Ground-breaking work in understanding of time

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.

>> figured out an experiment that may allow one to tell whether things are discrete or continuous. I'll post the description later.

I'm looking forward to it, Doc.<<

Simple:

FReeper posts on WOD, the Civil War, Gay Rights, Evolution and the 2nd Amendment (and now Kobe) are Continuous.

Posts on Science, Kalifornia, the Brain, and the advantages of cheese for your Dog are generally discrete.

This is a discrete posting. My other postings on the other subjects did not, in fact end. They were merely truncated in this dimension by a non-euclidean 3D plane. If you enter the tesseract, you will be able to follow the continuity.

See?

There have been other threads asking how could someone go about proving to themselves they definitely were or were not in a virtual reality simulation.

Our current understanding of the working of the computers that would drive such a virtual reality simulation is that they would have some very small but not infinitesimal clock cycle. Also, whatever reality they created would have some small but not infinitesimal resolution.

At one instant in time the virtual reality simulator could be stopped and polled to see where everything was located. So everything is as static as the arrow in Zeno's paradox during any one clock cycle.

The simulator, however, is outside the simulation and can move all of the objects in the simulator to the next state. If the simulator's clock cycle and resolution are finer than can be measured by those quasi-sentient objects in the simulator, then they will perceive themselves to be in a world with continuous time and space.

So I think a counterargument to Lynd is that so long as there is something outside the system (e.g. God outside the universe) to drive the objects from one static point to another, then motion will exist which will be observed by sentient components of the system.

There could still be a graininess to our universe which God can perceive, but that we are technologically incapable of perceiving. Some have suggested (whether or correctly or absurdly) that this graininess is the source of quantum uncertainty.

Or if there is no God outside the system, then even if we are currently in a virtual reality simulator with a certain graininess, there exist some beings in a real universe with no graininess. Either that or they are all frozen in time.

There's an equation from evolutionary theory (I can't remember the name) but the idea is to iterate something like X=A*X*Exp(-B*X) with A and B being positive constants. X can be considered to be a population. For continuous X, there is usually an analytical solution (often chaotic) to such systems. For a discrete system (X can take a limited number of integer values), the result X (the left hand side, LHS) can be set to the nearest integer to the RHS (or the greatest integer, etc., as long as we are consistent.)

What happens in the integer case is that there are cycles that depend on the factorization of the total number of allowed Xs. These cycles disappear in two cases: continuous X or a random component added to the RHS at each step.

My proposed experiment would be to find an analogous equation that could evolve in time such that periodic behaviour would be observed in the finite case but chaotic behavior in the continuous case. The difference in behavior would not depend on the resolution so much as on whether there is a finite number of states.

Of course, if there is a random component, the experiment fails. (Brownian motion would probably be sufficient to cause this failure. The dispersion relations seem to indicate that just having waves is sufficient.)

"Time is marching on And time is still marching on"

RiffRaff:
It's astounding;
Time is fleeting;
Madness takes its toll.
But listen closely...

Magenta:
Not for very much longer.

RiffRaff:
I've got to keep control.
I remember doing the time-warp
Drinking those moments when
The Blackness would hit me

Magenta:
And the void would be calling...

Transylvanians:
Let's do the time-warp again.
Let's do the time-warp again.

Narrator:
It's just a jump to the left.

All:
And then a step to the right.

Narrator:
With your hands on your hips.

All:
You bring your knees in tight.
But it's the pelvic thrust
That really drives you insane.
Let's do the time-warp again.
Let's do the time-warp again.

Magenta:
It's so dreamy, oh fantasy free me.
So you can't see me, no, not at all.
In another dimension, with voyeuristic intention,
Well secluded, I see all.

RiffRaff:
With a bit of a mind flip

Magenta:
You're into the time slip.

RiffRaff:
And nothing can ever be the same.

Magenta:
You're spaced out on sensation.

RiffRaff:
Like you're under sedation.

All:
Let's do the time-warp again.
Let's do the time-warp again.

Columbia:
Well I was walking down the street just a-having a think
When a snake of a guy gave me an evil wink.
He shook-a me up, he took me by surprise.
He had a pickup truck, and the devil's eyes.
He stared at me and I felt a change.
Time meant nothing, never would again.

All:
Let's do the time-warp again.
Let's do the time-warp again.

Narrator:
It's just a jump to the left.

All:
And then a step to the right.

Narrator:
With your hands on your hips.

All:
You bring your knees in tight.
But it's the pelvic thrust
That really drives you insane.
Let's do the time-warp again.
Let's do the time-warp again.

Thank y’all so much for your posts!

I was working on a reply last night, but a giant thunderstorm came through and I lost it. Sigh...

Your experiment sounds very interesting, Doctor Stochastic! Please let us know if you follow-through on it!

It seems to me that time is a dimension in wave propagation and hence time is contiguous in 4D, i.e. jumping is a technical deficiency of numbering and not time. But continuity of time is turned on its head when we examine betty boop's extra time dimension possibility! IOW, I believe betty has trumped Lynds.

It seems we always come back to randomness, Doctor Stochastic. I am not aware of any randomness that is uncaused (including Brownian motion) and thus the very definition of “random” as a natural event is a tongue-in-cheeker for me.

But with regard to the “Curse of Dimensionality” article – I read his use of the term “random points” as if it were “arbitrary points.” The bottom line is that the article is helpful to me in conceptualizing higher dimensions, e.g. hypercubes.

Thank you so much for your looking into the articles!

I thought you might be interested in the latest numbers on the subject of matter:

Astrobiology Magazine

The WMAP team found that the Big Bang and Inflation theories continue to ring true. The contents of the Universe include 4% atoms (ordinary matter), 23% of an unknown type of dark matter, and 73% of a mysterious dark energy. The new measurements even shed light on the nature of the dark energy, which acts as a sort of an anti-gravity.

That's the kicker. The Higgs boson is part of the ordinary matter, only 4% - and is yet to be proven by Fermilab or CERN. The largest, dark energy, is stranger still because it is like an anti-gravity.

That's why the first article I linked to you about the possibility of an extra time dimension is stunning. If you are right and gravity propagates through an extra time dimension, it would explain why we cannot see dark energy in the laboratory but it is so prevalent in the "vacuum" of space. IOW, local gravity would appear in our dimension due to the presence of ordinary matter - but in the extra time dimension in the absence of ordinary matter.

That would bring the whole issue back to Einstein's marble of geometry, i.e. structure of space/time in multiple dimensions!!!

Just a thought to ponder, taking your speculation to another level...

This is very, very good, wwfb, IMHO. Add consciousness and free will into the mix and the "objects" could move themselves to the next state. Were it also possible, and I think that it is, for the "Mover" to be simultaneously within AND external to the system, then I believe "our" model would even better represent reality.

As you see, some of my thoughts DO go "bump" in the night. Speculation is "free" is it not? ... ;-}

There was a hyperstring model developed by a grad student, I think in NY, that used 12 dimensions rather than 11. The extra dimension was a second time dimension. The 12-D model went around the circuit for a while, but it and the author have seemingly dropped out.

The problem was having two large time dimensions. If you destroy causality, which this would do, then all the physical processes, physics quantities, lose their application and the new scientific reality we are building is impossible. If the second time dimension involutes back on itself right away then there is not much problem. In fact, some quantization of time becomes possible. A sort of high frequency resonance would exist depending on the size of the involution. If it is of the order of a picosecond, then events would be localized to the space of an atom. If it's bigger, then multiple atoms are involved and the whole structure becomes unstable.

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Ground-breaking work in understanding of time

Mechanics, Zeno and Hawking undergo revision