Co-existence of Continuous and Discrete Physical Behavior by Ben J Baten

Hello Ben, I like the way I could read your essay despite being a non-mathematician. I admire your Author Bio statement "He hopes to make a contribution to fundamental physics by creating interest in, and contributing to, alternative approaches to current physics". I have something which may interest you in this area. It's a simple way to visualise a GRAVITON by use of an Archimedes screw mechanical model. Think about it. If this helical graviton travelled around a wraparound universe then it would emerge on the other side as a force of repulsion i.e. an ANTI-GRAVITON or DARK ENERGY. It's too good a model to ignore for any longer imo. Did Newton miss this simple idea to explain the mystery of a force at a distance?

Best of luck.

Alan

Ben

Nice essay, but you seemed to be pulling some punches and staying in the stream? I perticularly liked your simple, clear but pertinent itemised points towards the end. I also had a quick glance over your site, and wish to go though it carefully when I have time. I feel this ought to be higher and will certainly get a good score from me. I agreed with most of what I understood, but couldn't quite see how discrete time emerges from 'within' the particle motion. I hope this may paralell my own derivation of discrete time beween inertila frames via a simple scattering mechanism.

I hope you may be able to find time to read and comment on my essay. You'd need to read and think carefully as a quick scan almost always fails to get over the ket point. It's a bit like De Broglie struggling to derive 3 unified oscillations, but testing the brain to conceive and manipulate more moving variales than it's normally capable of, changing observer frames to compare, then seeing the fundamental consequences. more than I though are now succeeding. Do let me know.

(Be prepared for a very 'coal face' physical reality/localality empirical approach if you read it). There's also value in the string.

Best wishes anyway

Peter

Hi Peter,

Thank you for taking the time to read my essay. Hopefully, it does not come across too much as pulling punches. I'm in the process of reading essays and I will definitely read yours as well.

Many details underly what I have covered in my essay. Unfortunately, only a fragmentary overview can be provided in such a short write up and I'm afraid that this impedes clarity. Last year's essay provides a more elaborate description of some important aspects but still fall short on some details.

The theory I describe indeed partially overlaps with mainstream physics (if at least that is what you mean by 'staying in the stream'), which is good since existing well-established and experimentally verfied quantum and relativistic theory needs to be reproduced.

However, the theory is also significantly different. For example, main stream physics is not able to explain space and time, or attach a clear meaning to Planck's constant. In current physics quantum theory and relativity are disconnected and both theories are highly formal in the sense that one does not really obtains an understanding of the physical nature of earlier mentioned entities: it looks like one just manipulates equations without gaining a true understanding of their physical meaning and the entities involved (observables). In the theory (QFM) that I allude to, an oscillating process underlies the connection between quantum and relativistic behavior, dynamically created space and time, de Broglie's wave, particle mass, spin etc., and they all have a clear physical origin, which is lacking in current physics. For the mentioned reasons, I think this theory offers great potential although it describes phenomena in a rather different way than current physics. The long-range electromagnetic interaction theory (which covers e.g. Maxwell equations) and some results from General Relativity can be derived from within the basic theoretical framework. The details of the QFM are described in Kirilyuk's and my reports (use the slide deck on my website to get a quick impression).

How to address short-range interactions is somewhat unclear to me at this moment, but the analysis of the general state function solution that I mention in the essay should provide some insight. It could be that current short-range theories can be leveraged to a certain degree, although they may merely provide a mathematical approximation (emulation) of the actual extremely non-linear 'internal' behavior of particles.

In order to explain the existence of an oscillatory phenomenon as indicated in my essay one needs to conjecture the existence of two fundamental interacting fields, the electromagnetic and gravitational protofield. They are pre-space/pre-time fields from which space and time dynamically emerge as oscillatary phenomena.

