The Three and a Half Layers of Dynamics: Analog, Digital, Semi-Digital, Analog by Tejinder Singh

Dear Tejinder,

You write

---"the puzzling features of quantum theory"---

If a universe is to create itself out of nothing so particles have to create themselves, each other, then they are as much the source as the product of their interactions, the cause as well as the effect of each other's existence. If so, then there's nothing puzzling about quantum mechanics. For details see my essay.

Kind regards, Anton

I have been reading with pleasure your highly technical Essay and I think that may be useful to highlight some analogies and differences between our respective approaches.

As explained in my Essay, the canonical theory goes beyond less fundamental approaches as the superstring theory. This includes also the matrix formulation of M-theory (based in a Trace dynamics as that summarized in your Essay). The general state \hat{rho} of any system in canonical theory is defined on a generalized Liouville space (see pag 6 in my Essay). We can use an extension of Wigner techniques to derive an equivalent Wigner state \hat{rho}_W, but defined on a non-commutative phase space ({x},{p}), with associated N x N matrices like in Trace dynamics. However, the information contained in this non-commutative phase space is redundant and whereas the simplest dynamics (e.g. the S part of the canonical dynamics) can be adequately described by the geometrical star-products, there are difficulties to obtain the more general dynamics.

Indeed, the generator of the time translation in the canonical theory is not given by an operator but by a superoperator (e.g. the coefficients Omega are represented by superoperators in the quantum formalism associated to the post-Keizer form obtained at our Center). Those superoperators are defined in a superoperator space and are associated to (super)matrices of order N^2 x N^2. The evolution is described by an operator (matrix) Hamiltonian only as approximation in the 'pure' limit (see Box 1 in reference 8 in our Essay). From the Hamiltonian, we can obtain Lagrangians and actions using the usual techniques. That is, neither Hamiltonians nor Lagrangians and actions can describe the dynamics of the processes in the general case. Also the usual bosonic and fermionic commutators/anticommutators are valid only in the same 'pure' approximation.

Next, you introduce a statistical mechanics by coarse graining, using a maximum entropy method. There is several difficulties with this approach, which are solved in a natural way in the canonical theory. The first is that the canonical theory belongs to the modern statistical mechanics School of fine grained methods [FG], eliminating the extradynamical coarse graining considerations and their associated paradoxes. The second, is that the assumptions as your "the ensemble does not prefer any one state in the Hilbert space over the other" are derived rather than merely postulated. The third is that these assumptions work for equilibrium but not for far from equilibrium systems; therefore, we can obtain a nonequilibrium statistical mechanics of broad scope, whereas the work of Adler and others (reference 1 in your Essay) is limited to the simple case of (stable) equilibrium. The fourth, is that your work and the work of Adler and others relies on the Liouville theorem, which means that the resulting equations of motion cannot describe the evolution of the non-conserved variables, doing impossible the link with the phenomenological theory of nonlinear nonequilibrium thermodynamics. This is a well-known deficiency of the older approaches to statistical mechanics, which is solved by modern formulations of nonequilibrium statistical mechanics as that by Byung Chan Eu [Eu]. We can derive his nonequilibrium statistical mechanics as an approximation to the more deeper canonical theory.

As you correctly point, the next step in the scheme is to consider fluctuations. Again, at this point the work of Adler is based in further approximations. Effectively, he obtains a stochastic generalization of the Schrödinger equation and this generalization allows us to describe the nonlinear phenomena cannot be described by the usual Schrödinger equation, such as the collapse of wavefunctions. His work and that of others is very fascinating, because instead of the dual structure associated to the Copenhagen formulation of quantum mechanics, we have a single evolution, which gives reduction for measurements and the usual unitary evolution when the system is not measured! However, this kind of work is not fundamental. The canonical theory includes fluctuations (see Box 1 in reference 8 in our Essay) but cover a more broad spectrum. It is only when we approximate the canonical rate theory by its weak-coupling limit and take the Markovian limit that the fluctuations are Brownian. Moreover, Brownian fluctuations are related to what Nico van Kampen named "extrinsic noise", which is due to the fact that the system (the Brownian 'particle') is open. However, there is also another kind of noise, "intrinsic noise", which is related to the fact that the underlying structure of matter is discrete rather than analog. As van Kampen correctly noted, the noise observed in chemical reactions is of the intrinsic kind. It is not surprising that the canonical theory is able to describe both noises.

