Zeno's paradox seems to umply that motion is not possible. The paradox is easily resolved though by pointing to time intervals that get smaller if smaller space intervals are chosen in the formulation of the paradox. Like that there is no ground to make motion impossible.

If space or time are discrete though then there will be intervals from which a particle in motion can't travel to the next interval. If the basis unit of time is a Planck-time (10exp-43(s)) then how can time be measured between these intervals? In every interval everything is motionless so what determines the transition to the next interval in which things are slightly different? How can a particle move from space interval (a Planck interval is about 10exp-33(m)) to a from this interval spatially disconconnected next interval?

Now there are physical theories that include exactly discrete spacetime structures to account for a quantized version of gravity. One of these theories is loop quantum gravity. Such a discrete spacetime shouldn't be considered though as ordinary spacetime litterally built up from almost tangent chuncks of spacetime. But discreteness is involved. This doesn't automatically mean that continuity is gone though. Maybe there is a spacetime process going on between the intervals that we can't perceive. It looks like discreteness but behind the scenes there is continuity. But spacetime is no longer diffeomorph, which is a prerequisite in general relativity.

Does Zeno's paradox prove that this has to be the case? I mean, does the fact that things can move trough spacetime prove that there is continuity on every level? Can there be processes outside 4D spacetime that determine how each new interval must look like?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.