Dear Ian Durham,

as explained in my previous posts above, the existence of a lower limit to Dt (D is Delta) does not imply that the instantaneous velocity for light is not defined as, however, you believe.

As I showed, when one considers also the lower limit to Dx one obtains the exact equation for photons

Dx/Dt = c = dx/dt

which implies that expressions as (dx/dt) are perfectly well-defined and measurable.

You correctly point out Baten's mistake about Dx for electrons. However, again the lower limits for both Dx and Dt for relativistic electrons (or other particles) does not imply that the instantaneous velocity for those particles is not defined.

A rigorous analysis of relativistic localization for electrons was given in the reference 6 cited in my . One can easily obtain the next exact equation for fermions

Dx/Dt = (c alpha) = dx/dt

where alpha is one of the Dirac matrices.

Precisely the instantaneous velocity (c alpha) is used in QED to obtain the current density

j = e Psi* (c alpha) Psi

where e is the particle charge and Psi the field

Or in a more standard form

j = e c \bar{Psi} gamma Psi

with \bar{Psi} the adjoint field and gamma another of Dirac matrix.

There are other claims that you do that are corrected in the same reference 6.

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Ian,

Indeed. My knee-jerk reaction is a case in point. This part of relativity is abused so widely and often that it's blinded me to checking terms more carefully for definition.

Tom

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Dear Ian,

1. You're right that no classical theory of light was ever succesful. 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.

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Dear Juan,

See my last reply to Ian in which I have included an answer to the issue you bring up.

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Dear Dr. Ian Durham,

Iam a little bit confused of your thoughts on digital and analog nature of reality.Which one is more basic than the other one,analog or digital? Or do you want to say that it lies in our way of perception of reality. Any way historic background upon which you have based your essay is really absorbing.

But,I have other thoughts on the above problem in my essay.Why dont you,please,go through it and have a different view of the problem? Expecting your openion on it.

Best regards and wishing success in the competition.

Sreenath B N.

    Dear Ben,

    You are right on that we are talking about different things.

    By "x" both Ian and me are referring to the position as used, for instance, in QED. This is the instantaneous position of "point particles" as described in a quantum field theoretic framework. There is not such a thing as "internal motion" for point particles. Moreover, the nonzero Dx (D is delta) is not associated to real motion of any kind (althouth I know that some few references claim otherwise for the Zitterbewegung).

    If you want compute velocities/speeds you must use compatible positions and times. If "x" denotes position in QED, then "t" denotes time in QED and ratios as Dx/Dt and dx/dt are mathematically well-defined and with physical meaning. If by "x" you mean otherwise (as it seems that you mean with your "externally observable motion"), then you must also change "t" from that on QED to that in your own model.

    Finally, I want to emphasize again that the Dx ~ (hbar/mc) written in my above message is valid only for a stationary electron in QED and that it is neither the De Broglie wavelength lambda nor the Einstein-de Broglie 'wavelength' postulated in 1924 by de Broglie in his unfounded mixing of non-relativistic wave quantum mechanics with special relativity.

    To avoid further misunderstandings, I would add that the instantaneous velocity (c alpha), used in QED to obtain the fermion current densities, is not observable, although the speed and one of the components are observable.

    The reason which the vector (c alpha) is not observable has nothing to see with the existence of a lower limit for Dt, but is a direct consequence that the x in QFT is not Hermitian. This is the true reason which there is not position operator in QFT and position is downgraded to unobservable parameter, as emphasized in many texts.

    Hi Alan,

    Very interesting concept, but I still don't see why his theory of gravity is any different in that sense from electrostatics. In other words, just because he worded it in a certain way doesn't automatically make it incompatible with a particle model. It certainly could have affected the interpretation historically, but it doesn't a priori rule out a particle interpretation.

    Ian

    P.S. Fascinating bit on oranges and lemons.

    Robert,

    I'll print out your essay and read it. I'm interested in what you have to say on the topic.

    Ian

    Interesting points (both Ben and Juan). I still think, Juan, that we are fundamentally talking about different positions. I am not saying instantaneous velocities are not well-defined, nor am I saying that they do not exist. I am merely saying that, given existing technology, they cannot be measured to arbitrary accuracy.

    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 Ian,

    I have been analyzing another kind of statements done by you both in your Essay and in this forum. Relations as (Dx/Dt = c = dx/dt) given by me in this forum are independent of the "given existing technology".

