I just came across this very interesting article:

http://www.eurekalert.org/pub_releases/2003-07/icc-gwi072703.php

The author's conjecture is that there is no precise static moment underlying a process of dynamic motion. In essence, all measurements take place over an interval of time and as such space.

In brief, if you want to measure the position of an object at time -10.00 seconds, what you are in effect measuring is it's position during the interval 10.000000 seconds and 10.009999 seconds. Furthermore, no matter how small an interval of time you choose you, the object will always be in motion over that period and if you could measure it in a static position it would have to remain static( it could not keep moving).

I found this theory to be quite convincing, so I thought I'd toss it out there to see if anyone has any other views.

Cheers!

If you had a device that, say, measured the strength of the magnetic field, or some other thing related to motion, then the device could presumably have an instantaneous readout.

To carry the magnetic idea further:
Let's say that there is an electron at the origin. All motion is measured with respect to the electron. One way to measure the position of a particle is to measure the electric field strength at the particle. On way to measure the velocity of a particle is to measure the magnetic field strength at the particle. Neither one requires a differential measurement, just a slightly different slant on the notions of position and velocity.

Let's say that there is an electron at the origin. All motion is measured with respect to the electron. One way to measure the position of a particle is to measure the electric field strength at the particle. On way to measure the velocity of a particle is to measure the magnetic field strength at the particle. Neither one requires a differential measurement, just a slightly different slant on the notions of position and velocity.

That's sounds an awfully a lot like Heisenberg's uncertainty principle. as delta t -> 0, delta E -> INFINITY.

Originally posted by ryans
That's sounds an awfully a lot like Heisenberg's uncertainty principle. as delta t -> 0, delta E -> INFINITY. I didn't know that was HUP? I thought HUP was: [X,P]=ihbar. Anyway, I'm missing the part in my post that looks like Δt -> 0 => ΔE -> infinity. In fact, I didn't mean to stir up any QM sentiments; I was considering the electron and particle of interest as classical.

Upon closer examination, my post suggests a contradiction to Δt -> 0 => ΔE -> infinity. I am saying that, in literally no time at all, the velocity can be determined. Are you saying that you have a problem with this based on Δt -> 0 => ΔE -> infinity? Well, again, I was making a classical arguement, and I have been told that Δt -> 0 => ΔE -> infinity is not really a strict consequence of QM.

Quote from the link I provided above:
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.
End QuoteL


Contrarian:I probably didn't make myself very clear.The point that the author of the paper (Lynds') makes is that finding the velocity in literally no time at all is not the same as finding the velocity at one point at time and space.

Any measurement will have a take place between two times say between 1.00000000 sec and 1.0001000000 sec and, hence will involve an object moving between two different points. In other words we can never say that a moving object is at a particular point in space or time, but rather is travelling between two points at all times.

From this relatively simple seeming idea, he derives some fairly far-reaching consequences about time and space, not to mention producing a solution to a couple of Zeno's paradoxes.

Cheers,

That seems like an anthropocentric view to me. Just because we can't make a measurement in a certain way, doesn't mean that that certain way does not exist.

Hi errandir!

I am also a bit leery of this kind of approach, but I have to admit it seems logical.

A moving object is always moving by definition, therefor, arguments based on that object being precisely at a particular point in space at a particular point in time may be based on a flawed assumption, to wit, that there is a static point underlying a dynamically moving system.

Try as I might, this seems to hold up, logically.

I recommend the link above and also: www.peterlynds.net.nz

the author's website, with some intriguing additional information.

Cheers!

I don't think that a perfectly logic idea is necesarily true. I also agree that it seems logical, but I don't think that I agree with the premise.

I agree with errandir, and the mathmatician in the article who mentioned calculus:
the basic concept of calculus is that althoguh we, with necessarily inaccurate measuring devices, cannot measure a value at a single moment of time, does not mean that that single moment doesn't exist - we can takes our innaccurately measured single point, which Lynds correctly points out can only be an interval, a tiny section of the independent variable's (ie. time's) domain - delta t - and let it approach a limit which can exist despite the fact that we cannot reach it, obtaining a measurement at a single point in time. This was surely the great achievement of differential calculus.

