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.
ROFL!
Just wait, he's promising an article in a philosophy journal next.
"interval of time" is probably the terminology that fits best.
Phaedrus, I'm still working through these issues, so can't speak definitively of the problem you raise here, right this "instant." But the problem has my full attention. For openers, however, I think it's safe to say that the universe has a time process, which may or not closely correspond with the way the human mind considers/chooses/selects the frames in which time is "naturally" relevant for it.
But here's a "thought experiment," for what it's worth, that might shed some light on the relevant issues.
Here I am, betty boop, sitting in a chair, totally stationary. I'm here, not going anywhere for a while. I suppose it would be easy enough to locate my longitudinal/latitudinal space-time coordinates on, say, a map of Massachusetts. But would this exercise designate my "absolute" position in the universe? Let alone the question of relative position; for the latter begs the question: relative to what?
This was the point I was driving at, in reply #109. I'm beginning to think that the "relative to what?" is precisely the question that needs to be asked. So let's take stock of the possibilities.
First I would recognize that "relativity" has significance in two major modes: what is "beyond" myself, and what is "in" myself. That might sound totally mysterious; but it really is quite simple. To explain, I would like to apply the term "macrocosmic" as the "extra-me" component of the problem; and "microcosmic" for the "intra-me" aspect. (I seem to be the "conscious, that is self-aware mediator" that ties the two realms together, meaningfully.) Consider:
Exactly what coordinates could be established for my "absolute location" in present time, no matter how we might slice it, if -- as stationary as I presently am within my own limited sphere of reference -- I also happen to be the denizen of a planet that is rotating along its axis, and simultaneously orbiting in its course around the the Sun, our Star? Meanwhile, the Sun -- a star in a galaxy -- is travelling along its course, set by the primaeval explosion that propels stars and galaxies and nebulae into the further reaches of universal space-time? Every bit of this is "moving" in its own right; and I am borne along in this complex movement.
At the same time that we are considering the "position problem" that would seem to result from the above macrocosmic considerations, there are also problems of the microcosm: I am "moving" in every way at this level, too -- at the organic, cellular, molecular, atomic, subatomic, and quantum levels.
It might look like I'm a "couch potato," rooted to my chair, not going anywhere; but on closer inspection, it would seem I am teeming with movement, activity, in all directions and time scales....
So, if a careful observer wanted to locate my absolute position on a map in "real time" (three quite "naturally deduced," and yet still quite "relativistically artificial" human constructs right there), then by what relevant criteria amenable to human "measurement" would he be able to do this? How could I even be located, relativistically -- in the sense that the seemingly important relative items run outside of the categories of finite human time conceptions in themselves -- at both the macrocosmic and microcosmic levels?
This is what I mean about nature being "always moving," along multiple dimensions. And so we think we can simply designate an artificial time construct -- such as a second, or a minute, or a "now" -- and hope to capture a miracle, as if in a butterfly net?
Must stop for now. Probably more to follow, as these "lessons" sink in further....
Thank you so much for writing, Phaedrus.
LOL, we must bookmark this post for later reference!
You're older than you've ever been
And now you're even older
And now you're even older
And now you're even older
You're older than you've ever been
And now you're even older
And now you're older still
Time is marching on
And time is still marching on
This day will soon be at an end
And now it's even sooner
And now it's even sooner
And now it's even sooner
This day will soon be at an end
And now it's even sooner
And now it's sooner still
You're older than you've ever been
And now you're even older
And now you're even older
And now you're even older
You're older than you've ever been
And now you're even older
And now you're older still
After our conversation earlier, and some pondering since, I'm not so sure we can dismiss the possibility of extra time dimensions (with or without extra spatial dimensions.)
I’ve discovered that it is evidently the implications of an extra time dimension that causes the notion to be shunned by physicists.
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.
Nevertheless, a few brave scientists have ventured into the possibilities and the results are quite interesting.
I'm going to indulge in a little philosophical speculation here, which I am loathe to do in my debates with the Materialists and, in particular, the Evolutionists. The heavy irony of this is that Materialism itself is a philosophy that infuses the believers' thinking with that bias. The beauty, if you will, of Lynds' paper is that it gives us a new but not shallow view of some very old "problems". My take would be that only our understanding of reality involves seeming paradox. Reality itself is seamless and "paradox" is a tipoff that we don't understand something.
With this in mind, I believe that one of the best philosophical questions is "Why is there something and not nothing?". Its scientific counterpart might be "Why is there motion and not stillness?". Physicality is real enough. But without motion at all levels, would it "disappear"? I believe that it would. From whence comes the energy that powers the motion of the electron, alway perfectly regulated? The Materialists would say "It just is". Is that an answer?
I think we're missing something that is very, very fundamental.
Leonard Cohen, Anthem
Oddly enough, he dosn't seem to have a problem with saying a precisely defined point exists on a spatial coordinate.
But to those of us of the Plato mindset, Penrose et al, it is not finished until it also makes sense.
So to those of us in the second group, "Why is there something and not nothing?" is a most significant question. Penrose indicates that most mathematicians are at least weak Platonists, so let us keep asking that question and perhaps target it to the math centered disciplines.
But can theree be such a thing in reality, as oppoosed to a thought experiment? Can any real thing have an absolute position?
In fact, if you believe Newton's first law, that in the absence of external forces, objects with a fixed velocity continue to move at that velocity, and thus r = v t, then anything you say about t is automatically true of any of the three components of r.
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