As mentioned, the protofields can be used to explain the existence of the four observed fundamental interactions: gravity and e/m interaction, weak and strong interaction. One can understand the possible existence of an oscillating phenomenon caused by interaction between the fundaental fields also as follows. Imagine a stiff wired open (e.g. square) frame with a flexible membrane fixed to its edges and spanned accross it. Obviously, the frame and membrane interact and the presence of the frame allows the membrane to oscillate. The membrane can be viewed as the fundamental electromagnetic protofield in which oscillations (particles) exist. Obviously, in reality, such the frame does not exist. However, conceptually, replace the frame by the gravitational protofield, and assume that the protofields interact. Based on the frame-membrane analogy, the electromagnetic protofield should permit oscillating perturbations, which are facilitated and stabilized by the presence of the gravitational protofield (frame). This idea is mathematically supported by the very complex analysis in the first report on my website and which is described briefly in Kirilyuk's papers.

You indicated that you could not quite see 'how discrete time emerges from within the particle motion'. Discrete time emerges as period of the oscillating electromagnetic protofield. Discrete space emerges as individual space points which get created in the course of the oscillation behavior. During each oscillation period the perturbation created in the electromagnetic protofield moves at the speed of light from one dynamically created space-point to the next (giving rise to random Zitterbewegung).

One needs to distinguish internal particle motion, which is equal to the motion of the electromagnetic protofield perturbation, from externally observable particle motion, which is equal to the average beavior of a whole sequence of subsequently created protofield perturbations.

It is rather hard to describe this complex behavior in a simple manner, but I hope you get what I'm trying to convey.

Ben

Yes I get the feel of your approach. I hope you'll also get the feel of mine OK because I think, in fact I'm sure, it provides you with the short (& moderate) range interaction process you mention.

You also say of past theory basis;

"they all have a clear physical origin, which is lacking in current physics"

Which is precisely what the discrete field model (DFM) brings to the party. It explains the quantum mechanism for SR and the basis of GR, suddenly making the whole thing physically logical.

When you get to read it you must be prepared to do 3 things; 1) Suspend prior 'belief' temporarily (it will return better explained) 2) Read it slowly, as it demands visualisation and conceptual manipulation of more dynamic variables then our brains are used to dealing with, 3) Think the consequences through carefully, they are absolutely fundamental and massive.

So far only about 1 in 5 visitors have found the holy grail in there. I do believe you are able. From the initial difficulty of seeing it you will find it the simplest most Occam solution possible.

I believe conceptually it is perfectly consistent with your philosophy, but neither are complete and I can see both benefiting by unification.

I wish you luck. Best wishes

Peter

Dear Ben,

Thanks for an interesting essay discussing internal motion of particles. It is nice that the equations keep accurate units as the ideas are described for deeper reasons behind quantum mechanics and gravity. Note 8 seemed like a good analysis of Young's experiment with particle arrival probabilities.

I am curious about the concept of discrete time. As a single period of an electron's oscillation progresses, is there a notion that the electron moves continuously producing the quantum beat periods? If the detailed oscillation behavior could be observed, could finer definition be made for the rules of its motion?

I appreciate you sharing your ideas. It seems like this essay contest is showing that people really care about the reasons behind what is observed.

Kind regards, Russell Jurgensen

Dear Russell,

Thank you for you interest in my essay. The theory, originally developed by Kirilyuk, tries to create a realistic picture of particle behavior bases on minimal assumptions that are compatible with observations. This unification attempt is intriguing and since it is vastly simpler (not too simple) than other, mathematically dominated, attempts. The latter approach makes me suspicious, because it seems that complex mathematics is used to compensate for a lack of true understanding of physical behavior.

With respect to the units, the equations are indeed correct. However, more importantly, the equations themselves must provide a correct representation of the underlying physics. The Planck equations (for time, length and mass) are also correct in terms of units, but are likely incorrect with respect of the supposed physics. In Kirilyuk's work, the gravitational constant in those equations should be interpreted in a different fashion, see his reports and the QFM-II report on my website.

Note 8 is another example of an 'unexpected simple approach', in this case to explain quantum interference phenomena. There is no magic involved, conjecturing the existence of probabilistic learning processes is sufficient. The model used by the authors' for the devices may not exactly correspond to their real physical behavior. The authors have come up with a few ideas to test a some predictions of their work for cases that are not covered by quantum theory. Quantum theory only covers prediction of averages, not what happens during the 'start-up' behavior of e.g. a Mach-Zehnder experiment.

