Point particles moving in continous space

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SUMMARY

The discussion centers on the implications of continuous versus discrete spacetime on the movement of classical point particles. It asserts that if spacetime is continuous, a zero-dimensional classical particle would theoretically require infinite time to traverse between two points due to the infinite number of points in between. Conversely, if spacetime is discrete, classical point particles can move normally from point to point. This argument parallels Zeno's paradox, emphasizing that dividing space also divides time, leading to finite traversal time. The convergence of infinite series is highlighted as a relevant concept for further understanding.

PREREQUISITES
  • Understanding of classical mechanics and point particles
  • Familiarity with the concepts of spacetime in physics
  • Knowledge of Zeno's paradox and its implications
  • Basic comprehension of mathematical series, particularly convergent series
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  • Research the implications of continuous spacetime on particle physics
  • Study discrete spacetime models and their effects on motion
  • Examine Zeno's paradox in depth and its relevance to modern physics
  • Learn about the convergence of infinite series and its applications in physics
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This discussion is beneficial for physicists, mathematicians, and students exploring the foundations of spacetime theory and its implications for particle motion.

med17k
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does this statement make sense?
If Spacetime is continuous then a zero-dimensional classical particle would require infinite time to pass between 2 points in space because between any 2 points there is an infinite number of points but if classical particles have non zero space dimensions then they can move in the space from point to point . also if spacetime is discrete at the smallest scale then classical point particle can move ordinarily from point to point .
 
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Your statement is a modified version of Zeno's paradox. It doesn't take an infinite time between points, since dividing up space also is also dividing up time, so the time is finite.
 
Look up convergence of infinite series. Wikipedia article titled "Convergent Series" might be a good place to start.
 

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