So, what would you like more from us to read the article or die?

While I could be interested in looking at how you cope with the conservation of the number of particles if H is not Hernitian, the second part of your post is a shame

Hello Professor Goliney:

Nothing farthest from my purpose than displeasing you or objecting your authority. Please accept my humblest apologies if it happened otherwise.

Had you read the article you could have checked that in the natural model the number of particles --three in this case, as is the count of one proton, one electron and one photon-- never changes, at least if you are willing to accept that a totally absorbed photon, or "null cotangent vector", is still a photon. This makes sense because in the paper photons are cotangent vectors, hence the null cotangent vector is a photon. Alternatively, if you think that the zero cotangent vector is not an admissible photon, then perhaps you may be willing to accept that arbitrarily small non-zero cotangent vectors are photons, and the number of particles still will be three. Conservation of the number of particles does not look like a problem for the natural model.

There is no need to worry about Hermitian operators, since the concept does not apply to operators acting on vector spaces over the real number system, as is the case with Schrödinger operator acting on the (infinite dimensional) space E of real valued wave functions. We deal now with a real symmetric operator, and in future papers with real normal operators required to take care of angular momentum. Complex numbers may be used as a technical trick, but they are better avoided to minimize confusion with standard Quantism, full of complex quantities since its creation.

The natural model uses Schrödinger operator in a novel way. It postulates a Hamiltonian evolution equation on a space of states T*PE which is a symplectic manifold, in fact the (infinite dimensional) cotangent manifold of the real projective space PE, of the real linear space E. The potential energy is the Rayleigh quotient of H, the kinetic energy is the squared norm of the cotangent vector (energy of photon), and the total energy is their sum. The evolution equation is the Hamiltonian vector field of the total energy.

The natural model is non-linear in a deeper sense than usual. Instead of a non-linear expression for operators on some linear space, here we have an infinitesimal generator that is a vector field on an infinite dimensional manifold, and it is the manifold itself that definitely is non-linear, simply because it has non-zero Z2 cohomology, actually equal to the polynomial ring in one indeterminate Z2[W1]. If a large enough local chart could be found where the evolution equation had a linear expression, it may lead to very useful results; for various reasons, presently I do not think such chart exists. These concepts are familiar to any of the members of the celebrated --and much admired by me, an extremely modest author-- Russian school of topologists, which I am sure are within your reach, should a consultation be required.

The natural model already has enough structure to be reasonably proposed as a major breakthrough in the effort --started by Albert Einstein, Erwin Schrödinger, Louis de Broglie, David Bohm and others-- to get rid of Quantism.

And please, do not die before reading the paper. Preferably with a critical and constructive attitude. Many technical details are explained there for you to tackle with the skills of a well trained professional. If dominated by prejudices, you may go down into history as another example of useless argumentation against new, correct ideas. If convinced by the natural model, you could become one of its staunchest defenders. Anyway your comments are and will always be very welcome.

As is the case with beauty, shame is in the eye of the beholder. History sometimes takes strange turns and it may now leave practitioners of Quantism on the losing side.

With best regards and most cordially,

Daniel Crespin

Sirs: With all due respect to your experise, may I suggest that there is already a confusion about quantum states unitary evolution and quanrum transitions. By the original group of physicists, quantum transitions were regarded as showing the very heart of the new QM: they were considered as the quantum "jumps" between states, the typical QM-cal occurrence, characteristic consequence of the quantal nature of the microcosmos, belonging to, effectively, to the problem of QM measurement.

However, newly these transitions are treated as unitary time evolutions, taking place as a simple time dependent phenomena between all the states simultaneusly, as described as the usual time dependent phenomena of QM, described by martix mechanics or the time dependent Scrödinger equation. I would rather believe the original authors, though the transitions are evidently not immediate, there are stochastic distribution around theire occurrence in time as average lifetime of states in actual situations. One more note: It seems evident by now that specifically in biological systems, we need a description of non-stochastic, controlled and specific (constrained) quantum transitions, as the usual time evolution of the whole system. Mathematically, though, it seems to request Hilbert spaces with a non-trivial metrics (affine Hilbert spaces), meaning non-orthogonal basis vectors.

Dear András Balázs

Thanks very much for your clarifying comments. Biology is beautiful and mysterious. And yes, I definitely tend to agree with you. Somewhere there seems to be confusion.

With best regards,

Daniel Crespin

DC: My question is: With this natural theory of atoms already elaborated, what are the chances for its acceptance by mainstream Physics.

First you need to work out under what conditions the observable results predicted by your theory would differ from the conventional calculations.

Then you need work out how an experiment could be performed which would test this difference.

Then you need to do some research to find out if that, or something equivalent, has already been done.

If not, then you need to actually perform the experiment.

If the results match the conventional theory but not yours, you publish that as a finding. It may have falsified your ideas but if the test has not been done before, it is still of scientific value.

If the results match the your theory and disagrees with the conventional prediction, you publish that as a finding too.

Then comes the hard part, you have to convince a second researcher to repeat your experimental method based on your published description. If they get the same results, the experiment is "repeatable" and at that point people should take notice. The first response will be that your experimental method will come under scrutiny of course, and also your calculations of both theories.

Since I gather you also mean, as I do, that it is up to experiment to decide if a theory is right or wrong, I would wholeheartedly agree.

Dear Dishman:

Thanks very much. Your comments go straight to the center of the question. Very brilliant your ideas. I will see how to make an attempt on them.

Time ago I read Thomas Kuhn, a sort of scientist, philosopher, sociologist and historian. He was a remarkable character who wrote that, when truly new Science arises, the real problem is to change the hearths of already established scientists. He said that certain ideas, called paradigms, do not go away easily, nor are they accepted easily either, even if the old paradigms are plainly wrong and the novel paradigms are right (or less wrong).

