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In Newtons Principia he wrote:

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.

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?

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  • "Philosophically, or ontologically, though, is there a difference between saying that time flows or not?" This asks a question about words. The only thing relevant, however, is not which words are used, but what their intended meaning is. Aug 20 at 3:41
  • @David Asimov: No, I was being rhetorical, as should be obvious. There is obviously a difference. However, writers have been known to write sentences where the meaning of the words are at odds with the meaning of the sentence. The idea is to catch the readers attention. This is what I've done here. All words carry meaning as do equations. One of the jobs of mathematicians and physicists is to understand how to intrepret equations. And it makes a great deal of difference which words we use and how we present equations. Its not enough that we signify meaning with a private language; ... Aug 20 at 11:57
  • @Daniel Asimov: ... to facilitate communication public language must be used so that the public at large understand. After all, that is the point of communication. Aug 20 at 11:58

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Newton has only one form of time, Absolute Time, but with three atributes: absolute, true (whatever that means) and mathematical. He then identifies it with idealized form of subjective "duration" as well. The particle does not move "of its own volition" though, Absolute Time drags it along in synchrony with everything else. And synchronous motion of multiple disjoint particles is exactly the mathematical picture of ideal fluid flow. So Absolute Time flows, it is just a uniformized, depersonalized, mechanized, really really boring kind of flow.

But it is a flow, Newton specifically rejects relativity of motion, so contra Galileo uniform motion is not the same to him as rest, perception alone is not enough. The lake standing still with frozen present, past and future is metaphysically different. In Newton: A Very Short Introduction Iliffe writes:

"Newton remarked that ‘ordinary people who fail to abstract thought from sensible appearances always speak of relative quantities so much so that it would be absurd for wise men or even Prophets to speak to them otherwise’. Without the reference to theology, this significant view made its way into the Principia, where the vulgar were said to consider quantities only as they related to ‘perceptible objects’. However, Newton went on, ‘in philosophical discussions, we ought to step back from our senses, and consider things themselves, distinct from what are only perceptible measures of them’". See

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    I'm not sure that Newton rejected relative time, space and motion; he appears to derives them from his absolute notions. Jul 14, 2015 at 10:06
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    @Mozibur Ullah He rejected relative as being on equal metaphysical footing with absolute. They remained similar in "vulgar appearance" only, absolute velocities, etc. describe the "things themselves". He even demoted equivalence of motions in a uniformly moving container to a corollary in Principia from Law 4 in the drafts hsm.stackexchange.com/questions/2454/…, and looked for ways to distinguish absolute rest and motion as in the bucket thought experiment www-history.mcs.st-and.ac.uk/HistTopics/Newton_bucket.html
    – Conifold
    Jul 16, 2015 at 21:05
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    @confold: I just read in some notes that Newton took space to be 'Gods sensorium'; Jul 17, 2015 at 10:34
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    @ Mozibur Ullah “There exists an infinite and omnipresent spirit in which matter is moved according to mathematical laws” (Principia, book 3, prop 9). It is interesting that Newton came to be associated with clockwork universe, but "not a single example of Newton unambiguously referring to the universe as a clockwork system has surfaced". In 1690s he wrote that God is "constantly co-operating with all things according to accurate laws, as being the foundation and cause of the whole of nature" isaacnewtonstheology.files.wordpress.com/2013/06/…
    – Conifold
    Aug 26, 2015 at 22:55
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    that's a great find! I'd suspected that later generations had read back into Newton a purely mechanical philosophy, that he himself wasn't allied with; it didn't make sense given his later work in theology; plus I'd found the naming of his space and time concepts, by way of the absolute, suggestive of a theological orientation there; the quote also reminds me of Spinoza and neo-Platonism. Thxs for the references. Aug 26, 2015 at 23:06
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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) 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.

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.

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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.

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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 since the existence of a common moment across space is, or would be, unobservable.

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.

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Talk of time flowing is perhaps strange. It is not that parts of timelines themselves are moving along the lines; it is objects within them. But if time otherwise has no intrinsic "content," what is it that we call "time" that is "flowing"?

To avoid the picture of parts of time moving, or at least postpone this mystery, let's focus on, "Time flows," as metaphorically (if nothing more) predicating an action or event of time. (By "action" I do not mean a deed, but a positive determination from time, not something that "passively happens" to time.) Actually, I'd be hard put to explain a temporal event with no content: I would look for a change, but then I'd have to confront the idea of time changing, or of being different (even for some "static" 4-dimensionalist kind of reason) at different subtimes.

So as far as temporal action goes, I'd say that, "Time flows," means more that time, of itself, moves the objects in it, forward down time's lines. We flow through time, and not only on account of specific physical dynamics that we experience and engage with, but due to the whole ambient "purpose" of time overall.

This picture of time is, I hope, arbitrarily consistent with any well-evidenced scientific theory of empirical events. In an inherently dynamical universe, for instance, space too, and then rather the spacetime manifold as a more integrated system of functions, comes equipped with a force of action on its contents. On the other hand, that spacetime acts on its contents might seem less likely on a relational (Leibnizian) model, for such a model has spacetime "only" as relations between other objects and events. However, this relation-type itself could be construed as "acting on" its relata, perhaps. (Quick attempt: assume with Frege that concepts are Concepts, that existence is second-order predication (predication on other predication), so that the Concept of time can cause itself to be instantiated as much as it is instantiated by its physical relata; maybe then we have room to speak of time acting on its relata instead of just passively relating them.)

At any rate, if spatiotemporal relations are sui generis conceptually, we seem to have a sort of quasi-substantivalism on offer: at least in the mind of God, the irreducible relation-types of spacetime are compressed into mental objects, alongside all other monadic or polyadic structures of the relevant form.

Addendum. Kant seems to have had a humdrum thought (not necessarily false, though) about "time flowing":

Space and time are quanta continua, because no part of them can be given, without enclosing it within boundaries (points and moments), consequently, this given part is itself a space or a time. Space, therefore, consists only of spaces, and time of times. Points and moments are only boundaries, that is, the mere places or positions of their limitation. But places always presuppose intuitions which are to limit or determine them; and we cannot conceive either space or time composed of constituent parts which are given before space or time. Such quantities may also be called flowing, because synthesis (of the productive imagination) in the production of these quantities is a progression in time, the continuity of which we are accustomed to indicate by the expression flowing.

He also said:

For change does not affect time itself, but only the phenomena in time (just as coexistence cannot be regarded as a modus of time itself, seeing that in time no parts are coexistent, but all successive). If we were to attribute succession to time itself, we should be obliged to cogitate another time, in which this succession would be possible.

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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).

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