The theory has no effect on the detector, which responds only to charge. The wave superposition is only a general guide

or representation

to the statistics of the experiment.

Juan,

Don't you contradict yourself? If the theory has no effect on the detector, how the wave-superposition (in the theory) imposes the statistics obtained in the experiment?

Actually the status of a superposition is just a guess, it has not physical reality, other than after an experiment

establishing the statistics. People usually read too much into this.

Juan: "Actually the status of a superposition is just a guess, it has no physical reality, other than after an experiment establishing the statistics."

And what about interference patten obtained if we bring two components from the superposition to cross one another?

My Dear Sofia,

I think the answer is the number (2),

"The detector reacts with certainty to the electron charge, only when |α|2 = 1. Since |α|2 < 1, sometimes the detector feels the charge, and sometimes doesn't".

but how "sometimes the detector feels the charge, and sometimes doesn't. "?

I think that the particle itself choose which detector (A or B) want to react with it

(in my language: to appears on it :) ) then the detector feel it, so based on the staff of experiment the particle preferred some locations more than others.

With best regards.

Sofia

Then you use the creteria that the amplitudes add first, and then you find the square modulus. That is just part of the predicted statistics.

The prior use that you mentioned, is in the possible measurement results.

Another problem I am thinking about is if a quantum wave can really promote a transition delta(E) = hf,

as in the Franck Hertz experiment. I think it would, with modulated probability density, as the wave moves past some fixed point, creating a real frequency. That is how I think photons do also, but just using the electric field wave.

My lovely Mazen,

I think like you. What impinges on the detector is not a complete electron wave-packet, |1>a, but something that we don't know in classical phisics, an electron wave-packet of intensity |α|2 which is less than 1. If the intensity were 1 the detector would report the wave-packet with certainty (in thought-experiments we consider the detectors ideal). However |α|2|1>a is, in a way, part of the electron, although this part carries a full charge, -1e.

To put it is popular words, I think that the detector, as a macroscopic instrument sometime "understands" that an electron impinges on it, and sometimes doesn't. The closer is |α|2 to 1, the detector understands more times, i.e. in more trials of the experiment.

Behind the phrase "the detector understands" stands the fact that there is no such thing as the detector produces |α|2 from a click. The detector either clicks or not. Another fact is that if the wave-packet |1>a would have met, instead of the classical detector, another quantum object, e.g. an atom, |10> ( |10> meaning an atom in the ground state), an entanglement would have been generated

(1) (α|1>a + β|1>b) |10> → α|1>a |1e> + β|1>b|10>

(where |1e> means an excited atom).

But in the detector |1e> is extremely improbable because the number of atoms is huge. I think that the equation (1) should be replaced by

(2) (α|1>a + β|1>b) |N0> → α{|1>a [γN|Ne> + γN-1|(N-1)e>|10> + γN-2|(N-2)e>|20> + . . . . + γ2|2e>|(N-2)0> + γ1|1e>|(N-1)0>] + β|1>b|N0>}.

Neither this equation is fully correct, because what in fact happens is that in the detector where N is huge, all the contributions to the phases γmeγn of products like |n)e>b

Dear Sofia,

Your first question leads me to ask you a logical question: what exactly do you mean by cq. ? This logical question does your question stand or fall, so please answer this question. Thanks, Marc.

Dear Marc, Mazen, Juan, and all the users,

A process, is completely deterministic if for each input to the process we have ONE SINGLE output. There may be a couple of inputs producing the same output, what we call "many to one", but still, for each one of the inputs the output is unique.

A process is completely non-deterministic when for each input to the process may be more than one output - what we call "one to many", and the output is chosen in an arbitrary way.

In the text of my question is put in evidence a phenomenon. The measurement results of systems prepared according to the wave-function (1), i.e. the response of the detector A, although seem to be stochastic, though possess the following feature: in a series of trials of the experiment, the number of cases when the detector fires is proportional with |α|2. Therefore the response of the detector is not completely random.

