Please read this article, cause it is answering your question.

we cannot compare intelligent with mechanics (your car with yourself)

Article Intelligent Atom

Only eigenStates can be entangled, eigenValues cannot be entangled. There are no examples in nature of entanglement, despite many abberant suggestions such as electron orbitals being entangled. Electrons in an orbital are eigenValues, they are not in eigenStates.

Classical Physics deals with eiegenValues, classical psrticles, bang into each other.

EigenStates can however exist in nature under such extreme conditions such as the center of a star. Other than that, eigenStates do not occur in nature.

Entanglement, outside of a star, is purely an artificial phenomenon. Only man can create entangled systems, and using only tiny amounts of energy, such as a barium borate beam splitter, is totally passive, no energy transfer takes place.

In classical physics, entanglement as it is understood in quantum physics does not exist in the same form. Quantum entanglement involves a unique non-local correlation between particles, where the state of one particle instantaneously affects the state of another, regardless of distance, which cannot be explained by classical physics’ local realism. Classical physics, based on deterministic laws like Newton’s mechanics or Maxwell’s equations, does not exhibit this type of entanglement.

However, there are classical analogs of certain quantum phenomena, where similar correlations or synchronizations can be observed, but these do not exhibit the fundamental quantum properties, such as the violation of Bell’s inequalities, that characterize quantum entanglement. Some researchers explore classical systems with analogous mathematical descriptions, but these do not imply that the “entanglement” seen in classical contexts has the same physical or philosophical implications as in quantum mechanics .

The reference from the “Useless Mathematics” paper may be proposing a provocative or unconventional viewpoint, but as it stands, classical entanglement as described would not operate under the same principles as quantum entanglement, according to widely accepted physics theories.

Dear Ismail Abbas M. Abbas and Harri Shore :

I think that Harri´s comment expresses the accepted theories very well. My comment is over a recent theory that considers the quantum system as local, even if its space is divided by a double slit, beam splitter, or by the different trajectories of entangled particles. The core idea is that the system-space presence in 3D is oscillating with its 4th dimension: a random and intermittent presence in 3D. This in-and-out 3D explains Planck´s equation where the speed in the presence of action "h" is directly related to its energy (fast presence = small tau (tau = h/E) =>high energy). On each intermittent presence, the particles randomly assume one eigenstate solving the measurement problem. This 4th dimension is C*tau and not C* Minkowski's time of events. The periodicity tau is in the heart of quantum mechanics and energy is the one that gives the scale values of time-space-mass as expressed by Lorentz´s. So, entangled particles are local at the 4th dimension, and there is no issue with its 3D separation. Regards

This is just an introductory response, first to thank our fellow contributors for their helpful response and second to shed some light on the question and its answer.

The Schrödinger SE equation is incomplete and misleading because it operates, unlike nature itself, in 3D geometric space plus time as an external controller.

Any response from SE or its derivatives would be incomplete and misleading for all natural events.

Entanglement exists in classical physics situations such as audio rooms and the heat equation in 4D unit space where time t is a dimensionless integer woven into 3D geometry.

We assume that SE is simply the SQRT of the heat diffusion equation plus a law of vacuum dynamics.

The diffusion equation in 4D unit space can measure the speed of sound in audio rooms at 330 m s^-1 and the speed of light signal in heated metals at 3E8 m s^-1.

Additionally, Laplacian theorem and statistical theory of Cairo techniques predict the entanglement time (ταῦ) as finite and can calculate it.

Photon lifetime and entanglement time cannot be infinite.

@ismail abbas, Please explain why photon lifetime and/or entanglement lifetime cannot be infinite? photon and lepton lifetimes are defined in Classical QM (particle phtsics) as having infinite lifetimes.

in entanglement, time has stopped evolving altogether.

Estimating the lifespan of photons as infinite or 10 ^18 years is laughable.

Similar conclusions regarding the rotational entanglement of electrons makes you laugh.

(Wikipedia imagination: the lifespan of photons would be greater than 10^18 years!?)

Consider a cubic room with a side of 100 m filled with photons from across the frequency spectrum.

What happens when the light source suddenly goes out?

Laplacian's theorem predicts an exponential decay of the photon energy density U (number of photons per cubic meter) as follows:

U=U(0) Exp - K V/A . C.. . (1)

Where C is the speed of light, K is a constant function of the absorbance of the walls (K ∈ [0,1]) and V,A are the volume and area of ​​the control room.

Equation 1 also applies to the entire universe where we expect the photon to collide with an electron or nucleus and be absorbed completely or partially (Compton effect) and degenerate into a lower energy photon.

@ismail, then that is a personal hypothesis. in an expanding universe that is freezing out (Heat Death) and a vacuum, none of those parameters apply. there is no mass, no substance. those equations are for macroscopic populations of eigenvalues of solid particles, they have no relevance in QM.

if a photon does not interact with anything, its lifespan is infinite.

Normally I don't comment on answers from our contributing friends, but when this answer comes from our Australian friend in his best form approaching perfection, I find myself motivated to comment and step by step.

1-*(Quantum entanglement involves a unique nonlocal correlation between particles, where the state of one particle instantly affects the state of another, regardless of distance, which cannot be explained by the local realism of classical physics.)

