In Search of Continuity: Thoughts of an Epistemic Empiricist by Ian Durham

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.

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.

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

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

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

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

Dear Ian,

your essay has the merit, I think, to discuss with more clarity than other participants the distinction between the ontological and epistemological spheres.

There is a (minor) point on which I tend to disagree, or at least I need clarification. You write:

"This idea simply formalizes the somewhat intuitive notion that causality is somehow related to continuity. To get a better conceptual understanding of this, suppose two events, A and B, are causally connected. Then there must be some way to get information from one to the other without exceeding the speed of light (or, more formally, they must be either timelike or lightlike separated). If spacetime is discontinuous, how do we know that this information couldn't 'jump around' from point to point? Continuity guarantees that the information follows a nice, orderly 'path' between A and B. This should make it easy to see the conceptual attraction of a continuous reality."

I really do not see the coupling between causality and continuity as something that matches common intuition. In particular I am not sure I understand what you mean by writing that one might be worried by the possible uncontrolled jumps of information (possibly messing up causality, you probably imply) under a discontinuous spacetime assumption.

I am indeed tempted to say that a discrete spacetime assumption, as embodied in a partial order/directed-graph model (a causal set) would create less problems to intuition, as far as causality flow is concerned, due to the explicitly represented paths that information may follow in the discrete structure: you explicitly indicate which event influences which other event. (And Lorentz distance, in the continuum, in nicely approximated by graph-theoretic longest-path distance, in the discrete setting.)

Tommaso

Dear Ian,

Effectively, there is three different (dx/dt): the mathematical (dx/dt)_math where x and t are just mathematical objects; the theoretical (dx/dt)_th where x is the physical quantity "position" and t the physical quantity "time" (each with its respective unit); and (dx/dt)_exp related to an experimental realization given according to a concrete operational recipe and system.

However, for the case (dx/dt = c) discussed here, there is not difference between the theoretical and the experimental because the experimental value of c is exact in the SI and as said in a previous post: "Relations as (Dx/Dt = c = dx/dt) given by me in this forum are independent of the «given existing technology»".

Dear Lawrence B Crowell,

What "complementary principle"?

Hi Ian,

Another nicely constructed and argued essay -- and of course I'm glad you arrived at the conclusion that the next question to ask is whether it's possible to have a "quantum" theory that's not discrete. I'm looking forward to hearing more of your thoughts on that topic.

Only a couple of nitpicks:

- I didn't follow your leap from "imprecision" to "discontinuity". Yes, measurements are imprecise. Does that mean the knowledge we gain from them is "discrete"? Well, maybe, but that's not how I tend to think of the word. But then in your conclusion you used the word "discontinuous", which I think is a much stronger claim (and more akin to how I view "discrete" in the first place). Was that word a slip, or is that what you really mean?

- In my view of the world, "Classical, Newtonian physics" did indeed have competition after 1788 via Lagrange. A point I like to make, because I still don't think that people have properly wrapped their heads around how different variational principles are from what Lee Smolin calls the "Newtonian Schema".

Best,

Ken