Hi guys!

To errandir: A perfectly logical statement should be true IMO if it is factually accurate, and I can't seem to argue with either part of the theory.

To speeding electron:Calculus while interesting, does not really deal with the objection, IMO.

Taking the limit of something as it approaches infinity or zero or whatever is not the same as it actually reaching zero or infinity. In fact, this is not possible.

IOW, saying that an interval of time or distance is something which can approach zero, but never reach it is different from saying that an interval of time or distance can be a single point. As such, theories based on objects being at specific points and times may be based on this may be engaging in a logical fallacy ie. the limit as x goes to a is equivalent to x=a.

I have a grudging respect for this position, despite my misgivings, although I have trouble following some of Lynds' conclusions- any suggestions?

Cheers!

Lynds also points out that in all cases a time value represents an interval on time, rather than an instant.

Why does this have to be?

Sure with our methods of measuring instances we will never know the exact position of a moving object but that does not mean it doesn't have a precise position as is quoted below!!!

Consequently there is no precise moment where a moving object is at a particular point.

Hi John!

John:

Why does this have to be?

Sure with our methods of measuring instances we will never know the exact position of a moving object but that does not mean it doesn't have a precise position as is quoted below!!!

contrarian:

It seems to me that it is one thing to treat an object as though it is located at a particular point(assuming a point is an infinitesimally small bit of space) and something completely diiferent to say it actually is at that particular point.

The best analogy I can come up with is the difference is between watching a movie and experiencing real life. In a movie the picture is actually composed of imperceptibly many frozen frames strung one after the other, whereas real life is one continuous view of what is actually there.

I can see how these two conceptions could lead to some very different ideas about reality, although I can't follow many of the author's conclusions so far.

Cheers,

Originally posted by contrarian
A perfectly logical statement should be true IMO if it is factually accurate, ...I don't understand what you mean by a logical statement being factually accurate. A logical statement itself has nothing to do with fact.

If it rains, then the ducks come out.
There are no ducks coming out.

Therefore, I logically conclude that it is not raining based on the ducks.

I made this perfectly logically conclusion based on an axiom and a statement about the state of affairs. Either one of these could be false, so the perfectly logical conclusion could in fact be untrue, even though it is based on sound logic. What I'm arguing is that Lynd's axiom may not be (I don't see any good reason why it should be) true. I don't see any conclusive experimental evidence that point events do not exist. In fact, as precission technology progresses, we see evidence that the contrary is true: the more able we are to measure to finer detail, the finer detail we observe, which seems to be in direct contradiction (inductively speaking, another logical tool) to Lynd's axiom.




Originally posted by contrarian
... saying that an interval of time or distance is something which can approach zero, but never reach it is different from saying that an interval of time or distance can be a single point.I totally agree with this, but why would you even consider the issue of an interval of time or space being a single point in the first place. That doesn't even make sense. If this is what Lynd's was saying, then I misunderstood, and I agree with the axiom. I thought Lynd's was saying that points don't exist, not that intervals can't be points.

Consequently there is no precise moment where a moving object is at a particular point.

How about if u just look at this sentence again carefully (p.s. the arrow paradox was proven to be not paradox at all in another thread anyway so don't believe that)

What it says is that the object was never at any point !!!

no precise moment = never !!!

Therefore it has to be untrue by experimental evidence showing that particles do actually exist in space AND time.

very philosophical, excuse me!

Originally posted by errandir
I don't understand what you mean by a logical statement being factually accurate. A logical statement itself has nothing to do with fact.

If it rains, then the ducks come out.
There are no ducks coming out.

Therefore, I logically conclude that it is not raining based on the ducks.