Then you go over discussing the role of time and you introduce two concepts of time; at the one hand, the concept of dimensional time, which, as you correctly point out, is associated to a quantum operator of time and, at the other hand, the concept of "affine parameter". This is not very different from the Stuckelberg extension of string and p-brane theory (see reference 15 in my Essay). At this point, your essay looks ambiguous for me and you refer to a reference still in preparation. You say that you introduce operators (q,t) for each particle. However, next you write that this "introduce a non-commutative Minkowski spacetime". I assume that you mean a 4N dimensional non-commutative spacetime (for N particles), which would reduces to a non-commutative Minkowski spacetime only in the one-particle case.

In the Stuckelberg extension of string and p-brane theory, the introduction of a phase space as your (q,t,p,E) yields dynamical redundancies. These are 'solved' (or at least alleviated) by working off-shell. What approach do you take in your reference 11 in preparation?

Another point that I want to comment is when you take a Block Universe view where your "affine parameter" tau is not identified with time. Here your work departs from the Stuckelberg extension of string and p-brane theory (see reference 15 in my Essay). You seem to support what Pavsic names the interpretation "(i)", whereas he prefers the "(ii)". You give none technical reason for your interpretation, whereas others (mainly Horwitz, Fanchi, and others) have given many details on why the interpretation (ii) is the correct. In the references 17 and 18 cited in my Essay I showed that the parameter tau in the Stuckleberg, Horwitz, & Piron theory reduces to Newtonian time for interacting charged particles and for massive particles under gravity respectively, whereas the concept of dimensional time associated to spacetime rigorously fails to reduce in both cases.

You argue that the "transition from the lower analog layer to the upper analog layer also helps understand the

origin of the arrow of time". However, you give no technical detail and merely state that the question of the origin of the arrow of time is related to "why is the initial entropy of the Universe so low?". This is the well-known cosmological argument, but unfortunately it fails when one considers the details. A better approach to understand the origin of the arrow of time is given by the Brussels-Austin School [IRREV]. It seems that the Brussels-Austin School last theory for LPS with Poincaré resonances can be obtained from the canonical theory for systems with bifurcations [IRREV].

[FG] The quest for the ultimate theory of time, an introduction to irreversibility

[Eu] Nonequilibrium Statistical Mechanics, Ensemble Method 1998: Kluwer Academic Publishers, Dordrecht. Eu, Byung Chan.

[IRREV] Trajectory branching in Liouville space as the source of irreversibility

Dear Tejinder,

I wanted to let you know that I have read through your essay. I have not come across this kind of multilevel consideration of reality before and so it catch my attention. Although not having a mathematical background I did also find it hard to follow. The lack of beaks in the text also made it visually daunting. It is the kind of work that I would need to tackle slowly and a little at a time. However I appreciate that this was not written for the likes of me but rather mathematically competent physicists.

I have given a lot of thought to what is meant by reality and the question of time.You did point out an unknown underlying mechanism. That is something I am addressing in my essay. I am not sure if you were saying that the multilevel analysis was a potential solution or that it could not give full answers because of the unknown foundational mechanism. As you can probably tell I couldn't follow it very well, even though I think you had something very interesting to tell us. The fault lies with my lack of necessary mathematical education, abilities and skill.

I do hope that you find lots of interested readers, who are competent in maths and can give you more constructive and positive feedback.

Wishing you good luck. Georgina.

Dear Tejinder,

Thank you for taking the time to summarize the core of the essay. It is helpful.I do agree with the first paragraph of your summary. Also that QM is part of a deeper theory. I would have it as part of a greater theory, encompassing both QM and space-time. Time being the "problem child".

I also see a 3 level reality. Foundational level unobservable objects, data transmission( One might say the raw file of photon data) and emergent space-time image reality. QM models the unobserved timeless objects. Unique input selected by type and position of detector allows space-time construction. Emergent as a temporally distorted artifact from the transmission delay of data between object and observer.I suppose that as a non physicist my explanations may appear naive. Though Einstein did say "Everything should be made as simple as possible, but not simpler".

I have said I am not competent to comprehend the work that you discuss, let alone evaluate it. So please forgive me for not doing so. What a dull world if we all thought in the same way and had identical talents and interests. It is good that you have brought it here for others to see and consider.

