When one starts with a theory that nobody can understand, according to its defenders, everything is possible... So why not an electron which chooses its fate, and of course, to stay modern, it should be equipped with a computer. Ulrich, you miss something : the electron should be wired, it takes its computational power from the cloud, so there is no problem. The fairy tales were more entertaining.

I'm so sorry that I failed to entertain you. Instead of trying to rectify this omission I'll comment on some of your points. The theory under consideration is orthodox quantum theory (thus, according to Feynman, in fact a theory that nobody can understand). Specifically we are concerned with the basic question of measurement theory, how the deterministic evolution of a particle wave function can stop and produce a recordable classical event such as a click of some particle detector.

The basic argument is this: If the particle starts to interact with a system of many particles  the dimension of the effective state space grows exponentially so that even a very general notion of required resources allows us to conclude that these will be used up rapidly. For heuristic reasons I paralleled the view on the fate of the electron by a view on a concrete computer simulation of the wave function of the electron and all its effective interaction partners. In this view precise conclusions are possible whereas for the natural electron nothing is known so far about a underlying hardware which supports the dynamics of the wave function. Maybe wires (aka strings) are involved and the cloud(aka environment) so that your satire is not to far off.

Dear Ulrich,

your question appears to bear certain similarities to a philosophical problem posed by Hugh Everett III in his 1957 doctoral thesis on the first three pages. Enclosed the link

http://www-tc.pbs.org/wgbh/nova/manyworlds/pdf/dissertation.pdf

Unfortunately I got stuck there (somewhere below page 10) due to limited time. As far as I know, Everett's supervisor, John Archibald Wheeler, had high respect for him, despite the rather sad meeting with Niels Bohr in Kopenhagen... Maybe you get David Deutsch from Oxford to join this discussion...

Cheers, 

Markus

Dear Ulrich

Orthodox quantum theory has a great power : it has given the way for many academics to have a good life by teaching to their students a theory that nobody can understand. And for some of them to become even richer by winning a Nobel prize for inventing a new mystery.

I am to old to be in any way interested in all these shenanigans. There are more decent way to earn his living.

But just some considerations, based on something that all physicists focused on measure totally forget :

1. In most if not all experiments about atoms and elementary particles the models use a representation of variables (what ever) by functions which belong to infinite dimensional vector space.

2.So to estimate these functions requires an infinte number of values. That nobody can get. The solution is to adopt a more restricted specification of the map : it depends on a finite number of parameters. An then the statistical estimation from a finite number of data provides an answer.

3. Then happens a miracle : the infinite dimensional wavefunction has collapsed ! And of course the measured value is an eigen vector of the wave function.

With some maths everything is clear. But do not tell your students : they like the fairy tales muh better.

Dear Jean Claude,

let me comment your points 1-3:

1. As many physicists have observed, Quantum Mechanics works well in finite dimensional Hilbert spaces. Represent 'space' not as a 'continuum' but as a finite set of points and the Lebesgue measure by some sort of counting measure then all wave functions are defined by giving a finite number of complex values. Since we also replace the complex plane by a finite set of points this means finally that the wave-function is determined by setting a finite number of bits. Since this parallels what is done in computational quantum theory (sets of computer representable numbers are always finite even if any number is chosen to have millions of digits) there is a huge body of experience and knowledge along these lines of thinking. Although it is clear that any accuracy requirements in real-world applications can be satisfied by choosing a sufficiently fine net of points it also is clear that the execution time grows with the number of points. So, whenever a calculation is to come to an end the number of points involved has to be finite. 

Without any knowledge about Nature's ways to evolve wave functions over time it seems save to assume that a finite underlying structure ('computational resources') exists and that the time-stepping algorithms of computational quantum dynamics may serve as models for what goes on in nature within this finite structure.

2. Replacing the wave function by a function defined on a finite set is your remedy against the impossibility of specifying infinitely many numbers. You suggest  that this step is related to the statistical nature of quantum theory. It is not! The values of the wave function can neither set in an experiment nor can they be measured. Nevertheless they are not without physical meaning. If they are changed by interaction with a suitable experimental device the dynamic evolution changes as do the measurement values at the end of this evolution.

