[rrmm]

Check out section 10.3 in posted article.

The short of it is that lots of physical observables in nature are derivatives of things. So if the underlying thing contains a constant term, it goes away. Because it goes away, you are free to choose it however you like and still get the same observable result.

So the question then becomes how real you believe those underlying objects are. The linked article constructs a set up to challenge that.

[tel]

I think there's an odd sense where people think derivatives arise from "change in things" instead of being principal. It's sensible from our personal mindset to believe this but there's no reason a priori.

So that's kind of the question: can things like derivatives be the structure of space time or must they be arising from some underlying thing? Since the underlying thug involves some arbitrary, unobservable choice... it's a bit challenging.

[rrmm]

I've run across stuff in mathematical contexts where they'll throw in a derivative (or other operator) just to get the expression in the form they want.

It struck me as a bit odd, because hey, where's the change happening? But ultimately it was just a convenience, and maybe it had some underlying meaning in the original context, and maybe it didn't.

[tel]

But then sometimes it might be the case that the truly persistent thing is the derivative and the algebra forced your hand for good reason!