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.
If the answer to your question is affirmative, then the four dimension worldview (3 spatial plus time) can be seen as a fixed block and within the extra-dimension of time the entire panorama is revealed, i.e. beyond any conceivable timeline. This rings true to my Spirit and fits nicely with the Tegmark musings on a Level IV multi-verse of mathematical structures. IOW, instead of a separate universe per mathematical structure as Tegmark proposes, an extra dimensional time within which the mathematical structures exist.
The article on gravity raised even more flags for me – in particular, could dark energy be a manifestation of extra dimensional dynamics? It might help explain why dark energy, which is 70% of the mass of the universe, has not been detected in laboratories.
It may also help explain some of the apparent superluminal anomalies such as the Feynman one you discussed:
Indeed, simultaneous “action at a distance” seems to require some kind of field or substrate that is not constrained for space and time.
Thank you so very much for all these thought-provoking ideas! Hugs!!!
It depends. Hypoxia can be insidious so it does not always raise red flags. I can say that it is not unpleasant for me, at least as experienced in an altitude chamber.
Bingo! There is no content in the paper as far as I can tell, just a bunch of technical sounding mumbo-jumbo. The key to your observation is at the bottom of page 4 where Lynds destroys all of the quantities in physics (momentum, energy, etc.) and finishes on page 5 with "Moreover, the universe's initial existence and progression through time would not be possible. Thankfully, it seems nature has wisely traded certainty for continuity".
With regard to my use of the names Aristotle and Plato, I probably should have clarified that I was speaking in terms of mathematics.
According to the Aristotelian paradigm, physical reality is fundamental and mathematical language is merely a useful approximation. According to the Platonic paradigm, the mathematical structure is the true reality and observers perceive it imperfectly. In other words, the two paradigms disagree on which is more basic, the frog perspective of the observer or the bird perspective of the physical laws...
The Platonic paradigm raises the question of why the universe is the way it is. To an Aristotelian, this is a meaningless question: the universe just is. But a Platonist cannot help but wonder why it could not have been different. If the universe is inherently mathematical, then why was only one of the many mathematical structures singled out to describe a universe? A fundamental asymmetry appears to be built into the very heart of reality.
Hawking on physics and reality:
These lectures have shown very clearly the difference between Roger and me. He's a Platonist and I'm a positivist. He's worried that Schroedinger's cat is in a quantum state, where it is half alive and half dead. He feels that can't correspond to reality. But that doesn't bother me. I don't demand that a theory correspond to reality because I don't know what it is. Reality is not a quality you can test with litmus paper. All I'm concerned with is that the theory should predict the results of measurements. Quantum theory does this very successfully....
Roger feels that...the collapse of the wave function introduces CPT violation into physics. He sees such violations at work in at least two situations: cosmology and black holes. I agree that we may introduce time asymmetry in the way we ask questions about observations. But I totally reject the idea that there is some physical process that corresponds to the reduction of the wave function or that this has anything to do with quantum gravity or consciousness. That sounds like magic to me, not science.
Penrose on physics and reality:
Quantum mechanics has only been around for 75 years. This is not very long if one compares it, for example, with Newton's theory of gravity. Therefore it wouldn't surprise me if quantum mechanics will have to be modified for very macroscopic objects.
At the beginning of this debate, Stephen said that he thinks that he is a positivist, whereas I am a Platonist. I am happy with him being a positivist, but I think that the crucial point here is, rather, that I am a realist. Also, if one compares this debate with the famous debate of Bohr and Einstein, some 70 years ago, I should think that Stephen plays the role of Bohr, whereas I play Einstein's role! For Einstein argued that there should exist something like a real world, not necessarily represented by a wave function, whereas Bohr stressed that the wave function doesn't describe a "real" microworld but only "knowledge" useful for making predictions.