$-Classical physics in 4D xt unit space contains entanglement that involves a unique nonlocal correlation between particles (or energy density and furthermore between particles and boundaries) where the state of a particle instantly affects the state from another, whatever the distance.

2-**(Classical physics, based on deterministic laws such as Newton's mechanics or Maxwell's equations, does not present this type of entanglement.)

$-Classical physics, based on Maxwell's equations, exhibits this type of entanglement and much more when we reformulate Maxwell's first law to involve time [1].

3-***(Some researchers explore classical systems with analogous mathematical descriptions, but these do not only involve "entanglement")

$-The Laplacian theorem and Cairo statistical techniques imply the “entanglement” of energy density in its perfection.

4-****(The article reference “Useless Mathematics” may offer a provocative point of view.)

$-Excuse my provocation, I haven't found a better word than useless mathematics to describe a century of lies and denial.

-----

1-Is it time to reformulate the partial differential equations of Poisson and Laplace, ResearchGate , IJISRT journal, June 2023, Ismail Abbas's Lab

@Abbas, did you know there are 8,000 scientific papers published every day, seven days a week.

The idea that all of that math is useful is indeed absurd. Ive never seen so many upside down equations in my life as in the past two decades.

And I think rather than simplifying the math to its most rudimentary form, which displays true brilliance, they leave it in the most complicated, cryptic form possible, so as to appear 'smart.'

The acid test is, no one is building subsequent work on such mathematical scribble. You cant build on a platform of smoke.

Gentleman, if I may off some thoughts to consider.

Bothy of you are smart and have valid points, and I would wager that on most matters in (in Science & Math, et al) you would agree much more then you would disagree on.

William Bray - yes the rate of publication far exceed the ability for the peer group to discard and filter, let alone perform a critical review. And yes many would have exceedingly complex and often completely nonsensical at a glance.

But not all.

.... and I don't think its what you are saying, because , the sheer quantity of papers is prohibitive. What if the next leap forward is hidden there in the great unwashed...

So one can say there a non zero chance that some of the papers among those will contain useless mathematics, but cannot say with high degree of confidence that all of them do, as this will require critical evaluation tempo which exceeds that of publication.

Mathematics that are useless is not the same as saying Mathematics is Useless.

useless mathematics is describing the application -> thats a tonality and style choice.

Mathematics is useless --> ok, back it up and then give me something which can replace mathematics and can do it better, remain internally consistent, etc.

Ismail Abbas M. Abbas - same with labeling it ALL as lies and denial, if ALL of those are lies then by definition, they are all true as well, given theres no agreed standard of what is true. As they say, even a broken clock tells the right time twice a day.

I believe there are equations and theories out there which are evidently and elegantly true irrespective of the vector by which they found you.

So much so that vast majority of informed and uninformed know it to be such, yet there will always be someone or someones who will be 100% convinced it is an utter lie / abomination / etc.

One does not need to work hard seeking evidence of this; try typing Flat Earth in YouTube or Google and brace yourself.

M

Math is the greatest tool for one or two-dimensions static phenomenon only. unfortunately our past icon and even todays we think two-dimension fixed math that has been written in past can describe three-dimension of nature that is changing constantly.

Generally our manmade math, does not recognize temperature, pressure, colors, taste, smells, size, character of mass...etc. yet we close our eye and do not see this extremes discrepancies.

Here I can see unscientific arguments on math.

what can I do with an unscientific argument?

im not sure what that is ?

can you build a model to match observation and explain in a consistent way the natural world ?

I dont understand - we can observe and make tangible remarks in 4 dimensions. We also have set of mathematics that can describe movement and placements in that.

math doesnt "recognise" it is not an entity, it is a way to transmute, and annotate, make modles that can simplify and predict, etc. Colors exists without math, jsut as two things exists without calling them 2.

and some tht eother things you said are just wrong Im afraid....

I absolutely can use Math to define, measure and make exact and replicable exchange of meaningful information regarding pressure and tempature etc.

Tell me exactly how much hydrogen I can compress into a 2 cm by 2 cm cube without using any math or numbers?

Please read my above statement one more time .

Modeling nature to follow our model is not science, Prediction is not science, 4 dimension is made up thing from our icons last century

Tell me what did I say is not correct?

Please read this.

Article Intelligent Atom

Normally I don't comment on answers from our contributing friends, but when this answer comes from our best American friend in its almost perfect brilliant and thought-provoking form, I find myself motivated to comment and explain in detail.

The challenge is,

*-(Modeling nature to follow our model is not a science, prediction is not a science, the 4 dimensions are made up of elements from our icons of the last century

Tell me, what did I say that is not correct?

Please read this.)

$-This challenge statement is correct and perfect.

But here, in the numerical statistical method of the Cairo technique (discovered and applied only in 2020), there is a satanic entry that most people miss:

We do not model nature to follow our model. But nature itself imposes its response algorithm applicable to all physical events.

In a way we can say that the B matrix strings are a product of Cairo techniques: is it the unified field theory or the powerful and merciful divine law.

When you see a formula that can answer all classical physics questions, all quantum physics questions, and all math questions with the least amount of effort, what do you call it?

------

1-I. Abbas, Useless math, ResearchGate, IJISRT review, Oct 2024.

When you talking about nature, a flower is a good example. same tree might many tens or more flowers, but none of them the same, while they look alike.