3. Again, do you think that the mandatory restriction to considering only a finite sample of the wave function brings a about the restriction of measured values to the spectrum of some operator? And automatically satisfies Born's rule for the probability of  that value. You say that some math would make this clear.

Please present this math to us (or tell us where to look in your monumental book).

.

Dear Markus,

thank you very much for the Everett's thesis. Good to read, but so far I did not come to the end. Unfortunately David Deutsch can not be reached on RG. For an invitation through another channel I feel no sufficient motivation. I read some stuff from him and I locate him behind an impenetrable curtain, or in another version of the universe.

Best regards,

Ulrich

Dear Ulrich Mutze

Can practically an electron get enter in to your described situation with out welcome by potential difference into energy, regardless of wave or particle function plz ?

Regards,

Dear Raja,

since a bit of energy is released when the electron enters the crystal I expect that even a slow single electron will easily enter the crystal in vacuum if the surface is clean. If the electron comes with a whole beam of electrons we have to ground the crystal so that it does not accumulate charge.

Hope this answers your question.

Dear Ulrich

My objections are of a different nature.

In Physics (but it applies to any science, such as Economics) when you have a model and represent a quantity by a variable which belongs to an infinite dimensional vector spce - such as x(t) : a function - you have a problem because the knowledge of the map (x) would require a non countable infinite number of data. This is not  a matter of accuracy, but of discrepancy between the theoretical model and the physical limits of measure. So you adopt a simplified version of x(t), where it depends only on a finite number of parameters. This sums up to assume that x belongs to some restricted class of maps. You define an observable. This does not imply anything about the system and its behavior. The usual axioms of QM are not assumptions about the physical world (and indeed they do not contain a single word about it) but a set of theorems which can be proven and apply to any model meeting some general criteria.

By doing this I am by far closer to the way how actually physicists work. Before the physical measure there is a mandatory step which is the format and the use of the data. All the usual assumptions about 2 physics, the quantic world etc are just relics of the first part of the XX° century. This is just a pity that for 70 years academics go along with "interpretations" (there are officially more than a hundred of them) and not stop for a moment and look at the issue. But of course theoretical physics is not about innovation and deep thinking, but all about conformism and fashion.

Dear Ulrich!

I think that there is a possibility to explain the causes of the wave function collapse, which is not associated with any additional assumptions or creation of a new theory.

Collapse of the wave function - is only the limiting case, when measurement is performed by classical apparatus. The solution of the problem of collapse is connected with nonlinearity of quantum mechanics - this is the consequence of the creation (annihilation) of particles.

See, for example, Melkikh A.V. Nonlinearity of quantum mechanics and the solution of the problem of wave function collapse. Communications in Theoretical Physics. 2015. V.64, No. 1, 47-53.

You can download my paper here:

https://www.researchgate.net/publication/280062863_Nonlinearity_of_Quantum_Mechanics_and_Solution_of_the_Problem_of_Wave_Function_Collapse

Alexey

Article Nonlinearity of Quantum Mechanics and Solution of the Proble...

Dear Ulrich Mutze

Thanks for kind guidance. If the wave function can get collapse then is it equally possible that wave function can get adopt permanency (become permanent) as well ?

if so then particle nature  also become permanent or collapse ?

Regards,

Dear Raja,

in the framework under consideration the wave function is the formal representation of the particle's propagation through space. It assumes that there is a particle which propagates. So the situation does not have the logical symmetry that you seem to assume. The question: 'If we consider a collapse of the wave function why not consider a collapse of the particle' is the result of a false analogy.

Dear Ulrich Mutze 

what happens after when wave function get collapse, whats the scenario then ?

Regards,

Dear Jean Claude,

as far as I understand you, you have your way of understanding quantum mechanics. You derive it  'from some general criteria'. Unfortunately scanning through your opus magnum I found nothing that looked like a substantiation of this claim. But, only scanning writings that would deserve careful  reading is one of the problems with today's science and so I'm aware of the possibility that I missed something. Particularly puzzled I find myself by the problems that you see in continuously defined fields.