Bohr was perceived to have won the argument. In fact, according to the recent biography of Einstein by [Abraham] Pais, Einstein might as well have gone fishing from 1925 onward. Indeed, it is true that he didn't make many big advances, even though his penetrating criticisms were very useful. I believe that the reason why Einstein didn't continue to make big advances in quantum theory was that a crucial ingredient was missing from quantum theory. This missing ingredient was Stephen's discovery, 50 years later, of black hole radiation. It is this information loss, connected with black hole radiation, which provides the new twist.
Although the paper to which the post refers is not yet available, it's probably just a rewording of the Zeno paper online. In which case, there's not much to it.
That's true. The out of body or near death experience is a sure tip-off, but not everybody will experience that. And for some people a delusion is not recognized as such.
Here's a link to the paper: Time and Classical and Quantum Mechanics: Indeterminacy vs. Discontinuity in PDF. It's not simply a rehash of Zeno but says that in relative motion there isn't a precise position at a particular instant of time, etc. I guess I still don't get the significance of the paper.
A far more significant paper is Dodd's Compton Effect analysis which basically destroys the concept of a photon as an object (particle or otherwise). It shows how a free electron absorbs a fixed amount of energy and momentum from a classical circularly-polarized electromagnetic wave, independent of the wave's intensity (leading to E=hf and p = hf/c). The intensity of the wave determines the amount of time required to absorb this "photon" of energy/momentum.
There is one physicist that I know of who has the potential to bring this analysis to the forefront of physics: Princeton's Kirk McDonald. I enjoy reading his papers and he has been studying em-electron interactions intensively. He uses classical em to analyze his experiments - finding the limits of applicability, etc - then proceeds to muck it up by transitioning to QM. He won't make the jump to declare the photon dead as an independent object - it's like a giant elephant sitting in the middle of his papers that he won't acknowledge.
Very interesting speculation, Doc. Indeed, if the "resolution were fine enough," discrete "jumps" would look like a continuous process to us. But you suggest there's no "obvious" experiment that could be performed that would allow us to distinguish between the two theories.
But if "there would be no experiment that could give a result that was between one tick and the next," then how could we then demonstrate instances of cause and effect? If the two ticks are separate from each other, how could they affect each other?
Additionally, time divisions could be only countable but dense rather than continuous...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."
Thus we have two seemingly mutually exclusive theories and no obvious way to tell which is "correct." (Unless we say that time, like physical particles, has both a discrete and a wave form.)
Maybe these theories aren't testible in themselves, and the only way we can verify or falsify them is to load them into the assumptions of planned experiments and see what happens. But there's a problem even there: How would we know what the experimental results really mean if our assumptions haven't been "validated?" (And then, an even more extreme question: are they even susceptible to validation, in the scientific sense?)
I guess all this shows that "mind" and "matter" interact and can and do modify each other.... And then, perhaps there is the question of what "mind" wants to do here: recover traditional dynamics, or explore the fundamental structure of reality. I suppose motivations get loaded into our assumptions very early on; but this is rarely obvious.
Human beings get a whole lot "right." But sometimes, I wonder how, and why that is....
I wonder if you can help me understand the manner in which a discrete time division would display "density?"
Thank you so much for your fascinating and thought-provoking post, Doc.
This is a very great caution, Alamo-Girl. I'm going to have to give that a lot of very serious thought.
Thank you so much for your observations and analysis! And also, as ever, your generous help and encouragement! Will dive into those papers you bumped me to now, to catch up on this mysterious "dark matter...!"
Thanks, A-G, with HUGS!
If it were to open up new intuitions, even if completely equivalent, it would be useful even if not necessarily preferred.
But frankly, it sounds to me like the usual crank bullshit.
Aliasing leading to either an upper bound on possible frequencies of radiation, or at least indistinguishability beyond some frequency, would be an effect not in conventional physics.
The referee was right.
I was fortunate to have been exposed to delta-epsilon proofs with my first calculus class, and although the guy was not a good teacher, I am at least glad about that exposure. Infintitesimals and limits are difficult concepts for many to grasp, and I think this fellow has confused himself by trying to make it up on his own rather than understand what has already been found.
I'm looking forward to it, Doc.
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