Math cannot describe this flower with colors, taste, smells, grow....

Please read some scientific articles.

I read all thing you are telling me.

This article is telling you the truth,

Article Intelligent Atom

To describe quantitative entanglement, we introduce

the following example which is one of the most beautiful entanglement situations in classical physics:

Consider the Laplacian energy density diffusion PDE,

dU/dt)partial= α ∇^2 U + S. . . . . (1)

According to Laplacian theorem, the time-dependent numerical statistical solution of PDE 1 is given by [1],

U(x,y,z,t)={B+B^2 +B^3 . . . . . . +B^N}.(b+S) + B^N.IC . . . (2)

Or,

The Dirichlet boundary conditions are described by the vector b, the source term is given by the vector S in joules s^-1 and the vector of initial conditions is IC.

B is the well-defined transition matrix and the first in the history of mathematics.

Equation 2 is quite surprising.

It shows that mother nature has an almost satanic intelligence:

The solution of the Laplacian system is divided into two parts,

The first part is entangled with the walls b and the source term S.

The second part deteriorates exponentially and is neither linked nor entangled with an external cause.

............

1-Useless mathematics - The complex untold story, ResearchGate, IJISRT journal, October 2024.

The two things are related but not quite the same(@mammanrawagana)

The question arises: does the Laplacian PDE of classical physics, which we call the Laplacian PDE of motion, have an eigenvector solution and a corresponding eigenvalue in the same way as in quantum physics?

This is a serious question and the short answer is yes.

And yet we cannot study the question via the current inadequate definition of the eigenvector itself.

The current definition in the separable space R^4 is that if a vector in the original space retains its direction after multiplication by the matrix A in the transformed space then it is an eigenvector of A.

It is better to replace this with a 4D unit space definition,

The eigenvector of the 4D unit Laplacian matrix partial differential equation of motion is simply its solution in 4D unit space with its corresponding principal eigenvalue λ = 1.

The classic Schrödinger equation,

I h dΨ/dt)partial=-h2/2m. Nabla^2 Ψ+ V Ψ . . . . (1)

OR,

H^Ψ = EΨ. . . . . (2)

reduced form,

Should be conveniently replaced by its square Ψ^2 to conform to the Laplacian PDE,

dU/dt)partial=D.Nabla^2 U + S(x,y,z,t). . . . . . (3)

where U=ψ^2=ψψ*.

which is logical and makes sense.

Note that V Ψ in equation 1 is replaced by S(x,y,z,t).in equation 3.

The hypothesis S(x,y,z,t).=Const. ψ(x,y,z,t).appears naturally inevitable.

In other words, the square of the classic Schrödinger PDE, which is equation 3, must be completed by the basic rule of the source term in vacuum dynamics, namely:

S(x,y,z,t) =Constant * V(x,y,z,t) . . . . (4). .

Then the solution of PDE 3 proceeds in a simple way, analogous to the heat diffusion equation, to obtain ψ^2 and finally Ψ itself is found by calculating the square root of ψ^2.

This process is illustrated in Figure 1.

Fig.1. ψ^2(x) and ψ(x)

@Ismail Abbas, I appreciate that you conatrained your argument to four observable dimensions. Most people pop off into the realms of the gods. It is a display of superior problem solving skills.

I would like to remind my esteemed colleagues that mathematical physics differs from mathematics in principle in that in the former case we must interpret mathematical quantities from the point of view of their connection with measurements (or at least with possible measurements). Formal logic is present, of course, in the description of nature, but it is not physics without a connection with measurements. When considered from this position, entangled states do not exist in classical physics, if by the latter we mean the framework of non-low-temperature observations in the macrocosm. If we try to construct combinations based on the formulas of classical physics, similar in content to quantum-mechanical entanglement between states, then I think they can be done in countless ways and therefore lead nowhere.

No, entiglement does not exist in classical pysics in the same way it does in quantum physics. Quantum Enteglement is a uniquely quantum phenomena where particles become interlinked an the state os one particle instantaneously influences the state of the other, no matter the distance between them. this non-local conection defies the principles os classical physics, which relies on local realism an deterministic intercation.

in classical physics, there's no concept that directly parallels quantum enteglement. classical system follow well-defined paths and behaviors bases on initial conditions and forces acting on them, without the spooky action-at-adistance that characterizes quantum entenglement.

Enteglament is one of fundamental feature that sets quantum mechanics apart from classical mechanics. its's what allows phenomena like quantum computing and quantum teleportation to be possible.

King Regards

Gastaõ Soares Ximenes de Oliveira

UTPR-PG

UNTL-Physics Department

2024

Here is one proof among too many others that the entanglement of classical physics (heat diffusion, energy density, sound intensity in audio rooms, electrostatic potential energy in the control volume V, etc.) exists in classical physics in the same way as in quantum physics and even more:

Using Laplacian matrix algebra, we show that the infinite power series [(1+x)/2]^N is equal to (1+x)/(1-x), ∀x∈[0,1[ .

We propose an axiom or a mathematical hypothesis:

[For a Laplacian power matrix B,B^2,B^3. . ,B^N ., the sum of their igenic values ​​​​is equal to the eigenvalue of their power series sum]

We call it Axiom 1.

To this end, we can present the well-defined stochastic transition matrix B (which is replaced by A in the current analysis for convenience) previously explained in refs 1, and verify the above hypothesis.

