What is the meaning of 2^1/2 in quantum physics?

Ismail Abbas M. Abbas @Ismail-Abbas-Abbas

25 May 2025 20 9K Report

This crucial question was posed and received a relevant answer in the ResearchGate Q&A section on July 23, 2023.

A simple way to answer it is to use the 2020 second theory of quantum mechanics, using tensor dynamics [1], supplemented by the author's proposed artificial intelligence [2].

This doctrine was so dangerous that the manuscript describing it had to circulate under the ground, through publications and distribution.

The former iron guardians of the original first theory of the Schrödinger equation in 1927 know that sooner or later, the classical Schrödinger equation will disappear and be replaced by the second theory of quantum mechanics, and that they will disappear with it.

1-Fundamentals of quantum mechanics-Theory and Practice.

2-BOOK- Fundamentals of quantum mechanics-Theory and Practice.

Juan Weisz

Thats just a number! No meaning!

Vlasie Catalin Mircea

Preprint Calculating 2(1/2) (2) in IOMM: "Complex" vs. "Light" Pitic ...
In IOMM, a mathematical value like 2(1/2) doesn't "exist" with infinite precision until a Pitic actualizes an approximation of it through a TIO-limited process.
This could be paralleled with the concept of a quantum state "collapsing" or becoming definite upon measurement. Before Pitic Radix performs the calculation, 2(1/2) might be considered an "unactualized potential" within the IOMM mathematical framework. The Pitic's computation is the act of actualization.
The Pitic's Kp (skill) and chosen algorithm influence the outcome (the specific SNM approximation and its precision within TIO limits), analogous to how the choice of measurement apparatus affects quantum outcomes.

Ismail Abbas M. Abbas

This is just a preliminary answer to demonstrate the importance of √2 in quantum mechanics:

i- The statistical transition matrix/tensor B defining advanced artificial intelligence and the solution to heat conduction is positive and has a unique square root.

ii- The square root of the real tensor B is another tensor Q, which is the complex transition matrix of the quantum system.

iii- The elements of the tensor Q and its energy eigenvalue are based on √2.

The factor √2 represents the Phythagorean theorem or the orthogonality of the 4-dimensional unitary x-t space.

The indoctrinated iron guardians of the classical Schrödinger equation claim that its solution contains √2 by chance and order the smartest to shut up and calculate.

To be continued.

Manfred Geilhaupt

it's coming up by calculating an effective value. In AC circuits useful for to pay electric energy used. If you use the U0,I0 maximum values - possible too - but not correct. (Sometimes called "Expectation Value")

Vlasie Catalin Mircea

My theory The IOMM (Theory of Fatigued Infinity and the Minimal Number Series) is based on 2 theories developed by me. The first is the Theory of Fatigued Infinity (TIO) where the infinite is idealized, in the sense that you cannot reach the infinite because the complexity grows exponentially, and at some point the complexity will be so great that you cannot continue, that is the tired infinite, and the other theory is the Granular Fundamental Space and the Minimal Number Series (SNM) theory which says that 0 is an ideal number and that it does not exist in reality (I also have a postulate that proves that 0 does not exist) instead there is a number 0A which has the smallest possible value. If we use this theory I tend to think that we are getting closer to the answers we are looking for, because this theory eliminates singularities.

Manfred Geilhaupt

(I also have a postulate that proves that 0 does not exist)

Zero does not exist in nature: Energy=const (zero would be nonsense)

Ismail Abbas M. Abbas

The above answer was theoretical. Here's the application:

i. The well-known statistical transition matrix/tensor B defines advanced artificial intelligence, and the solution for thermal conductivity is,

0 10416667/62500000 10416667/62500000 0 10416667/62500000 0 0 0

10416667/62500000 0 0 10416667/62500000 0 10416667/62500000 0 0

10416667/62500000 0 0 10416667/62500000 0 0 10416667/62500000 0

0 10416667/62500000 10416667/62500000 0 0 0 0 10416667/62500000

10416667/62500000 0 0 0 0 10416667/62500000 10416667/62500000 0

0 10416667/62500000 0 0 10416667/62500000 0 0 10416667/62500000

0 0 10416667/62500000 0 10416667/62500000 0 0 10416667/62500000

0 0 0 10416667/62500000 0 10416667/62500000 10416667/62500000 0

ii. The square root of the real tensor B is another tensor Q, which is the complex transition matrix of the quantum system, Q = √B,