Once again, Good luck, Georgina.

Dear Tejinder,

While your approach is quite different from mine, and quantum theory is not my primary concern, I nonetheless appreciate your list of belonging problems.

I am not sure whether a peculiar 'influence' outside the light-cone has really been experimentally verified in EPR experiments. You gave no reference for your sentence: "The 'action-at-a-distance' in an EPR type experiment, which Einstein called spooky, has been experimentally proven to exist [however, we know it cannot be used for signalling]." If you refer to Nimtz type claims, I strongly disagree. To my knowledge there is no correct evidence for action at a distance.

I tried to explain why Planck's constant has nothing to do with the non-commutativity.

What I am tempted to ironically call the Schulman length between micro and macroworld might have a simple explanation: Quantum theory is affected by erroneous interpretation after arbitrarily choosing a complex ansatz. You may trust in my competence in this case.

What about the allegedly compelling accuracy of agreement between predicted and measured values, I see two question marks. First I recall Lighthill's theory of cochlea whose results were tweaked very close to reality, even too good as to be honest, because the passive model did not yet consider cochlear amplification. I also recall not yet understood discrepancies, in particular concerning a paper by Gompf et al. Secondly, I suspect there might be a qualitative mistake even in case of quantitative agreement. Before I abandon the causality conjecture I am ready to put any theory in question, even spacetime.

Please do not take it amiss if I consider it justified to look for possible mistakes at the most basic level, and this layer is in my understanding the fundamentals of mathematics. Do you object?

Regards,

Eckard

Dear Tejinder,

Thanks by confirming my above assumption about the 4N dimensionality of the spacetime in your Essay.

When classical dimensional time is raised to dimensional time operator, the Stuckelberg-like evolution time continues labeling the evolution of the generalized quantum states, without any need to take a Block universe viewpoint. Indeed, as showed in the references cited in my Essay, the picture based in an evolution time is more fundamental.

The cosmological argument cannot explain the arrow of time because initial low entropy states lead to evolutions incompatible with the second law. In the Chapter 1 of the BAS reference that I gave to you in the forum of my Essay, the authors show how an initial low entropy state belongs to both semigroups Lambda^{} and Lambda^{-}, whereas only Lambda^{} is compatible with the second law and the observed phenomena. They then choose the correct semigroup by comparison with observation. It is this selection which explains the arrow of time. Their demonstration can be extended to initial pure states with zero entropy and also to more general classes of dynamical systems.

Your essay was thought provoking and I gave it a high score. I do take some pause with the conclusion that quantum theory is purely a statistical result. Experiments with W and GHZ states illustrate Bell inequalities for a single experiment. I will have to read this again to see how this can be reconciled accordingly.

Cheers LC

Dear Dr. T P Singh,

Your essay is thought provoking,because you are trying to explain how digitality arises out of continuous (analog) nature of reality;for that you are inventing the concept of mesoscopic physics.It is a good idea. But in my essay,Iam trying to reconcile digital and analog nature of reality in a different way.Why dont you,please,go thro' my essay and express your openion on it.

Best regards and great success in the competition.

Sreenath B N.

Dear Dr. Singh,

Ingenuous your vision of a fundamental continuous layer underlying the quantum one, then the classical level, interfaced through the semi-digital layer, in the context of trace dynamics. It seems to capture a deep meaning of the quantum world and its relation with the classical level. The title is very suggestive; it also makes me thinking at the three and a half layers of the dynamical energy.

Best regards,

Cristi Stoica, Infinite Resolution

Dear member Tejinder Singh,

You wrote: "... your criticism is most welcome. I plan to read your essay soon and will leave my comments on your page."

Regards,

Eckard

Dear Tijender

My spirits were raised by your exceptional essay. In my view you are absolutely correct in virtually all your assumptions and conclusions (at least all those I think I understood).

I believe the concepts within our essays completely parallel each other, yet yours is a physics paper and mine is in a wholly different, naive but fully falsifiable and predictive, empirical language. I offer a link between the micro and macro space time structures, equivalent to non commuting matrices or discrete manifolds, with time emerging from it's simple dynamics. You may read my essay title as equivalent to the block universe, using a discrete field model (DFM) and well known boundary mechanism. http://fqxi.org/community/forum/topic/803

Duality emerges as the simple symmetry transition to implement any change to the analogue energy of motion, i.e. changing f and Lambda to preserve c and E locally.