Note that the matrix B and all its integer series are symmetric physical matrices and are not simply a set of numbers, because much information data is inherent in their structure and can be applied to many physical and mathematical situations.

For a simple cubic geometry, the square matrix A 8x8[1] is given by,

1-RO (1-RO) / 6 (1-RO) / 6 0.0 (1-RO) / 6 0.0 0.0 0.0

2-(1-RO) / 6 RO 0.0 (1-RO) / 6 0.0 (1-RO) / 6 0.0 0.0

3-(1-RO) / 6 0.0 RO (1-RO) / 6 0.0 0.0 (1-RO) / 6 0.0

4- 0.0 (1-RO) / 6 (1-RO) / 6 RO 0.0 0.0 0.0 (1-RO) / 6

5- (1-RO) / 6 0.0 0.0 0.0 RO (1-RO) / 6 (1-RO) / 6 0.0

6- 0.0 (1-RO) / 6 0.0 0.0 (1-RO) / 6 RO 0.0 (1-RO) / 6

7 - 0.0 0.0 (1-RO) / 6 0.0 (1-RO) / 6 0.0 RO (1-RO) / 6

8- 0.0 0.0 0.0 (1-RO) / 6 0.0 (1-RO) / 6 (1-RO) / 6 RO

Step 1

Note that matrix A implies a specified RO.

For example, if RO is arbitrarily chosen equal to 0.2 then the numerical entries of the Laplacian matrix above A reduce to:

0.2 0.8/6 0 0.8/6 0.8/6 0 0 0

0.8/6 0.2 0.8/6 0 0 0.8/6 0 0

0 0.8/6 0.2 0.8/6 0 0 0.8/6 0

0.8/6 0 0.8/6 0.2 0 0 0 0.8/6

0.8/6 0 0 0 0.2 0.8/6 0 0.8/6

0 0.8/6 0 0 0.8/6 0.2 0.8/6 0

0 0 0.8/6 0 0 0.8/6 0.2 0.8/6

0 0 0 0.8/6 0.8/6 0 0.8/6 0.2

The eigenvalue of matrix A above is 0.6, which is equal to (1+RO)/2.

Step 2

Continuing, the square of the Laplacian matrix A^2 is expressed as follows:

7/75 4/75 8/225 4/75 4/75 8/225 0 8/225

4/75 7/75 4/75 8/225 8/225 4/75 8/225 0

8/225 4/75 7/75 4/75 0 8/225 4/75 8/225

4/75 8/225 4/75 7/75 8/225 0 8/225 4/75

4/75 8/225 0 8/225 7/75 4/75 8/225 4/75

8/225 4/75 8/225 0 4/75 7/75 4/75 8/225

0 8/225 4/75 8/225 8/225 4/75 7/75 4/75

8/225 0 8/225 4/75 4/75 8/225 4/75 7/75

And its eigenvalue is equal to 0.36, or [(1+RO)/2]^2.

In general, the eigenvalue of the matrix A^N is equal to [(1+RO)/2]^N.

Moreover,

ev A^N=[(1+RO)/2]^N =ev1^N for all RO ∈[0,1[. . . .Rule 1

The type of proof or validation for rule 1 is statistical proof never before known but well explained above in question/answer 2.

Note that the Laplacian eigenvector is composed of the constant element vector, (k, k, ...., k), k different from zero, and its elementary eigenvalue ev1 is equal to (1 + RO) / 2 for all RO in the interval [0, 1].

For convenience, we denote the eigenvalues ​​ev,s for A, A^2, A^3, ...., A^N by,

ev2 = evA^2=ev1^2, = [ (1 + RO) / 2] ^ 2

ev3 = evA^3= (ev1) ^ 3 = [(1 + RO) / 2] ^ 3, etc.

. . . . . . . . . . . . . . . .

evN = evB^N= (ev1) ^ N=[(1 + RO) / 2] ^ N

We do not know how to perform the summation of infinite series [(1+x)/2]^N but we know how to perform the summation of infinite series of power matrix A^N given by,

E(N) = B^0 + B + B^2..... +B^N......(1)

Or,

A^0 = I

Note that for N sufficiently large, it is easy to find E by an algebraic mathematical series or by simple matrix inversion, i.e.

E = [(I-B) ] - 1

And we define the transfer matrix D by equality,

D = E-I. . . . . . .(2)

Step 3

Calculate the transfer matrices D and E.

For a large N and an arbitrary R=0.2 as parameter,

The transfer matrix D is given by,

8/21 11/42 2/21 11/42 11/42 2/21 1/21 2/21

11/42 8/21 11/42 2/21 2/21 11/42 2/21 1/21

2/21 11/42 8/21 11/42 1/21 2/21 11/42 2/21

11/42 2/21 11/42 8/21 2/21 1/21 2/21 11/42

11/42 2/21 1/21 2/21 8/21 11/42 2/21 11/42

2/21 11/42 2/21 1/21 11/42 8/21 11/42 2/21

01/21 02/21 02/11 02/21 02/21 02/11 08/21 02/11

2/21 1/21 2/21 11/42 11/42 2/21 11/42 8/21

It is clear that the eigenvalue of the transfer matrix D above is equal to 1.2 which is exactly equal to [(1+RO)/(1-RO)]

Needless to say the result above,

ev D=[(1+RO)/(1-RO)] . . . (32)

is valid for all values ​​of RO ∈[0,1[.

