Zeno's Paradox Considered Federal Criminal Case

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Discussion Overview

The discussion centers around the application of Zeno's paradox in the context of a federal criminal case involving an individual fleeing an immigration checkpoint. Participants explore the implications of Zeno's paradox on concepts of space and time, particularly in relation to quantum physics and theories such as string theory and loop quantum gravity.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant links Zeno's paradox to a legal case, questioning how one can traverse distances despite infinite subdivisions.
  • Another participant asserts that quantum physics implies space is discrete, suggesting that this resolves Zeno's paradox.
  • A different participant challenges the claim about quantum mechanics, stating it does not address the discreteness of space.
  • Some participants discuss the lack of scientific evidence regarding the quantization of spacetime, noting philosophical implications and potential resolutions through theories like M-theory.
  • One participant mentions the Planck length as a possible scale where space might be discrete, referencing quantum tunneling as evidence against Zeno's paradox.
  • Another participant introduces loop quantum gravity as a framework that quantizes area and volume, suggesting it supports the idea of discrete spacetime.

Areas of Agreement / Disagreement

Participants express differing views on the nature of space, with some arguing for its discreteness and others maintaining that it is continuous. There is no consensus on the implications of quantum physics for Zeno's paradox or the nature of spacetime.

Contextual Notes

Participants acknowledge the complexity and unresolved nature of the relationship between quantum mechanics and the concept of spacetime, highlighting various theoretical frameworks without reaching definitive conclusions.

ohwilleke
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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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