Kuhn looked at the beliefs of great past scientists finding that they had many wrong ideas. Great scientists of the past could commit gross errors. Why not contemporary scientists? The infallibility of Science was then placed in serious doubt. Nowadays nobody knows if, and when, absolute knowledge will ever be attained.

Is the existence of paradigms itself a paradigm? Perhaps a "metaparadigm"? And if it is, was it accepted too easily? Are metaparadigms easier to impose or to debunk than plain paradigms? Kuhn metaparadigm will ever go away? And if so, what can replace it?

A philosopher, called Karl Popper, had some influence on Kuhn. This Popper proposed something he called "falsifiability". He said that with falsifiability one can check whether apparently scientific theories are true. He may have meant theories like Darwinism, Marxism, Psychoanalysis, Economics and Quantism. Falsifiability may have some resemblance with what you tell. Can falsifiability be falsified? Or is falsifiability itself beyond Science, a non-scientific eternal truth?

Another philosopher, Paul Feyerabend, did not believe Kuhn or Popper. He said that in Science there are no rules and "everything goes". It was rumored that Feyerabend was actually an anarchist, that is, he preferred to reject all rules and regulations. What a strange bias. Although some rules he obviously respected, like the Grammar to write thing others could understand.

I very much appreciate your comments and expect to be able, in some future time, to do something about them.

With hearty thanks,

Daniel Crespin

Sir:

Concerning paradigms, I don't have much to say, never went to such depths, still, I think there is generally such a thing as the spirit of the (social) age. I would believe our new age brings a new paradigm based on fundamentally the electronic communacation age, so now everybody seems to be crazy in official science by the "bit", that the Universe is said to evolve towards the information-founded subject, swallowing every matter and turning them into "bits". Never thought it so, and don't incline to believe it. I try to hold myself to Heisenberg's words: to change only when it seems to be absolutely necessary. I would add: but if so, you must be prepared to defend it through every trouble with not blind belief but with well fought for scientific conviction.

Physical reality is based on a simple structure. This structure is believed to be a relational structure that in mathematics is known as an orthomodular lattice. That structure extends automatically into a separable Hilbert space. The set of closed subspaces of this Hilbert space has exactly the relational structure of the orthomodular lattice. The Hilbert space is a kind of repository for dynamic geometric data. It owns a unique companion non-separable Hilbert space. This couple can be turned onto a dynamic model in which part of the Hilbert spaces scans over the Hilbert space as function of a real valued progression parameter. This model cannot generate its own dynamics. It needs additional stochastic mechanisms that generate the locations of elementary modules. These mechanisms ensure the coherent dynamic behavior of these elementary modules. The mechanisms apply inhomogeneous spatial Poisson point processes that own a characteristic function. The elementary modules hop around in a stochastic hopping path and after a while the hop landings form a hop landing location swarm that owns a location density distribution. Due to the existence of the characteristic function the location density distribution owns a Fourier transform and therefore the swarm owns a displacement generator. This means that in first approximation the swarm moves as one unit. The location density distribution is the squared modulus of the wave function of the elementary module.

docs.com/hans-van-leunen

DC: Thomas Kuhn ... wrote that, when truly new Science arises, the real problem is to change the hearths of already established scientists.

He did, and I think it's partly true, for example there is currently great resistance to the acceptance of string theory but that is also based on good scientific principles, there are many versions and no testable predictions as yet. Acceptance will require evidence. On the other hand, when dark energy was discovered by Perlmutter etc. in 1998, it was accepted with the barest of ripples because it came directly from reliable observations by two independent teams.

On falsifiability, I would suggest you think carefully about Russell's Teapot (see the link). The point was that the proposition that such a teapot existed could never be falsified, hence we should not believe in it. Science embraces that too, it only accepts propositions where it can be shown that there exist tests which would show the proposition to be false if it is not in fact true, then those tests must be performed and the proposition must survive the test.

A more concrete example was the acceptance of general relativity over Newton's law of gravity. The test in question was that of bending of light by the Sun which was measured by Eddington during an eclipse. The value matched that predicted by general relativity but was double what Newton's Law predicted, thus the older law was falsified while GR was not.

String theory is in a difficult place because it so far does not predict anything different from existing theory. Some theorists are suggesting that "mathematical beauty" should be sufficient for its acceptance over the older maths but there is also a great deal of resistance to that, and IMHO rightly so.

https://en.wikipedia.org/wiki/Russell%27s_teapot

Sir: You are perfectly right in generaliy. The trouble with QM, you see, that it was formed enfocedly to comply with expriment, if with nothing else on Earth. So you cannot falsify it within pure physics, is my point, but seek such a material system, where it apparently does not function. That is the case with biological systems, you know. This is not because one wants something new anway, but because the contradictions are there, like in the famous Measurement Problem

Dear Daniel Crespin,

In my view the problem has already been solved by Einstein, when

translating the incompleteness of quantum mechanics into an

ensemble interpretation of the wave function. Note, that this

ensemble interpretation has experimentally been proven, for

instance by Tonomura and by Lichte (references can be found in a

number of my papers and in my book on the Foundations of quantum

mechanics, all to be found on my website

http://www.phys.tue.nl/ktn/Wim/muynck.htm ).

By Einstein the discontinuous change of the wave function due to

measurement was interpreted as a selection of a subensemble based

on selections of a particular measurement result among all

possible measurement results obtained from the ensemble. The states

of the different subensembles can be found in a simple way

discussed in sect. 3.2.6 of the above-mentioned book as

`conditional preparation', in general yielding a result different

from that described by von Neumann projection (once more being in agreement with observation).

Excellent response and good discussion

Dear Professor Muynck

Thanks very much for your interest.

I am extremely pleased with a message from someone that seems certain about these questions of quantum interpretation, and perhaps also about indeterminacy, uncertainty and similar controversial aspects of QM. That Quantum Mechanics is incomplete, incorrect or unsatisfactory was certainly solved by Einstein et al, but there may still be opportunity for additional criticism. Hopefully, those that choose to ignore or distort Einstein results will be eventually exposed.

