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.

    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

      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.