Fundamentals of Quantum Mechanics

Theory and Practice

Abstract

The Schrödinger equation, with its Bohr/Copenhagen interpretation, was born in 1927 from the imagination of Schrödinger, Bohr, Heisenberg, and others.

This theory is inherently incomplete, unreliable, and doomed to disappear sooner or later.

It fails to explain complex microscopic situations such as vacuum dynamics, nor macroscopic situations such as the formation and explosion of the Big Bang, nor the formation of black holes.

We believe that the main reason for the incompleteness of the Schrödinger equation is that it exists and operates in a three-dimensional geometric space plus t as an external controller (R^4 space), which is an incomplete and inadequate space.

It is noteworthy that this is the first time that the incompleteness of the classical Schrödinger equation has been linked to its operating space.

Over the past century, several attempts have been made to combine the three-dimensional Schrödinger equation with the theory of general relativity in a four-dimensional unitary x-t space to extend its range and remove its shortcomings, but without any improvement.

The West is losing the battle of quantum mechanics!

Recently, in 2020, a new breakthrough statistical theory in 4D unitary x-t space based on B-Transition matrix chains which is a product of the theory of Cairo techniques emerged [1].

It is an advanced concrete theory of artificial intelligence, called Cairo Techniques Theory.

This theory, which models the behavior of nature, has proven capable of solving temporal situations in classical and quantum physics in the most general cases, as well as pure mathematical problems.

In conclusion, we can hypothesize the following:

It is true that Cairo intelligence techniques = natural intelligence = artificial intelligence in the strict sense = unified field theory.

The same theory proposes replacing SE with its square combined with the advanced artificial intelligence as an essential improvement.

So we now have two distinct theories of quantum mechanics: one based on the original 1927 theory of the Schrödinger equation supplemented by the Bohr/Copenhagen interpretation, and the other based on the 2020 square of the Schrödinger equation, supplemented by advanced artificial intelligence.

This is the subject of this article.

The author introduces and defines the concept of a control volume (in a 4D unitary x-t space), previously unknown in either classical or quantum physics.

The concept of a closed control volume, delimited by a closed surface A subject to Dirichlet boundary conditions, replaces the concept of an infinite space R^4, which is of limited utility.

In this article, we also demonstrate that the squared Schrödinger equation preserves, or even improves upon, the quantum concepts of the original Schrödinger equation, such as quantum entanglement and quantum superposition in addition it allows for .

Quantum entanglement exists in both quantum and classical systems, between the elements and walls of the system, and its speed is limited to C, the speed of light.

The speed of entanglement can never be infinite, and the supposedly spooky action at a distance is merely a phantasmagorical fantasy.

Once again, the West is losing the battle of quantum mechanics!

I.INTRODUCTION

The Schrödinger equation, with its Bohr/Copenhagen interpretation, was born a century ago, in 1927, from the imagination of Schrödinger, Bohr, Heisenberg, and others.

This theory is inherently incomplete, unreliable, and doomed to disappear sooner or later. It fails to explain complex microscopic situations like vacuum dynamics, nor macroscopic situations like the formation and explosion of the Big Bang, nor the formation of black holes.

Once again, the main reason for the incompleteness of the Schrödinger equation is that it lives and operates in R^4 space, 3D plus t, as an external controller, which is incomplete and inadequate. Almost all of modern physics is based on two theories: general relativity and quantum mechanics.

It is worth noting that Einstein's relativity, special relativity, and general relativity were developed in the unitary 4D x-t space, which explains why these two theories have remained valid and robust for over a century.

Recall that over the last century, several attempts have been made to combine the three-dimensional Schrödinger equation with the theory of general relativity in a four-dimensional unitary x-t space, but without any improvement.

The West is losing the battle of quantum mechanics!

As a result, we now have two distinct and competing theories of quantum mechanics: one based on the original 1927 Schrödinger equation theory, and the other based on the 2020 square of the Schrödinger equation, enhanced by advanced artificial intelligence.

Which of these two theories will ultimately prevail is the subject of this article.

In this article, we also demonstrate that the transformation of electromagnetic field energy into gravitational field energy and vice versa is possible and that, combined with the second theory of quantum mechanics, it provides a basis for combining the theory of general relativity with that of quantum mechanics.

This was a fundamental assumption in the search for a unified field theory (theory of everything), including the theory of general relativity.

In order not to worry too much about the details of the theory let us move directly to the Applications and Numerical Results.

III. Applications and Numerical Results

This section of applications and numerical results will be presented in the form of a dozen questions and answers covering most of the persistent and resistant topics in quantum mechanics for the sake of convenience and clarity.

Q1

Are there two distinct theories of quantum mechanics today?

A1

In 1925, E. Schrödinger formulated his famous quantum mechanical equation, and in 1927, N. Bohr and E. Heisenberg, among others, invented his so-called superposition interpretation for this equation, despite opposition from A. Einstein and E. Schrödinger himself.

Over the past century, ardent defenders of the original quantum theory have attempted to present it, alongside the theories of relativity, as the unified field theory, but to no avail.