Yes, an electron is internally always in motion and continuously produces quantum beat periods as a consequence of the internal; oscillation. Note that, although an electron is internally always in motion, externally, as observed average behavior it may be stationary. How can an electron be internally in motion while being stationary? Consider the fact that we have two protofields (as they are called in the essay) with completely different mobilities. The quantum beat oscillation must necessarily result in a rotation in the electromagnetic protofield due to the different protofield mobilities and their mutual attraction. So, we have co-existing oscillating, 'internal motion' and rotation (spin). It seems that all of this simultaneously occurring behavior must cause perturbations in the electromagnetic protofield which are, for a stationary particle, move such that they are located on a 'circle'. In this way the electromagnetic protofield perturbation can move at the speed-of-light while the particle is stationary. The on-circle perturbations give rise to the observed Bohr magneton of an electron. For an electron in motion, the on-circle behavior gets stretched in favor of forward motion of the electromagnetic protofield perturbations.

This is a bit finer definition of the internal motion of an electron. Some of those aspects are cover in the QFM-I and QFM-II papers on my website in which you can see that this picture is fully supported by a self-consistent mathematical theory. This demonstrates that long-range electromagnetic and gravitational interactions can be unified into a single consistent theory. The qualitative and quantitative description of short-range interactions requires much more work. A particle model described in a report on my website may be a starting point.

Part 1 of a discussion with Ian Durham about his essay. Since it has some relevance to my essay, I thought it would be worthwhile to repeat here.

Dear Ian,

I enjoyed reading your essay. Several of the issue that you discuss have been paradoxical for ages and have not been resolved satisfactory. There is, however, a way to get around those issues, which I will explain below by addressing them specifically.

1. Page 4. the second expression for the average speed makes the assumption that the limit can be determined, because dt (read d as Greek delta) can be made arbitrary small. This is not the case. As I describe in my essay, for electrons, dt has a lower bound equal to 10 exp (-20) sec. A The electron would cease its existence by 'making it smaller'. In other words, mathematically, one can determine the stated limit, but it is unphysical. The velocity of a massive particle is well-defined, even although dt is different from zero. The velocity of a particle does not need to be described in terms of a mathematical limit at all: a definition in terms of a discrete ratio is sufficient, i.e. v = dx/dt, where dx and dt are constrained by quantum condition (4) stated in my essay. In this way, an electron can be assigned a velocity without measuring this (see page 6 of your essay where you discuss the issues around this).

2. Page 5. Classical Light. I assume you mean light described in terms of classical theory.

3. Page 5. "by Brukner and Zeilinger to argue that the continuum is nothing but a mathematical construct, a view I wholeheartedly endorse". I do not necessarily agree with this view. As I describe in my essay, continuity needs to co-exist with discreteness. In the theory I describe, two underlying continuous fundamental fields are needed to explain the existence of particles, interaction between particles, and dynamically emergence of local discrete space and time.

4. Page 5. "So what happens in the limit as dt --> 0 for classical light?" As I indicated under 1., dt cannot be smaller than 10 exp (-20) sec. Light cannot be attributed a discrete time, unless one wants to define it as wavelength/c. The latter is not very useful, since the time would be wavelength dependent.

5. Page 5. "Suppose we decrease dt while leaving dx unchanged. As dt gets smaller and smaller, it implies we are measuring the difference between x1 and x2 more and more rapidly. Lest we forget, classical physics limits how rapidly information can propagate. At some point, without changing dx, we will be empirically prevented from further reducing
dt since the ratio of
dx to dt cannot exceed the speed of light. So, if we wish to take
dt --> 0, we must take dx--> 0 in order to keep the ratio at or below the speed of light."

There is an implicit assumption made that dt can be made arbitrary small, which is not the case as I explained earlier. For a stationary electron dx=0, while dt=10 exp (-20) sec, such that the ratio dx/dt=0 and there is no issue with violating the speed-of-light as one would get by assuming that dt can be made arbitrary small. When the speed of an electron increases, both dx and dt increase, but their ratio cannot exceed the speed-of-light c. In my essay, I explain that this is due to the fact that the internal speed of random spatial motion of an electron is equal to the speed-of-light. The details can be found in the second report on my website.