Dear Alexey,

I'm aware of the Weber/Rimini approach of adding a non-linear term to the usual many body Schrödinger equation. However, your understanding of interacting quantum fields as a non-linear system  which forbids super-positions of solutions is definitively a misunderstanding. The field operators are operators in a linear space and all observables you built from them are linear operators featuring a spectrum and a set of eigenvectors just as in quantum mechanics of few-particle systems.

Moreover, your cited work is hardly more than a sketch of ideas since it gives no hints how Born's formula for the probabilities of potential measurement results would come out.

Dear Raja,

the answer is that the collapse would not purge the wave function but would simplify it. The simplified wave function would display a measurement result and would allow further time-evolution with the available resources.

Deqr Ulrlrich

Any time a model is designed with variables which meet some - usual - mathematical specidications, the variables show properties like those of QM. This is just mathematics and theorems, there is nothing to substanciate. But of course one can disregard mathematics...

Dear Ulrich!

What about nonlinear system of equations - let's imagine classical case. What is the fundamental system of equations for classical mechanics? Of course this system contains Newton's equations of motion and Maxwell equations for fields. The system, I discussed is the generalization of this classical system for quantum case. That is, this is the most gereral systems of equations for quantum particles and fields.

What about its nonlinearity - this is the consequence of the fact that the sources of fields are currents and charges densities. They are real values and proportional not to wave function but to probability density.  

Dear Alexey,

the non-linearity of the field equations of, e.g. QED, accounts for interaction not for destruction of superpositions of states. Or, put differently: non-linearity of the field equations give you Feynman diagrams with nontrivial vertices and linearity of the theory lets you add the contributions from different Feynman diagrams. So, I see no support for your view that particle creation lets the wave function collapse.

Dear Profs. Dutally and Mutze in particular,

                                                                            I think it is important to distinguish between an equilibrium system for example when the waves in a pond become correlated in order to redistribute their combined energy to a higher potential, so that further waves can form with the same surface and disequilibrium when the sea waves require the coastline to break the waves and absorb their energy to determine the balance between land and sea. Even if there are hidden variables we can explain the system by using the Laws of classifying the waves systems Please refer to my Econophysics paper on String Theory of Environmental Political Uncertainty and Information etc.. on my RG website if you will. We (Soumitra K. Mallick, Hamburger, Sandipan Mallick) have worked on these systemic resolutions of forces to develop material systems also using String Theory, Quantum Mechanics and Physical Chemical Analysis Technology (partly mind experiments like Prof. Schroedinger's Cat in the Box experiment) and the above Laws.

Earl Chair Prof. Dr. SKM QC EPS Fellow(In) MES MRES MAICTE

Dr. Nick Hamburger, Dr. Ing., HN Consulting and,Megatron Consulting, USA

Earl Prince Sandipan Mallick, MAICTE, MPCI, NSHM & MAKAUT, Undergraduate student and researcher, India

Dear Dr. Soumitra K Mallik,

it is important to distinguish between and equilibrium system ... and ????

As it looks to me, you have not completed your thought. So, I don't know what to distinguish.

My question deals with a single particle which, when coming under the influence of an increasing number of interaction partners, is required to follow intractable equations. So the problem occurs long before an equilibrium system had a chance to come into existence.

This problem does not exist in a model which treats particles (such as water molecules in the ocean) in terms of classical mechanics.

