Quantum Calculus: Fund. Theorem & Plank Time?

[duffbeerforme]

Hi, first post. I'm not a physics buff at all and this is probably an easy question to answer.
when looking at the fundamental theorem of calculus you take the limit as say t goes to zero (t being time). But does quantum physics say that t is not continuous.. something like a smallest time step such as plank time?.. and would this change calculus when dealing with real world problems?

thanks

 

[lbrits]

Well, t need not be time, and as far as calculus is concerned, it can be anything. In quantum mechanics time and space are usually treated as being continuous variables, and it is usually only when you throw gravity (or field theory) in the mix that you need to ask questions about discreteness of time.

Aside: In quantum mechanics, things are sometimes discrete and sometimes not. It's not fundamental to quantum mechanics, but rather the spaces on which the quantities are defined. For example, angles live on a compact space, and so angular momentum gets quantized. On the other hand, distances are unbounded and so these aren't quantized.

Back to your question. I don't know if this would really change real-world problems. The definition of a limit says that you never actually have to take t=0, but just "as close as you need to". That's sort of the heart of the delta-epsilon definition of the limit.