I made this perfectly logically conclusion based on an axiom and a statement about the state of affairs. Either one of these could be false, so the perfectly logical conclusion could in fact be untrue, even though it is based on sound logic. What I'm arguing is that Lynd's axiom may not be (I don't see any good reason why it should be) true. I don't see any conclusive experimental evidence that point events do not exist. In fact, as precission technology progresses, we see evidence that the contrary is true: the more able we are to measure to finer detail, the finer detail we observe, which seems to be in direct contradiction (inductively speaking, another logical tool) to Lynd's axiom.

I totally agree with this, but why would you even consider the issue of an interval of time or space being a single point in the first place. That doesn't even make sense. If this is what Lynd's was saying, then I misunderstood, and I agree with the axiom. I thought Lynd's was saying that points don't exist, not that intervals can't be points.

Hi errandir!

In terms of logic fact and truth, I was trying to say that if an argument is correct in terms of it's facts and its' logic then it must be true. I apologize for the confusing wording. I think we agree though.

In terms of your point in re: the finer detail producing evidence of points, I don't think I follow your point here. A more precise method of measurement SEEMS to produce only a more precisely defined interval not a specific point in space.

You may have a more accurate idea of what Lynds is getting at than I do. I can follow his idea of time being a flowing property and his solution of Zeno's paradoxes, but so far I haven't been able to make sense of the broader implications.

Cheers!

Originally posted by contrarian
In terms of your point in re: the finer detail producing evidence of points, I don't think I follow your point here. A more precise method of measurement SEEMS to produce only a more precisely defined interval not a specific point in space.Yes, and I agree that there is no conclusion made (see below), save by induction alone. But, without induction, we would all be lost.




Originally posted by contrarian
You may have a more accurate idea of what Lynds is getting at than I do.Actually, I must confess that I'm not paying very much attention to the Lynd's factor, and, IMO, we can do without him. It was OK for a thread seed, but I think we can meaningfully carry the discussion without him. The primary issue on the table, as I see it, is whether or not points (events) exist. My basic claim is sort of a cop out. I don't think that this is a question for physics, because I don't believe any experiment will ever be able to make such a conclusion one way or the other. To entertain the philosophical aspect, though, I will appeal to the TV analogy:

Let's say that the video camera periodically exposes photosensitive material to light. Each exposure represents a frame. The frequency of exposure represents the resolution of the time scale. So, is this frequency limited by the fact that an instant in time does not exist? Or, is it limited by technology (sensitivity of the material, shutter speed and what have you)? I'm not trying to say that, just because we can measure arbitrarily small time intervals, that these intervals are themselves instants. What I am trying to say is that, since the intervals are arbitrarily small, then, if there is no such thing as an instant in time, we should start to observe multiple redundancy for exposures above some frequency. But, even assuming we have a sensitive enough material, and a fast enough shutter, it would still be hard to determine such redundancy, because, as the frames get arbitrarily closer together in time, they get arbitrarily closer together in likeness, and, the complexity of comparison would have to scale with the frequency to some order.

Probably a more practical approach would be to attempt to observe the waveform of a gamma ray. Then, when this is accomplished, try to observe the waveform of something of even higher frequency. Of course, this is still just an inductive approach. What I would be interested in hearing is at what frequency we should start observing evidence that time does not exist in instants.

If Peter Lynds is talking about physics rather than mathematics, it seems to me that he is merely stating that at some very small scale, calculus does not provide an exact model for moving objects. If this is what he is saying, it does not seem so profound. In some sense, we have always known that mathematics describes an ideal rather than a reality.

When continuous mathematical equations describe the motion of a zero-dimensional point, calculus can be used to describe a specific position at each specific instant in time. I hope that Lynds is not claiming that calculus is invalid, which seems preposterous.

From the point of view of pure mathematics, I have always considered the Zeno motion paradoxes absurd. The Zeno point of view does not describe the reality of a race between Achilles and a tortoise or the motion of an arrow. Calculus does an excellent job of describing the motions of Achilles and the tortoise, including an instant in time and a point in space when the tortoise is overtaken. Experimental evidence is on the side of calculus.

