Exploring the Concept of Time as a Scalar in Mathematics and Physics

[uiulic]

Why is time a scalar?

Sb says time is scalar because under two different FRAMES, t and t' are the same (for describing the same event?). However, if one frame is moving to the other, how can this be generally true? Isn't time RELATIVE in physicists' eyes? Therefore, " time is a scalar" is ONLY AN ASSUMPTION? I mixed mathematics and physics?

 

[uiulic]

I consider myself to be physics illiterate because I do NOT understand any of the following physical concepts such as time, mass, force,energy... AT ALL.

 

[Timo]

The term "time" is ambiguous and can stand for:
(1) a coordinate used to characterize a point in 4D-spacetime ("let's meet at the white tower (~3 cordinates) at 6 pm (4th coordinate)". That's not an invariant quantity under changes of coordinate systems (18 o'clock).
(2) a measure for length of curves (smartassname("curve")="trajectory") in spacetime. "I've waited for 3 hours at the f***ing tower and you didn't show up!". I do have aged 3 hours between ariving at the tower and leaving, loudly cursing people who never show up in time. These 3 hours have a physical reality and cannot be dependent on whether you count the hours 0-12 twice a day or 0-24 once or if someone moves very fast relative to me. No way you're going to talk yourself out of it by using a different coordiante system for spacetime.

I think your confusion stems from thinking of coordinate time (your question "for the same event?" hints there, at least) while the person claiming time was invariant is talking about length of curves (also called "eigentime"). Seperating between cs-independent properties and different classes of cs-dependence is one of the most important steps for understanding relativity. But it's something that simply takes time to get used to, even though there's tons of classical analogies. Example: Draw an arrow on a piece of paper. The question how much the arrow is pointing up (coordinate time) depends on the orientation (coordinate system) you chose for pinning the piece of paper on the wall. The length of the arrow (eigentime) stays the same.

 

[uiulic]

Timo,

Thanks very much for your reply. You have convinced me of some points about "time" to an extent. But my "time" problems (in my mind) come from everywhere. It is a shame that I only heard of RELATIVITY theory (and am guessing what it is only).