Posted on 07/31/2003 7:13:14 AM PDT by Nebullis
A bold paper which has highly impressed some of the world's top physicists and been published in the August issue of Foundations of Physics Letters, seems set to change the way we think about the nature of time and its relationship to motion and classical and quantum mechanics. Much to the science world's astonishment, the work also appears to provide solutions to Zeno of Elea's famous motion paradoxes, almost 2500 years after they were originally conceived by the ancient Greek philosopher. In doing so, its unlikely author, who originally attended university for just 6 months, is drawing comparisons to Albert Einstein and beginning to field enquiries from some of the world's leading science media. This is contrast to being sniggered at by local physicists when he originally approached them with the work, and once aware it had been accepted for publication, one informing the journal of the author's lack of formal qualification in an attempt to have them reject it.
In the paper, "Time and Classical and Quantum Mechanics: Indeterminacy vs. Discontinuity", Peter Lynds, a 27 year old broadcasting school tutor from Wellington, New Zealand, establishes that there is a necessary trade off of all precisely determined physical values at a time, for their continuity through time, and in doing so, appears to throw age old assumptions about determined instantaneous physical magnitude and time on their heads. A number of other outstanding issues to do with time in physics are also addressed, including cosmology and an argument against the theory of Imaginary time by British theoretical physicist Stephen Hawking.
"Author's work resembles Einstein's 1905 special theory of relativity", said a referee of the paper, while Andrei Khrennikov, Prof. of Applied Mathematics at Växjö University in Sweden and Director of ICMM, said, "I find this paper very interesting and important to clarify some fundamental aspects of classical and quantum physical formalisms. I think that the author of the paper did a very important investigation of the role of continuity of time in the standard physical models of dynamical processes." He then invited Lynds to take part in an international conference on the foundations of quantum theory in Sweden.
Another impressed with the work is Princeton physics great, and collaborator of both Albert Einstein and Richard Feynman, John Wheeler, who said he admired Lynds' "boldness", while noting that it had often been individuals Lynds' age that "had pushed the frontiers of physics forward in the past."
In contrast, an earlier referee had a different opinion of the controversial paper. "I have only read the first two sections as it is clear that the author's arguments are based on profound ignorance or misunderstanding of basic analysis and calculus. I'm afraid I am unwilling to waste any time reading further, and recommend terminal rejection."
Lynds' solution to the Achilles and the tortoise paradox, submitted to Philosophy of Science, helped explain the work. A tortoise challenges Achilles, the swift Greek warrior, to a race, gets a 10m head start, and says Achilles can never pass him. When Achilles has run 10m, the tortoise has moved a further metre. When Achilles has covered that metre, the tortoise has moved 10cm...and so on. It is impossible for Achilles to pass him. The paradox is that in reality, Achilles would easily do so. A similar paradox, called the Dichotomy, stipulates that you can never reach your goal, as in order to get there, you must firstly travel half of the distance. But once you've done that, you must still traverse half the remaining distance, and half again, and so on. What's more, you can't even get started, as to travel a certain distance, you must firstly travel half of that distance, and so on.
According to both ancient and present day physics, objects in motion have determined relative positions. Indeed, the physics of motion from Zeno to Newton and through to today take this assumption as given. Lynds says that the paradoxes arose because people assumed wrongly that objects in motion had determined positions at any instant in time, thus freezing the bodies motion static at that instant and enabling the impossible situation of the paradoxes to be derived. "There's no such thing as an instant in time or present moment in nature. It's something entirely subjective that we project onto the world around us. That is, it's the outcome of brain function and consciousness."
Rather than the historical mathematical proof provided in the 19th century of summing an infinite series of numbers to provide a finite whole, or in the case of another paradox called the Arrow, usually thought to be solved through functional mathematics and Weierstrass' "at-at" theory, Lynds' solution to all of the paradoxes lay in the realisation of the absence of an instant in time underlying a bodies motion and that its position was constantly changing over time and never determined. He comments, "With some thought it should become clear that no matter how small the time interval, or how slowly an object moves during that interval, it is still in motion and it's position is constantly changing, so it can't have a determined relative position at any time, whether during a interval, however small, or at an instant. Indeed, if it did, it couldn't be in motion."
Lynds also points out that in all cases a time value represents an interval on time, rather than an instant. "For example, if two separate events are measured to take place at either 1 hour or 10.00 seconds, these two values indicate the events occurred during the time intervals of 1 and 1.99999...hours and 10.00 and 10.0099999...seconds respectively." Consequently there is no precise moment where a moving object is at a particular point. From this he is able to produce a fairly straightforward resolution of the Arrow paradox, and more elaborate ones for the others based on the same reasoning. A prominent Oxford mathematician commented, "It's as astonishing, as it is unexpected, but he's right."