In such situation Sir, with due regards and pardon my lower dimensional approach to such questions, in as yet not publicly published material that I have referred to before we have shown that in computer systems one can control the path of such particles which operate in Higgs Englert Bosonic fields and satisfy certain cybernetic systems laws as I have mentioned with certain engineered nanomaterials which say have controllable dielectric properties to control the paths of quantum mechanical motion by using an ensemble intrepretation of probability and either using lower dimensional semiconductance or classical-quantum Archimedean potential kinetic flows to complete circuits if you will. We have tested some such systems, which we have to admit are very rare as of now, because of their genetic property requirements of natural algorithmic flows and representation. So we almost completely agree with you, in that, such systems can be perfectly engineered to be a perfectly correlated particle system capable for example magnetic linear acceleration. We have even invented some engineering applications like sustainable (both information and energy) e-commerce applications. SKM, NH, SM

Sharing link,

https://www.google.es/url?sa=t&source=web&rct=j&url=https://www.sciencedirect.com/science/article/pii/0960077994E00706/pdf%3Fmd5%3D0b481da0b13f6d81580ef40c2b8928e2%26pid%3D1-s2.0-0960077994E00706-main.pdf&ved=2ahUKEwj-k8vn7d_ZAhUDNxQKHbT-BqUQFjAHegQIBBAB&usg=AOvVaw1dJjBkydUz88bCvXXPZ1DX

Regards!

Nature is not a computer. Natural law might sometimes be computational, but that is a fact of observation and not a fact of ontology. I recommend reading Howard Pattee's work on this point.

https://www.informatics.indiana.edu/rocha/publications/pattee/index.html

Best wishes,

Damian

The ratio essendi should not be confused with the ratio cognoscendi.

- Ratio essendi: why something is what it is.

- Ratio cognoscendi: how something is known to be what it is.

https://student.cc.uoc.gr/uploadFiles/%CE%9210/Reason_Piaget.pdf

Cheers,

Fabian

@Damian and Fabián

Unfortunately I can't discover any relation of your contributions to the present question.

Dear Prof. Mutze,

to get back to this old discussion, which I value very much, especially since Breakthrough Physics Prizes and Nobel Physics prize has been made an objective for our newly planned "Ramanujan-Hardy-Mallick-Hamburger-Mallick School of Mathematical Sciences Thinking" and ofcourse our present employers (we mean for Dr. Somak Raychaudhury, Director, IUCAA, India, Mr. Sandipan Mallick, young student and researcher of B.Pharm. at NSHM College of Pharmacy and Maulana Abul Kalam Azad University, Kolkata, India and Prof. Dr. Soumitra Kumar Mallick, IISWBM & Calcutta University, India), not canvassing please, I think it is a very important question of Quantum Physics especially as we have discovered that it operates through String Theory AGNNNetworks (www.researchgate.net/profile/Soumitra_Mallick) when you quantise the system by our discovered Vector Diffeotopy of Embeddings of the "String Matching Field" established experimentally by experiments on Globalised internetworked E-Stock Exchange Networks and Quantised Machines i.e. after the events. Now we have used NASA's Juno Probe Field Match experiment also (courtesy Dr. Dave Newmann) see the above reference, to obtain Dbranes String Theoretic and Higgs-Englert-Bosonic Mechanism Quantum Mechanism for the Systems Stock & Flow for the Field Match (somewhat casual remote experimentation via the internet).This we have established is the MTheory of the String Matched Field System. So if you would like to see our roadmap the outline is here.Thanks.

Soumitra Kumar Mallick

Ulrich,

You are right! Is up to you to decide the level of observation and confine your inquire accordingly.

Nevertheless, I must confess that it is hard for me to imagine the realm of quantum mechanics lacking the observer’s operations, and their associated descriptive tools involved in its determinations.

My call is a meta-reflection (please forgive me if this is a triviality for you) regarding the role of the cognitive operations performed by the cognitive agent, and the mathematical tools that support this activity to get new knowledge.

Cheers,

Fabian

Nice response, Fabian.

Ulrich,

Your question is about "Nature's computational resources" which presupposes at the outset that Nature has any computational resources of its own. And it doesn't. Computation is a description we can apply, but that's the observer that Fabian points out you leave out with such proposals laid at the level of ontology (i.e., of "what Nature can compute"). Since you ask the RG crowd, we are here to tell you--Fabian and me both--that your answer leaves out the observer in a quantum-focused question. Fabian is putting his point well, and my own point is that observers make Nature a computational problem, Nature is not in itself a computational process.