I never thought of any real object as being a zero-dimensional point, so it does not bother me that calculus cannot provide an exact description of the motion of any physical object. A minimum quantum of time and/or distance does not seem any worse than a minimum quantum of energy. My intuition is not comfortable with either notion, but neither concept seems totally outrageous in view of the experimental evidence supporting Quantum Theory. Quantized time and/or space seem quite compatible with the Uncertainty Principle.

Has anybody here read and done a careful analysis of the Lynds article?

Is he claiming that calculus cannot even model ideal motion? Is he claiming that the existence of a zero length interval of time (an instant) precludes the possibility of motion even in the ideal world of mathematics? This would be a profound claim.

BTW: There have been numerous articles refuting the notion of a flow of time from past to future, which might very well be an abstraction in our minds.

Originally posted by Dinosaur
Quantized time and/or space seem quite compatible with the Uncertainty Principle.I am no experimentalist, but you seem to contradict the theory that I understand. According to such theory, upon a measurement of position, the system collapses to a position eigenstate, which is precisely a point in space. All uncertainty says is [X,P] = ihbar, so, after this measurement, you have no idea what the momentum of the particle is.

Errandir: I am sorry that I mentioned the Heisenberg Uncertainty Principle, which might result in this thread being led far from the concepts proposed by Lynds.

Your post seems to say that a position measurement makes momentum totally unknown, which is not what the HUP states. This is only true if the position measurement is exact. The HUP states that the more precise the position of a particle, the less precise the momentum & vice versa.

There is at least one thread that discusses the HUP. Discussion of the HUP should be posted there or perhaps a new HUP thread should be started.

This Lynds concept seems too interesting on its own to be lost in a maze of HUP discussions.

Originally posted by Dinosaur
Your post seems to say that a position measurement makes momentum totally unknown, which is not what the HUP states. This is only true if the position measurement is exact.Like I said, I'm no experimentalist, but the <i>HUP</i> (as I was taught) doesn't say that an exact position measurement is impossible. Furthermore, the Copenhagen interpretation says that a position measurement itself causes the state to collpase to a position eigenstate (and therefore gives the position with utmost certainty, to the limit of the resolution of the measuring device).




Originally posted by Dinosaur
This Lynds concept seems too interesting on its own to be lost in a maze of HUP discussions. Well, then don't use HUP in support of your arguement.

Dinosaur

Here is a critique of Lynds based on his use of reductio ad absurdum.

http://philsci-archive.pitt.edu/archive/00001333/01/ZENO.html

Here is another critique:
http://www.thequantummachine.com/analysis.php

Here is a partial response by Lynds:
http://www.peterlynds.net.nz/notes.html

I personally don't feel either of these critiques are that effective, but maybe you'll have a different opinion.

In terms of your point in re calculus, I think one of the consequences of Lynds theory is that it makes one question the use of infinitesimals when discussing physical properties.

Sum of infinite series and other uses of calculus may provide the mathematically correct answers, but that is not equivalent to stating that this is a "true" conception. In fact, infinity is by definition an unreal quantity.

Now, I am unable to really follow most of the ideas Lynds puts forward, but they are interesting, anyway. Hopefully, at some point the issue will resolve itself in my head. :)

Cheers!

Originally posted by contrarian
... infinity is by definition an unreal quantity.What dictionary are you using?

Sorry, I should've said an undefineable, unmeasurable quantity

If you are trying to suggest that infinity (and/or zero) doesn't exist (outside of math), then I disagree. For instance, we don't know that the universe is not infinitely expansive. We don't know that there are not places where there is nothing. As a matter of fact, any set of two mutually exclusive properties demonstrates definitively that zero exists. And there is no way to prove that infinity does not exist.

Originally posted by errandir
For instance, we don't know that the universe is not infinitely expansive. We don't know that there are not places where there is nothing.

I dont believe that infinity exists in our universe. The idea exists alright but not physically. The universe cannot be infinite in size if it started out with a finite size (at the big bang). Most physicists now believe there to be a maximum size to the universe.

