Question

In introductory analysis, the discussion the derivative emphasizes that while average rates of change are measurable, instantaneous rates of change are a "limiting abstraction". While this makes perfect sense from the formal view of analysis, I wonder how it maps to the view of physisists.

Are instantaneous rates of change, such as velocity, only ever inferred from observable average rates of change (measured or imagined over arbitrarily small intervals), or can they be directly observed?

Answer 1

Instantaneous velocity can never be measured since there is no way in the real world to do anything instantaneously. All measurements take some amount of time to peform.

For example the comment to the question mentioned using the Doppler effect to measure instantaneous velocity. That is not possible since to measure the frequency of a wave you have to observe it for something on the order of a cycle of the wave, so the Doppler effect will only ever measure the average speed of the object over some small time interval.