Recently, in 2020, the author presented the square of Schrödinger's partial differential equation as a new quantum mechanics theory [2,3].

We believe that these two descriptions of quantum mechanics can not be merged into one but their numerical results can be compared one vs the other.

In other words, one must apply the statistics of the Cairo technique theory to a well-defined quantum physical situation, then apply the original Schrödinger partial differential equation to the same defined situation and find the affinity zones with respect to the decoherence zones of the two solutions.

Note that:

i- The original Schrodinger equation of 1925-1927 exists and operates in R^4 space (3D plus real-time as an external controller), which is an incomplete and inadequate space.

ii- The new quantum mechanics based on the square of Schrödinger's original PDE exists and operates in the 4D unitary space x-t, which is the complete space [4].

Q2

Is the second theory of quantum mechanics tensor mechanics?

A2

An m × n matrix: the m rows are horizontal and the n colons are vertical.

The entries, or input elements, of matrix [A] are the values ​​Ai,j, where i is the ith row and the jth column.

Matrices can be of type (m = n) or other, and of similar type (Aij = Aji) or other.

Thanks to matrix technology and artificial intelligence, we have various components and similar matrices capable of modeling or simulating the natural grace of AI statistical algorithms.

An automatrix, or nxn transition matrix B, is an array of n^2 (nxn) entries (sometimes called inputs or elements) capable of describing energy density statistics in a 4D unitary x-t space.

The intelligent technology embodies the techniques used in several consecutive sections:

If we now write the statistical transition matrix B in the form:

Bi,j,kN

where i, j, k lowercase indices and N uppercase indices.

where:

x=i dx, y=j dy, z=k dy

and t=N dt where N is the number of iterations or time jumps of dt, then the tensor nature of the matrix B is revealed.

Q3

Is it is true that Cairo intelligence techniques = natural intelligence = artificial intelligence in the strict sense = unified field theory

A3

The answer to this question emerges from the following 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, sound intensity in audio rooms.. etc.) [1,2,6,7,8].

The challenge is as follows:

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

Thank you.

Q4

What is the relationship between thermal diffusivity and the speed of light?

A4

The numerical statistical theory of the Cairo techniques predicts a relationship between thermal diffusivity α and the speed of light C in a natural cooling curve.

For example, for a metallic cube whose side l is [1, 2, 3],

the strings of the B matrix provide the first unique and rigorous proof of Sabine's experimental reverberation formula in a century:

U(t) = U(0). Exp -t [Constant. Area / C. Volume]. . . . . . (1)

C is the entanglement velocity. The reverberation velocity of sound is obviously the speed of sound in air at NPT = 330 ms^-1.

The same thing happens in the free cooling curve of metal cubes and leads to the following formula,

C = T½ * log 2 * L²/ (thermal diffusivity α) . . . . (2)

T1/2 is the half-life of the cooling curve of a metal cube of C.

T1/2 should be measured experimentally.

T1/2 of a free cooling curve T1/2 for a 10 cm aluminum cube at 45 seconds

and that of a similar iron cube at 100 seconds

The thermal diffusivity α is determined from thermal tables:

α (Al) = 1.18 E-5 MKS units

α (Iron) = 2.5 E-5 MKS units

If we substitute the above numerical values of α, L and T1/2 ​​into equation 2, we obtain C, the speed of light, equal to 2.95 m s^-1 for both cases.

But the question arises: what is going on here and why is the thermal diffusivity α related to the speed of light C?

Rise and fall of matrix mechanics, January 2024.

Q5

Is it true that the Fourier transform is only an optional mathematical tool?

A5

The assertion that the Fourier transform is merely an optional mathematical tool overlooks its fundamental significance in many areas of mathematics and applied sciences. While it may appear dispensable in some contexts, it is essential for analyzing and solving problems in signal processing, differential equations, and physics.

In your discussion, the statistical theory of Cairo techniques offers a framework for solving time-dependent partial differential equations (PDEs), but it does not negate the utility of the Fourier transform. The Fourier transform provides a comprehensive solution framework, particularly for linear systems, allowing us to work in the frequency domain, which often simplifies the problem-solving process.

Regarding the limitations we mentioned, while it’s true that the Fourier transform traditionally assumes infinite domains, various adaptations—such as the Fourier series or windowed Fourier transforms.

We assume that the Fourier transform is merely an optional mathematical tool that can be dispensed with.

The statistical theory of Cairo techniques predicts the general solution of a time-dependent PDE as follows [2,3,4,5,6]:

f(x,y,z,t)=D(N).(b+S) + B^N.IC..(1)

where D(N) is the transfer function = B+B^2+B^3 +...+B^N

b is the vector of 1D, 2D, and 3D boundary conditions, arranged in the appropriate order.

IC is the vector of initial conditions.

B is the well-defined transition matrix for the considered closed control volume. One drawback of the mathematical Fourier transform is that it predicts the solution for 1D, in the x domain GT -∞ and LT ∞, and is not defined for the domain of the x elements of [a,b]. The Fourier transform itself predicts the wave solution for 1D, over the entire interval -∞