My own viewpoint, as far as the hydrogen atom is concerned, is this:

1.- Schrödinger self adjoint Hamiltonian operator H partially redeems Quantism in the sense that its eigenvalues and real valued eigenfunctions (but not the complex valued functions in general) are closely related to a correct description of stationary electron energies and stationary electron states.

2.- The space of quantum states is definitely incorrect. Such mistaken quantum space of states can be any of the following

2a) The complex preHilbert space $E$ of complex valued wave functions, \Psi(x,y,z) or \Psi(r,\theta,\phi), as well as its Hilbert space completion $\bar{E}$.

2b) The unit sphere of $E$ or $\bar{E}$, respectively denoted $S_1E$ or $S_1\bar{E}$, consisting in normalized complex wave functions.

2c) The complex projective space $PE$ or $P\bar{E}$ made up of complex lines, these being also called complex Hilbert rays.

3.- The quantum unitary evolution equation, say the unitary flow $U_t$, is totally incorrect as well. This includes the flow on the preHilbert space, the flow on the Hilbert space, the flow on the unit sphere, and the flow induced on the complex projective space. In all cases there are no trajectories of the flow in the space of states joining stationary states of different energies. This erroneous evolution allowed the gestation, birth and growth of quantum indeterminacy, quantum uncertainty, quantum duality, quantum interpretation and other spurious physical "principles".

4.- Many parts of Quantism can be rescued, particularly those related to the calculations of eigenvalues and eigenfunctions, but this is a formidable future task requiring the concerted effort of many able scientists.

I thank you for dedicating time to this discussion and wish you the best of times.

Most gratefully,

Daniel Crespin

@ All P.T. Followers of this question,

The physics of quantum phenomena is really very complex. Any explanation of all features of the observed world in a consistent way, seemingly is impossible, which is not surprising for everybody thinking seriously about the nature. However we have some selfconsistent models describing correctly huge areas of the reality. Quantum mechanics is one of them. It is not true that there is no possibility in explanation of changes of the quantum state. In my opinion a quite satisfactory model is the one, where the result of the observation of the world is the reduced state of the observer (formally expressed by partial trace). In such setting, everything known to the observer is the reduced state, which involves the information about the state of the outer world (i.e. the environment) in amount dependent on the interaction between the two worlds. Then everything goes without any difficulty, incluging the possibility that we can restore the (in general - convex combination of) stationary states of the total sytem. I have pointed at this possibility in my article put into RG at the address linked below.

This possibility is shown for examples with product initial state, under hamiltonians suitably containing non-commuting terms. Let me stress, that in such setting I do not refer to the particular way the observer knows its/his/her state! It is assumed, that the system knows the own state perfectly at each instant.

Obviously, I do not have to add much comment on the well-known phenomenon that the process describing changes of observer's reduced states already in rather simple cases exposes possibility of evolution from the pure state to mixed states. The only detail important for the current question is, that there are (usually) no jumps! The jumps appear only as a necessity when we want to try to present in one model the meaning of the probability of a particular pure state with the picture seen by an ADDITIONAL SUPER OBSERVER. This is completely another story. Why nobody doubts that a probability model describes, say the street traffic, simultaneously BEING CONVINCED THAT IT DOES NOT PREDICT AN ACCIDENT happened to a particular car within a particular time interval?

Best regards

Conference Paper Quantum Systems' Measurement through Product Hamiltonians

“Are random quantum jumps the only possibility? ”

- yeah, that is fundamentally so. There cannot be some continuous change of anything [which isn’t absolute infinite, though; but that is inessential here since any system in physics is limited] including – continuous changes of material objects/systems of objects. The reason – fundamental logical self-inconsistence of the notion/phenomenon “Change”: if something changes continuously every “now state” is simultaneously “past”, “now” and “future” states; when all these states are different by definition. This fact was discovered 2500 years ago, when Zeno predicted the quantum mechanics.

Thus quantum transitions and the uncertainty of objects’ states between/at transitions is fundamental and so, say statements as “…Quantum Mechanics is incomplete, incorrect or unsatisfactory was certainly solved by Einstein et al…” aren’t correct; the uncertainty problem cannot be “solved” by some interpretation; including by “translating the incompleteness of quantum mechanics into an ensemble interpretation of the wave function.”

In the reality there is no [and cannot be] really always [simultaneously] existent [e.g. Multiverse’s] “ensembles”, that is impossible by the energetic reason.

That is another thing that all what happens in our Universe now in the reality “had happened already always” and “is happening always” absolutely infinite “number of times”, now given observers simply observe a given movie of the Universe evolution, as that they have made/make infinite “number of times” also.

And this evolution of unique Universe every time proceeds in accordance with the unique scenario, where all/every wave functions collapse by some unique ways, all coins fall on the same unique sides, etc.

If that would be not so, Achilles never could overtake any turtle. But deltaP*deltaX>h-bar/2 allows that…

More – see https://www.researchgate.net/publication/260930711_the_Information_as_Absolute  

Cheers

Cheers

Article the Information as Absolute

Sergey,

The fact that universe is fundamentally stochastic is not explained by the fact that dynamics asks for it. Digital computers can generate quasi random numbers with cyclic algorithms. The fact that we judge reality as stochastic can be based on the fact that the period of the cycle of the generator of the locations of elementary particles is enormously large.

I would not go into any discussion here,my corresponding standpoint was exposed at related topics in my comments at RG.

.Hans,

“…The fact that universe is fundamentally stochastic is not explained by the fact that dynamics asks for it…”

The fact that Universe is fundamentally stochastic fundamentally follows from logical self-inconsistence of the notion/phenomenon “a Change”, thus every changing system is fundamentally stochastic without any necessity in other additional reasons – though the stochasticity of concrete systems can have some additional reasons/sources.

