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Who is Peter Lynds? The question has been troubling the world of physics since articles began appearing in newspapers and websites around the world earlier this month claiming that Lynds, a 27-year-old college dropout from New Zealand, had developed a radical new theory of time. Those who had glimpsed Lynds' ideas - which a physics journal has agreed to publish - were predicting they would shake the science world to its foundations and would solve philosophical and mathematical conundrums that have puzzled the best minds for thousands of years. Some were already comparing the young author with Albert Einstein.

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Guardian Story

A couple days later, I see this Lynds guy in the Globe, saying the same thing and being called "the new Einstein" for it.

Fuckin' hell! If I'd thought to write up my "insight" in a paper, I coulda been famous too!

'Course, I'm not even remotely qualified to know whether this "insight" is full of crap or not. I'm no theoretical physicist, nor a mathemetician.

Aristotle: died, 322 BC, several instants before Peter Lynds was born.

However, this is not the best solution to the paradox.

[ 18 August 2003: Message edited by: rasmus_raven ]

What I've observed, though, since starting this job, is that the minutes are not constant. At my desk, there are three, and sometimes four clocks visible, and all of them say a different time--but it doesn't matter. It's always what time it is, regardless of what the clocks say. And also, not all minutes or seconds pass at the same rate of speed, or some minutes take longer than others.

Is this what the dude's talking about?

[ 18 August 2003: Message edited by: Lima Bean ]

Time was occurring way before anybody ever invented the concept of minutes or any measurement of time passing, and it's still the same time happening now. There is only one time, and it's always now...

Isn't time the fourth dimension?

[ 18 August 2003: Message edited by: Lima Bean ]

Leibniz and Newton independently came up with notational schemes for subdividing apparently continuous phenomena like time into pseudo-discrete units called "infintesimals". This became the basis for the branch of mathematics called "calculus" and involves considering quantities like "ds/dt" which is the limit value of the function s(t) as t approaches,but does not reach the value t. For ease of caculation, dt is considered to be zero, though it clearly can't be if we want to avoid a division by zero error, and "ds/dt" is calculated by a formula familiar to anyone who's taken an introductory calculus course.

The point is that ds/dt doesn't exist in physical reality, because no matter how arbitrarily close to zero we make "dt", there is an infinity of smaller dts.

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Originally posted by beluga2:
It's absolutely bizarre, but I was thinking the exact same thing as this Lynds character just a couple days before I first saw this story! I was pondering Zeno's Paradox, the one about Achilles racing a turtle and never catching up, trying to figure out why it was wrong. (Why I was pondering it I haven't a clue -- I haven't taken any physics courses in years.) Finally I muttered something like "That's easy! Time can't be divided into precise intervals like that -- there's no such thing as a precise instant in time!", and then forgot about it.

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Calculus can be used to disprove Zeno's Paradox by showing that the sum is finite (or convergent, as we math geeks or math-pretender geeks say).

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Originally posted by Sisyphus:
Leibniz and Newton independently came up with notational schemes for subdividing apparently continuous phenomena like time into pseudo-discrete units called "infintesimals". This became the basis for the branch of mathematics called "calculus" and involves considering quantities like "ds/dt" which is the limit value of the function s(t) as t approaches,but does not reach the value t. For ease of caculation, dt is considered to be zero, though it clearly can't be if we want to avoid a division by zero error, and "ds/dt" is calculated by a formula familiar to anyone who's taken an introductory calculus course.

The point is that ds/dt doesn't exist in physical reality, because no matter how arbitrarily close to zero we make "dt", there is an infinity of smaller dts.

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If I may be permitted a digression, I like to think of calculus in terms of incrementals or infinitesimals, so that if you talk to me about math stuff, you will often catch me talking of "volume increments" or "area increments", for example, rather than a more "mathy" perspective of just treating them as quantities all by themselves It's partly due to my chemistry and physics background that leads me to treat changing quantities as "actual" infinitesimals.

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From the article in the Guardian:
His big idea, put simply, is that time cannot be thought of in physical, definable quantities. To the uninitiated that may seem obvious, but to some physicists it's heresy. Current thinking in quantum mechanics relies on time being made up of tiny, discrete packages - just like light and energy.