On the paradoxes Lynds said, "I guess one might infer that we've been a bit slow on the uptake, considering it's taken us so long to reach these conclusions. I don't think that's the case though. Rather that, in respect to an instant in time, I don't think it's surprising considering the obvious difficulty of seeing through something that you actually see and think with. Moreover, that with his deceivingly profound paradoxes, I think Zeno of Elea was a true visionary, and in a sense, 2500 years ahead of his time."
According to Lynds, through the derivation of the rest of physics, the absence of an instant in time and determined relative position, and consequently also velocity, necessarily means the absence of all other precisely determined physical magnitudes and values at a time, including space and time itself. He comments, "Naturally the parameter and boundary of their respective position and magnitude are naturally determinable up to the limits of possible measurement as stated by the general quantum hypothesis and Heisenberg's uncertainty principle, but this indeterminacy in precise value is not a consequence of quantum uncertainty. What this illustrates is that in relation to indeterminacy in precise physical magnitude, the micro and macroscopic are inextricably linked, both being a part of the same parcel, rather than just a case of the former underlying and contributing to the latter."
Addressing the age old question of the reality of time, Lynds says the absence of an instant in time underlying a dynamical physical process also illustrates that there is no such thing as a physical progression or flow of time, as without a continuous progression through definite instants over an extended interval, there can be no progression. "This may seem somewhat counter-intuitive, but it's exactly what's required by nature to enable time (relative interval as indicated by a clock), motion and the continuity of a physical process to be possible." Intuition also seems to suggest that if there were not a physical progression of time, the entire universe would be frozen motionless at an instant, as though stuck on pause on a motion screen. But Lynds points out, "If the universe were frozen static at such an instant, this would be a precise static instant of time - time would be a physical quantity." Consequently Lynds says that it's due to natures very exclusion of a time as a fundamental physical quantity, that time as it is measured in physics, or relative interval, and as such, motion and physical continuity are possible in the first instance.
On the paper's cosmology content, Lynds says that it doesn't appear necessary for time to emerge or congeal out of the quantum foam and highly contorted space-time geometrys present preceding Planck scale just after the big bang, as has sometimes been hypothesized. "Continuity would be present and naturally inherent in practically all initial quantum states and configurations, rather than a specific few, or special one, regardless of how microscopic the scale."
Lynds continues that the cosmological proposal of imaginary time also isn't compatible with a consistent physical description, both as a consequence of this, and secondly, "because it's the relative order of events that's relevant, not the direction of time itself, as time doesn't go in any direction." Consequently it's meaningless for the order of a sequence of events to be imaginary, or at right angles, relative to another sequence of events. When approached about Lynds' arguments against his theory, Hawking failed to respond.
When asked how he had found academia and the challenge of following his ideas through, Lynds said it had been a struggle and that he'd sometimes found it extremely frustrating. "The work is somewhat unlikely, and that hasn't done me any favours. If someone has been aware of it, my seeming lack of qualification has sometimes been a hurdle too. I think quite a few physicists and philosophers have difficulty getting their heads around the topic of time properly as well. I'm not a big fan of quite a few aspects of academia, but I'd like to think that whats happened with the work is a good example of perseverance and a few other things eventually winning through. It's reassuring to know that happens."
Lynds said he had initially had discussions with Wellington mathematical physicist Chris Grigson. Prof. Grigson, now retired, said he remembered Lynds as determined. "I must say I thought the idea was hard to understand. He is theorising in an area that most people think is settled. Most people believe there are a succession of moments and that objects in motion have determined positions." Although Lynds remembers being frustrated with Grigson, and once standing at a blackboard explaining how simple it was and telling him to "hurry up and get it", Lynds says that, unlike some others, Prof. Grigson was still encouraging and would always make time to talk to him, even taking him into the staff cafeteria so they could continue talking physics. Like another now retired initial contact, the Australian philosopher of Science and internationally respected authority on time, Jack Smart, who would write Lynds "long thoughtful letters", they have since become friends, and Prof. Grigson follows Lynds' progress with great interest. "Academia needs more Chris Grigsons and Jack Smarts", said Lynds.
Although still controversial, judging by the response it has already received from some of science's leading lights, Lynds' work seems likely to establish him as a groundbreaking figure in respect to increasing our understanding of time in physics. It also seems likely to make his surname instantly associable with Zeno's paradoxes and their remarkably improbable solution almost 2500 years later.
