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.
"...now is the time of God's favor, now is the day of salvation." Paul, 2 Cor. 6:2
"...tomorrow is another day." Scarlett, Gone with the Wind
This is a clever bit of writing. The start of a cat fight.
Certainly it's worth a mention by Hovind on how Creationism is unchanging, yet science always seems to get it wrong, and how some schmoe beat the establishment at their own game.
It looks like an airy, hand-waving dismissal. Zeno's paradoxes are like the geometric demonstration that two unequal-length line segments contain the same (infinite) number of points, and/or the demonstration that every point in the real number line has a corresponding point in the subset segment of the line between 0.0 and 1.0. In fact, Zeno's paradoxes basically are those paradoxes turned into word problems.
Cantor for sure, who explored the properties of infinite sets, deserves better than he seems to be getting from Lynds here. So there will probably be hackles raised.
Every bump and hiccup is proof that the Hovinds of the world are really right.
Good question. I'm not positive I've thought this all the way through, but so far, I don't see that it has any effect on the "outside of space and time" idea. Primarily because Lynd's theory attempts to describe what is "in", rather than what is "out".
In reality, which much of the posers discussed have little to do with, I've always thought it was silly to try to assign a static point to something so elusive - and always in motion - as time. Of course, "common sense" and science don't always gibe. :^)
Reminds me of a book by someone else in that general vicinity of the world. Permutation City, by Greg Egan. Mindblowing read. In a virtual cyber world, the inhabitants all experienced "normal" time, even though in the realword computer which was running the simulation, it was running at 1/17 speed. Not just that, but when different "moments" of the virtual world were run backwards, or out of order, at random, the inhabitants still experience normal "time".
To return to Zeno‘s paradoxes, the solution to all of the mentioned paradoxes then, that there isn‘t an instant in time underlying the body‘s motion (if there were, it couldn't be in motion), and as its position is constantly changing no matter how small the time interval, and as such, is at no time determined, it simply doesn't have a determined position.In the case of the Arrow paradox, there isn‘t an instant in time underlying the arrows motion at which it‘s volume would occupy just —one block of space“, and as its position is constantly changing in respect to time as a result, the arrow is never static and motionless.
The paradoxes of Achilles and the Tortoise and the Dichotomy are also resolved through this realisation: when the apparently moving body‘s associated position and time values are fractionally dissected in the paradoxes, an infinite regression can then be mathematically induced, and resultantly, the idea of motion and physical continuity shown to yield contradiction, as such values are not representative of times at which a body is in that specific precise position, but rather, at which it is passing through them. The body‘s relative position is constantly changing in respect to time, so it is never in that position at any time. Indeed, and again, it is the very fact that there isn‘t a static instant in time underlying the motion of a body, and that is doesn‘t have a determined position at any time while in motion, that allows it to be in motion in the first instance.
Moreover, the associated temporal (t) and spatial (d) values (and thus, velocity and the derivation of the rest of physics) are just an imposed static (and in a sense, arbitrary) backdrop, of which in the case of motion, a body passes by or through while in motion, but has no inherent and intrinsic relation. For example, a time value of either 1 s or 0.001 s (which indicate the time intervals of 1 and 1.99999….s, and 0.001 and 0.00199999…. s, respectively), is never indicative of a time at which a body‘s position might be determined while in motion, but rather, if measured accurately, is a representation of the interval in time during which the body passesthrough a certain distance interval, say either 1 m or 0.001 m (which indicate the distance intervals of 1 and 1.99999….m, and 0.001 and 0.0019999….m, respectively).
Therefore, the more simple proposed solution mentioned earlier to Achilles and the Tortoise and the Dichotomy by applying velocity to the particular body in motion, also fails as it presupposes that a specific body has precisely determined position at a given time, thus guaranteeing absolute preciseness in theoretical calculations before the fact i.e. ∆d/∆t=v. That is, a body in motion simply doesn‘t have a determined position at any time, as at no time is its position not changing, so it also doesn‘t have a determined velocity at any time.
Lastly, and to complete the mentioned paradoxes, William James‘ variation on the Dichotomy is resolved through the same reasoning and the realisation of the absence of a instant in time at which such an indivisible mathematical time value would theoretically be determined and static at that instant, and not constantly changing. That is, interval as represented by a clock or a watch (as distinct from an absent actual physical progression or flow of time) is constantly increasing, whether or not the time value as indicated by the particular time keeping instrument remains the same for a certain extended period i.e. at no time is a time value anything other than an interval in time and it is never a precise static instant in time as it assumed to be in the paradoxes.
5. Closing Comment
To close, the correct solution to Zeno‘s motion and infinity paradoxes, excluding the Stadium, have been set forward, just less than 2500 years after Zeno originally conceived them. In doing so we have gained insights into the nature of time and physical continuity, classical and quantum mechanics, physical indeterminacy, and turned an assumption which has historically been taken to be a given in physics, determined physical magnitude, including relative position, on its head. From this one might infer that we‘ve been a bit slow on the uptake, considering it has taken us so long to reach these conclusions. I don‘t think this is the case however. Rather that, in respect to an instant in time, it is hardly surprising considering the extreme difficulty of seeing through something that one actually sees and thinks with. Moreover, that with his deceivingly profound and perplexing paradoxes, the Greek philosopher Zeno of Elea was a true visionary, and in a sense, over 2500 years ahead of his time.
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I think he's arguing that the traditional math is right, but it doesn't model reality. It's beyond my pay grade.
I can picture this perfectly; it looks like motion-blurring in still photography. The problem is that fast film and a fast shutter greatly reduce motion blur. I once was startled to develop pictures of an air show and see the rotors on flying helicopters looking crisply defined as if stationary. Certainly, I didn't remember them looking that way on my retina as they flew overhead.
To return to Zeno‘s paradoxes, the solution to all of the mentioned paradoxes then, that there isn‘t an instant in time underlying the body‘s motion (if there were, it couldn't be in motion), and as its position is constantly changing no matter how small the time interval, and as such, is at no time determined, it simply doesn't have a determined position.I hate that as a "solution." All "isn't" and "doesn't."
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