6. Page 5. "The classical theory of light assumes light is a wave which is an inherently non-local phenomenon". Indeed. This result in a paradoxical behavior. However, is is also known that light consists of photons, which propagate at the speed-of-light, and posses a kind of corpuscular behavior when detected. When one assumes that photons are oscillating blobs, then they do not behave as a classical wave. Still, a 'wavelength' can be assigned, which is equal to the length of the oscillation.

Ian Durham's reply:

Thanks for the comments, Ben. Regarding your point number 6, the corpuscular theory of light is inherently quantum. No classical corpuscular theory of light was ever successful as far as I am aware.

I think we fundamentally agree. In all your points where you say there's a lower limit to dt (and then you cite it), that's precisely my point. There is a lower *empirical* limit. The assumption that dt -> 0 is a purely mathematical one and is not grounded in reality, as you correctly point out.

I would, however, disagree on two points. First, if we assume an empirical limit on dt, then we need to also assume an empirical limit on dx such that v can never be zero since zero motion for point particles is ultimately prevented by quantum effects as is well-known. Second, on your point number 3, there are ways to take the ontological status of a field out of the theory without altering the mathematics, i.e. the "field" interpretation of the mathematics is only one possible interpretation of them.

Part 2 of a discussion with Ian Durham about his essay.

My reply:

Dear Ian,

1. You're right that no classical theory of light was ever successful. That is not the point I wanted to make. Photons are quantum like entities can be detected by particle detectors. In interference experiments they exhibit a wave-like character. This dual behavior could be reconciled by assuming that they are oscillating 'blobs in motion' to which a frequency (temporal periodicity) and 'wavelength' (spatial periodicity) can be assigned and which is detectable as a particle.

2. Your reply: "I would, however, disagree on two points. First, if we assume an empirical limit on dt, then we need to also assume an empirical limit on dx such that v can never be zero since zero motion for point particles is ultimately prevented by quantum effects as is well-known.

This is not correct. We are talking about two different things, namely the internal random motion (Zitterbewegung) and the external observable average motion of a particle dx (which you use in your essay). In case of a stationary particle, obviously, the externally observable motion dx=0. However, the internal random motion is created in 'discrete portions' equal to dx sup 0 = h/mc (Compton's 'wavelength). In my essay I talk about dx sup 0, from which dx sup 0= h/mc can be derived via h v sub 0 = m sub 0 c sup 2 (de Broglie's equation, see (1) in my essay).

3. Your reply: " Second, on your point number 3, there are ways to take the ontological status of a field out of the theory without altering the mathematics, i.e. the "field" interpretation of the mathematics is only one possible interpretation of them."

I would like to remark that, by assuming the existence of two fundamental interacting fields (protofields in my essay or whatever you want to call them) one can show that the existence of massive particles, their interaction, the notion of particle spin, particle charge, mass, wave function all can be explained consistently within one coherent model (see the complex non-perturbative considerations in ref 2/3 of my references). The true nature of those 'fields' will likely never be known: we can only observe their consequences in particle interaction behavior and detectors. The issue with current (multi-body) interaction models is that, unfortunately, either they are too simple or they cut out essential pieces if the math 'gets too difficult'. When applied to the conjectured interacting two protofields it is shown that those cut-out pieces are essential to understand the complete quantum and relativistic behavior of particles. The internally random quantum behavior of massive particles can be identified with Zitterbewegung.

Ian Durham's reply:

Ben, as for your point number 2, while conceptually I see where you're coming from, I would argue that no such measurement has ever been made in a laboratory. In other words, we've never achieved absolute zero in a laboratory. As for your point number 3, I think I agree with it.

Dear Ben Baten,

I enjoyed your essay, as I too am focused on deBroglie 'pilot waves' as the explanation of the particle-wave duality.