Besides the uncertainty of states of changing objects/systems for any/every dynamic system to solve this self-inconsistence and, e.g., to evolve in some, say, determined [principally limitedly] way,

additionally is necessary to spend something, what for material objects in physics is called “energy”; when non-material system “human’s consciousness” changes, for example when thinking, she spends an energy also, a difference is only in that in Matter humans can  measure relative portions of the energy measuring kilograms, meters, and seconds, when corresponding set of variables for the consciousness till now is unknown – besides the seconds.

“…The fact that we judge reality as stochastic can be based on the fact that the period of the cycle of the generator of the locations of elementary particles is enormously large. ..”

- it seems as rather rational to suggest that a generator of pseudo-random numbers of the locations of elementary particles doesn’t exist, since even only in Matter there are too many particles and all of them always move randomly somehow and to somewhere...

Cheers

The Schrödinger equation that allows to find the energy levels is the time independent Schrödinger equation, where the time derivative is replaced by the energy eigenvalue.  The Schrödinger equation that describes the evolution of a quantum state is the time dependent Schrödinger equation. The wave function need then not be an energy eigenstate.

The quantum jump is a concept of old quantum mechanics, that have been replaced by wave mechanics by Heisenberg and Schrödinger, it no longer applies. A transition is described by the time dependent Schrödinger equation, and happens when there is an external perturbation, such as vacuum fluctuations. Then, the interaction term creates an overlap among the energy eigenstates, and their complex amplitudes change with time.

Now the measurement intervienes. According to the type of measurement, the wave function is projected onto a corresponding eigenstate.  If the energy level is measured, the wave function is projected onto a level which is not necessarily the same as in a previous measurement. If the radiation is measured, a photon is either observed or not. If it is, that is correlated with a change of energy level.

OK, this image is pretty simple and acceptable. But:

What does it mean that energy level is measured?

What does it mean that the radiation is measured?

Answering this questions we necessarily come to  observer's subsystem, and then in such a consistent model the only cause of changes is the interaction hamiltonian which causes the information to pass from the observed subsystem. I prefere the opinion that  the implied evolution of the reduced  state of the observer is the only result of the measurement (obviously and unfortunately  a posteriori, only). In this fashion no jump appear and the subject of measurement (=observation(?)) depends in a strict way on the terms of the interaction and the  hamiltonians desribing self evolution of the subsystems (some other details are provided at my former answer)

Sergey,

The Hilbert Book Test Model is a purely mathematical model that is based on a rather simple foundation, which was discovered eighty years ago by two scientists that called their discovery "Quantum logic". Mathematicians give this relational structure a different name. They call it an orthomodular lattice. This lattice gets a direct realization in the set of closed subspaces of a separable Hilbert space. Every infinite dimensional separable Hilbert space owns a unique companion non-separable Hilbert space that can be considered to embed the separable Hilbert space. This model can easily be converted into a dynamic model. However, in order to achieve that target, this base model must be extended with stochastic mechanisms that provide elementary modules with their locations.

See: docs.com/hans-van-leunen or TheHilbertBookTestModel by Hans van Leunen

https://doc.co/WmxXCB 

Joachim, that doesn't work, in quantum mechanics, measurement is non local.

Claude, 

there are two parts in your answer:

1. An empty part with the answer on your definition of the quantum measurement of the energy level

2. Evaluation of my answer "(that doesn't work)" with arguments related to lack of nonlocallity (probably, of my proposal of a definition of quantum measurement)

With respect to  2: Could you please be more precise showing places where my proposal implies any relation to locality or non-locality of the measurement? And what does not work, with respect to which aims?

Ragards

How do you describe a measurement in an EPR type correlation experiment? Reality proves to be non local, and Quantum Mechanics is a modelling of that.

Hi, Daniel!

I just want to tell you that only the ground state is a stationary state. The Hamiltonian that predicts the excited states is a ZERO ORDER approximation Hamiltonian.

The excited states are, as I already told you, RESONANCES. The correct Hamiltonian for these states is the zero-order Hamiltonian plus a correction which includes the Hamiltonian of the e.m. field and the interaction Hamiltonian between the e.m. field and the atom.

In a semi-classical view, the excited atom behaves as a DIPOLE which oscillates under the influence of the e.m. field of the vacuum. Ultimately, the dipole emits a photon. There is no "jump" between stationary states as you say, the oscillation takes some time proportional with the inverse of the width of the excited level (excited levels do not have a sharp energy, the distribution is a Lorentzian). 

Dear Sofia

Next week I should have enough time to reflect on these, and previous, remarkable comments, and to reply in more technical terms. Until then, a good literary expression of my appreciation of the complexities of Quantism is the following paragraph of J. L. Borges, a celebrated Argentinian writer:

"Around 1916, I decided to devote myself to the study of Oriental literatures. Working with enthusiasm and credulity through the English version of a certain Chinese philosopher, I came across this memorable passage: “A man condemned to death doesn’t care that he is standing at the edge of a precipice, for he has already renounced life.” Here the translator attached an asterisk, and his note informed me that this interpretation was preferable to that of a rival Sinologist, who had translated the passage thus: “The servants destroy the works of art, so that they will not have to judge their beauties and defects.” Then, like Paolo and Francesca, I read no more. A mysterious skepticism had slipped into my soul. "

                                                                                Translated by Eliot Weinberger 

With most cordial regards,

Daniel Crespin

Hans,

“…The Hilbert Book Test Model is a purely mathematical model that is based on a rather simple foundation, which was discovered eighty years ago by two scientists that called their discovery "Quantum logic"…” , etc.

Sorry, but I was educated as  experimentalist, not theorist; an so cannot comment this problem professionally. But as to me the above quoted passage isn’t completely correct – the Hilbert space in QM isn’t some arbitary abstract space, it is the space where just physical operations are formalized, by introducing just “physical” operators – of  momentum,  energy, angular momentum, etc.

