# Do physicists talk about instants and infinitely small moments in time? [duplicate]

Do physicists talk about instants and infinitely small moments in time?

If so, how do they measure something like that? If they don't measure it, why do they think it exists?

• No, "instantly small" isn't even correct English. Do you mean an instant in time? An infinitesimal time interval? Please edit your question to clarify it. – user4552 Nov 18 '19 at 2:58
• well, it's very bad english -- not what i meant to write -- but might say what i wanted [time that is as small as an instant]. anyway, apologies – user3293056 Nov 18 '19 at 3:00

Time and space are modeled in most physics theories as continua because there is no evidence that they are discrete.

Models are just models. We may eventually discover, or become convinced theoretically, that time and space are discrete and not continuous.

An instant is not an infinitely-small time interval. It is a zero-size time interval, the analog of a point in space.

• Yes. For example, we talk about the position $x(t)$ of something at the instant $t$. – G. Smith Nov 18 '19 at 3:08
• No. Nothing can be measured exactly. Physicists are very happy when they can measure something to, say, one part in a trillion. Often they have to settle for more much worse precision. – G. Smith Nov 18 '19 at 3:10
• It makes sense to talk about the present instant at any location. It doesn’t make sense to talk about the present everywhere in space, because there is no absolute time. – G. Smith Nov 18 '19 at 3:14
• The present is an instant, a zero-size time interval. – G. Smith Nov 18 '19 at 3:17
• We deny the existence of a Newtonian present that is the same for everyone everywhere. – G. Smith Nov 18 '19 at 3:20

Many quantities in physics depend on derivatives of functions as evaluated at a specific point in time. It makes perfect sense to assert the existence of an instant in time in this context because it allows you to solve for the value of that derivative.