Hence Q =

((3+3*i)*104166670^0.5+(1+i)*312500010^0.5)/200000 ((1-i)*104166670^0.5+(1-i)*312500010^0.5)/200000 ((1-i)*104166670^0.5+(1-i)*312500010^0.5)/200000 ((-1-i)*104166670^0.5+(1+i)*312500010^0.5)/200000 ((1-i)*104166670^0.5+(1-i)*312500010^0.5)/200000 ((-1-i)*104166670^0.5+(1+i)*312500010^0.5)/200000 ((-1-i)*104166670^0.5+(1+i)*312500010^0.5)/200000 ((-3+3*i)*104166670^0.5+(1-i)*312500010^0.5)/200000

((1-i)*104166670^0.5+(1-i)*312500010^0.5)/200000 ((3+3*i)*104166670^0.5+(1+i)*312500010^0.5)/200000 ((-1-i)*104166670^0.5+(1+i)*312500010^0.5)/200000 ((1-i)*104166670^0.5+(1-i)*312500010^0.5)/200000 ((-1-i)*104166670^0.5+(1+i)*312500010^0.5)/200000 ((1-i)*104166670^0.5+(1-i)*312500010^0.5)/200000 ((-3+3*i)*104166670^0.5+(1-i)*312500010^0.5)/200000 ((-1-i)*104166670^0.5+(1+i)*312500010^0.5)/200000

((1-i)*104166670^0.5+(1-i)*312500010^0.5)/200000 ((-1-i)*104166670^0.5+(1+i)*312500010^0.5)/200000 ((3+3*i)*104166670^0.5+(1+i)*312500010^0.5)/200000 ((1-i)*104166670^0.5+(1-i)*312500010^0.5)/200000 ((-1-i)*104166670^0.5+(1+i)*312500010^0.5)/200000 ((-3+3*i)*104166670^0.5+(1-i)*312500010^0.5)/200000 ((1-i)*104166670^0.5+(1-i)*312500010^0.5)/200000 ((-1-i)*104166670^0.5+(1+i)*312500010^0.5)/200000

((-1-i)*104166670^0.5+(1+i)*312500010^0.5)/200000 ((1-i)*104166670^0.5+(1-i)*312500010^0.5)/200000 ((1-i)*104166670^0.5+(1-i)*312500010^0.5)/200000 ((3+3*i)*104166670^0.5+(1+i)*312500010^0.5)/200000 ((-3+3*i)*104166670^0.5+(1-i)*312500010^0.5)/200000 ((-1-i)*104166670^0.5+(1+i)*312500010^0.5)/200000 ((-1-i)*104166670^0.5+(1+i)*312500010^0.5)/200000 ((1-i)*104166670^0.5+(1-i)*312500010^0.5)/200000

((1-i)*104166670^0.5+(1-i)*312500010^0.5)/200000 ((-1-i)*104166670^0.5+(1+i)*312500010^0.5)/200000 ((-1-i)*104166670^0.5+(1+i)*312500010^0.5)/200000 ((-3+3*i)*104166670^0.5+(1-i)*312500010^0.5)/200000 ((3+3*i)*104166670^0.5+(1+i)*312500010^0.5)/200000 ((1-i)*104166670^0.5+(1-i)*312500010^0.5)/200000 ((1-i)*104166670^0.5+(1-i)*312500010^0.5)/200000 ((-1-i)*104166670^0.5+(1+i)*312500010^0.5)/200000

((-1-i)*104166670^0.5+(1+i)*312500010^0.5)/200000 ((1-i)*104166670^0.5+(1-i)*312500010^0.5)/200000 ((-3+3*i)*104166670^0.5+(1-i)*312500010^0.5)/200000 ((-1-i)*104166670^0.5+(1+i)*312500010^0.5)/200000 ((1-i)*104166670^0.5+(1-i)*312500010^0.5)/200000 ((3+3*i)*104166670^0.5+(1+i)*312500010^0.5)/200000 ((-1-i)*104166670^0.5+(1+i)*312500010^0.5)/200000 ((1-i)*104166670^0.5+(1-i)*312500010^0.5)/200000

((-1-i)*104166670^0.5+(1+i)*312500010^0.5)/200000 ((-3+3*i)*104166670^0.5+(1-i)*312500010^0.5)/200000 ((1-i)*104166670^0.5+(1-i)*312500010^0.5)/200000 ((-1-i)*104166670^0.5+(1+i)*312500010^0.5)/200000 ((1-i)*104166670^0.5+(1-i)*312500010^0.5)/200000 ((-1-i)*104166670^0.5+(1+i)*312500010^0.5)/200000 ((3+3*i)*104166670^0.5+(1+i)*312500010^0.5)/200000 ((1-i)*104166670^0.5+(1-i)*312500010^0.5)/200000