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This part is true. In conventional quantum mechanics there's the notion of a "Planck time" - the smallest discrete time increment possible (see, there I go with my increments! ), which is about 10^-43 seconds. This, by the way, is not a coincidence as far as the Big Bang goes; since it is the smallest time increment possible, it means that QM says that we can't really talk about what happened between zero time and the 10 to the negative forty-third second after it.

However, it is my understanding that Planck Time and Planck Length arise out of studies of spacetime behavior near the Big Bang, and how spacetime collapses down to four dimensions from 10, 11, or 26 or whatever.

My basic problem with the paper is that Lynds seems to be mixing a hodgepodge of things together and incorporating some old, some new, concepts together and presenting the whole thing as revolutionary.

It can be shown without reference to any Planck Time at all that the uncertainty principle is valid both with respect to position/momentum complementarity and energy/time complementarity (what I mean is, it can be shown without use of the Planck Time that changing one of the two makes the other less accurate. Measure energy more precisely and the time interval over which to do it gets larger. Snapshot your energy in a specific time and the energy uncertainty goes through the roof).

[ 19 August 2003: Message edited by: DrConway ]

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i think the important issue here is "does this get me any closer to owning a time machine or being able to teleport?"

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This explanation is based on Mark Sainsbury's book "Paradoxes":

The paradox of the arrow is framed as follows. At any given instant, an arrow occupies a space equal to itself. Since an instant is like a point, of no duration, the arrow is therefore at rest. Wherefore the arrow never moves, because at every instant, it is at rest.

However, we don't need to accept that an arrow's being "at rest" at an instant entails that the arrow is at rest, period; we can say that the notion of being at rest must refer to a sequence of instants, not a single instant. We can define being at rest as follows: an arrow is at rest if it occupies the same space in each of a sequence of neighbouring instants; if it occupies a different space in neighbouring instants, it is in motion. So there is no paradox.

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Originally posted by rasmus_raven:
One can defeat Zeno's paradoxes without reference to the ideas of calculus, even while accepting the terms of the paradoxes.

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Well then you've done more reading than I have on that - I only ever learned how to treat them using concepts from calculus.

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The paradox of the arrow is framed as follows. At any given instant, an arrow occupies a space equal to itself. Since an instant is like a point, of no duration, the arrow is therefore at rest. Wherefore the arrow never moves, because at every instant, it is at rest.

However, we don't need to accept that an arrow's being "at rest" at an instant entails that the arrow is at rest, period; we can say that the notion of being at rest must refer to a sequence of instants, not a single instant. We can define being at rest as follows: an arrow is at rest if it occupies the same space in each of a sequence of neighbouring instants; if it occupies a different space in neighbouring instants, it is in motion. So there is no paradox.

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This seems to be a roundabout way of considering the frame-of-reference situation with respect to the paradox. In the arrow's frame of reference, it appears to be at rest but at each time increment, if all objects around it are displaced by some finite distance, then the arrow has moved in the stationary observer's frame of reference. (I'm cheating a little bit here, mind you, but this is to keep the physics simple)

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Damn it, where did I put volume IV?

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Only volume IV?! Get in line, buddy. I'm giving Gibbon a run for his money.

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At my desk, there are three, and sometimes four clocks visible, and all of them say a different time--but it doesn't matter. It's always what time it is, regardless of what the clocks say. And also, not all minutes or seconds pass at the same rate of speed, or some minutes take longer than others.

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Well, just so. Einstein at some point explained relativity thus:

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When a man sits with a pretty girl for an hour, it seems like a minute. But let him sit on a hot stove for a minute—and it’s longer than any hour. That’s relativity.

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For this, he got the Nobel Prize.

It's all a question of having the right press agent.

[ 20 August 2003: Message edited by: 'lance ]

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Sisyphus: The point is that ds/dt doesn't exist in physical reality

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[ 20 August 2003: Message edited by: satana ]

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Neither does "time", "distance", ... etc. They are all mental contructs our minds create to help us make sense of the world. These words, definitions, equations are not necessarily "reality" (another mental construct). Think of them as "tools".