    Another issue is our current ability to measure arbitrary physical, chemical, or biological quantities using the technology at our hand. This would be the debate of the difference between (dx/dt)_th and (dx/dt)_exp, for instance.

    Juan,

    So you are, in essence, you are saying that there are really three ways in which we can understand dx/dt and not two: first, there is the purely mathematical sense of an instantaneous value such as dx/dt which has no real meaning outside of pure mathematics (i.e. it's purely symbolic); then there is dx/dt with the added meaning attached to it when it becomes associated with a theory; and finally there is the experimental realization of dx/dt.

    I make no distinction between (dx/dt)_math and (dx/dt)_th in my essay which I think has been the source of confusion here. In fact the entire point of my essay is to argue that limitations on (dx/dt)_exp mean that we can never know whether (dx/dt)_th is real or just a mathematical approximation.

    Ian

    I will add your essay to the list of them that I am reading.

    Indeed, the divide between analog and digital lies in how we perceive reality.

    The relationship between the continuous and discrete aspects of the world seems to be an example of a complementary principle. I am not sure how this can be formally demonstrated. Yet it appears that wave functions and continuous structures of that nature are not directly observed, whereas what we do observe are particle or the discrete event of a particle occurrence.

    Your essay was pretty good and enjoyable.

    Cheers LC

      Dear Ian

      I'll need to read your essay again more carefully and will do so, but your response above to Robert Spoljaric interested me as much and seemed to be fully consistent with the basis of my own essay rather than the ruling paradigm.

      There also seems to be a similar strong consistent and broad 'new physics' theme emerging in a number of others, including our current leader Jarmo, also Edwin, Robert, Willard, Georgina, Rafael and the list goes on.

      Do you think FQXi may at last be engendering the fundamental paradigm shift it was conceived for? or do you feel the new green shoots will be trampled on yet again? or are not worth nurturing? I'd be interested in your views on mine and the above if you have time to add them to your list!

      Best of luck.

      Peter

        Thanks, I'm glad you liked it! I think the continuous v. discrete debate was actually at the true heart of the original complementarity principle. If you read Bohr's writings and those of people who adhered to his principles, I think you'll find that this is precisely at the core of what they were talking about.

        Peter,

        Unfortunately, I'm a bit of a cynic so I don't necessarily think FQXi is engendering any paradigm shift (though I think it does a great deal of good). There are just too many people out there who see FQXi as an organization of cranks (ignoring the fact that there are five Nobelists among us).

        That said, there may be a slow shift happening in foundational circles. But I don't think anything will truly change until there is a major breakthrough in experiment. Just my opinion (though one shared by a few other people).

        Ian

        Ian

        Thanks. Cynicism seems difficult to fight in current conditions, and experimental results now seem consistently defined by the ruling paradigm not the other way round. Who would now volunteer for the 'crank label by being inconsistent?!

        If you really are am empiricist I really do hope you might look over my essay and advise what may be physically wrong with the empirically consistent solution to unification at it's heart.

        You'll need to slow down and think carefully at a few key points. It appears it's only lack of that care that has prevented the solution being seen before now.

        There was something very moot late in your essay I'd like to return to, in the meantime I'd be richly honoured by any views on mine. (2020 Vision, a model of discretion..)

        Best wishes

        Peter

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          Dear Ian,

          I have just had a quick read of your essay. I was very pleasantly surprised as I had thought it might be far to complicated for me to understand. I will certainly read it again when I have more time and am less tired.It is written in an accessible and clear way.

          The introduction is excellent. You are the first, that I have read , who plainly asks what is actually meant by continuous and discreet, as well as asking what is meant by reality. You are right to highlight the limits to objective knowledge. We can not know because our knowledge is limited by the need to make detections and interpret them. There is some overlap with last years question here.

          Any way It looks like you have done a very good job of addressing the essay question in an enjoyable and relevant way.

          I was sorry to hear of the loss of your father in Law.

          Good luck. Georgina

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            I find it hard to understand why one would identify radical reversals of known science with a great creative surge of knowledge, when the facts say otherwise. Arguably, the most revolutionary ideas in physics in the last 300 years -- Einstein's -- were founded in the revolution that Newton started, not in any new way of doing physics. Even now, where relavitity meets quantum mechanics, most bets are on quantum field theory to extend Einstein's work, not overturn it.

            Regardless of the charatcerizations of popularizers, objective knowledge viewed in an objective manner is hard won and incremental -- like the process of evolution itself.

            Tom