Contrapositively, if the universe has infinite size, then it started out with a non-finite size. This still doesn't help conclude the validity of infinity, since we don't really know either of the two, one way or the other.

I'm a bit surprised that Lynds suggestions are controversial , not being a physicist. I understood that in the orthodox view spacetime is viewed as being a continuum, which seems to be basically what Lynds is saying.

I also understood that Zeno's paradoxes proved that Lynds conclusion about the non-existence of 'instants' is correct long before Lynds was born. After all, nothing can happen in one instant, so nothing can happen in a series of instants. Instants therefore don't make sense. This is precisely what the race between Achilles and the tortoise shows to be the case.

Why does anyone argue for 'instants'?

Canute: People consider instants a reasonable notion because of mathematical equations, particularly calculus. Instantaneous velocity and position at an instant of time are self consistent concepts. Furthermore, calculus does an excellent job of modeling classical reality. When 3D position is described using parametric equations of a 1D time variable, the conclusions are usable for many practical purposes. Even without calculus, such equations can describe instantaneous velocity.

The above is the reason that the quantum world seems so weird. It is counterintuitive.

Calculus does a good job of explaining the Zeno paradoxes, when it uses limit concepts to add up an infinite series. In reality Achilles overtakes the tortoise with no problem and seems to do it at the point predicted by the mathematics.

I have not been able to fully understand the Lynds point of view, but agree with the concept that instants of time do not exist in the real world. They certainly do not seem to occur in the quantum world, and we cannot measure instantaneous velocity in the classical world. We can only measure time intervals and approximate the motion that takes place in intervals.


I cannot say more until (or if) I understand Lynds better than I do now. I consider his view silly in the mathematical mindscape, but I do not think he is talking about that arena.

Dinosaur

Quite agree. Instants have a mathematical existence but should not be reified. That seems to be Zeno's very point.

Originally posted by errandir
Contrapositively, if the universe has infinite size, then it started out with a non-finite size.

Agreed

This still doesn't help conclude the validity of infinity, since we don't really know either of the two, one way or the other.

No, but it concludes the invalidity of infinity as I have just said that the universe started out finite.

Originally posted by John Connellan
... I have just said that the universe started out finite. How do you know this? On what do you base this?

Originally posted by errandir
How do you know this? On what do you base this?

The big bang theory states that the universe was a finite size (had a beginning and so time is also finite).

Originally posted by John Connellan
The big bang theory states that the universe was a finite sizeWell, I don't know really anything about the big bang theory. Could you cite me a reference?

A thought.

If there are 'instants' then the slowest possible speed of motion is one fundamental quanta of distance ('qd') in one instant.

Let's now race Achilles against a tortoise. To make the race really unfair the tortoise must go as slow as possible. In each instant of time it will travel one qd.

Then let's make Achilles go much faster, say 10^10 qds per instant.

In any instant Achilles is smeared over 10^10 qds, and is therefore nowhere in particular.

The notion of 'instants' of time therefore makes no sense.

Any objections?

Originally posted by Canute
A thought.

If there are 'instants' then the slowest possible speed of motion is one fundamental quanta of distance ('qd') in one instant.

Let's now race Achilles against a tortoise. To make the race really unfair the tortoise must go as slow as possible. In each instant of time it will travel one qd.

Then let's make Achilles go much faster, say 10^10 qds per instant.

In any instant Achilles is smeared over 10^10 qds, and is therefore nowhere in particular.

The notion of 'instants' of time therefore makes no sense.

Any objections?

An instant in quantum (Planck) terms is the time it takes light to cross the Planck length. Do u understand now?

Originally posted by errandir
Well, I don't know really anything about the big bang theory. Could you cite me a reference?

Sure,
any of Stephen Hawking, Roger Penrose, and Robert Gerochs papers will testify to the existance of a singularity at some point in the universes past.