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I am familiar with this perspective and find (particularly as I am taking another valiant, but certainly ultimate stab at Of Grammatology) that I have lost patience with it, though I used to argue the same thing after waking up from an Ayn Randian coma in my teens. The radical subjectivism (sometimes morphing into solipsism) that underlies statements of the type "All is but a mental construct" has served as fodder for undergraduate philosophical navel-gazing since long before I was a navel-gazing undergraduate. Time, mass, distance are all measurable and equivalent between equivalent inertial frames of reference, regardless of the observers' "mental constructs". The signifiers and their definitions are mental constructs, granted, but communicable between different interlocutors to the point that extremely subtle and precise predictions of experimental results can be made on the basis of generally-accepted definitions of these by people from different cultures in different experimental settings, using different paradigms. For example, the photoelectric effect and wavelike diffraction patterns are both observale whetther you consider light to be a wave or whether you consider it to be a particle.

Note that the above does not assume that any definition of said signifiers is anything but provisional and operational: it is in no sense "complete".

Edited to remove gratuitous brusqueness and unwarranted snippyness.

[ 20 August 2003: Message edited by: Sisyphus ]

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Originally posted by DrConway:

...In conventional quantum mechanics there's the notion of a "Planck time" - the smallest discrete time increment possible (see, there I go with my increments! ), which is about 10^-43 seconds. This, by the way, is not a coincidence as far as the Big Bang goes; since it is the smallest time increment possible, it means that QM says that we can't really talk about what happened between zero time and the 10 to the negative forty-third second after it.

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I wonder: does Quantum Mechanics really claim that "Planck Time" is the smallest time increment possible, or just that it is the smallest unit of time that has any possible meaning to us? Perhaps time is continuous rather than discrete, or perhaps smaller increments could exist (in theory), but how could we possibly know? The hypothetical smaller units of time would be completely unobservable and have no meaning to us, because any increment of time smaller than "Planck Time" could not reveal any change, even in a photon travelling at the speed of light.

Maybe the idea is analogous to that of "absolute zero" temperature? Perhaps it could get colder and colder infinitely, but how could we know? Once Hydrogen freezes there can be no observable effect of any theoretical "lower" temperature, so you couldn't even prove the existance of it.

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Perhaps it could get colder and colder infinitely, but how could we know? Once Hydrogen freezes there can be no observable effect of any theoretical "lower" temperature, so you couldn't even prove the existance of it.

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Problem with that idea is that temperature is a measure of the average kinetic energy of the atoms of whatever has the "temperature", so I think two limitations apply:

1) If there is no matter present in a volume then the concept "temperature" has no significance.

2) Once the kinetic energy is zero, unless there is a physically plausible way to achieve negative
1/2mv*v (negative mass?, negative V*V (keep an i out for me willya? )?) I don't see how it can be.

Personally, I think Krishnamurti has the correct statement of the problem, which is that all movement of the mind is in the past so that we are always trapped in the past by thought. Any attempt by thought to apprehend the eternal (or momentary) "now" will fail, just as will any attempt to catch it on a device, which would only be, like the brain, another way of recording the past.

[ 20 August 2003: Message edited by: Sisyphus ]

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Originally posted by Sisyphus:
As a note, DrC, we all treat the infintesimals as "real" when we have to compute with them and treating ds/dt as a simple fraction, while egregiously sloppy to a mathematical purist, comes in handy all the time .

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What it really means, though, is that when my BF says "you're late!" I can say "no I'm not, there is no 'late;' there is only one time and it's now, and I'm here, so it's impossible that I could be late" and that'll be the end of that discussion!

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Anyone interested in a great and hugely entertaining fictional meditation on Zeno's paradoxes might want to find a copy of Italo Svevo's novel The Confessions of Zeno (1923). (Svevo was his Italian name; a citizen of Trieste, he is also known by his Austrian name, Ettore Schmitz. Many consider his discovery the greatest thing that James Joyce ever did.)

The funniest metaphors in the novel are plays on the paradoxes, on the apparent impossibility of motion through time and space, or at least on the human self-consciousness that seems to reveal/create that apparent impossibility.