Step 4

Since the transfer matrix D is given by A +A^2 + A^3. . +A^N for N tends to infinity.

Then, applying rule 1, we get,

(1+RO)/2 +[(1+RO)/2] ^ 2 +[(1+RO)/2] ^ 3 +.....[(1+RO)/2^N =[( 1+RO)/(1-RO)] . . . . (3)

therefore, for a large N,

If we replace RO with x in equation 3, we obtain the required proof.

It is worth mentioning that here,

i- the proof or validation of the above analysis, valid for all values ​​of the main diagonal inputs RO in the interval [0,1[, is only a statistic.

ii- Laplacian theorem generated an important rule 1 never before known

Once again, Laplacian's theorem and Cairo techniques can correct many of today's useless mathematics and generate an infinite number of integer series formulas.

Also note that B-transition matrix chains provide a classic and rigorous chaining.

The Laplacian PDE system,

dU/dt)partial=D.Nabla^2 U +S(x,y,z,t) . . . . . .  (4)

And its solution,

U(x,y,z,t)= D(N) . (b+S) + IC. B^N. . . . . (5)

is entangled to boundary conditions b, source term S and to itself.

--------

1-Useless math.

Why do people have difficulty defining time?

The only adequate definition of time is found solely at the heart of Cairo techniques. It is the only theory of 4D xt unit space where time is defined as a dimensionless integer woven into a 3D geometric space.

This brilliant definition of space-time is in fact the inherent source of entanglement phenomena in classical physics, quantum physics and even pure mathematics.

Entanglement, whether classical or quantum, in 4D unit space appears clearly in the Cairo techniques and Laplacian theorem and can be used to generate definitions and rules of physics and mathematics never before preceded.

The Laplacian process or the Laplacian system itself can be described or defined in three different equivalent formats,

dU/dt)partial = α ∇^2 (U) + S. . . . . (1)

U(x,y,z,t+dt) = B. U(x,y,z,t) . . . . . . (2)

U(x,y,z,t)= (B+B^2+B^3+ . . +B^N) . (b+S) + IC. B^N. . . . . (3)

In normal conventions.

Note that the Schrödinger equation in particular and quantum mechanics as a whole are actually nothing more than the SQRT of the Laplacian PDE and the Laplacian system.

Also note that equations 1,2,3 are all equivalent without any sort of overspecification.

Equations 1,2,3 can be used to find an expression for the speed of sound Vs in cubic audio rooms of side L like [1],

Vs=T1/2 L^2 / α (sound). . . . (4)

Note that Equation 4 shows that sound energy is entangled in the walls via the sound wave speed Vs.

Using Sabines' experimental values ​​for T1/2, the numerical result for Vs at NTP is 330 m/s.

Similarly for the speed of EMW C in a metal cube of length L is given by,

Cemw=T1/2 L^2 / α (metal). . . . (4)

Note that equation 5 shows that the thermal energy in the metal cube is entangled in the walls via the EMW velocity C=3E8.

In 2022, the author carried out thermal experiments on the cooling curves of metal cubes with a side of 10 cm and found the half-time cooling curve of Egyptian aluminum and Russian iron (poor carbon) as follows [1], T1/2 for an aluminum cube with a side of 10 cm = 45 sec, T1/2 for an iron cube with a side of 10 cm = 100 sec [1]. Substituting the above values ​​for α from the Google search thermal tables and the experimental T1/2 into equation 2, we arrive at a value of Cemw close to,Cemw = 2.9 E3 in both cases .

Again, classical R^4 mathematics is useless for finding the value of energy diffusivity α in metals or for finding the correct relationship between α and Cemw. Again, it is not strange to find a relationship between the speed of light c and the thermal diffusivity of metals since the entanglement signal from free nodes to boundaries or walls and vice versa propagates at the speed of light c. It is obvious that Laplacian theorem and numerical statistical theory of Cairo technique can measure the speed of sound in audio rooms and the speed of EMW in vacuum while classical R^4 mathematics is useless in this appearance.

1-I. Abbas, Useless Mathematics – The Complex Untold Story. ResearchGate, IJISRT review,  October 31, 2024.

@Ismail Abbas, why dont you just put it all in a paper and publish it here on RG? No one is going to read pages of Hex Latex.

Also, you seem to be forgetting that Entanglement is the embodiment of the departure from Classical Ohysics, which was the dilemma at the turn of the 20th century and remains so to this day.

Classical Physics is all about observables and predictability. Entanglement is proven unpredictable, 2022Nobel, Bell and Aspect. That Nobel also proved the second departure from Classical Physics, that Observation determines the system. There are no equations for that.

Another serious question arises:

Can B-statistical matrix chains solve the Bohr hydrogen atom?

Niels Bohr presented his classic atomic model of hydrogen in 1913.

He combined Newton's laws of motion for a particle in a central field with his famous equation for quantizing angular momentum,

mv.2πr = n h. . . . (1)

n =1 2 3, ... infinity is called the principal quantum number.

He concluded that the permitted stationary energy states are those given by,

n=1 for E1=-13.6 ev

n=2 for E2=-13.6/4 =-3.4 ev

n=3 for E3=-13.6/9=-1.51ev

. . . .

etc, as shown in Figure 1.