((-3+3*i)*104166670^0.5+(1-i)*312500010^0.5)/200000 ((-1-i)*104166670^0.5+(1+i)*312500010^0.5)/200000 ((-1-i)*104166670^0.5+(1+i)*312500010^0.5)/200000 ((1-i)*104166670^0.5+(1-i)*312500010^0.5)/200000 ((-1-i)*104166670^0.5+(1+i)*312500010^0.5)/200000 ((1-i)*104166670^0.5+(1-i)*312500010^0.5)/200000 ((1-i)*104166670^0.5+(1-i)*312500010^0.5)/200000 ((3+3*i)*104166670^0.5+(1+i)*312500010^0.5)/200000

iii. At first glance, we notice that √2 is scattered among the elements of the vector Q, and that its energy eigenvalue/eigenvector is based on √2

The factor √2 represents the Pythagorean theorem or the mutual perpendicularity of x, y, z, and t.

iv. The eigenvalue equation of the tensor Q is,

equals,11111111

0.70710679

,has an energy/eigenvector eigenvalue of ,

0.70710679.

Whereas √2/2 is equal to,

0.707106769

which represents remarkable 8-digit precision.

Ismail Abbas M. Abbas

BETTER TYPING:

============

The above answer was theoretical. Here's the application:

i. The well-known statistical transition matrix/tensor B defines advanced artificial intelligence, and the B 8x8 matrix entries for simple cubic shape is:

The statistical hypothesis is that quantum equation is the square root of heat conduction equation and also Q = √B,

NOW B matrix 8x8 is ,

0 1/6 1/6 0 1/6 0 0 0

1/6 0 0 1/6 0 1/6 0 0

1/6 0 0 1/6 0 0 1/6 0

0 1/6 1/6 0 0 0 0 1/6

1/6 0 0 0 0 1/6 1/6 0

0 1/6 0 0 1/6 0 0 1/6

0 0 1/6 0 1/6 0 0 1/6

0 0 0 1/6 0 1/6 1/6 0

the quantum mechanical transition matrix Q is the square root of classical physics transition matrix B,

Q = √B,

Hence Q =

iii. At first glance, we notice that √2 is scattered among the elements of the vector Q, and that its energy eigenvalue/eigenvector is based on √2

The factor √2 represents the Pythagorean theorem or the mutual perpendicularity of x, y, z, and t.

iv. The eigenvalue equation of the tensor Q is,

* [1 1 1 1 1 1 1 1]

equals,

0.70710679

,has an energy/eigenvector eigenvalue of ,

0.70710679.

Whereas √2/2 is equal to,

0.707106769

which represents remarkable 8-digit precision.

Juan Weisz

Manfred

What happens when your car has 0 gasoline?

Vlasie Catalin Mircea

It's easy, the gas exists somewhere, either you have too little, or it's too far away, so it's not 0 it must exist, or it existed once, just because you don't have gas doesn't mean it doesn't exist. In response the car doesn't have gas, but gas does exist. So 0 has a value.

Manfred Geilhaupt

Juan Weisz

What happens when your car has 0 gasoline?

God question! (I take my electric car)

Seriously: If my car has 0 gasoline, that does not mean gasoline (energy) generally is zero possible in our universe. Zero is math-like here. (My tank is empty instead to use zero is equivalent locally, relatively.) Think you made a point on this point above?? (And on the other hand Energy can not be infinite as well)

By the way 010011 in your computer zero is not zero

Juan Weisz

Well, i never thought such massive misunderstandings of QM , were even possible.

Even some cursatory reading of introductory books imtended for lay persons shoul straiten out

what is talked about in the microscopic world.( ie B. Hoffman)

Manfred Geilhaupt

Juan

If your wallet is empty, where do you think the money has gone?

Vlasie Catalin Mircea

It is true that when the wallet is empty, there is no money. Let's say you have an empty wallet and you want to fill it with 100 euros, in mathematics there is an imaginary number i, this does not mean that the wallet will not be filled with 100 euros in reality, but it is precisely your imagination that transforms 0 into i, that is, you imagine that there is money in the wallet. Thus, instantly 0 is transformed into i, just through your imagination, this imagination increases the chances that the wallet will be filled (they are not high, but they exist). The value 0 appears when the wallet is lost and no one imagines that that wallet is filled with money, therefore imagination is an action that in the future may fill the wallet, or not, but it still remains an action i.

Manfred Geilhaupt

It is true that when the wallet is empty, there is no money....

One reason why Einstein invented Relativity

Juan Weisz

No sweat

I dont keep it all in my wallet.

Transform 0 into i ? How is that?