Generally speaking mathematics is nothing more then a language that allows to depict physical objects and processes by utmost complete and compact way; as well as there can be different corresponding mathematical models at describing the physical reality – most known cases are Heisenberg’s and Schrödinger’s QM representations; so appearance of a next version cannot be excluded; the unique condition – this representation should be equivalent to existent representations in points where the lasts are adequate to the reality – and the new one must be in accordance with experimental data and must not contain possible logically inconsistent inferences as well, of course.

But it is well known that existent formulation of QM seems as complete enough and a new  QM representation has a sense first of all if it contains some new just physics…

Cheers  

Sergey,

If I were a pure experimentalist, then I could live with your view on the usage of mathematics in  physics. My experience during my career as a developer of image intensifier devices has enforced me to think otherwise, because my task required a deep understanding of the features and the behavior of quanta. Without the application of mathematical models this was impossible. For me mathematics was not only a description tool. Instead it was impossible to understand what was going on without the support of Hilbert spaces and field equations. Applied physics can exist without the usage of Hilbert spaces, but understanding the origins of the features and behavior of quantum physical objects is impossible without the availability of a suitable mathematical model. In order to get a full picture you need the full capability of the Hilbert space and that capability you only get in a combination of a separable quaternionic Hilbert space and its (unique) companion non-separable Hilbert Space. Only that base model offers you the reason of existence of electric charges, color charges, creation and annihilation events and entanglement.

Physicists tend not to take the restrictions that mathematics poses to their models for serious limitations. Read the paper of John Baez.

http://arxiv.org/abs/1101.5690

Mathematics is a tool useful only for checking the consistency of the basic assumptions, and for solving problems, including by posing them well. It doesn't allow a real understanding of what happens, precisely because of its problem solving role.

Hans,

“…In order to get a full picture you need the full capability of the Hilbert space…Only that base model offers you the reason of existence of electric charges, color charges, creation and annihilation events and entanglement…”

- again, any mathematical construction by any means cannot offer any reason of existence of any material objects/processes. Fundamental Nature forces, charges, colors, energy, momentum, etc. exist in the system “Matter” quite objectively, without any link to – how their existence, interactions and changes can be depicted in some mathematical models; including they existed, interacted and were uninterruptedly changing rather long before the time when Hilbert space appeared in mathematics.

Cheers

Sergey,

Apparently, you do not comprehend that most of mathematics is derived by investigating the structure and the behavior of reality. Especially the foundation of reality is easily comprehensible.

Hans,

“…you do not comprehend that most of mathematics is derived by investigating the structure and the behavior of reality…”

again – in this fact there is nothing surprising.  Matter is rather simple informational system that is built basing on a rather small set of logical rules/links; thus on the one hand mathematics is the language that is fundamentally suited for utmost [comparing with other languages that use mostly not rigorously formalized words/notions] complete and compact description of material processes; from another hand – by the same reason it was quite natural that mathematics appeared at humans’ practice at attempts to describe natural processes and that turned out to be successful.

I.e.  “Mathematics indeed knows practically everything about Matter”, but it “knows” also very many other things; the human’s problem is – where mathematics indeed relates to Matter and so can be correctly applied at analyzes of physical reality? - and here exists practically one criterion in this problem – mathematical symbols must have physical sense. A brick falls on Earth under force GMm/R2 with the acceleration 9.8 m/s2 not because of  mathematics contains the function f(x)=1/x2, operations of multiplication and division, and the number 9.8; it falls because of action of physical gravity force that acts according to Newton gravity physical law; and the application of Hilbert space in QM by no means differs principally from this example.

Again – till a physicist doesn’t point  – to what new physics a new mathematical approach relates, any mathematical novations are nothing else then mathematics scholastic exercises. There exist a huge number of papers like you linked, including in very respectable physical journals, and in every paper is written that presented mathematical approach is an next revolution in physics.

But the result is well known – in the reality physics-2016 contains practically nothing new comparing with, say, physics-1980…

Cheers

Meters, seconds and kilograms are invented by humans in a situation that they do not yet understand the relation between these parameters. Otherwise many of these values would have been taken equal to unity. Planck's constant represents another category. It indicates the number of elements that are contained in the swarm that represents an elementary particle or the number of fronts that constitute a photon.

I have to thank  Claude for his last two remarks, since answers to the posted questions could be interesting for other ResearchGaters.

1. In the model of measurement presented in my first post, there are no new mathematical assumptions about the quantum evolution of isolated systems: only deterministic dynamic governed by suitable hamiltonian is accepted.

New-old notion is that the state of a subsystem is the reduced  state obtained by partial trace. With respect to this the new interpretation is, that the reduced state in the only knowledge of a subsystem (modelling the observer) about the entire system. Therefore the assumed definition of  the result of  measurement is formally the equivalence class of all system's states which imply the same reduced evolution of the observer.

2. The problem of locallity is not a problem of the assumed QM, but just a problem of interpretation. The system of notions sketched above exposes the locality of quantum measurement as follows:

There are such  tri-partite systems , where (for reasons explained below)   "2" is the observer whereas "1" and "3" form a compound bi-partite observed subsystem, and such  that the entangled state of  "1+3" can be indicated by the observer  even in the absence of interaction between  "1" and "3".