Now, my question tries to get into the process that happens in each SINGLE TRIAL of the experiment. You see, in order of having an ordered circulation of cars on a road, each car has to respect the circulation rules. In the same way, for having along an experiment the statistics that the number of clicks of A is proportional with |α|2, in each trial of the experiment the measurement process should go in a particular way: the greater is |α|2, the process should tend to produce an avalance of excited atoms.

It is obvious to me that since |α|2 < 1, the measurement cannot produce a click compulsorily, in each trial. It is also obvious to me that an avalanche of excited atoms (eventually, most of them ionized) is a macroscopic phenomenon which either appears, or not.

The result deciding seems to me as if a little daemon who is aware of the value of |α|2, picks a number in the interval [0, 1]. If the number is ≤ |α|2, the daemon allows the avalanche, but if the number is greater than |α|2 the daemon stops the formation of the avalanche.

What is not clear to me is which item in the measurement acts as the daemon.

Thank you too,

Sofia

QM is not deterministic. The only problem in quantum mechanics is related with the measurement process, whereby classical mechanics substitutes the QM probability (Pascal) probability to calculate with experiments numerous experimental data to validate the results. For example, the discovery of the Higgs-Guralnic boson was validated by thousands of processes of measurement with he CERN supercollider.

A deeper theory, compared to conventional QM, is available (see, for example, https://arxiv.org/abs/1807.08603 with references therein, along with “Sorry, Albert!” on my website www.soiguine.com). In that theory qubits are lifted to geometrically feasible even elements in geometrical algebra formalism with the opportunity to explicitly define “complex” plane(s). Probabilities in that frame are defined as relative measures of fibers (level sets) of measured observable values.

Dear Alex,

itself is logically contradictory, i.e. how can quantum parallelism be binary? Thank you for the added reply. Marc.

Dear Mark,

Qubit is just unit value linear combination, with complex coefficients, of two two-dimensional vectors. That's it. Probabilistic interpretation via the squares of coefficients is just interpretation. Parallelism, in conventional QM, is engaged through qubit tensor products that is fully formal and has no feasible physical implementation. Due to that realization of quantum computers based on conventional QM remains yet in the area of dreams. The deeper theory I talked about opens the way to quantum computers as analog devices. Probabilities there are just relative measures of the level sets of the results of measurements that means any result can be received through (infinite) amount of states acting on observables. That is parallelism in that theory.

Understanding of the theory requires some efforts, it is not one day job. Also important for understanding is not to be fully zombied out by existing QM formalism, all that Bohr's interpretations, etc.

Dear Alex,

Your reply leads me to other questions:

(i) does linearity belong to QM?

(ii) does complexity belong to QM?

(III) does dimensionality belong to QM?

(iv) is there any non-conventional QM?

Thanks for your reply. Marc.

My Dear Sofia,

I want to say something,

1- In classical mechanics (which is a deterministic theory) we have what we called initial velocity, it can be anything (in non-relativist case and less than c in relativist case) so no velocity is more preferred than another, so in general case when we didn't have any information about the initial velocity, we build a statistical solution based on all possible values of velocity.

My question is what is the alternative of initial velocity in a quantum mechanic?

I think the alternative is the quantum jump, but based on the formulation of quantum mechanics we found that the particle prefers some quantum jumps more than other quantum jumps, that lead us to the special probability density of existence.

2- So the hidden variable in quantum mechanic is this quantum jump, and this quantum jump is not local I mean that the particle does this jump based on what exists in the staff of experiment,

(and this jump, in my opinion, is the events of disappearance and appearance..)

so if you can prepare the particle with one specific quantum jump it will do exactly this quantum jump, so based on this idea we can say that the quantum mechanics is a deterministic theory, but because we can't know the quantum jump until it really happened we can't deal with it, so we go to statistical description.

3- The number |α| 2 is related to the stuff of experiment (you need to change the stuff to change this number), in my opinion the particle know the stuff, so the particle know this number so the particle prefers some location more than others based on this number , so we have simple choices as we have in the ordinary probability theory (I demonstrated mathematically this idea in my theory).

