Zeno's Paradox Considered Federal Criminal Case

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The discussion revolves around the application of Zeno's paradox in the context of a legal case involving an individual fleeing an immigration checkpoint. It explores the implications of quantum physics on the nature of space, suggesting that while space may appear continuous macroscopically, it is discrete at a quantum level. Participants debate the validity of Zeno's paradox, with some asserting that quantum mechanics does not support the idea of discrete space. The conversation touches on concepts from string theory and Loop Quantum Gravity, which propose quantization of spacetime and challenge traditional notions of continuity. The idea that particles can "jump" through space, as seen in quantum tunneling, is also mentioned, further complicating the discussion of space's nature. Overall, the thread examines the intersection of philosophical and scientific perspectives on space and motion.
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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.
 
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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.
 
properphysicist,

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

- Warren
 
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.
 
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.
 
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.
 
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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.
 

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