If you publish these days, you dont make money, you loose some.

Then, if you are lucky, your article will be remembered for at most 1 month.

Juan Weisz

Anyway, action in physics is an integral over L dt=S

Manfred Geilhaupt

No sweat

Yes sweat

I dont keep it all in my wallet.

God's way too

Transform 0 into i ? How is that?

If 0 energy is possible in our universe this contradicts the conservation of energy - not math.

If you publish these days, you dont make money, you loose some.

I only would if I get much :)

Then, if you are lucky, your article will be remembered for at most 1 month.

Broterwerb und Streben nach Erkenntnis sollten voneinander getrennt sein. (A.E.) Man sollte selbst seine Erkenntnis widerlegen zu versuchen, bevor es anderen gelingt. (ICH.) Macht zufriedener. Noch mehr, wenn es nicht gelingt. Ich vertrau auf Einstein in diesem Falle. Und auf den Dalai Lama.

Ismail Abbas M. Abbas

The core of the statistical theory, called Cairo techniques, is based on matrix/tensor B transition chains in a closed volume or control volume, which allow for an exact simulation of nature in all time-dependent physical and mathematical processes.

In conclusion, the hypothesis that the statistical theory, called Cairo techniques, is the unified theory for all domains, or the theory of everything. It has been successfully proven since 2020, generating more than 50 original papers [1,2] in various fields of classical physics, quantum physics, and mathematics.

The theory asserts that there is nothing new in quantum mechanics.

The solution to the Schrödinger equation is simply the square root of the solution to the heat diffusion equation. And the transition matrix of the quantum system Q is the square root of the transition matrix of the heat diffusion system B.

To find Q = √B, use the simplest 8x8 matrix B for a three-dimensional cube. B=

0 1/6 1/6 0 1/6 0 0 0

1/6 0 0 1/6 0 1/6 0 0

1/6 0 0 1/6 0 0 1/6 0

0 1/6 1/6 0 0 0 0 1/6

1/6 0 0 0 0 1/6 1/6 0

0 1/6 0 0 1/6 0 0 1/6

0 0 1/6 0 1/6 0 0 1/6

0 0 0 1/6 0 1/6 1/6 0

Therefore, the transition matrix Q of quantum mechanics is the square root of the transition matrix B of classical physics,

Q = √B. Its complex Q matrix is therefore expressed as follows:

i)*104166670^0.5+(1+i)*312500010^0.5)/200000 ((-3+3*i)*104166670^0.5+(1-i)*312500010^0.5)/200000 ((1-i)*104166670^0.5+(1-i)*312500010^0.5)/200000 ((-1-i)*104166670^0.5+(1+i)*312500010^0.5)/200000

5)/200000 ((1-i)*104166670^0.5+(1-i)*312500010^0.5)/200000

At first glance, we notice that √2 is scattered among the elements of the vector Q, and that its eigenvalue/energy eigenvector is based on √2.

The factor √2 represents the Pythagorean theorem or the mutual perpendicularity of x, y, z, and t.

At first glance, we notice that √2 is scattered among the elements of the vector Q, and that its eigenvalue/energy eigenvector is based on √2.

The factor √2 represents the Pythagorean theorem or the mutual perpendicularity of x, y, z, and t.

iv. The eigenvalue equation of the tensor Q is:

Q . IC = Constant * eigen value . IC . . . (1)

where IC is an initial condition or an arbitrary eigenstate simply assumed to be arbitrary like [1,1,1,1,1,1,1,1]

Solution to Equation 1 or energy vector in arbitrary units:

0.70710679

This means that Q has an energy/eigenvector eigenvalue of ,

0.70710679.

Which is exactly equal to √2/2.

( √2/2)=0.707106769

Q-matrix has remarkable 8-digit precision which is quite striking.

There is an undeniable connection between quantum mechanics and 2^1/2, where the Schrödinger equation fails to find it.

Q-matrix claims that in the superposition of two or more energy/eigenvector states, we must multiply by 0.70710679.

Is this convincing enough?

Ismail Abbas M. Abbas

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.

Badges
Science topic

More Ismail Abbas M. Abbas's questions See All

What is the difference between mathematical R^4 space and physical 4D unit space?

We assume that the difference is huge and that it is not possible to compare the two spaces. The R^4 mathematical space considers time as an external controller and the space itself is immobile in...

10 August 2024 6,678 14 View

Is it true that the vacuum bomb is about to arrive?

We assume this to be true. We also assume that the vacuum bomb is the latest version of explosives with an explosive power of a few to ten kg of TNT equivalent. It has the unique characteristic of...