With best regards.

(i) The operators of the quantum are linear, the superposition of solutions is typical of linear equations.

(ii) Depends on ones outlook. Formalism itself does not suggest complexity, but some imagine a complex sub reality.

(iii) Quantum problems can be solved in different dimensionalities and experiments may be pseudo one or two dimensional,

as well as three dimensional.

(iv) There are several interpretations of the quantum (but formalism fairly standard) Some more conventional than others.

You think contradictory if one of two events excludes the other, but you can have 50% probability for each, and this is not contradictory. The later is quantum.

Dear Mark,

(i),(ii) Linearity and complexity (if you mean complex numbers) are tightly related in conventional QM. In the deeper theory I am developing we get the same if everything happens in the same plane in 3D.

(iii) Dimensionality is a bit different thing. In conventional QM it brings in tensor products that are impossible to physically interpret, though they are used as part of formal justification of entanglement. In my theory dimensionality causes linking between actions of states with different planes, generalizing formal, unspecified "complex" variable plane of conventional QM.

(iv) That's what I am working on.

Mazden,

Classical mechanics has initial conditions but the quantum has not (except for initial probability density distributions)

This has to do with lack of determinism in the quantum as to path or trajectory.

Regards, juan

Dear Juan Weisz,

Sure I know that "Classical mechanics has initial conditions but the quantum has not (except for initial probability density distributions)"

and this is the standard formulation, but I token here about the non-local hidden variable that is behind the probability density distributions, I suggest like this idea in this paper:

Preprint The theory of disappearance and appearance

With best regards

I know non local effects, but the idea that there is a variable there drives me wild. Maybe some can enlighten me.

For me nonlocal is a kind of continuity from local.

Dear Juan Weisz,

In my opinion, the no-local behavior tells us that the particle know (somehow) what is exists in the stuff of experiment (the environment) and take a decision in its motion based on this knowledge and based on some degrees of freedom (like quantum jumps)

With best regards.

Thanks Mazen,

electrons making decisions sounds spooky.

I would describe jumps, either as transition probability, or the physical influence of a probability density modulated wave

with a certain frequency, where you can show the elastic conversion of pp/2m energy over to a term hbar omega.

(Frank Hertz experiment). That is why Im interested if a quantum wave is described by exp(ikx) or by cos(kx).

Best Regards, Juan

Dear Juan,

How can be described whereas it is 'fluid'? Why do you use 'a'?

Thanks for your reply. Marc.

Dear Juan Weisz,

1- You said:

" where you can show the elastic conversion of pp/2m energy over to a term hbar omega. "

In my theory I put this section:

"First, we mean specifically by "quantum jump" one period of movement between two appearances of a particle.

As we know, based on Newton's First law of motion "In an inertial reference frame, an object either remains at rest or continues to move at a constant velocity,

unless acted upon by a force".

But this law is not compatible with the disappearance and appearance idea!,

this law is not always true since the particle might easily appear (if the quantum jump is enough) in a forbidden (have a variation to very large potential field like for example particle in box) place after some quantum jumps in the direction of the movement of the particle!, so for a huge number of particles that jump in the subatomic level the Newton law may put our universe in

unstable situation!, and this might happen specifically when the length of the jump is close (or greater) to the length of the field's fluctuations.

But in the case where the length of the quantum jump is very small compared to the length of the field's fluctuations then the first law of Newton will be applicable because in this case, we can be sure that the particle will feel the force before that the force gets altered so all initial velocities are acceptable."

So based on p2 /(2m) of the particle and based on the distribution of fields in the space environment the particle follow classical mechanics or quantum mechanics ...

2- Sorry, what you mean by "That is why Im interested if a quantum wave is described by exp(ikx) or by cos(kx)." ?

With best regards

Quantum theories can be understood from several viewpoints; I particularly like the versions of quantum field theory by Rudolf Haag, who was my teacher, but I also like the approach to quantum field theories by Richard Feynman, who also was was one of my teachers.