Fig.1.Bohr hydrogen atom in classical quantum mechanics.

It is quite surprising that the stationary energy levels of the hydrogen atom can be calculated directly from the eigenvalue relation in a central field, i.e.

eigenvalue N = N^2 eigenvalue 1 explained above.

So, total energy E at level 1 = eigenvalue for N = 1

e.e/4πr^2 ε0 =-13.6 ev for (eigenvalue 1)

which means,

If eigenvalue 1=-13.6 ev, then,

If eigenvalue 2 * 4=-13.4 ev

Or, eigenvalue 2=-3.4 ev

and, eigenvalue 3*9=13.6 ev,

Or, eigenvalue 3=-1.51 ev

etc.

Note that the total energy of the H atom comes from the expression above,

dU/dt)partial = α ∇^2 (U) + S. . . . . (1)

for stationary states, i.e.

dU/dt)partial=0

And,

S(x,y,z)=const*Ves(x,y,z).

Does Planck's law of radiation belong to quantum or classical physics?

It was a "battle for the world" at the time, but as we know, Einstein lost to the greatest scientists of the time, Bohr and Heisenberg among others.

This particular unanswered question where classical mechanics and quantum mechanics meet and interact in an equation is always of great importance and helps to understand the two subjects.

1-Consider the formula of Max Planck, which replaced the complete failure of those of Wien, s and Rayleigh Jeans, for the density of the thermal radiation of the black body u (f, T):

du (f, T) = {(2 h f ^ 3 / c ^ 2). 1 / (e ^( hf /kB.T) -1)} df. . . . . . . . (1)

with h = Planck, s constant and f = frequency of radiation, kB = classical statistical Boltzmann constant and T = classical thermodynamic temperature.

A first glance at the exponent hf / kB .T shows that the numerator hf is pure quantum mechanics QM while the de-numerator is purely classical physics without forgetting that a quantum temperature is not yet defined by unique way.

And now should we call the equation. 1 Classic, Quantum or half and half?

2- What QM interpretation is introduced into equation 1? Einstein QM interpretation or Bohr-Copenhagen QM interpretation?

Keep in mind that the new numerical statistical theory called Cairo Techniques, which operates in a 4D unit space never known before 2020, is the only one that can rigorously prove Planck's radiation law.

Furthermore, this theory shows that to derive equation 1, it is not necessary to assume that the quantized Max Planck oscillators have energy hf, 2hf, 3hf. . etc or any quantum number 1,2, 3, N, ... where N is a large infinite number.

However, Einstein lost the battle at the Copenhagen conference in 1928 and the case seemed closed.

So what?

To be continued.

@Ismail

what is it with you guts who post endless things that are not being read and do not read the comments or replies? what is the point of you being here?

Useless quantum mechanics:

Here are some comments on the last answer,

1-A. Einstein and N. Bohr continued their scientific debate but maintained their mutual friendship until the end of their lives by having frequent friendly dinners and discussing the future interpretation of quantum mechanics and Schrödinger's PDE. (Picture 1.)

Photo 1. Einstein and Bohr having dinner together and discussing for hours the correct interpretation of SE.

2-The year 1927 became decisive when many physicists and mathematicians became fans of the Iron Guards and indoctrinated by Bohr's interpretation of SE and defended it until their last breath.

What is dangerous is that these brainwashed fans have formed a Christianity circle with the slogan: Shut up and calculate!?

3-E. Schrödinger himself announced his objection to the

Bohr plays SE in his famous Cat in a Box paradox but ultimately withdraws under pressure from the Iron Guards.

4-Many physical and mathematical problems can be solved if we admit that mother nature has a face to show and a way of speaking to herself.

Modern physics (classical physics plus entanglement transition probability), including its universal laws, is the mother of quantum physics and not the other way around.

To be continued.

@ismail, so you actually read a comment. fascinating.

you are obviously in here with the fantasy that someone would read your work, because your stats clearly indicate no one is reading your work.

what you have to admit, as per your own statement, that it is you, not the fantasy, that is not producing work of value. easily solved, just change your approach. if you cannot do that, then you will luve and die a failure.

just make the right choice.

try learning the subject. you only have a surface knowledge of qm and gr. you dont even have knowledge of the various forces, qed, qcd, qtd, qzd, temporal mechanics, holographic theory, ads/cft models, and so on, just a four year basic undergrad exposure to physics 101.

you cant rewrite physics without even knowing the language. pay attention to your own limitations rather than accusing the world of not tuning into you "infinite wisdom," which obviously does nit include knowledge of the subject. take the sting and make the change in you, you are not changing the world or going down in history.

The following equation 1 is Planck's well-known formula for black body radiation,

du(f,T) = {(2hf^3/c^2). 1 / (e ^( hf /kB.T) -1)} df. . . . . . . . (1)

with h = Planck, s constant and f = radiation frequency, kB = classical statistical constant of Boltzmann and T = classical thermodynamic temperature.

A close look at equation 1 shows that it is made up of two parts,

the first to know (2 h f^3/c^2) or a constant. f^3/c^2.