The burden on this questions of yours is to demonstrate that Nature is computational. And I wish you good luck in that demonstration.

Best wishes,

Damian

@Damian,

I don't think that anyone has a sufficiently clear notion of a computational process that would make 'Nature is a computational process' a meaningful statement. In formulating my question my intention was to refer to computation only as a metaphor. As most physicists see the role of the observer in quantum theory the 'observer' may also be a measuring device combined with a computer-based storage system. The instance who 'makes Nature a computational problem' is the scientist (most often a physicist) who tries to understand a natural phenomenon. In writing down mathematical expressions he prepares the way to computer based simulations for which 'computational resources' (storage space and execution time) are meaningful notions. If all acceptable simulations can be shown to need exponentially growing resources for increasing numbers of particles under consideration it is a natural conclusion that for some range of particle numbers Nature needs to deviate from the path for which the simulation was reasonable. This is the 'breakdown' to which my question refers.

Whether Nature is computational or not seems not to be important here. It suffices to observe that all understood physics turned out to representable in the language of mathematics and, therefore, to be in principle programmable.

Ulrich,

I understand better your question, and it is a significant one. The issue is the limit to our knowledge, not in the way it is usually understood in QM, that is the impossibility to measure some phenomenon Whatever our model, when they involve continuous maps or functions, it is impossible to collect all the data which would be required to get a faithful estimate. So we proceed practically to simplify the map, so that it depends only on a finite number of parameters. The problem is not a problem of measure, it is a statistical problem. But it has far reaching consequences on the model itself, and indeed this is the base of QM.

Ulrich,

It is perfectly fine for me to accept that you are dealing with “simulations of Nature” and their properties (using computational models) not with “Nature”. The value of this exercise will be its predictive power. If you want to derive a explanatory narrative (by any means), I think its value will be mainly “heuristic” to produce better predictive models. Of course you could be interested in produce just an “explanatory” tale about the “properties of Nature”. Whatever is the case, I think it is very important to acknowledge the contributions of the operations performed by the cognitive agent in the construction of knowledge.

By the way, “metaphors and analogies” are produced by “reflective abstractions” derived from the operations and the tools (this include mathematical devices) that a cognitive agent uses to acquire knowledge. Please see Chapter -6 in Piaget, Jean and Campell, Robert L., "Studies in reflecting abstraction", Psychology Press (2014).

Cheers,

Fabian

Dear Prof. Mutze and other readers,

At some point in the past I had mentioned about models under zero gravity and then I had mentioned about systems classification into gravitons and other particles, now two years later I have to withdraw my statement about zero gravity because I was thinking then in terms of partial systems modelling and abstracting from gravity but it was not necessary to do so. So my later communications are more systems integrated one can say. I am hereby correcting myself.Thanks.

Soumitra Kumar Mallick

for the RHMHM School

@Jean Claude

Replacing continuous functions by finite lists of numbers of finite precision is inherent in any computer simulation of natural phenomena. It is easy to experiment with changing number precision and discretization lengths. Nobody, so far, has observed the emerging of quantum-mechanical behavior. Actually, many years ago, I tried hard to enforce quantum mechanical behavior by reducing numerical precision - without any success. What can be seen in such numerical experiments is that interference patterns that are seen in simulations of quantum dynamical phenomena may disappear. So, what you see as the basic reason for quantum mechanics can at least be considered a model for decoherence.

@Fabián

I would be interested to learn in which part of the game, in your view, a cognitive agent plays a role. Is this agent simply the scientist? And are his 'operations' simply the reasonings that text-book writers formulate in support of their attempts to formalize natural phenomena?

Ulrich,

- Yes the scientist is the cognitive agent.

- The work that I have suggested for you to look is “experimental work”, so the "reasoning" presented there is not performed in the solitude of pure abstract thinking, is “experimental” thinking with all the due control. I hope you can have time to review that reference. I am afraid that will be the shorter ride for you to satisfy your curiosity. Anyway, I am not escaping from your request, I am just trying to make the things easier for you and me.