Mazen,

the two expressions seem equivalent as per Schrodinger theory, but not in terms of probability density, one is constant and the other is modulated. Also only one of the two is a momentum eigenstate.

Im wondering if one is ineffective as to electron promotion, while the other is.

The time of one wave cycle is the time between the dissapearance of one and the apearence of the other?

Regards, Juan

Claudio,

Thank you for telling us your preference, but I am sure that each one of us has some preference. The question asked here is whether the QM is completely non-deterministic, or has some stub of determinism in it. See further explanations in the question text.

Dear Juan Weisz,

First, in my theory the time of one wave cycle is not the time between the disappearance and appearance, in non-relativistic case this duration is almost zero.

In fact, the complex number exp(ikx) only makes the calculus easier, and we can build all the quantum physics only on trigonometry function like cos(kx) or sin(kx).

For me, I don't like to view the complex number in the main physics equations, because I think it hides the physics meaning of the subject of equations.

Anyway, I demonstrate this in the following paper (section 4 and 5):

Preprint The theory of disappearance and appearance

With best regards

Sofia

I will vote for completly non deterministic, the undelying reality, if any, is left unspecified. However it is very hard to distinguish

the two cases, due to the statistical interpretation I believe in. QM is at the level of a phenomenology and very risky

scientifically to go any deeper right now. I always have a provisional image of the quantum.

Mazen,

with your half wave length periodicity of the wave to cause jumps, I think you are saying that it is probability density and not the wave that does it. I tend to agree, but from completely different basis. The frequency would come from the speed of the wave moving past some fixed point. I would use p instead of L to indicate linear momentum. If you do the math properly you will get

pp/2m equal to hbar omega. If you use the wavelength of the wave you just get half this, the wrong answer.

My dear Juan,

I have no idea what happens here, I answered you already, but my answer disappeared. So I write it again. I advise to withdraw your vote for complete non-determinism because you'd quarrel with QM. Complete non-determinism means that results of a measurement appear with equal probabilities. However, look at eq. (1) in my question. Would the wave-function allow the responses a and b appear with equal probability? What you talk about?

With kindest regards

There are several approaches to quantum mechanics: the algebraic approach, due to Rudolf Haag, the Feynman approach, with quantum field theories, the stochastic approach to QM. But, in spite of the dissimilarities between the various approaches, they are all equivalent and lead to the same verifiable and the same results with respect to the experimental confirmations.

That is not my meaning. One probability can be greater than another, but there is still no interpretation of underlying causality.

Besides the replies I gave in my previous answer, I should add another remark to the question about the interpretations of quantum mechanics: there are other approaches to QM: the stochastic approach, where - instead of the standard probability of QM quantum theory - one uses stochastic processes as the model. The standard and the stochastic approach give the same results, except for short-time processes.

Juan,

Quantum probabilities are not fully random, they have propensities.

Sofia

You must still have to say what is behind the propensities, of course it is not classical probability, it is based on a wave.

I am trying to have a theory that sais that the wave has to do with the exclusion principle of Fermions, nilpotency

of creation and destruction operators, but it always comes back to just mathematics, never any real causality as is understood

in Classical terms. It just connects to other mysterious stuff. Also I try to figure out how the wave causes jumps.

Regards, Juan

Dear Juan

"You must still have to say what is behind the propensities, of course it is not classical probability, it is based on a wave."

I think that the propensity is given by |α|2, see option 2 in the question. But there are also options 1 and 3. The option 3 tries to get into the phenomenology of the propensity, but is not successfull. The formation of an avalanche is sometimes allowed, and sometimes stopped. BY WHAT IS IT STOPPED? This is the problem.

". . . creation and destruction operators, but it always comes back to just mathematics, never any real causality . . . "

Oooo! I absolutely agree with you, mathematics won't answer the question. The mathematics leaves us at a certain point, beyond which we have to try our intuition, e.g. make hypotheses as I do. (By the way, I think that you wanted to say phenomenology, not classical causality. The latter is not a good term in non-deterministic processes.)