My approach differs somewhat in that I base it on Maxwell's 'gravito-magnetic' field, updated to reflect recent measurements and calculations. Maxwell noticed that Coulomb's equation and Newton's equation had the same form, and decided to replace Electric field by Gravity field and charge by mass in the other EM field equations. But to complete this translation he needed an analog of the electro-magnetic field, and he termed this the gravito-magnetic field. Just as moving charge induces a circulating magnetic field, moving mass will induce a circulating gravito-magnetic field. This field, accompanying a corpuscular electron adds a wave-like aspect, while the description of such is a solution of Schrodinger's equation.

So if you're interested in an alternative perspective on deBroglie QM, I invite you to read my essay here. I would appreciate any comments.

Edwin Eugene Klingman

Dear Edwin,

I have read you essay and found the summary on page 8 about the 'serious problems' current theories cannot solve interesting. Those types of issues are hardly ever discussed.

In your essay you start with a master equation that requires the pre-existence of a coordinate structure otherwise the gradient cannot be determined and distance (r) cannot be measured. The phi field is identified with gravity. On page 3, a C field is introduced. So, I get the impression that both of us need to fields to describe physics although both approaches are very different.

In my essay, I mention the need for two interacting protofields to explain the currently observed 4 short/long-range interactions and the existence of particles. Displacement and time dynamically emerge. The typical equations from current quantum theory, relativity theory and electromagnetic theory can be derived from the conjectured existence of the interacting protofields and require dynamically created time and particle displacement. I merely give an overview of some of the results of this theory in which the math follows from the physics. Many details can be found in the references and require a fair amount of time to plow through. A slide deck on my website gives a summary overview.

There are probably some more differences that can be identified between our essays. I think we need to leave it to others to assess the merits of both approaches.

Best regards.

Ben,

Thanks for looking at my essay and commenting. I agree with your conclusion.

Good luck in the contest and with your researches.

Edwin Eugene Klingman

Dear Ben,

I enjoyed your essay and I particularly agree that space and time should dynamically emerge with mass-energy. Quantum Mechanics has never been agreeable to me, do to its inherent incomprehensibility. I wish you success in your endeavors to supplant QMs.

You also wrote: "In case of gravity, the mathematical extension of the metric to empty space is a mathematical generalization which cannot be derived from the theory described in this report and appears to result in an unphysical description of a dynamically evolving space-time of the universe as a whole. Consequently, any supposedly observed evolution dynamics of the universe remains to be explained in a different manner than current physics maintains."

Let me point you to my essay for a different perspective on the universe as a whole. I have defined a cosmic spacetime that is a superposition of local spacetimes and I believe it is a model that would fit well with your theory. I have also reached some conclusions and offered alternative hypotheses for some cosmological mysteries that you might enjoy. I hope you will find the time to read it.

Best Regards,

Dan

Dear Dan,

Thank you for your feedback on my essay. You are one of the few thus far. I have also read your essay and must admit that have will probably have to read it a few more times to fully comprehend it.

I also appreciate your alternative thinking. In my opinion, the approach of current physics is is getting more and more 'problematic'. There are some issues with current cosmology that you touch upon with which I fully agree, such as the large amount of unexplained energy and the known theoretical issues with black holes.

I also agree with the statements on page 2: 'Time in relativity is simply defined by that which is measured by perfect clocks' and 'time is (possibly) an elementary ordered process of change, and footnote 2: ' In our approach, we will not assume that events are perfect point-like mathematical objects, only that they are infinitesimal in extension and duration compared to the scale our geometry represents.' All those remarks nicely match what I try to convey in my essay where this is made more explicit.

I'm not clear about the notion of cosmic time. For me, time originates from particle dynamics and only a single notion of (discrete) time is needed to describe physical events.

In the theory that I describe, the notions of time, space, particle motion, energy, momentum and Planck's constant are all well-defined and directly connected to the behavior of an electron (these notions can be generalized to other types of massive particles and for photons those concepts can only be defined in terms of massive particle behavior (see material on my website). I get the impression that in current physics the notion of 'energy' is very loosely used.