Remember the big bang implies a start of time and since time and space are essentially connected (spacetime) then this in itself implies the creation of space.

Originally posted by John Connellan
An instant in quantum (Planck) terms is the time it takes light to cross the Planck length. Do u understand now?
What's that got to do with what I posted?

Originally posted by John Connellan
The big bang theory states that the universe was a finite size (had a beginning and so time is also finite).

the big bang theory does not make any assertions about the finiteness of the universe.

Originally posted by Canute
What's that got to do with what I posted?

Think a little. What I said means that an instant is an incredibly short period of time. Such a short period that traversing 10 planck lengths in an instant is impossible coz u are going 10 times faster than light.

The slowest speed would be traversing 1 planck length in 10^10 instants not the other way round!

Originally posted by lethe
the big bang theory does not make any assertions about the finiteness of the universe.

If the big bang was indeed a singularity then the universe had to be finite in size. If we can speculate on temperatures reached just after the big bang then we must also conclude that the universe was finite. If we can estimate the age of, or the amount of matter in the universe then it must be finite. If we say that there is only a finite amount of energy in the universe then it must be finite.

Originally posted by John Connellan
Think a little. What I said means that an instant is an incredibly short period of time. Such a short period that traversing 10 planck lengths in an instant is impossible coz u are going 10 times faster than light.

The slowest speed would be traversing 1 planck length in 10^10 instants not the other way round!
Please read my post again, you're misunderstanding it. Forget about how long an instant is, or Planck lengths, it doesn't matter what units you use, its the principle that matters. Just assume that they're as small as the can be.

Originally posted by Canute
Please read my post again, you're misunderstanding it. Forget about how long an instant is, or Planck lengths, it doesn't matter what units you use, its the principle that matters. Just assume that they're as small as the can be.

OK speed is distance/time right?!
Get rid of Achilles and replace it by light (the fastest thing).
The tortoise can be anything else. As u say it doesn't matter what units u use so we wont mention Plancks anymore. The smallest distance there can be is defined by how far light travels in the shortest tme, u agree? The shortest time is how long it takes light to travel the shortest distance u agree? Remember space-time is defined by light!

This means that in an instant, light will only travel this distance. Anything else will not have travelled! Even with a very fast object it will take a good few instances before we can tell that it has moved any distance. Nothing is spread out here!

If I am still not answering ur question can u please rephrase it with a different analogy or something?

John

You keep changing the conditions of my thought experiment. Why not try it as written? The upper speed of light is not an issue, assume that there isn't one. Make the turtle go as slow as possible, and quantify how slow that is in finite units of your choice, one fundamental unit of distance per instant. Then study how Achilles manages to go faster. Strange problems arise, as Zeno asserted.

This suggests, as Lynd's argues, that it's illogical to suppose that there can be motion within an instant.

OK I thought u were talking about the quantisation of space-time. This is actually Zenos paradox. I thought u meant the smallest unit of time and the smallest unit of distance. Are u saying it still works by taking any time or distance? Im gonna think about it now. BYE

Sorry, I should have made that clear.

I have concluded that there cannot be motion within an instant as u say. This also implies that there cannot be motion within a Planck length as I have always assumed. Motion is a series of 'quantum jumps' through space and time. Is that better?!

Hmm. Isn't it better to assume that spacetime is a continuum rather than that motion a series of quantum jumps?

Originally posted by Canute
Hmm. Isn't it better to assume that spacetime is a continuum rather than that motion a series of quantum jumps?

No, cant we assume that space-time is quantised as well as motion or am I missing something. That would be my preference. I have always assumed space-time to be quantised intuitively even as a kid!

Originally posted by John Connellan
No, cant we assume that space-time is quantised as well as motion or am I missing something. That would be my preference. I have always assumed space-time to be quantised intuitively even as a kid!
But then how do you deal with Zeno's arguments? How can motion be a jumping from place to place, where is the arrow when it is between places?

To put it another way. If the turtle is in one place at one instant, how can Achilles be smeared across a large number of places in that same instant, and thus catch up?

