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: 
My tuppenceworth: A second is defined according to the natural resonance frequency of the cesium atom (9,192,631,770 Hz), so scientific time is Aristotelian, based on motion. However, in a higher gravity region a second may pass, say, 5 times slower. A traveller to that region will return younger than his stay-at-home twin. Both twins age, but while time advances generally, it does so at different local rates.

[![enter image description here](https://i.stack.imgur.com/k2427.png)](https://i.stack.imgur.com/k2427.png)

The OP states: "*Newtonian time flows everywhere in space at the same rate.*"

The question for Newtonian time is whether *absolute* time—if it exists—is advancing uniformly, even though the local rates of Aristotelian time differ. Newtonian time would amount to advancing moments of universal simultaneity, which is a [disputed issue](https://ndpr.nd.edu/reviews/einstein-relativity-and-absolute-simultaneity/) since the existence of a common moment across space is, or would be, [unobservable](https://www.nature.com/articles/140963b0).

Of Aristotelian time the OP writes:

> 
> 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.
> 
> 
> 

In the absence of particles (or flux motion) there would be no Aristotelian time.
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).