Here is a brief explanation of why the scattering wavefield follows an exponential decay √2 and √3 in 3D and 2D energy density systems during free fall (zero boundary conditions and zero source vector S).

In any closed control volume CV bounded by a closed surface A, two fields act simultaneously:

i) the classical/quantum scattering energy density field U;

ii) the information field that controls and directs the classical/quantum scattering energy density U.

This means:

DIFFUSION IS PROHIBITED WITHOUT PERMISSION.

Any attempt to measure the scattering energy density U will disrupt the entire information field and cause it to collapse completely.

This phenomenon is sometimes referred to as "measurement-induced wavefunction collapse."

Dear Professor Abbas M. Abbas,

I wondered about the factors 2 and √2 cropping up in relation to the "entanglement current" of two close but separate Josephson Junctions.

Preprint Brief Summary of the relations describing the 'Entanglement ...

What kind of joke is this?

Our Argentinian friend's impromptu response lacks professionalism and therefore deserves no comment.

The history of matrix mechanics began in 1925, with the aim of explaining the new world of quantum mechanics, energy, and momentum, such as the mysterious spectrum of the hydrogen atom, a quantum particle in a potential well, the stationary Bohr-Einstein distribution, etc.

The "Heisenberg-Born-Jordan matrix" is the first matrix formulation of quantum mechanics, developed by Werner Heisenberg, Max Born, and Pascual Jordan in 1925. This formulation was a major breakthrough, providing a consistent mathematical framework for describing quantum phenomena using matrices representing quantum physical properties such as position and momentum.

The matrix itself is expressed as follows:

0 -i√1 0  0

i√1 0 -i√2 0 . .

0 i√2 0 -i√3 . . .

0 0 i√3 0 -i√4 . .

etc

Note that the leading authors of the time claimed that √2, √3 . . etc. had their place in QM.

The real numbers √2, √3 . . etc., and more precisely √10, would have more space in the output results.

The author recommends two modifications to the above matrix:

i- Transform the matrix into a real matrix by removing the complex unit i.

ii- Reshape the above matrix into a sawtooth pattern, which is the most efficient for a quantum matrix.

Bo sequence.

A bit far feched mumbling only.

No physical constant!

The physical significance of the "Heisenberg-Born-Jordan matrix of 1925," which was a major breakthrough, is obvious: it is a matrix formulation of quantum mechanical systems equivalent to the classical Schrödinger equation (1927). Its expression is:

Ψ = h

0 -i√1 0 0

i√1 0 -i√2 0 . .

0 i√2 0 -i√3 . . .

0 0 i√3 0 -i√4 . .

etc.

The Heisenberg matrix Q is the energy operator of the quantum mechanical system in the sense that:

E= ∭Ψ^2 (x,y,z,t) dx dy dz. where E is the total energy of the quantum mechanical system E (x,y,z,t) = ΨΨ* =Ψ^2.

Between 1927 and 1930, the Q matrix definitively lost the battle against the Schrödinger equation, which is called the decline of matrix mechanics.

In 2020, another breakthrough was made: describing the Q matrix by the square of SE, and not SE itself, the subject of this question.

We propose here two major modifications to improve the Q matrix above:

i- Transform the matrix into a real matrix by removing the complex unit i.

ii- Transform the matrix above into a sawtooth pattern, which is the most efficient for a quantum matrix.

This improvement actually constitutes a revival, or even the rise of matrix mechanics.

To be continued.

The "Heisenberg-Born-Jordan matrix," the first consistent matrix formulation of quantum mechanics in 1925, is a bit strange.

It states that:

Ψ = √h

0 -i√1 0 0

i√1 0 -i√2 0 . .

0 i√2 0 -i√3 . . .

0 0 i√3 0 -i√4 . .

etc.

. . . Q1

It is clear that the Heisenberg matrix Q1 is the energy operator of the quantum system in the sense that:

E= ∭Ψ^2 (x,y,z,t) dx dy dz. where E is the total energy of the quantum system E (x,y,z,t) = ΨΨ* =Ψ^2. Equation Q1 suggests that the imaginary Heisenberg matrix describes the square root of the energy density of the mechanical system, not the energy density itself.

We suggest the following improvement, both physical and logical.

This improvement is the subject of this question.

We propose two major modifications to improve the matrix Q1 above:

i- Transform the matrix into a real matrix by removing the complex unit i and replacing Q1 with its square Q^2.

ii- Transform the matrix above into a sawtooth pattern, which is the most efficient for a quantum matrix.

We believe that this improvement actually constitutes a revival, or even the rise of matrix mechanics.

The new matrix Q^2 will be written as follows:

Equal to,0 -1^0.5      0      0      0      0      0      0      0      0      01^0.5      0 -2^0.5      0      0      0      0      0      0      0      00 2^0.5      0 -3^0.5      0      0      0      0      0      0      00      0 3^0.5      0 -4^0.5      0      0      0      0      0      00      0      0 4^0.5      0 -5^0.5      0      0      0      0      00      0      0      0 5^0.5      0 -6^0.5      0      0      0      00      0      0      0      0 6^0.5      0 -5^0.5      0      0      00      0      0      0      0      0 5^0.5      0 -4^0.5      0      00      0      0      0      0      0      0 4^0.5      0 -3^0.5      00      0      0      0      0      0      0      0 3^0.5      0 -2^0.50      0      0      0      0      0      0      0      0 2^0.5      0

Q=

-1     0   2^0.5       0       0       0       0       0       0       0     0

0    -3       0   6^0.5       0       0       0       0       0       0     0

2^0.5     0      -5       0 2*3^0.5       0       0       0       0       0     0

0 6^0.5       0      -7       0 2*5^0.5       0       0       0       0     0

0     0 2*3^0.5       0      -9       0 30^0.5       0       0       0     0

0     0       0 2*5^0.5       0     -11       0 30^0.5       0       0     0

0     0       0       0 30^0.5       0     -11       0 2*5^0.5       0     0

0     0       0       0       0 30^0.5       0      -9       0 2*3^0.5     0

0     0       0       0       0       0 2*5^0.5       0      -7       0 6^0.5

0     0       0       0       0       0       0 2*3^0.5       0      -5     0

0     0       0       0       0       0       0       0   6^0.5       0    -2

Note that the new matrix Q contains √2, √3, √5, etc. in addition to √10, all with 8-digit precision.

To be continued.

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 inherently included in Equation 1 by simple substitution Q=SQRT(B).

This is why the input elements of the transition matrix Q are all non-rational, such as √3, √2, etc., in the world of quantum mechanics.

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.