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Is there any limit on the speed of changing something?

For example a particle is transformed to some other particle; This takes some time or is absolutely instant?

If every change takes some time, what is the fastest change? what phenomenon? What is the maximum possible speed?

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Welcome to Physics SE! -1 Your topic is not well defined. It is unlikely to give a physical context to compare different changes/derivatives of functions, because they will have different units. You could rephrase the question to ask specifically for "time". –  Stefan Bischof May 22 '13 at 19:39
    
Possible duplicate: physics.stackexchange.com/q/9495/2451 –  Qmechanic May 22 '13 at 20:35
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marked as duplicate by Waffle's Crazy Peanut, Emilio Pisanty, Qmechanic May 22 '13 at 20:39

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There's no formal minimum duration for a process that takes place in one location that we know of. Quantum field theories tend to break down on the "plank scale", though, and the plank time is $5.39106(32) × 10^{−44} s$. We don't know how to mathematically describe processes that take less than this amount of time right now, but this isn't a minimum time. It's just the timescale at which quantum gravity becomes important, and we don't really have that figured out yet.

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