"instance of time" vs. "instant of time"

Question

The following two sentences quoted from this scientific paper (emphasize added) actually mean the same thing: at any moment.

For such plants this is related to the choke/valve openings, compressor, and pump settings at every instance of time. These are the control elements.

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The idea is to operate the plant, at every instant of time, as near optimum as possible.

Are "instance of time" and "instant of time" interchangeable?

If not, which one should be used? The phrases often occur in Physics textbooks with the same meaning.

Answer 1

An instance is a particular example of something. This is an instance of an answer on EL&U.

An instant is a moment, an infinitesimal point in time.

Now, every instant is indeed an instance of time, because every infinitesimal point in time is an example of a time. There's a subtle difference, but it amounts to the same thing in some cases.

The overlap between the two is very small though.

It would be unusual to think of it this way though, unless perhaps you were someone who often thought about different examples of things moving through time and how they were alike or different from each other. In other words, unless you were a physicist.

It's much more idiomatic to say "instant of time" or simply "instant" when you mean such a point in time. I would recommend it.

If however you were taking several readings or measurements of something, then you would have several instances, and in the case of physics these might very well be of time. Here "instance of time" is the only correct one. Which is probably what leads these physicists to say "instance of time" when the rest of us would more likely say "instant of time".

Answer 2

It is most unlikely that a physicist would think of instance as synonymous with instant. I never met such usage. Any instance (example, case, occasion) of something may occur at a particular instant but this does not imply synonymity.

The first sentence is incorrect if the author refers to particular times as instances. These times are instants.

Only if the author is thinking of instances as cases, examples or occasions of "this" aspect of control (note that we are not told what "this" is, but I assume it to be an occasion when control is applied) would a physicist use "instance" rather than "instant". When using "instance" in this way there is no need to add of time, because the instances are of control, and not of time.