About nilpotency, I have no idea what it that, won't you define it? Though, I don't see what the exclusion principle may have to do with my question. The wave-function (1) could have represented single bosons instead of single fermions. The problems would have been the same.

With kind regards

Sofia

Nilpotency of an operator is when some power of in is equal to zero. So if you try to create two electrons at the same place with

the same spin you get zero, the power in this case is 2. This is the exclusion principle.

ad^2 = 0 where ad means the dagger of a; this in turn follows from a slightly more complicated Canonical quantization formula

with antisymmetry. Same happens with destruction operator.

If you think the wave is more or less the same as the electron, then it is not so clear that the wave is a boson.(I admit that waves usually are treated as bosons)But I also saw certain mathematical reasons for doing this,

take too long to explain right now. What fluctuated as a wave was the occupation number operator ad(l)a(l) , between the limits of 0 and 1 for a given spin, and different sites l, equivalent to a fluctuating probability density.(not the actual eigenvalues which are only 0 and 1, but a probability of finding the respective eigenvalues)

Regards, juan

The problem is that if you start off with a probability model, you have to exclude zero and one. There is no deterministic event in QM, by the very model.

Dear Ed,

Correct, even by definition! Thanks for your reply. Marc.

QM can be formulated in several ways, all non-deterministic, such as the quantum probability of Feynman - which is probably the best - or with the Kolmogorov probability or Nelson's version of chaotic processes. Apart from transient temporally short phenomena, the various approaches are mutually equivalent.

But the standard approach by Feynman is the best, because it allows the generalization to quantum field theories.

QM cannot be formulated in Kolmogorov probabilities because these probabilities fail to explain entanglements.

Besides, the question does not ask how can QM be formulated, but what causes an answer yes or no of a detector. The answer is not entirely random, as yes and no don't have equal probability. The question is what stands behind the propensities and how phenomenologically it is done.

Please read my answer to Juan. It's waste of time to throw comments that represent no answer to the question.

My dear Juan,

what's your problem?

"If you think the wave is more or less the same as the electron, then it is not so clear that the wave is a boson."

I din't say that the wave of an electron is a boson. Why don't you read what's written? I said that to think in the direction of mixing the exclusion principle in the present problem, leads nowhere, because instead of woking with electrons I can work with bosons. By α|1>a + β|1>b I can represent the wave-function of a boson.

Also, I don't know what is "ad(l)a(l)". Do you mean â†â ? (You have to learn to do copy-paste of symbols from a doc-file. Create to yourself a doc-file with special symbols and copy from there.)

NOW, TO YOUR SUGGESTION: you see, the wave-function α|1>a + β|1>b is an eigenfunction of the number operator. There is no fluctuation in the number. Even each one of its truncations, α|1>a and β|1>b are eigenfunctions, respectively of the number-operators â†â and b̂†b̂. So, the number of particles does not fluctuate, neither on the path a, nor on the path b. Therefore, IF the detector A sees the wave α|1>a , then it sees one particle, no less. But, DOES the detector A see allways the wave α|1>a ? I am not sure.

Maybe it always sees the wave; but it seems to me that for the detector A the fact that the wave intensity α2 is less than 1, is a problem. If α2 were equal to 1, there were no problem, the detector A would have fired with certainty. But α2 < 1 is a problem. Well, so far so good. The question is, what the detector does in face of this problem?

With kind regards

Not having equal probabilities is NOT a reason to not be entirely random.

Sofia

By the present problem, you mean your problem? Mine is Fermionic.

I suppose you can get quantum waves from Bosons also, but you would have to start from different statistics (The Bose Einstein)with commuting algebra. There is no exclusion.

Fermionic:

The number operator gives both the eigenvalues (0 and 1) and the eigenstate for each case. The eigenstate for 0 is orthogonal to the eigenstate for 1

The number operator is symmetric, so with the characteristic of a Hermitian operator, and you interprate the result as you always do.

the result of measurement can only be 0 or 1, but wave charactristics for amplitudes, depending on site.

