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I apologize in advance for the wording. Human languages - and most especially English, or so it seems - are not very good with time. If you understand what I've written but can think of a better way to say it please mention it.

Now, I am neither a Physicist nor a Philosopher, but...

Of the various models of time, many seem to require that there be some existence that extends beyond the instantaneous 'now.' Time in those models is a place that has reality outside of now, such that it may in principal be possible to alter one's location in time to visit either the past or the future or both, depending on the particular model.

If time is in fact a continuum, with past and/or present being simply locations along that continuum, then it seems that one's rate of experience of duration should necessarily relate to movement through the time dimension. To experience one second of duration is to advance one second along the line of time, just as advancing one meter in a particular direction is to move to a new location one meter removed from the previous point along some arbitrary spatial axis.

In the physical dimensions traveling between two points requires the same magnitude of physical movement regardless of the rate at which that movement occurs. By analogy, travel between two points in time requires the same magnitude of duration regardless of the 'rate' at which that duration occurs.

Given that objects that experience different degrees of time dilation can travel between temporal locations without passing through the same duration, does the existence of time dilation imply that the temporal continuum does not in fact exist?

Presentism does not seem to be in conflict with time dilation - the passage of time is a measure of the rate (for want of a better word) at which one experiences duration relative to others in different frames of reference.

So... does time dilation demonstrate that models of time that treat it as a continuum are flawed or have I missed something in my line of thought?

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Human languages are appropriate for what they're used for; in what they've evolved for, which is to facilitate communication in our every-dayness, that is in our usual mode of living: ordering pizza, arranging to meet up with a friend, getting a doctors appointment and so on.

In specialised domains of life where more precision matters then language adapts, in say logistics; but science (or natural philosophy) too is a specialised domain, and in there we have theorising about time - from Aristotle to Einstein; and language here includes the hieroglyphics of mathematics (but possibly not diagrams - these being more pictorial).

The model of time that you're interested in, the physical one modelled in physics is not the only one: there is, I think on ontology of time by Bergson where on the present (la duree) exists; the past and the future do not; so here time continuum doesn't exist.

In Newtons sense of time, it is time that flows (and it flows uniformly); so objects do not in a sense move in time; this is fundamentally different from how they move in space. The two dimensions - space and time - are ontologically very different; but we do have a time continuum.

In Einsteins conception of time, time assumes the spatial character of space; but also our motion takes on the character of time in that our motion is always uniform even when we're standing still; if I move then I move just that bit slower in time so that the two motions when summed come to a constant value (in fact the speed of light). Light for example does not move in time at all, it just moves in space (hence it travels at the speed it must - the speed of light).

In Einsteins conception there is no sole time continuum, in fact it makes by itself no sense; there is only as Minkowski pointed out, the spacetime continuum.

I'm assuming from your use of 'time dilation' that it is Einsteins conception you are probing; so strictly speaking there is no time dimension. So no time continuum.

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