* It follows directly from the second corollary of Laplacian's theorem, product of the statistical theory of Cairo techniques,

Corollary 2 states that [1],

The volume integral of ∇2 U(x,y,z,t) over the closed volume V for any source/sink distribution inside V is equal to the closed surface integral of U.C.

It is clear that C is the speed of the wave in the medium considered.

C= 330 m s-1 for the sound wave and 3E8 m s-1 for the EMW.

In mathematical language [1],

∫∫∫closed volume ∇2 U(x,y,z,t) dV = ∫∫closed surface U(x,y,z,t).C dA

Corollary 2 implies,

(L/λ)^3=number of harmonic oscillators of wavelength λ and frequency f=C/λ.

In other words, the density number of harmonic oscillators of frequency f is given by

a constant * f^3/c^2.

**In order to proceed with the demonstration of the second part of Planck's formula for black body radiation, we propose the following:

Planck's law for the spectral electromagnetic energy U(λ,T) radiated per unit volume by a cavity of a black body BB in the wavelength interval λ and (λ + Δλ) can be written as terms of Planck's constant (h), speed of light (c), Boltzmann's constant (k) and absolute temperature (T):

I(Lambda,T)= 2 h c^2/Lambda^5 *{ 1/[exp hc/ λ.K.T)]-1} . . . . . . (1*)

Where λ is the wavelength of the emitted radiation.

Max Planck derived equation (1) via his postulate of quantizing the energy of the quantum atomic oscillator:

E(osc)=n. h. f, that is to say

E(osc)= hf, 2hf, 3hf, . .  infinity. . . . (2)

in the form of non-continuous but discrete or quantized energy values.

Planck's hypothesis led to a revolutionary correction of the classic Rayleigh Jeans formula and Wiens' law for BB radiation.

However, it is rarely mentioned that the author, among others, intuitively assumed that Planck's postulate of energy quantification**. In order to proceed with the proof of the second part of Planck's formula for black body radiation, we propose the following:

Planck's law for the spectral electromagnetic energy U(λ,T) radiated per unit volume by a cavity of a black body BB in the wavelength interval λ and (λ + Δλ) can be written as terms of Planck's constant (h), speed of light (c), Boltzmann's constant (k) and absolute temperature (T):

I(λ,T)= 2 h c^2/Lambda^5 *{ 1/[exp hc/ λ.K.T)]-1} . . . . . . (1*)

Where λ is the wavelength of the emitted radiation.

Max Planck derived equation (1) via his postulate of quantizing the energy of the quantum atomic oscillator:

E(osc)=n. h. f, that is to say

E(osc)= hf, 2hf, 3hf, . .  infinity. . . . (2)

in the form of non-continuous but discrete or quantized energy values.

Planck's hypothesis led to a revolutionary correction of the classic Rayleigh Jeans formula and Wiens' law for BB radiation.

However, it is rarely mentioned that the Author among others intuitively assumed that Planck's postulate of quantizing the energy of the quantum atomic oscillator Eq 2 was inherently a statistical assumption and that the derivation of Planck's radiation law could be carried out by replacing it with other adequate statistical approaches.

The discovery of the laser theory of atomic spectral lines which belongs entirely to A. Einstein is the required adequate statistical approach..

A brief explanation to clarify the connection between Einstein's atomic LASER and Planck's atomic radiation formula can be presented as follows:

The history of the laser undoubtedly began in 1916 with Albert Einstein, who assumed that there were three distinct processes essentially involved in the formation of an atomic spectral line:

Spontaneous emission and absorption (well known before Einstein) and stimulated emission of radiation SER (discovered by Einstein).

Consider three quantized electron levels 1, 2, 3 where the intermediate level 2 is a meta-stable state.

Obviously, the existence of a meta-stable state E2,N2 between E1,N1 and E3,N3 is essential for population inversion and light amplification where we obtain two coherent photons out of one.

But how did Einstein find his SER coefficient?

Another thought experiment was added to his two remarkable thought experiments on the theories of general and special relativity.

consider a cavity with two-level atomic systems N2 and N1 and the radiation density of frequency f0 is u (f0) is in thermodynamic equilibrium.

1-The classic Boltzmann statistic determines the N2/N1 ratio.

Einstein assumed that atomic quantum energy levels at thermal equilibrium obey classical Boltzmann statistics, viz.

N2 / N1 = exp - (E2-E1) / kT... . . (3)

2-With f0 or f obeys the Bohr relation, namely,

f = (E2-E1)/ h ....(Bohr relation)

3- The absorption rate for the upper level N2 must be equal to the emission rate (Reciprocality of mother nature).

The laser equation immediately follows,

dN1/dt] absorption = dN2/dt] spontaneous. emission + B21 u (f0) N2 . . . (4)

B21 is the Einstein coefficient of stimulated emission of radiation.

Note that B12 and B21 are inherently statistical as nature itself.

SO,

U(f) = (A12/B21) / ((B12/B21) N1/N2 - 1). . . . . . (5)

Eq. 5 is the laser equation.

Obviously, the Einstein coefficients of spontaneous and stimulated emission B12 and B21 are equal, viz.

B12 = B21.

Finally, We feel excited when we observe that Planck's quantization law for black body radiation Eq(1) could be derived from Einstein laser equation 5 by the substitution

A21=8 π h f ^3 B21/ c^3.. . . . . . (6)

Equation (6) is the formula for the number of standing waves in a 3D blackbody box used by Max Planck and later by A. Einstein.