More precisely, it is possible thatthe following conditions are fulfilled:

condition 1:  the hamiltonian is a sum of two interactions A+B, where :

A - involves the coordinates of  "1" and"2", only

B -  involves the coordinates of   "2" and "3", only

condition 2: the reduced states of system "2"  at  instants  t  contains the corresponding mixed terms substantially, which makes the result of measurement dependent on the entanglement. The notation of subsystems is in accordance with subsection

4.2. Three-partite systems - non-commuting factors

in the presentation referred to in my first post (currently - number 15 on page 2 above), where a strict fomulation of such examples can be found. In particular, one can use formula on page 47 suitably adapted to entagled states of  "1+3". For instance, if the system state is represented by the wave function of the form:

( \pi^{1} \otimes \psi^{1} + \pi^{2} \otimes \psi^{2} ) / \sqrt{2} \otimes \phi

with orthonormal  pairs  

{\pi^{1},  \pi^{2}} \subset l_2  and  {\psi^{1}, \psi^{2}} \subst L_2(R),

and with \phi \in L_2(R),  which  is the initial state of  "2". Then the above named mixed terms at instant  t  depend  among others, on the reduced term

\sum_j  \int_R

[ \exp{ i t m_j ( x - x') }  \pi^{1}_j  \psi^{2} (y) (\pi^{2}_j \psi^{1} (y))* ]

\cdot  \phi( x + ty ) \phi( x' + t y )*  dy

which is non-zero for some sufficiently strongly varying  sequences  m_j , j \in S, and functions \phi(x) , x \in R (the initial wave function of the observer).

Let me stress again, that my proposal does not solve the problem of a single act of quantum measurement, also, it does not relate to locality or nonlocality of, say, interaction between elementary particles. What it does, and I think it works sufficiently well, is an explanation of  the possibility of measuring  entaglement between two subsystems by observing them separtely.

Additionally, the given class of examples confirms the idea presented by Sergey, that mathematics expresses only our knowledge of the nature. Since my proposal does not use any new formal assumptions about the model of the quantum dynamics, the result could not be more complete than it is well known. E.g. nothing new about the sought full description  of a single act of quantum measurement, in particular of the existence or not of the random quantum jumps, especially those which should apear at some mysterious instants of measurement).

Finally, I am even not trying to find the definition of measurement of the energy level:)

Best regards

That is the usual answer: non locality doesn't apply here. It does. In the orthodox description of a Bell type experiment, there is not one observer, but two independent ones (entanglement also occurs when there is only one system, two entangled systems are used for practical reasons.) That is indeed inherent to quantum theory, including all of its interpretations. Now when we talk about information about a system, this information is not shared among the two observers, then most of the interpretations fail. The wave function can't reflect the knowledge of a system, since this knowledge depends on the observer, while the wave function is the same.  

@ Claude

Dear sir, you are discussing the theoretical model related to reality without showing which elements of the model correspond to which elements of the reality. Therefore the exchange of point of view becomes very hard.

       The main problem is the definition of the measurement by two independent observers. Obviously you know, that the Bell type experiments (as they are described in the literature) derive the existence of the correlation AFTER the by comparing the two effects caused by say BOTH photons by coincidence. Where is here place for two observers?Note that even if the say independent observers exchange information by phone, they form ONE observer consisting of two parts!

       Next is your misunderstanding of my idea, that the result of the observation is determined exclusively by the state of the observer (if you wish, including appropriately involved model of the human being!)

       Another important difference, not repairable without strict vocabulary from real to theoretical notions and back, is reflected by your opinion:

"The wave function can't reflect the knowledge of a system, since this knowledge depends on the observer, while the wave function is the same"

In my proposal every system knows its own (reduced) state perfectly, and this is the key of the system of notions. You are trying to introduce an observer whose knowledge is (by assumption?) not accompanied by mutual influence of the changes of the joint state of the observer and the observed. This is too far from my model, and  even inconsistent if the measurement should be seen as a result of interaction between physical objects.

And finally, it is not my point of view that "non locality doesn't apply here". Contrarily, my example from the last post illustrates that non locality holds as a possibility to determine existence or absence of the entanglement of the state of a bi-partite subsystem by an observer which interacts with each part separately. By the way, I cannot state "independently", since the hamiltonian in use is a sum of two non-commuting terms, representing the interaction between the first  and the second party, respectively. As it is well know, the unitary evolution of the global state generated by this sum is not a  composition of two unitary evolutions generated by each term separately. And this separability is indeed the only requirement about the relation between the observer and the observed subsystems.

Regards

I don't say there are two observers, but that in orthodox quantum theory there are two independent observers. Actually, they communicate only classically. Your interpretation makes no exception, since you only postulate a single observer, without modifying the formalism so that it be possible.

In the case of the two slits experiment, when there is only one observer on the screen, no problem appears.  But it appears when there is a second observer at one of the slits, yet they need not to communicate.

If  they do not  communicate then no correlaration can be stated, just due to this lack of exchange of results. Isn't this correct?

If you don't listen to and take into account the objections, then it is pointless to wonder nobody is interested in your work, that's just because of that.

Hello to all

This has been an interesting and intense exchange of ideas. I have been traveling since a few weeks and, against my wishes, being on he road prevents me --the originator of the thread-- to participate more actively. I now drag a heavy backlog of pending comments. Nevertheless, and at the risk of distorting my initial question, I will add here more questions.

There has been mention in the thread of the observer as an important component of quantum systems. It is then natural to ask:

Has anyone written in a more or less explicit way the quantum Hamiltonian operator Hob of the observer?

Assuming there is positive consensus about the existence of Hob, and that the formula is manageable, let us add a few important technicalities asking also:

In what linear space is Hob defined?

What are the eigenvalues and eigenfunctions of Hob?

In particular

Is the collection of eigenvalues continuous or it has a discrete part?

Are all the eigenfunctions square integrable?

What is the shape of the orbitals?

It will be fodder for all the tabloids of the world if the orbitals resemble the human figure. Questions about the universality of DNA, evolution, brain, sex and alien intelligence would aquire a different perspective.

With most cordial regards,

Daniel Crespin

Dear Claude,

Surely, the discussion wouldn't end with such evluation of my presentation if you admitted any mathematically strict and consistent  model of the reality, not necessarily equal to my. Frankly, starting the discussion I have expected critics about the correctness of the model first, and its relation to reality at the second place. Therefore the presentation  I call a proposal. In particular, from opponents  I expected rather any definition of the observer and  of the measurement (in particular the one of the energy level:). Let me stress, that I didn't change and didn't add  any postulate to  the standard quantum theory. 