Cheers,

Fabian

@Fabián

Unfortunately to get hold of Psychology Press (2014) would not be easy for me. Having scanned your link .../Reason_Piaget.pdf I'm not confident that Piaget's ideas can help to improve my understanding of quantum physics. So I'll not follow the Piaget-path and hope you can forgive me.

Ulrich,

No worries. I was not interested in improving your understanding of quantum physics. I was pointing to the mental processes involved in acquiring knowledge that are at play in any cognitive interaction between an epistemic subject and the Nature.

Cheers,

Fabian

Fabian:

The book originates from 1977. I think it is directed towards learning of joungsters and as such I followed lectures in pedagogy

I cannot remember what it says about adults

Harry,

I should have mention from the beginning the work by Piaget y Garcia “Psychogenesis and the History of Science”. Here you will find the same tale for adults (scientist). What Piaget discover is that children, like scientists, have to actively manipulate their environment in order to construct knowledge. The mechanisms described by him are common no matter the age or the occupation of the individual. It is my personal opinion that this work is a “must read” for any scientist.

Cheers,

Fabian

Ulrich,

Don’t you reckon that it is a wee bit naughty to recommend an opinion from someone who is doubtful about his memory regarding the matter at issue, just because you don’t want to know about it?

I know you start the party but, please don’t be a party pooper, just because some of us are not dancing at the rhythm of your music.

Cheers,

Fabian

@Fabian

I understand that you are enthusiastic about the work of Piaget that armed you with impressive notions such as cognitive agents and epistemic subjects. But, a response to a question at RG is expected to contain at least an element of a partial answer.

Ulrich,

To be honest I don’t like much to repeat myself, but I understand that the individuals and historical memory is feeble. Knowing that you like metaphors, please allow me to try a “veronica” to deal with your charging horns.

Your question was:

“Can 'the collaps of a wavefunction' be understood as a computational breakdown due to Nature's limited computational resources?”

My colleague Damian and myself answered, NO

The bottom line of our answer pointed that the “knowledge of Nature” is not “Nature”. Knowledge is not a copy of Nature, it contains inextricable elements from the Observer-Nature interaction (like in an experiment). To my knowledge, this idea is at the core of quantum mechanics and also in the manner in which we understand the psycho-genesis of knowledge, in this matters what Piaget said (from experimental sources) is in line with the conceptions of quantum theory.

Please forgive me that there is no English translation for the following text illustrating my point.

"Introduction à l'épistémologie génétique (II). La pensée physique: Chapitre VII: Les enseignements épistémologiques de la microphysique" (pag 260-261)

“ Sur le plan microphysique enfin, c’est-à-dire à l’autre extrémité des échelles d’observation, l’interaction entre le sujet et les objets se présentera sous un jour ne laissant plus guère d’occasions à ces illusions réalistes propres aux échelles plus grandes. Pour connaître les objets, le sujet est, en effet, toujours obligé d’agir sur eux, c’est-à-dire de les modifier d’une manière ou d’une autre. Mais, tandis qu’aux éche lles moyennes et surtout supérieures, cette modification consiste surtout à les enrichir de rapports nouveaux sans les altérer rofondément, les objets sont cette fois d’un ordre de grandeur considérablement inférieur à celle du sujet et de ses appareils, les actions de localisation, ou de mesure des vitesses, etc., introduisent des changements relativement très grands dans la disposition de ces objets. Il s’ensuit alors que la réalité connaissable est constituée par un complexe indissociable de rapports dus, les uns aux objets et les autres à l’intervention opérative du sujet: celui-ci ne se trouvant jamais en présence que d’un tel complexus ne saurait donc plus tomber dans l’illusion d’atteindre un réel situé au delà de son action.

Mais inversement, cette activité est conditionnée comme il va de soi par les propriétés des objets, puisque c’est la valeur du quantum d’Action qui, comme celle de la vitesse de la lumière à l’autre extrémité des échelles, oblige le sujet aux complications expérimentales que l’on sait”

Cheers,

Fabian

https://informationandreality.com/2022/01/17/an-interpretation-of-the-collapse-of-the-wave-function/