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Instantaneous Velocity

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(edited 7 years ago)
Original post by Dooderman
Hey.

As far as I understand, instantaneous velocity involves the velocity of travel at a infinitesimally small fragment of time - this is fairly simple.

However, it appears this would conflict with the Zeno effect, a.k.a. the Turing Paradox, according to which time, if spliced into units small enough, is found in still "frames," where no velocity happens, meaning that, in a small enough time frame, the instantaneous velocity must always be zero.


I think you (or I?) may have misunderstood the Zeno effect. This is just an aspect of quantum 'weirdness' where one can hold a system in an 'unstable' state indefinitely by repeatedly interacting with it. Perhaps there is some confusion with the philosophical 'Zeno's paradox'?

Instantaneous velocity is just velocity at an instant of time; at a specific moment t.. Mathematically, velocity is defined to be distance/time as we let the time become zero - it's just a special case of the derivative.
___
(edited 7 years ago)
Original post by Dooderman
Hey.

As far as I understand, instantaneous velocity involves the velocity of travel at a infinitesimally small fragment of time - this is fairly simple.

However, it appears this would conflict with the Zeno effect, a.k.a. the Turing Paradox, according to which time, if spliced into units small enough, is found in still "frames," where no velocity happens, meaning that, in a small enough time frame, the instantaneous velocity must always be zero.


Remember that the instantaneous velocity you're talking about is classical physics, if you start mixing quantum and classical physics you're always going to end up in trouble.
Original post by Dooderman
Aaah yes, it appears I mixed up the Zeno Quantum Effect and the work of Zeno the Man.


Easily done - I believe the quantum Zeno effect was named after Zeno 'the man' because it does vaguely resemble one of his paradoxes!


The actual effect shows the effects of observation on atomic decay, i.e. if you know something is likely to have decayed within 5 seconds, and observe it every 2 seconds, it will not decay.


Strictly speaking, it could actually decay in that situation. However, if you 'observed' it every .2 seconds it would be less likely to decay, every 0.02 seconds less likely still, so with 0.002 etc. The idea is to imagine that we interact with the system (and 'collapse the wavefunction') at n evenly spaced time intervals. As we increase n (and hence decrease the time intervals), the probability of decay decreases. In the limit of n increasing indefinitely (i.e. approaching infinity), the probability of decay approaches zero.


Zeno the Man, however, said that if time could be cut into the smallest increments possible, all things would be completely still, meaning there is no motion.


That sounds like one formulation. I think among physicists (rightly or wrongly) this paradox is probably considered to be little more than semantic trickery and the armchair hand-waving of philosophers. Among philosophers (and possibly mathematicians), the issue is probably slightly more contentious - however, many believe they have 'solved' it (https://en.wikipedia.org/wiki/Zeno%27s_paradoxes#Proposed_solutions).

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