Apparent time yields multiple times: apparent solar time, apparent lunar time, and so forth, ticking irregularly with respect to one another. Among the reasons that
Gassendi gives against a relationist conception of time is that such an identification of time with actual motions would lead to multiple times. Gassendi asserts that this is to be rejected in favor of a single, unifying time (see Gassendi 1972, 393-94). In Gassendi, the question of whether there is one time or many is to be settled by broadly a priori argumentation, whereas in Newton’s hands the issue becomes empirically tractable.
Newton distinguishes between true and apparent time. True time, just like true motion, is a property of the body or system itself, not of the appearances. In the equation of common time, we search for a single time parameter to be used in common for all bodies, relative to which we can construct a theory of their motions. If successful, this time parameter corresponds to the true time of the system of the world. For example, the lunar day and the solar day are different apparent measures of time, ticking irregularly with respect to one another, but belief in true time is the belief that (i) underlying these differing apparent measures is the one true time which these motions approximate to a greater or lesser extent, and crucially (ii) the irregularities in the motions of the moon and the sun relative to true time can be precisely quantitatively accounted for, without remainder, by our theory of forces by which the bodies in our system interact. The assertion that time is true is the assertion that there is one time, not many, in this specific sense.
True time for Newton, I suggested, is time that is unique and proper to the system of the world. The “system of the world” for Newton is the solar system, but the issue of true time (on the view I advocate) is system-relative and therefore independent of whether the “system of the world” is our solar system or some other system or the material universe as a whole. The issue is whether, for the system of interest, there is any such thing as true time. In the context of Descartes’s project, and in the hands of Newton, this is transformed into the following empirical question: can we construct a satisfactory physical theory for this system using a single time parameter?
There are at least two ways in which this could fail. One possibility is that we could get close but not quite there, so that we are left with irregularities that cannot be accounted for either by modifying the time parameter or in terms of forces: we are not able to come up with a satisfactory physical theory using a single time parameter, and so we are unable to supply this empirical warrant for the existence of a true time associated with that system. A second possibility concerns a specific way in which this might happen: subsystems dominated by different forces might tick irregularly with respect to one another with no common underlying metric. For example, there is no guarantee a priori that an atomic clock, governed primarily by the laws of quantum mechanics, will tick regularly with respect to a pendulum, whose rate of ticking is governed primarily by gravitation; the two could turn out to tick irregularly with respect to one another with no common underlying metric. There would then be no such thing as “true time” for any system in which both quantum mechanics and gravitation play a role. Specifically, were it to happen for the solar system, then there would be no such thing as true time for the system of the world.
It is, therefore, an empirical question—and an open empirical question at that— whether any such single time parameter can be constructed. In Newton’s hands, the appropriate methodology for tackling the question of whether there is one time or many has been utterly transformed. Whether there is one time or many is something that we discover not through a priori argumentation alone but through attention to the details of empirical enquiry. The question of whether there is one time or many has become an empirically tractable question, one that is appropriately addressed by paying attention to the details of empirical enquiry, and through the progress of that enquiry.
-  Thus, the question also becomes more complex: for any given system, we can ask whether time is true, and alsofor the collection of all systems we can ask whether time is true.