🚀 go-pugleaf

Physics is about properties of nature on which we all agree.
The bottom-line is common-sense intuition, not mathematics.
To emphasize this obvious fact, a long boring story follows.

`Time flows' expresses the following intuition, in which we
all *believe*: if we have a point of a material object, then
the set of events happening in that point can be linearly
labeled from `past to future' in a way that we all agree
upon (using common sense). Any device that sepatates the
`different' events (common sense again) by correctly ordered
labels is called a clock.
If one has some material coordinate grid (x,y,z), and one has
clocks in each point, it follows that each event happening
in the grid gets a unique label (t,x,y,z).

Now comes the mathematical *idealization* of that intuition:
Forget about the fuzziness of the intuitive concepts `point'
and `event'. View the grid as a continuum, and t as a contin-
uous parameter in each grid-point. We then *believe* that we
will be able to cover all of spacetime whith such local
coordinate-patches, such that these patches relate differentiably.
i.e. we believe that spacetime can be given the structure of
a manifold. The intuition above tells us that each point in
a material grid describes an `oriented curve' in spacetime.
To give this rigorous meaning, one can use a Lorentz metric
on spacetime to define `time-orientability' precisely.
And blah blah blah.

Bottomline (as promised) : First intuition, the n mathematics
(and with the mathematical results, back to intuition; if 
you can't, you've waisted your *time*, just like I've been
doing now).

marc.