Question: In Newtons *Principia* he wrote:

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> Absolute, true and mathematical time, of itself, and from its own nature flows equably without regard to anything external, and by another name is called duration.
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Hence, Newton distinguishes *three* forms of time - absolute, true and mathematical - and then identifies them.

Whereas for Aristotle, time was an aspect of change, and of which one aspect is physical motion; Newton reverses this conception, in a sense.

Thus, Newtonian time flows everywhere in space at the same rate; so for a man positioned somewhere in space he can 'see' in a sense (as in McTaggarts 'tensed' time) the future coming forward becoming the present and then going behind to the past; or in Heracleitian imagery time is like a river.

But it's the relative motion here that counts.

So, one might equally say that time rather than flowing like a river, stands still, like a lake it's surface is unruffled; until one puts a particle on it, which then moves ahead of its own volition.

This in fact is the usual way that one describes the classical trajectory of a cannonball in a space and time diagram; an exercise that one might do at school, say on graphed paper with the horizontal axis for time and the vertical one for displacement.

So, here - time does not *flow*; the cannon-ball *moves* in time.

The difference between the two pictures, Newtons original conception and the standard one taught is not usually remarked on. 

Philosophically, or ontologically, though, is there a difference between saying that time flows or not? 

Even when the physical picture, the expressed by calculations in Newtonian Physics, give the same result?

Answer: 
I will answer from our understanding of time as modeled by the **theory of relativity**. In that context the "flow of time" is nothing else than a consequence that every normal material observer moves forward in time (this is a consequence of the conservation of energy, since our mass is positive the *tangent vector to our trajectory in space-time* gives a forward component). In fact, antiparticles can be considered as particles moving backward in time for the same reason.

Therefore, that time does not flow for a material entity would be equivalent to the *tangent vector to its [trajectory in space-time (worldline)](https://en.wikipedia.org/wiki/World_line)* having timelike component equal to zero. The point is that different physical observers would differ on how to describe the object. For one observer it could be that this body does not extend in time and occupies for an instant several positions in space, but for another observer in relative motion with respect to the first one, the same object would be perceived differently, namely, as a [tachyon](https://en.wikipedia.org/wiki/Tachyon).

The summary is that although theoretically we could find bodies that do not move in time (and for which time does not flow), this condition would depend on the observer and would not be an intrinsic property of the "tachyonic object". Moreover, there are many doubts as to whether we could ever interact with such a tachyonic object, and it is doubtful that in nature there are physical processes that lead to such situations.
I think this has more to do with the idea of *fluxion* and the cohesiveness that surface tension gives to fluids, not of relative motion.

To think of the thing that allows for motion as moving seems like a logical trap that can only lead to paradoxes.

We segment the metaphor of fluidity into at least three aspects. Time 'flows' in that it maintains continuity (as in the way hair or robes flow, even if they don't move) not in that it arrives at a given rate (the way bullets might flow out of a machine gun) or that gets from one place to another (the way traffic flows).