You'll see from the thread there are a number of other very consistent essays which build to a fuller picture consistent with yours.

Our failure would prove to have been in ability of dynamic conceptualisation.

I truly hope you are able to read and understand the structure behind the model. I will be as happy with any scientific (rather than belief) based falsification as with confirmation, as I have as yet had none.

I currently have papers in preprint and under consideration further exploring important fundamental consequences. If you have time I will post links.

Very best wishes and thank you humbly in advance for your views on my essay.

Peter Jackson

Dear Dr.TP Singh,

Thanks for your reply and query.I have identified QG field to 'exponentially varying accelerated field' in which the gravity/acceleration varies exponentially.So it is possible for us to derive GR from QG but not vice-versa.Regarding how I have done this can be seen in my article on QG,which you find in my web-site I have mentioned in my essay("http://www.sreenath.webs.com" and click on abstract).The path described in QG field is Logarithmic (Equiangular) spiral path on a plane and conical spiral path in three dimensions.So QG field is a 'Torsion" field.When torsion vanishes QG field becomes uniform accelerated field i.e.,GR.

I have different views on QM which you see in my above article.In it,I have tried to connect the Schrodinger equation to 'how a particle gains energy in the QG field'.If you want me to send my article by e-mail to you,please,inform me and your mathematical frame work to my work I welcome most.

Best regards

Sreenath B N

Hi to both of you,all, you are relevant.here is some ideas for fun.

The caratheodory method of axiomatization seems universal and I like it, I suppose you also, in logic the kelvin Planck satetment of the the second law is interesting also.Because all is under these universal thermodynamical laws.The specification of an intergrer is always logic respecting the momentum and the kinetic energy.It's really the base of many things our thermodynamics and this heat.The quantum statistical mechanicsis precise and the real degrees of freedom are there in a pure thermodynamical logic.A little of maxwell law of velocities and vibrations and a Boltzmann helping with the correct finite numbe, and it's very relevant.1/2mv²...1/2m alpha²..1/2m beta².....correlated with volumes.The pression and the volumes dance with the velocities of rotations orbitals and spinals and the kinetic energy.....more mvV constant, general for all physical entangled spheres and hop all our thermodynamics and all our Quantum statistical mechanics is simplified and generalized in a spherical logic as the ideal gas.Avogadro will agree no hihii, in all case if the time operator is inserted, thus the relativity can be inserted rationally respecting the entropy and the arrow of time.But the axiomatization still is essential with its limits due to the finite universal serie.That implies an intrinsic cause in the gravitational stability, thus of course not actions at distance, but simply some informations arriving in the gravity and which fuses, it's totally different than a instant action from an other point inside this Universal sphere.The thermodynamics prove that.

Best to all and good luck in the contest.

Steve

Tejinder,

Masterful!

To your point of experiencing spacetime as classical, while acknowledging the infinite linear superposition of quantum states (and the challenge of computability in finite time) -- you might appreciate a less technical treatment of the same conclusions in my essay ("Can we see reality from here?")

Best,

Tom

I am having to read your paper again. I forgot that I had written on your space here. I responded to your comments on my space at

http://fqxi.org/community/forum/topic/810

and I will try to comment further. I will have to finish reading your paper on Monday.

Cheers LC

Tejinda

I greatly appreciate your supportive comments on my essay and the discrete field model, (DFM). I repeat me response below;

"Thanks for your agreement and sympathy. I'm acutely aware of the need to extend it with mathematical proof to allow physicists to "feel more at home". If you feel you may be of any help in collaboration I'd be delighted. As it's a logic and empirically based 'conceptual' theory the first problem is what to calculate!"

Perhaps nature is too complex for a single human brain process to make sense of. In the Architectural profession astonishing things are only achieved by teamwork. I not only have to have specialist skills but conceptual overview, and understand and co-ordinate a wide range of brilliant specialists, with entirely different ways of looking at things, into the whole. It seems physics as a whole may benefit from more of that, being more inclusive and holistic rather than exclusive and disparate. I'd be interested in your view, generally and specifically to exploring the DFM.

Very many thanks for your time.

Peter