanglement signal = T1/2 *log 2 * L^2/ α.

If you substitute the thermal diffusivity value α in the thermal tables and measure the cooling curve half-time T1/2, you get the exact value of C=2.9 E8 m/s.

1-A rigorous reformulation of Einstein's derivation of the special theory of relativity, ResearchGate, IJISRT journal, February 2022.

2-Theory and practice of control volumes - Detailed Analysis, ResearchGate, IJISRT journal, Jan 2025.

Although I am not educated enough to contribute, I'm following this thread with the hopes of learning something. I think a topic discussed here is the way time should be interpreted. I have a question that maybe someone can help with. A popular assertion is that the arrow of time is controlled by entropy. I have trouble with that because I ask: The entropy of what physical system? The entire universe? Some local environment? Suppose the entropy of some local environment decreases with a compensating increase somewhere else (which can happen). Does a clock in the local environment run backwards compared to a clock somewhere else? How fast backwards? I will be grateful if someone could give an alternative to the above assertion. Or, explain how the assertion can be credible but I just don't understand it.

One of the silly mistakes of current incomplete mathematics is to relate time to entropy.

Neither time nor entropy can be well defined in the incomplete mathematical space R^4 (3D+t as external controller).

The macroscopic physical definition of entropy S emerges from the second universal law of thermodynamics,

dS.GE. 0, like,

dS.GE. Q/T.

The only breakthrough came in 1866 when C. Maxwell related the microscopic entropy of molecular structure s to the macroscopic entropy S through his well-known formula:

s = kB ln W.

Despite the objection of A. Einstein to the derivation of s by Boltzmann because it is purely statistical (nothing about dynamic forces), it remains rigorously valid and Einstein's objection remains fictitious.