What is the Smallest Unit of Time for Measuring Acceleration?

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SinghRP
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Is there a quantum of time?
What’s the smallest interval of time in which acceleration can place? – on the earth? – on the sun? – on a black hole?
A chronon is the time that light takes to cover classical electron radius. The other is the Planck time. But these won't serve my purpose, when I am trying to study (classical) acceleration.
 
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There is no evidence that time is quantized and some folks believe it is, some believe it isn't.

EDIT: I seem to recall reading somewhere that if time IS quantized, then the measure of quantization is WAY less than the Plank time, but I cannot provide you a reference for that and in fact I may misremember it entirely.