Dan, I get the impression that you are assume the existence of expanding space time. Since space has a different meaning in the theory I describe, there is no notion of expanding space. Consequently, the observed 'expansion of space' needs to be explained in a different fashion.

Best Regards.

Dear Ben,

I was glad that you had the time to read my essay. I, like you, am taking an alternative approach as I have seen many issues arise with the Standard Model of Cosmology, in particular DM and DE, only to receive the band-aid treatment. I appreciate people, such as yourself, taking a similar stand against the fundamental issues with QT and trying to provide a more reasonable and inclusive theory. I have not had the opportunity to check your website or the cited work of Kirilyuk. I plan to do this as time allows.

As for my notion of cosmic time, this is a definition based upon the need to combine all local spacetimes, each with their distinct time coordinate based on local conditions, into a cohesive whole (namely the universe) and constrained by the singularity in the distant past. IOW everything in the universe has a shared history, regardless of the rates of their local clocks.

As for the expansion of space, I have accepted the commonly held view that the cosmological redshift is evidence of its expansion. But my model, by having an intrinsic curvature, unrelated to the total mass-energy content, IMO is a more natural way to explain many open cosmological questions. I must have misinterpreted the quote cited from your essay in my previous post. Nevertheless, I do plan to study your approach more thoroughly in the near future.

Wishing you the best,

Dan

Dera Ben,

as was saying in my post it is very interesting to find a convergence of view with you.

The Kirilyuk's works deserve special attention. I hope that my answers to your questions were useful.

Good luck and stay in touch.

Donatello

Part 1 of a discussion with Donatello Dolce about his essay. Since it has relevance to my essay, I thought it would be worthwhile to repeat here.

Dear Donatello,

I have read your essay. I also believe that de Broglie's original ideas are essential to accomplish unification. You will see similar statements about the non-mathematical aspects in both of our essays. Some of the main ideas in your essay are identical to the ones I pose in my essay, althought the origin is very different. The main differences between your and my description that I could identify are:

1. Page 1. Abstract. Cyclic Space-Time. In my essay time I describe that, under the stated conjectures, time and space are dynamically emerging by the interaction of two fundamental fields. Time is equal to the oscillation period, space dynamically emerges during the highly non-linear oscillation as high-density points of the dynamically combined protofields. This is different from the displacement (motion) of a particle, which should not be equated to dynamically emerging space.

2. Page 1. In the work I cite, there is no need to introduce a lattice, letting N--> infinity, or bosonic fields. The interacting fundamental fields can be describe in terms of state function equation. Its solution can expanded in terms of eigenfunctions, which also results in a 'matrix description, which is in turn equivalent to an effective potential equation. The highly technical analysis of this equation shows that dynamic state function solutions must exist, which give rise to internal spatial randomness.

3. Page 2. The 'uncertainty' relation is derived in the work I cite. However, they are exact relations, not 'uncertain' relations. See QFM-II report on my website.

4. Page 3. Expression 3. You provide an expression for the action in terms of a Langrangian density. Langrangian densities are not needed in the Quantum Field Mechanics I describe because the Lagrangian of a free massive particle has the conventional non-quantum field theory form: L= - m_0 sqrt (1 -v sup 2/c sup 2), where m_0 is the rest mass. The particle in a box quantization is not needed. See also QFM-II report on my website.

Finally, I would like to say that there are some very good general observations in the body of your essay and the conclusions!

Best regards.

Dear Ben,

thank you for reading my essay. I am happy to see a sort of convergence of views between us. I think that also the Kirilyuk's works will be source of inspirations for my future studies. I particularly I like how you describe the appearance of a particle from the a de Broglie periodic phenomenon. It is what I have found plotting the modulo square of one of my periodic field (see the presentation http://wwwthep.physik.uni-mainz.de/~dolce/tmp/seminario-3.pd

f). Moreover I hope you'll find interesting the other discussion given in arXiv:0903.3680v1-v4 (note that v5, i.e. ref.[1], contains only an half of the original paper posted on arXiv nearly 2 years ago).