Lynds' plans for the near future the publication of a paper on Zeno's paradoxes by themselves in the journal Philosophy of Science, and a paper relating time to consciousness. He also plans to explore his work further in connection to quantum mechanics and is hopeful others will do the same.
Well, that works for Rosie O Donnell, but what about the rest of us?
That reminds me of my statement to physicist which he did not understand. I stated - If something(anything) moves, everything moves.
With a single time dimension we have a timeline where order exists, i.e. before this, after that. Add another time dimension, and that timeline becomes a plane – and there is no past or future hence cause and effect get muddled (physics must have causation) … objects travel faster than light, etc.
“Shunned by physicists!” Well, of course, A-G, and entirely understandable. It’s nice to have a single timeline where order exists, a nice linear one that moves from past, to present, to future. It’s difficult to conceive of causality outside this framework.
But the question I wonder about is, because the human mind needs to work this way, and thus must impose itself in this manner on reality, could this then mean that somehow we are making reality “fit” our categories instead of the other way around? And if this is so, then could it be possible that there are aspects of reality that must remain forever unknown to us on principle, because we have no other method by which to engage or deal with them, given our present state of consciousness and our resulting notions WRT the problem of Time?
Personally, I rather “shun” the idea of understanding myself as a “composite” built entirely out of the activity going on in a multiplicity of fields – gravitational, EM, and various levels of quantum fields, certain of which are yet hypothetical; e.g., the Higgs field, which has been predicted mathematically, but whose characteristic particle, the Higgs boson, has yet eluded experimental confirmation. Then I learn that there’s yet another little “crittur” – the Goldstone boson(?) (with its related field) that has recently been predicted on the basis of mathematics – presumably even finer and lighter than the Higgs. I haven’t a clue how or when that will be experimentally validated or falsified.
But “shunning” is silly, if what I wish to “shun” is the actual truth of reality: Which surely seems to be that I am composed of a multiplicity a different fields (or “ontological levels”). Truth is truth! My “opinion” of it matters not in the least.
The point about all these fields out of which I (and everything else in the universe) am made up is, as I understand it, that they are universal fields. Every one of them is as “big” as the entire universe itself.
Here’s what I wonder about, as it seems particularly related to our understanding of time. Isn’t in a certain sense something that is “universal” effectively “timeless?” In the sense that it never does move from past to present to future, it just IS? Just as physical laws themselves are effectively “timeless?” They do not build up randomly over a long chain of causation; they are that which constrains apparent randomness into the forms we see all around us; and without them, there could be no forms? It probably sounds pretty “Greek” to simply say that universals are timeless on principle – which in a certain way gives them a value as some kind of order of “time” – so to speak (if only to indicate negatively what is not subject to temporal change).
Incidentally, Prof. Kafatos suggested in a recent paper (you’ve seen it) that the masses of particles derive from their interactions with the field(s) that are appropriate to their particular level of activity. Which, following my reasoning above, means they are vested with their primary qualities/characteristics by virtue of their participation in the universal field. Thus in a certain sense, we have time-subject properties and activities deriving from a “substrate” that is essentially not in time.
Plus Richard Feynman has suggested that, at state vector collapse, one of the photon pair “must calculate” all possible routes to find its photon twin before it actually settles on one. This seems a little nutty to me (maybe he was speaking tongue-in-cheek); but if it’s true, it seems that calculation must proceed at a rate faster than the speed of light; for on state vector collapse, the photon twin “instantly” gets the same “information” as the original photon. So I don’t see why there cannot be “superluminal” velocities; especially if the field in which they are taking place is substantially “out of time” – and thus not constrained by our ordinary notions of space and time.
Indeed, simultaneous “action at a distance” seems to require some kind of field or substrate that is not constrained for space and time.
Or at least, that’s what it looks like to a rank (though quite passionately enamored!) beginner with a fertile imagination! :^)
Seriously, I’m speculating on the basis of logic and the (yet) quite limited information that I have regarding these subjects. I’ve printed out the two PDFs you linked me to, and will study them over the weekend. I’ve been thinking about writing a short article on the universality of consciousness as a potential fundamental field or principle of the Universe, based on some recent papers I’ve read from Raman, Rifat, and Grandpierre, that might shed further light on these issues, and perhaps aid in focusing our present speculation further.
All I can say about it right now is that it will be a “bear” to write! I want to thank you for all your help and encouragement, so very deeply appreciated....
