Why discretize time?

There are several reasons why we might want to discretize time, the following being a list of those that readily come to mind.

1. We might believe as a matter of principle that time really is discrete, rather than continuous or part of a continuum, as will be discussed in Section 28.1.

Our motivation here might be a belief in some deeper and more comprehensive view of space and time, such as Snyder's quantized spacetime algebra (Snyder, 1947a, 1947b).

2. We want just to explore the advantages and disadvantages of an alternative model of time, with no prejudice one way or another.

This is the point of view that we find most appealing in this list. There is no proof that time is continuous or discrete. It is conceivable that DT (discrete time) mechanics might lead to a testable prediction that could not be formulated in CT (continuous time).

3. We might be sampling some quantity at regular or irregular intervals of time.

This is in fact how all experiments are done, because matter is discrete, not continuous. All information is acquired discretely and there really are no truly continuous processes of information acquisition, if we believe in quanta and the atomic theory of matter.

4. We want to approximate a continuous function as a discrete function in order to make a numerical estimate of some integral or the solution to a differential equation.