Eric Mutta wrote:
Hi All,

Though I am a computer programmer by profession, I do occassionally
wander into physics and have a general interest in it. Experience wise,
I'm familiar with elementary physics but I never got into the heavy
stuff, which brings me to my question.

Well, what one considers to be elementary and what heavy is a quite
subjective viewpoint... ;-)


I keep hearing about curved space-time in a variety of articles but
can't seem to get my head around the notion space being curve-able and
of time and space being fusable.

First off, when I think of space I think of the absence of matter to a
given degree. Vacuo are at one extreme being completely empty space,
while dense solids are at the other extreme with very little space in
them.

I think you go wrong already here. "space" isn't just simply the stuff
"between" the particles. Space is everywhere. A block of steel with a
volume of 1 m^3 has just as much space as 1 m^3 of vacuum.


Then when I think of time, I think of a man-made logical device used
for measuring the "distance" between the occurrence of two events of
interest.

One could as well say that space is a man-made logical device used
to measure the distance between two material things.


(Time seems to be one of those things you can't define easily
without using the word "time" itself, though I am aware of the
definition of a second in terms of transitions of state in the
cesium-133 isotope).

Physicists usually say simply "time is that which the clock measures". ;-)



Now then, how do you fuse/combine space (the general absence of matter)
and time (a logical device for measuring)?

By first noting that your notions of space and time aren't really
adequate for the question.


Or is this fusing a purely mathematical concept?

One could say so, yes. Einstein showed that space and time measurements
are not unique, but depend on (relative) motion; Minkowski then pointed
out that Einstein's equations can be formulated as coordinate
transformations in a four-dimensional space (with a non-positive
definite metric...)



Furthermore, how can space curve?

How couldn't it? ;-)


That sounds like taking "nothingness"
and giving it shape which doesn't seem to compute in my mind.

Equating "space" with "nothingness" is a bad idea. You could as well
ask "how can nothingness have a volume"?


OK, suppose that it could curve and we treat it as a hypothetical fourth
state of matter coming after the gaseous state.

*Very* bad idea. Why on earth should we do that?


Wouldn't it need to be
contained in something and hence take on the curved shape of that
something (much like a liquid in a container)?

No. General Relativity uses Riemannian geometry. In that, curvature
of something can be defined without referring to anything outside.



Or looking at it another
way, how would curved space maintain its structure?

The curvature is determined by the matter (or, actually, energy)
content. As long there is matter, there will be curvature.

Think of the (bad!) analogy of a rubber plane, with marbles lying on
it, depressing it, forming troughs.



I believe these questions should be answerable in the same language as
they were posed: English.

Only partly. After all, if everything in physics were explainable in
plain English, it wouldn't take years of study!

Do you also think that the question "Why are the possible orbits in
a gravitational field around a central mass parabolas, ellipes and
hyperbolas"? That's classical Newtonian physics...


[snip]

Bye,
Bjoern