04 August 2024 4,534 1 View

Is it true that science is leaving the era of mathematics and entering the era of matrix mechanics?

We assume this to be true. Science leaves the era of mathematics and enters the era of matrix mechanics and the turning point is the discovery of numerical statistical theory called Cairo...

31 July 2024 3,900 2 View

Which filtration method to go for run off water from dirty solar panels to be used again?

We are working on a robot that cleans solar panels using fresh water supply and a rotating brush. We are trying to conserve as much water at possible by recycling the dirty water that is collected...

28 July 2024 5,778 2 View

Can we find a statistical matrix mechanics equivalent to the Schrödinger equation?

We assume that we can find a statistical matrix mechanics equivalent to Schrödinger's PDE in two consecutive steps: i-Transform the Schrödinger PDE describing the wave function Ψ into its square...

27 July 2024 3,959 4 View

Has anyone looked into the stability of FEM methods on curved meshed?

Google scholar isn't giving me any results on this

27 July 2024 595 2 View

Is it true that there is a physico-statistical meaning to the constant π other than circular geometry but the iron guardians of the SE deny it?

We assume that there is a physico-statistical meaning to the constant π other than circular geometry, but the iron guardians of the Schrödinger equation deny this. The iron guardians of the...

22 July 2024 4,285 9 View

How many samples size should I select to compare both groups?

I want to study the differences between two groups: the treatment group and the comparison group. The total population consists of 60000 women in the treatment group, distributed across different...

21 July 2024 669 3 View

Is it possible to calculate finite numerical integration via matrix mechanics?

We assume that it is possible to calculate finite numerical integration via statistical matrix mechanics (a product of the statistical method of Cairo techniques). It is obvious that here it is...

21 July 2024 6,809 5 View

Assuming that the vacuum explodes spontaneously, how is this explosion sustained and amplified?

We assume that the energy in infinite free space (in addition to flammable particles if any) is drawn toward the center of the hottest point, as if to add more fuel to the fire. The Big Bang...

20 July 2024 503 1 View

1. If I can quantize the atom using this hyperbolic spiral and classical physics, could nature do the same?

If we map as a continuous motion an ionising electron (beginning its journey at n=1) in an H atom, a specific hyperbolic spiral appears (see animation). When we solve this spiral formula, we find...

07 August 2024 5,343 2 View

How are iso-frequency contours plotted?

Let's say we have a standard, regular hexagonal honeycomb with a 3-arm primitive unit cell (something like the figure attached; the figure is only representative and not drawn to scale). The...

07 August 2024 1,937 1 View

Stability of the Solar System: Insights from Einstein’s Equations ?

The stability of the Solar System is a complex subject that blends the classical framework of Newtonian mechanics with the modern insights provided by General Relativity (GR). Understanding this...

07 August 2024 2,569 1 View

How to use Density Functional Theory to calculate carrier mobilities of solid system?

Hello, everyone. I have tried to determine carrier motilities of some materials, by Density Functional Theory, using Quantum ESPRESSO. There are a few methods to do it, like a package called...

04 August 2024 8,894 1 View

Can we find a statistical matrix mechanics equivalent to the Schrödinger equation?

27 July 2024 3,959 4 View

How can I use DFT-D3 correction ( Siesta version 5.0.1)?

Dear Siesta Users, I installed Siesta 5.0.1 and I want to use Grimme's D3 correction. According to the 5.0.1 manual, I could use a few parameters to include the D3 correction in the...

27 July 2024 5,748 0 View

Can we eliminate the stress singularity at the tip of the crack by manipulating the elastic constants?

The aim of the research here is to prevent the propagation of the crack in the fabricated elastic medium with useful applications.

25 July 2024 9,976 3 View

Can anyone kindly suggest research topics in the area of thermodynamics, heat transfer, fluid mechanics or renewable energy?

I am an undergraduate mechanical engineering student seeking suggestions on topics related to either thermodynamics, fluid mechanics, heat transfer or renewable energy for my final year project....

24 July 2024 4,058 5 View

Is the zero-zero component of the metric tensor equal to 1 for accelerating reference frames?

Consider the case of negligible gravity but there is an accelerating reference frame. Its origin traces out a trajectory, or world line, seen in some inertial reference frame. The Lorentz metric...

24 July 2024 1,608 15 View

Is it true that there is a physico-statistical meaning to the constant π other than circular geometry but the iron guardians of the SE deny it?

We assume that there is a physico-statistical meaning to the constant π other than circular geometry, but the iron guardians of the Schrödinger equation deny this. The iron guardians of the...

22 July 2024 4,285 9 View