1) I consider that one of the beauty of my theory is that it does not require any hypothetical element not yet observed in nature. It is base only of relativistic space-time and boundary conditions, even the wave nature can be regarded as arising naturally from the assumption of periodicity through Discrete Fourier transform. The most elementary periodic system is a vibrating string and the fields of my theory are exactly the four dimensional generalization of sound waves and sound sources, see ref.[1]. Thus I don't need any pre-field. I suspect that if you tray to formalize your idea of protofield in a consistent way, you'll end up to my periodic field.

2) The lattice assumption was only used to show the connection of my theory with the 't Hooft deterministic model. In my case I have continuos (digital) cyclic coordinates. In your description of field, if you don't use space-time coordinates our only choice left to describe the randomness is to assume hidden variables, with all the problems coming from the no-hidden variables theorems. In my theory there are no hidden variables, the only variables I have are cyclic (analog) space-time and (thus) quantized (digital) energy-momentum.

3) the uncertainty relation as well as the commutation relations are direct consequences of the cyclic space-time. There is not intrinsic (indeterministic) uncertainty. Is the (discrete) process counting of the number of cycles that gives an indeterminacy on the frequency of the ciclic phenomena. To have infinite accuracy of the frequency we need to count an infinite number of cycles, just as in an ordinary wave.

4) A field is a very wide concept and it is perfect to describe periodic phenomenon. The idea comes from de Broglie and evolved in string theory (in my case you can find both these aspects). You say that your theory is base on a protofield, so you should involve some field lagrangian at some point. By the way the field lagrangian and the particle lagrangian are dual if you assume periodicity. You can find the technical proof of this statement for instance in arXiv:0903:3680v4 par.4.1. You will see that a cyclic field, through Poisson summation, can be written a sum of path described by "non-quantum field lagrangians". Moreover the evolution of periodic fields is exactly described by the ordinary Feynman Path Integral and the lagrangian that appears in the exponential is again the "non-quantum field lagrangians".

I really thank you for your interest in my work and you are always welcome for discussions. As you probably noticed, the assumption of intrinsic periodicity opens a new way in physics full of premises!

Best regards,

Donatello

Part 2 of a discussion with Donatello Dolce about his essay. My reply to him.

Hi Donatello,

I read you reply in the thread of my essay. I also think that periodicity is a very important element to eliminate many of the inconsistencies in current physics and is potentially a promising field of research. There are a few other essays that make references to periodicity, but do not expand upon it as we do in our essays.

I summarized some aspects of Kirilyuk's original theory on Quantum Field Mechanics (QFM) in my essay and linked it to de Broglie's thinking and current theories. On my website, I have cast Kirilyuk's work in a more accessible form with extensions following from the basic theory.

About your feedback:

1. The electromagnetic and gravitational protofields are notions introduced to match observed fundamental interactions with minimal assumptions to construct a theory. They should be viewed as real physical fields of which the detailed characteristics may never be known apart from they way they facilitate particle interaction. They should not be interpreted as mathematical fields.

2. In QFM-I (see my website) hidden variables indeed appear, but in a completely different fashion than in current theory: they are not measurable since they pertain to the protofield interaction.

3. No comments.

4. You state that 'You say that your theory is base on a protofield, so you should involve some field Lagrangian at some point.' The basic theory (see QFM-I on my website) describes protofield interaction and from that dynamically emergent space and time. It does not rely on a Lagrangian yet, since it addresses the existence of particles. The next layer of the theory (QFM-II) introduces physically rationalized action conditions to describe electron motion (with stationary state is a special case), from which eventually the Lagrangian of a free electron follows. This does not seem to be a very important result, but a free electron can be viewed as the prototypical particle of nature given its stability and low complexity. A correct physical description of this case should be viewed as a stepping stone for subsequent theoretical work. I have attempted to come up with a 'simple description' of more complex massive particles in line with some of the results of QFM, but this description remains to be compared to measurement results. This is clearly work in progress and can be criticized in some areas.

I will take a look at the references that you mentioned since I'm always interested to learn something new.

Best Regards.

Thanks for your answers to my questions!

Kind regards, Russell