It is worth mentioning that in the above derivation of Planck's law for the spectral electromagnetic energy U(λ,T)

the quantization numbers of the harmonic oscillators is not needed!?

*** Think about the meaning of the Schrödinger equation and the brainwashed iron guards when they use black magic unnecessarily to prove Planck's radiation law.

***-The fact that the exact value of Planck's constant h = 6.63 E-34 J s is it an inherent property of a quantum universe ? that is to say that Planck's constant is a universal law inherent and a useful tool for studying

1- Useless mathematics - The complex and untold story.

Moreover, we also assume that the statistical theory of Cairo techniques, Laplacian theorem and B-matrix chains can provide a magical iterative method to solve the eigenvector problem of the Laplacian system by producing sequences of solution of initial vectors that converge to the eigenvectors quickly. , stable and unique.

There is no need to use other mathematical algorithms to produce vector sequences that converge to eigenvectors in a much more complicated way.

An illustrative example is the summation of the statistical chains of matrix B as follows:

B+B^2+B^3+. . . +B^N = D for n free nodes =7, RO=0 and sufficiently large N is is as follows:

D=

3/4 3/2 5/4 1 3/4 1/2 1/4

3/2 2 5/2 2 3/2 1 1/2

5/4 5/2 11/4 3 9/4 3/2 3/4

1 2 3 3 3 2 1

3/4 3/2 9/4 3 11/4 5/2 5/4

1/2 1 3/2 2 5/2 2 3/2

1/4 1/2 3/4 1 5/4 3/2 3/4

If we start from an arbitrary initial eigenvector of solution of constant elements inputs all = 1, we proceed as follows,

[D].[1]= [IT1]

6

11

14

15

14

11

6

First iteration numerical result, i.e. [D].[IT1]=[IT2] is,

71

131

171

185

171

131

71

And similarly [IT3] is given by,

860

1589

2076

2247

2076

1589

860

Note that IT3 is the principal eigenvector required with λ=1 (Main eigenvalue).

Striking precision.

Question:

Boltzmann's formula for the microscopic entropy s = kB Log W, why was it criticized by A. Einstein?

* This is a serious question showing the importance of modern statistics (classical statistics plus modern definition of probability which is in itself a kind of entanglement) in proving physical events.

One of the most important and precise formulas in the history of science was published in 1877:

s = kB Log W ...... . . . . . . . . (1)

with s approaching 0 as the temperature T in degrees Kelvin tends towards zero.

This relationship is considered to be Boltzmann's best achievement and is engraved on his grave in Vienna.

It is the only derivation of the agreed definition of macroscopic thermodynamic entropy S which appeared as early as 1850.

In fact, the thermodynamic entropy S was introduced by Clausius, Kelvin and others through the second law of thermodynamics:

S = d Q reversible / T. . . . . (2)

Only then did the macroscopic entropy S have a mathematical basis based on a well-defined molecular system of binary interaction.

A. Einstein objected to its pure statistical derivation followed by Boltzmann and asserted that the proof should be made on both statistical mechanics and Newtonian dynamics, which was clearly absent.!

It's quite astonishing that Einstein missed to approve or improve Boltzmann's pure statistical derivation, .

Formula 1 appears to be one of many prominently subjects where math still lags behind physics.

How do thermodynamic entropy dS = dQ (rev) / T and Boltzmann microscopic entropy S = k log W match?

As early as 1850, there was an agreed definition of thermodynamic or macroscopic entropy as S = dQ reversible / T with S approaching some constant or zero as T approaches zero.

However, a breakthrough came in Boltzmann's equilibrium statistical mechanics known as the relationship or proportionality between macroscopic entropy and probability of microscopic states of gas molecules W (Boltzmann called W number of complexions of state known as S = k log W early in 1877).

It worth mentioning that Boltzmann statistics is equivalent to Newtonian dynamics and laws of motion.

Moreover, relationship 1 is considered the best of Boltzmann achievements and is engraved on his grave in Vienna. Only then, the macroscopic entropy had a mathematical basis based on a well-defined molecular binary collisions.

Surprisingly, though, both definitions 1,2 match.

Einstein raised a finger against Boltzmann's derivation [1] based on probabilistic assumptions without any dynamic laws ?

Finally, this is not to discount from Einstein great achievements who slipped only twice (this one and the specific heat of crystal structure where statistics is a must) during 50 years of theories and research discoveries.

1-I. Abbas, Quora Q/A 2021.

Albert Einstein criticizes Boltzmann's formula for microscopic entropy, S = k_B * log W, because he believed it did not fully capture the complexities of thermodynamic equilibrium fluctuations. Einstein interpreted the formula as a large deviation formula, which he used to develop his theory of thermodynamic equilibrium fluctuations. He argued that the likelihood function of any system composed of two probabilistically independent subsystems should be factorizable into the likelihood functions of each subsystem.

yeah sure, in classical physics correlation can be made and showing past behaviour but in QM an entanglement is a truly superposition of two or more particles to each other and cannot be separated

Please take a look at,

Useless Quantum Mechanics – The Complex and Untold Story, ResearchGate, November 2024.

Please take a look at:

Useless Quantum Mechanics – The Complex and Untold Story III

ResearchGate, IJISRT journal.