The number operator is parametrized per site, so it is different on each site, and so is the corresponding eigenstates.

You are correct in the interpretation of the number operator, but you have many.

The characteristic for Bosons would be similar, but perhaps then you deal with infinite matrices, more complicated.

The simple harmonic oscillator is the simplest in that category.

ccupation number is 0,1,2,3,4,.....in that case. If they are all orthogonal, measurement should give you only one.

Maybe you would have to use some kind of super detector. I suspect we are not using comon language.

I do not understand why a probability should be excluded fro 0 or 1...if you change the problem also proves nothing.

Regards, Juan

Juan,

"By the present problem, you mean your problem? Mine is Fermionic."

By the present problem, I mean the problem in the question. When I ask a question I do it because I need an answer to my question.

"I suppose you can get quantum waves from Bosons also, but you would have to start from different statistics (The Bose Einstein)with commuting algebra. There is no exclusion."

Bose-Einstein statistics enters into play when you speak of condensates, not when you speak of single-particle wave-functions. Condensates are multi-particle systems. As to exclusion, whith whom do you expect a simgle particle to do exclusion?

Sofia,

No they were not specifically directed.(sorry) However I gave you my thought about a Bosonic wave.

However your question was about electrons originally. The detector is triggered by charge, is all I can say.

Ed

Your remark about probability not including 0 or 1 is really not necessary.

The outcome of a measurement cannot be predicted with certainty, but right after it you jump to one of the eigenvalues,

and you can say for certain that is the result.

When I say non deterministic I mean only the first part.

That is what I would answer Sofia also. The theory does not mandate what a detector does. For this you need a different analysis. The theory (only before measurement) is just statistical and sais nothing about a particular triggering of a detector.

Perhaps only after a long sequence of measurements can you judge the detector adequacy.

Dear Juan Weisz

The half wavelength periodicity is for the classical limit when we enter to classical physics, but for the quantum world, the jump can be anything and sure it is compatible with the probability density of the particle.

with best regards.

Entanglement is a question of definition of object.

Is it two separate pieces, or is it only one single object? That creates many difficulties.

Juan Weisz: the contrarians will just have to believe it, if they continue to refuse to hear reason.

Sofia Wechsler: You wrote, "Quantum probabilities are not fully random, they have propensities." This is false.

The problem is that if you start off with a probability model, you have to exclude zero and one. There is no deterministic event in QM, by the very model. Even eigenvalues have a width, look for Lamb shift.

Ed,

I already explained that if you include the measurement part, you have to regard this as an amaturish remark. No theory of probability excludes P=0 or 1. If you never attain these values , that is one thing, that is no bother, but why exclude them from math? What you really use is probability density anyway.

Theory of probability, any theory, must exclude 0 or 1. It is not sound math to use probabilities, and "complain" that 0 or 1 are missing... or, that 0 or 1 are excluded.

To the second part of the question by Sofia, with the first part being a YES as it MUST be, the answer is UNDEFINED a priori -- and any attempt to define a priori MUST be false by the very model used. You'd have to change models, Sofia, for further resolution.

The contrarians have no resort but to believe this; if they refuse to reason then the only way left is to abandon reason.

That is why I dont complain, because 0 and1 are there, even if I never have to use them.

Someone in math, answer this.

Yes, QM is completely deterministic. the concept of non determinism traveled from uncertainty principle which is failure of QM itself most commonly misinterpreted. there is no probability in QM. The same question was asked by Schrödinger, He and his famous followers never could prove that if there is such an element, here is the Schrödinger's reply asked during an interview, "I am sorry I ever created QM". So see the reply of the developer on it. And u will be surprised to know that all these.... even we do not understand QM as well as CM all we know only end results on that we are applying randomness not on the cause. As the important link is missing.

Bell's theorem smashed in one blow by String Mechanics, one of the biggest achievement of this century, as it was based on the consequences of the randomness on the results (outcomes) not on the very cause of it. Unless we know the proper mechanism things are statistical (mind it not random, otherwise there would have been no geometries, shapes, structures, periodicity... had been possible in the world we live), QM basically fails and misinterpret it.