Thank you anyway for your comments and questions. After this I still continue to stay on the position, that the observer - doesn't  matter one- or multi-partite -  should be involved as a part of the system staying equal in r\^ole with all other part(icle)s? Finally, please take into account, that some of your sentences like the following one

"The wave function can't reflect the knowledge of a system, since this knowledge depends on the observer, while the wave function is the same."

are presented as the unique and  absolute  truth, which made the discussion pretty hard, at least for me.

Best regards,

Joachim

Daniel Crespin,

Maybe you can free some time to read the paper The Hilbert Book Test Model. This purely mathematical model offers two views. One view is the creator's view. In this view universe has a Euclidean structure and the model is interpreted as a structured repository in which all historic, recent and future dynamic geometric data are stored in the form of discrete quaternions and quaternionic continuums. Special mechanisms use stochastic processes that generate the locations of elementary modules.

The other view is the observer's view. Observers are modules that travel with a vane that scans over the model as a function of progression. These observers get their information from the past. They cannot access information that arrives from the future. The field that embeds them is the continuum that brings information to these observers. Therefore, the observers experience a spacetime structure that has a Minkowski signature.

The first view describes what actually happens. The second view describes how that scene can be observed. The two views describe the same model.

If you have less time, then you can look through docs.com/hans-van-leunen

https://doc.co/WmxXCB

Joachim, in the context I gave "quantum theory, including all of its interpretation," it is a logical and absolute truth. If you find it hard, probably it is, but it is no less true. I'm not the one who should answer the questions, it is the one who proposes a model. Measurement is defined in all textbooks on elementary quantum mechanics. That's not I don't want to help, but you make it hard to me.

Claude,

thanks again.Perhaps sometimes, somewhere we attain at least agreement that not everything stated as interpretation (one among many other) is the truth, whatever it means.

Sincerely yours,

Joachim

@Daniel

Thanks for your humorous questions. Fortunately, we do not have to describe observers by means of a theory having been construed to have microscopic objects as its domain of application. Actually, the human observer does not play any other role than observing the macroscopic positions of the measuring instruments he is using in order to obtain knowledge on microscopic objects, or even just looking at the graphs produced by his

printer after the measurement results have been processed by his computer. 

It is even questionable whether quantum mechanics is able to describe completely the interaction of a microscopic object and a macroscopic measuring instrument. Presumably we should even  content ourselves with describing quantum mechanically the interaction of the microscopic object with a microscopic part of the measuring instrument that is sensitive to the microscopic information, amplifying that information by means of semi-classical theories.

Hello Willem Marinus

You are very much welcome, Willem. Nevertheless my questions were not intended to be humorous. I think they should be taken seriously. I simply added one final comment that --depending on the reader-- can be taken humorously. I would be delighted if you smiled at it.

As for the questions themselves, if observers are quantum systems they should have observables, particularly an energy observable, which according to Quantism determines --via Schrödinger time dependent equation-- how the observer evolves. For observers there should be stationary energy values, orbitals, total quantum angular momentum, intrinsically random "quantum jumps", and consequences of quantum uncertainty, of quantum indeterminacy, of quantum wave-particle duality, of quantum tunneling, and of any other quantum principle or phenomenon as well.

Many may dodge the questions by hiding behind the Correspondence Principle, or under any other defense of Quantism of the type "Classical Physics is the limit of Quantism". But it would be preferable for them --so I think-- to be corageous and try to advance their faith in the special role of Quantism. 

Skeptics may be exempted, but if someone really belives in Quantism, and that the quantum nature of observers is important to understand Physics, Philosophy, History or any other topic, he must be willing to face the challenge.

Very serious Quantists have advanced the idea that the Universe is anthropic, namely, that it exists for "us". Could there be a more dramatic proof of this proposition than finding --after due calculations-- that observer orbitals are anthropomorphic? I myself side with the very scarce unfaithful --those that do not believe in Quantism, nor in an Anthropic Universe-- and feel free from any burden of proof.

It is my humble opinion that at its most basic level Quantism contains serious mistakes requiring urgent attention. Please give a look to my papers, already referred in this thread, where the big mistake (Schrödinger time dependent equation) is analized and an appropiate correction is described.

Willem, please forgive my persistent dissent from Quantism, but for the sake of Science I cannot remain silent on these issues.

Most thankfully and very cordially,

Daniel Crespin

Dear Daniel,

I do not know what you mean by Quantism. Assuming that you mean by

this the belief that quantum mechanics is the `theory of

everything', I can tell you that I, too, side with the unfaithful.

Although quantum mechanics has a formidable domain of application,

I do not think that its domain is universal, in particular not in

terms of applicability. We do not describe the behaviour of

billiard balls with the Schroedinger equation because we have much

better theories for that. By the same token, I would not try to

describe human observers by quantum mechanics, even though I

believe they consist of atoms. However, although also billiard

balls consist of atoms, does it seem silly to me to apply quantum

mechanics with the intention to win your game of billiards.

In my view quantum mechanics is a very useful theory describing

certain aspects of the microscopic world, however being neither

applicable to the submicroscopic nor to the macroscopic world

(although certain aspects of these worlds might be dealt with by it

in an approximate way).

Willem de Muynck

My dear Willem

By Quantism I mean the doctrine --oportunistically based on the inadequacy of Schrödinger time dependent equation (STDE)-- proposing that electrons make intrinsically random transitions, or random jumps, from stationary states having a given energy level, to some other stationary state having a different energy level. These assumptions have many additional consequences that play the role of important courtiers in the household of Quantism. In particular Quantism claims that the random transitions break down causality and are discontinuous.

We owe to Isaac Newton the discovery that causal laws can often be expressed mathematically as differential equations. Newton, a bachelor, embracing Nature and brandishing differential equations sired Mathematical Physics. 

When using differential equations a "cause" is an initial state, say ψ(t0); a "consequence" is any of the the states ψ(t), t>t0; and the cause itself has in turn its own previous causes that are the values ψ(t), t

According to Schrödinger 1926, there are no quantum jumps. And indeed, newer experiments show that a transition is completely canceled, if it has not been completed.