Originally posted by Canute
To put it another way. If the turtle is in one place at one instant, how can Achilles be smeared across a large number of places in that same instant, and thus catch up?

I can only guess - because the turtle does not move across as much planck lengths in any time interval than Achilles. In other words, the turtle will be at a location for a few 'intances' while Achilles quickly closes in.

Originally posted by John Connellan
I can only guess - because the turtle does not move across as much planck lengths in any time interval than Achilles. In other words, the turtle will be at a location for a few 'intances' while Achilles quickly closes in.
That doesn't work. Achilles [I]must[I] move across more than one fundamental (and indivisible) unit of length in one instant if he is ever to catch up. Therefore he cannot ever be at any particular place, and his position in each instant must be something like a wavefunction rather than a precise location.

Originally posted by Canute
That doesn't work. Achilles [I]must[I] move across more than one fundamental (and indivisible) unit of length in one instant if he is ever to catch up. Therefore he cannot ever be at any particular place, and his position in each instant must be something like a wavefunction rather than a precise location.

Of course it works! The turtle stays in the same place for more instances so Achilles catches up. Read again!

Originally posted by John Connellan
Of course it works! The turtle stays in the same place for more instances so Achilles catches up. Read again!
But we have defined the speed of the tortoise as being one unit of distance per instant. That's as slow as a turtle can possibly go without stopping. You can't solve the problem by making him go even slower, he can't.

In other words, it's impossible for anything to go slower than one (indivisible and fundamental) unit of distance in one (indivisible and fundamental) instant. Nothing (travelling at a constant speed) can go slower than that.

Originally posted by Canute
But we have defined the speed of the tortoise as being one unit of distance per instant. That's as slow as a turtle can possibly go without stopping. You can't solve the problem by making him go even slower, he can't.

In other words, it's impossible for anything to go slower than one (indivisible and fundamental) unit of distance in one (indivisible and fundamental) instant. Nothing (travelling at a constant speed) can go slower than that.

No, ur big misunderstanding is that quantised motion cant involve stopping! Thats exactly what its all about. There are jumps between each Planck length and so the turtle stays in that 'cell' so to speak for more 'instances' than Achilles. If motion were continuous then u are right but for quantised space-time, motion cannot be continous but a series of steps. Think of life as one large motion picture where the units of instances (planck time) are so small that we cannot yet detect its quantised nature even experimentally.

Originally posted by John Connellan
No, ur big misunderstanding is that quantised motion cant involve stopping! Thats exactly what its all about. There are jumps between each Planck length and so the turtle stays in that 'cell' so to speak for more 'instances' than Achilles. If motion were continuous then u are right but for quantised space-time, motion cannot be continous but a series of steps. Think of life as one large motion picture where the units of instances (planck time) are so small that we cannot yet detect its quantised nature even experimentally.
If you're assuming that constant motion is a series of stop-start steps then you're right. But I hope you're not going to tell me that anyone believes anything as illogical as that.

Originally posted by Canute
If you're assuming that constant motion is a series of stop-start steps then you're right. But I hope you're not going to tell me that anyone believes anything as illogical as that.

U have to believe in 'steps' if u believe in quantisation of both space and time as steps are implicit in these theories.

I am afraid I DO believe in these theories and I suggest u do too!

Originally posted by John Connellan
U have to believe in 'steps' if u believe in quantisation of both space and time as steps are implicit in these theories.

I am afraid I DO believe in these theories and I suggest u do too!
I agree with the first sentence but I definitely don't with the second. In fact I think that such theories are completely self-contradictory for the reasons I've given and which Zeno gave a lot earlier. You may be right of course, and me wrong, but I don't have any reason to think so yet. As far as I know yours is the unorthodox opinion, but to be honest I'm not quite sure what the orthodox opinion is on this one.

regards
Canute

Fair enough, each to their own opinion. All I know is that I am comfortable with quantisation and always have been from an early age. We will just have to wait for experimental evidence I guess:o