Seems perfectly reasonable, or at least conceivable to me, AndrewC. For everything is "connected" to everything else by virtue of their mutual/collective participation in the fields that altogether constitute all of life. So if something moves, it moves its "neighbor," and the moving "neighbor" moves what it touches, and movement is thus propagated to the furthest reaches of the relevant field(s). The only potential constraint seems to be an entity's access to a "free energy" store/source that could lead to a countering/dampening effect of that propagation somewhere along the line of transmission....
Of course, I'm just speculating here.
AG, for the sake of Aristotle, your comment needs fixing. Aristotle refutes the materialists in his Metaphysics. And in the mindset of Aristotle, the very ones who proceed beyond the "it just is" have wisdom:
For men of experience know that the thing is so, but do not know why, while the others know the 'why' and the cause"Why" in Greek is dia ti: on account of which something is. It asks for a cause. Aristotle expanded from a monistic view of causes (contra the materialists) to a pluralism of causes, including immaterial causes."Again, we do not regard any of the senses as Wisdom; yet surely these give the most authoritative knowledge of particulars. But they do not tell us the 'why' of anything-e.g. why fire is hot; they only say that it is hot.
"Evidently we have to acquire knowledge of the original causes (for we say we know each thing only when we think we recognize its first cause), and causes are spoken of in four senses. In one of these we mean the substance, i.e. the essence (for the 'why' is reducible finally to the definition, and the ultimate 'why' is a cause and principle).Whatever Aristotle said about the why contained in the how, this criticism has no right to dismiss Aristotle's recourse to formal causes learned from his teacher.
The connections you make (Aristotle-materialists-Hawking) yield effective conclusions on the basis of wrong and partial information.
Add my endorsement to A-G's here, Phaedrus: So beautifully stated! You also wrote: "I think we're missing something that is very, very fundamental." So do I. Thanks so much for this elegant post.
It is not yet available online. The most recent edition of "Foundations of Physics Letters" available online is April 2003. (This appeared in the August 2003 edition). Be patient. Meanwhile, you can always go read Lynds' "Zeno's Paradoxes: A Timely Solution" if you are so inclined. I posted the link earlier. But I'd be glad to post it again, if you wish.
I strongly doubt it, cornelis.
I think what his paradoxes show is that, if you load an unfounded/incorrect assumption into an analysis of a problem, you could find yourself "proving" something that isn't true. The incorrect assumption in these cases is that time is divisible into discrete units. Thus all the results obtained contradict the types of results that we would expect to obtain on the basis of direct observation, knowledge, and experience.
Zeno's logic wasn't faulty. His "trial assumption" was faulty. And I think he knew that. That was the point. He probably took some pleasure in the effects his paradoxes had on people who engaged them, perhaps thinking it would be difficult for many if not most people to spot the fundamental problem that lies at the root of their construction. Of course you're right: "puzzles can work within their own definitions." Whether those definitions have anything to do with objective reality is the real question.
I think Lynds, if anything, wants to thank Zeno for showing how our own mental constructions of methods to solve problems can be self-defeating, leading to absurdity. I get the sense that Lynds goes Zeno one better: That if time were actually divisible into discrete units, nothing could "move" at all.
cornelis, for whatever it's worth, my sense is that Zeno and Parmenides were working on different problems entirely. Thus they aren't directly comparable, for our purposes.
I thought I was the only one who thought along these lines. In effect, his final moments become eternity for him, which is why, for me, it is so extremely important to have a pleasant "final moment", if possible.
Past and future co-exist only with in the mind of Man...and G-d.
Or will it simply result in a slight variation in color (for visually observable wavelengths) or the appropriate counterpart in other invisible spectra? If so, what standard of non- distorted wavelength would one use to compare the subject wavelength to?
Not necessarily. Things could occur by jumps. There might be a system where one measures the position of a particle and "later" does another measurement for which the particle is somewhere else. (This describes discrete space.) Were time discretized, one could look a the "fundmental clock" and only see discrete units. There would be no experiment that could give a result that was between one tick and the next. If the resolution were fine enough, all of ordinary dynamics can be recovered (and there would be no obvious experiment that could distinguish a really fine discretization from a coutinuous theory). There are discrete models (used in numerical analysis) where energy, momentum, etc. are exactly conserved. The accuracy of the discrete mechanism is roughly of the square of the finest division.
Additionally, time divisions could be only countable but dense rather than continuous. This would recover all of dynamics easily because the Riemann integral is sufficient for such cases. (Continuous time requires a Lesbegue integral. I'm not sure there's an experiment that shows one rather than the other to be "correct.")
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