Hello Enders

You state that "According to Schrödinger 1926, there are no quantum jumps." Please allow me the following comments.

A set of articles by various authors are collected in a book edited by Wolfgang Pauli

Pauli, W. (ed.) - Niels Bohr and the Development of Physics. Pergamon Press, London. 1955.

Among the articles there is one by Werner Heisenberg

The Development of the Interpretation of the Quantum Theory

The following lines can be found in the article (page 14 of the book)

At the invitation of Bohr, Schrodinger visited Copenhagen in September, 1926, to lecture on wave mechanics. Long discussions, lasting several days, then took place concerning the foundations of quantum theory, in which Schrodinger was able to give a convincing picture of the new simple ideas of wave mechanics, while Bohr explained to him that not even Planck's Law could be understood without the quantum jumps. Schrodinger finally exclaimed in despair:

"If we are going to stick to this damned quantum-jumping [verdammte Quantenspringerei], then I regret that I ever had anything to do with quantum theory,"

to which Bohr replied:

"But the rest of us are thankful that you did, because you have contributed so much to the clarification of the quantum theory."

May be the above paragraph is the ultimate source of your statement.

The displeasure shown by Schrodinger has a different interpretation. It may mean that he understood quantum jumps, that he had a clear picture of the reach of the Schrodinger time dependent equation (STDE), and in particular that STDE contradicted quantum jumps. Therefore he knew that something very fundamental was missing in his elegant STDE. Nowhere he said something equivalent to "quantum jumps do not exist". He was annoyed by having to accept the existence and crucial phenomenological role of quantum jumps for the description of the basic atomic phenomena of absorption and radiation.

If you have a different historical source to justify your interpretation please share with us the reference as it would be extremely interesting

With most cordial regards,

Daniel Crespin

Daniel, informal citations are good, but I have read the Schrödinger's articles in the text, there is no need of quantum jump, as it is defined in old quantum mechanics. There is the wave function collapse, but it doesn't happen between the levels of an atom, it requires a measurement by a macroscopic apparatus, and the eigenfunctions of the Hamiltonian don't play a privileged part. Moreover, it is a projection and not a transition between different states, there must be a significant overlap between the initial and the final state, which is not true between the levels of an unperturbed atom. Bohr botched it up too with Einstein, who subsequently proved that the collapse leads to at least one of these problems: non completeness or non locality. That is such continuously spread confusions that makes QM so difficult to teach.

Dear Claude and Daniel,

It is appropriate that Claude is referring to the old pre-1925 quantum theory, which was still a classical theory, intended to describe individual microscopic objects. Lack of distinction between de Broglie waves and Schroedinger's quantum mechanical wave functions has smuggled pre-1925 elements into post-1925 quantum mechanics, one of which being quantum jumps, based on the idea that values of quantum mechanical observables are properties of microscopic objects being able to jump stochastically between their possible eigenvalues (or even are created by the measurement) .

At present we have empirical evidence that Schroedinger's quantum mechanical wave function is not a description of an individual object, but a description of an ensemble of such objects (see e.g.

http://www.hitachi.com/rd/portal/highlight/quantum/index.html#anc04

(on that page see Video clip 1)). It seems to me that Einstein's idea of the incompleteness of quantum mechanics is in an observational way corroborated by

this measurement, and that von Neumann projection c.q. its generalization describing preparation of subensembles conditional on the measurement results that are obtained, can be seen as unproblematic properties of a statistical interpretation of quantum mechanics, more or less in the sense in 1970 proposed by Ballentine.

Willem, in the hydrogen atom, there is an individual electron, yet we observe energy levels as predicted by the Schrödinger equation. It is true that there is a probabilistic interpretation similar to the case of a statistical ensemble, but we must think in terms of probability amplitude, because the measured observables may be different. It is not possible to define a joint probability density in the phase space, save for very special states.

Very much in agreement with Claude here: we have in fact observations of individual systems following quantum mechanics. The electrons in the double-slit experiment described by Willem are one example, but in atom traps, for example, we do observe a single particle effecting quantum transitions between states. So, while I do agree that the ensemble interpretation is unobjectionable, I do not think we can view it as a final description of quantum systems, or a definitive interpretation of quantum mechanics, since the latter also does quite well for individual systems.

CPM

I do not understand at all your writing about the hydrogen atom

What observable(s) do you mean? and what probability that is associated with that parameter

And also: the energy levels are NOT observed only the transition or rather the energy differences

Harry, that you observe the level or the photon emitted by a transition, including its angular momentum, is the same.

The photon's energy is the energy difference between levels.

Angular momentum of what: the photon?

and what about the probability that you mentioned above?

Harry, it is a discussion here, not a textbook on elementary quantum mechanics.

Dear all,

The only things we have ever observed are reactions of our measuring instruments on interactions with microscopic objects. We never saw these objects themselves, let alone their properties which I, like most of you, believe are there, but of which we can obtain knowledge only through the intermediary of our measuring instruments. For those who still believe in the logical positivist idea of basing theory on direct observation, please read Frederick Suppe ed., The structure of scientific theories : symposium, 1969, Urbana, Ill.: outgrowth with a critical introduction and an afterword by Frederick Suppe,

University of Illinois Press, 1977 (or maybe have a look at my website, see link).

http://www.phys.tue.nl/ktn/Wim/muynck.htm

Claude Pierre,

Can you, please, explain what you mean writing:

"...we must think in terms of probability amplitude, because the measured observables may be different."

Please, make your answer as it were a scientific discussion here, not an unprecisely written  text book for pre-school children :(

I just would like to add my little comment that at a certain time have been thinking in terms of the observer's introduction in such a way, and found the best were to represent it in the dual space, the complex conjugate one, and, mind you, that is how I found out the reverse time progress picture.