Zeno's Paradox Considered Federal Criminal Case

ohwilleke · Dec 22, 2004

This case:

http://pacer.ca10.uscourts.gov/pdf/03-2243.pdf

presents an interesting application of Zeno's paradox (i.e. how can you get from point a to point b despite the fact that you must cross half the remaining distance to get there an infinite number of times), in the context of an individual who fled an immigration check point in his car.

properphysicist · Feb 2, 2005

According to Quantum Physics space is discrete, not continuous. i.e. there are a certain finite number of intervals of space between a and b each of which is either crossed or not. Space is discrete on a very small scale, therefore, macroscopically speaking, space appears to be continuous.

Thus, Zeno's paradox does in fact not exist.

chroot · Feb 2, 2005

properphysicist,

Quantum mechanics says nothing at all about the discreteness of space.

- Warren

Chronos · Feb 3, 2005

For a logically rigorous discussion of Zeno's Paradox:
http://faculty.washington.edu/smcohen/320/zeno1.htm

properphysicist · Feb 3, 2005

chroot, yes you're right, it talks about discrete energies of bound particles. I assumed there was something about space in there too.

perhaps I'm thinking of string theory. if that's also wrong then what does say space is discrete because I thought that was the case.

Canute · Feb 3, 2005

As far as I can tell there is no scientific evidence either way on the quantisation of spacetime. There are physicists who argue that the notion of 'points' and 'instants' is incoherent, sometimes citing Zeno. On the other hand the idea that spacetime is continuous also leads to problems. (How can something that is one thing also be many? How can something that is one thing have physical extension? etc.). Perhaps M-theory will solve this riddle, for it suggests that there is a sense in which spacetime does not exist. Maybe what Buddhists say about spacetime will turn out to be right after all. That'd be ironic.

jackle · Feb 3, 2005

properphysicist said:

According to Quantum Physics space is discrete, not continuous... Space is discrete on a very small scale, therefore, macroscopically speaking, space appears to be continuous...

You might be thinking of the Planck length, which is very small. Don't know if this helps.

Also, I think QM does suggest that particles can jump areas of space without ever being in between. eg. Tunnelling, quantum leaps. I think Zeno was wrong too.

ahrkron · Feb 5, 2005

properphysicist said:

perhaps I'm thinking of string theory. if that's also wrong then what does say space is discrete because I thought that was the case.

The closest I know to that assertion comes from Loop Quantum Gravity (an alternative to String Theory). It is a way of quantizing the gravitational field starting from the GR perspective. Within the LQG framework, it has been shown that area and volume should be quantized. They have even calculated the spectrum of the corresponding operators.

Zeno's Paradox Considered Federal Criminal Case

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