Quantum Zeno?

Most recent answer: 10/22/2007

Q:
Hi. I’ve long wondered about this and would like your answer/opinion from a physics perspective: Some object (my finger or a bacteria, whatever) moves a finite distant from point a to b. Does that object move (jump) through a finite number of indivisible spaces, much like a dot moving across a computer screen from pixel to pixel (the dot cannot be in between pixels)? Or does the object move in a continuous flow across the whole distance? Logically, it must jump through some finite indivisible spaces, otherwise we can argue it would become an infinite distant and the object would never get to point b. This is starting to sound a bit like Zeno’s paradox, but shouldn’t, and converging series or some time answer certainly won’t satisfy me. Actually if an object does not move by "jumping" through indivisible finite spaces then I could use that to argue that time does not exist (which I don’t think it does anyway, but not because of this line of thought). Perhaps there is a better quantum answer that removes the "logic" and can better answer my question? Thanks.
- Brian (age 29)
Australia
A:
Actually, I should be careful about the name- the ’quantum Zeno’ effect is something different

In any standard formulation of either classical or quantum descriptions, space and time are fully continuous and the object moves in a continuous way. You say that that’s illogical, but I can’t respond to that claim without knowing your line of reasoning. The little bit that you give seems to simply ASSUME the answer, rather than demonstrating it from agreed-upon postulates.

There is one possible paradox, but it could not have been known to Zeno. Standard attempts to combine General Relativity and Quantum Mechanics lead to infinite answers for all sorts of simple quantities, unless one adds an infinite number of carefully adjusted special new parameters to the theory. Among the attempts (most prominently, String Theories) which try to fix that problem, many involve some breakdown of the idea of continuous space-time on a very small scale. That does not mean, however, that it will be replaced by a set of discrete lattice points of the type you suggest, although some people are trying to make theories of that type.

Mike W.

One buzzword in the field about space and time at the very very very small scale (or very very high energies) is "Quantum Foam", trying to describe what space and time would be like if it is all bent around very small local density fluctuations.

The lattice approach is championed by Steven Wolfram of Mathematica fame (see "A New Kind of Science"). Not everyone is convinced of this line of reasoning, however -- there is no experimental evidence to believe in a discrete grid of space and time.

Tom

(published on 10/22/2007)