Sam
2003-09-24 00:24:38 |
New answer to Zeno's Paradox
Hey, I don't know if this is the right place to post these sorts of topics, but I thought you all might be interested in this.
A previously unknown, not-college educated physisist has recently made huge waves with his new theory on time. He has written two srticles on it and one of them deals directly with Zeno's paradox. The solution that we had all been told (Zeno was wrong 'cause he didn't know calculus) may well be wrong, and it could just be that we have an incorrect view of time. Lynds, the guy, says that it simply doesn't make sense to ask where something is at a specific moment in time, because time doesn't have any "moments" in it, and things that are moving aren't in any specific position at any specific time.
Anyways, just thowing that out there, as so many paradoxes and logic puzzles seem to be based on the fact that we can ask where something is at any time.
http://philsci-archive.pitt.edu/archive/00001197/02/Zeno_s_Paradoxes_-_A_Timely_Solution.pdf |
TomM
2003-09-24 12:19:28 |
Re: New answer to Zeno's Paradox
That relates to the Heisenberg Uncertanty Principle and the fact that the mathematical models used to describe the physical world do not match it perfectly. (E.g. Newton's laws are close enough in most cases, but there are situations in which they "break down" and you need to switch to Relativity or Quantum Mechanics).
Most puzzles and paradoxes are based on the mathematical models, or on "pure mathematics. Real Physics, especially on the Quantum Mechanics level need to take Heisenberg into consideration: if you pin down one parameter too closely, there is a paired parameter which can vary far too greatly. The most common of such paired parameters are time and position (location in space): the same two parameters that your synopsis indicates.
At the moment I am on a library computer and cannot read *.pdf files. I'll take a look at the article from my own computer later. |
Sam
2003-09-25 11:50:46 |
Re: New answer to Zeno's Paradox
Indeed, with most puzzles of this sort to mathematical answer is the one expected, as it's rather a bore when know-it-alls start telling you "you can't split quarks" or whatever when dividing things by infinity.
In this case though it's interesting because people say, Zeno's paradox seems to make sense, so why *does* Achillies pass the Tortois? At which point people normally bring in calculus as the real-world answer. This answer, though, is instead telling us that the entire question makes no sense, as is is a contradiction in terms to say "where is Achillies at time T?" |
Alan
2003-09-25 16:12:01 |
Re: New answer to Zeno's Paradox
I read that and I have a lowcomprehending of what was being said/portrayed (I did understand a good portion of it though) and I must say that was very interesting to read. I just must ask this. Was one of the concepts that was being portrayed that nothing is relative to any other thing? Or that space and time can't be relative to eachother. |
Sam
2003-09-25 19:03:38 |
Re: New answer to Zeno's Paradox
Though I can't pretend I understood it all myself, I think that's it's neither of those things. Rather I think he is saying that there is no such thing as an instance in time, only intervals, and that if it were a series of instances, motion would be impossible:
"Time enters mechanics as a measure of interval, relative to the clock completing the measurement.
Conversely, although it is generally not realized, in all cases a time value indicates an interval of time, rather than a precise static instant in time at which the relative position of a body in relative motion or a specific physical magnitude would theoretically be precisely determined.
...
[if that were not so] the relative position of a body in relative motion or a specific physical magnitude, although precisely determined at such a precise static instant, it would also by way of logical necessity be frozen static at that precise static instant. Furthermore, events and all physical magnitudes would remain frozen static, as such a precise static instant in time would remain frozen static at the same precise static instant: motion would not be possible." |
TomM
2003-09-26 19:00:17 |
Re: New answer to Zeno's Paradox
Like the two of you, I can't pretend to have understood it all, but what I got out of it was that Zeno was trying to point out the difference between the real world and a mathematical model of the world by showing that the mathematical model could not explain motion.
The invention of calculus allowed the mathematical model to catch up with the real world (thus creating the science of Physics).
But Quantum Mechanics returns us to Zeno's old questions, but with a twist. The mathematics (calculus) are there to accomodate motion, but the experimental "real-world" data is what seems to be denying it now. |