Dear Dinesh,

Please explain me further what exactly you mean by: (a) randomness; (b) Heisenberg's uncertainty principle; (c) is the latter (i.e. uncertainty principle) lies deeper where our logic and language (which is the base of every science including QM) should neccessarily be impossible to utter it?

Thanks for your reply. Marc.

Dear Dinesh,

What do you mean by classical mechanics? Please tell me whether any non-classical mechanics exsists and how and which it exsists. Thank you for your answers.

Yes, Dinesh wants everything to be Classical Mechanics,

unfortunately he is very wrong.

classical Mechanics is identified with Newton and followers,

Lagrage and Hamilton. Special theory of relativity is also included.

Then Classical field theory covers Maxwell theory of Electromagnetism, and the General theory of relativity.

In summary almost everything that is non quantum is called

Classical.

The quantum markes a sharp break in methods and results.

In fact irreducible randomness is a characteristic, which

Dinesh would rather not admit.

Thermodynamics and Statistical Mechanics also admit randomness, although at not so fundamental level, unless it is quantum statistical mechanics.

Ed

In some sense events with probability zero still occurr.

Consider a perfectly defined trajectory of a particle, among all the other possible trajectories.

Since all the other trajectories constitute an infinite set, the given trajectory has probability zero, and yet occurrs.

This gives you some idea of conserving P=0 or 1

I proved it. Nothing to say further.

Juan Weisz

and all. I proved it by deriving various results, that was derived by QM by simply using Classical Mechanics and even those which have never been derived by QM itself e.g. explanation of Black body radiation.....Photo electric effect.....Bose Einstein condensation....all the postulates of QM, even Plancks E=nhv.... de Broglie's hypotheses ..Classical analogue of QM oscillator (experimental finding) ....almost everything, what more is to be expected by this Classical Mechanics in which finally QM emerges as the particular case of CM, this is a recent news so it is quite possible you all may be surprised or taking it as a biggest joke in the scientific community. I am also surprised how this can be possible, through my reading and arguments seen so far would have not been so clever enough to accept the CM as the winning design of nature , but recently discovered one of the hidden variables makes this possible. Please visit the page Paired statistics (which is name of the project) I have kept there all the results achieved so far in project description in order to stop unintentional increase in impact factor, one may freely visit or comment or suggest any thing to me or take part in it, but currently , please, do not impose or advertise randomness on this occasion, as this has not been applied with a general view in the mind in the old theories of CM, QM...SM.

I also do not know how to comprehend all these, but, perhaps by this Einstein was correct in his deep insight about quantum mechanics. At the moment I have nothing more to say, only rebirth of Classical Mechanics!

Juan Weisz

Sir, you wrote

>>Consider a perfectly defined trajectory of a particle....

if the trajectory is perfectly defined so the probability is 1. There can be no 0 probability.

Same thing (loop hole) I observe in QM. perhaps you may not agree with me, just consider the general view of randomness. All the SM, QM.... consider equal a equal priori probability which is just a postulate, please don't be confused with it and also do not confuse others we all are expecting the hidden generous residing in you.

I would have agreed with your previous comment, but see what I was pointing at.

Marc Carvallo

sir, here is something...

A) requires lengthy writing.....illustrations

B) just a measurement problem which also believed and held long even by Heisenberg.

C) uncertainty principle does not lie deeper and it is not the base of every science including QM....

@Juan's reply and others, especially your past education should be sufficient to understand what is not classical mechanics, If you are really exploring.

Welll, I do not argue with those that know nothing.

Tired of seeing baloney on some threads.

Classical probability is no. of favoured events, divided by all possible events. This gives me zero.(1 divided by infinite)

Quantum probability is given by the square modulus of a wave function.

Dear Dinesh,

Please explain me why the uncertainty principle does not lie deeper and it is not the base of every science including QM....

Thanks for your answer. Marc.