Why is Time Considered a Scalar in Mathematics and Physics?

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Discussion Overview

The discussion centers around the nature of time in mathematics and physics, specifically addressing whether time is considered a scalar quantity. Participants explore the implications of time being scalar versus its relativity in different frames of reference, touching on concepts from both theoretical and conceptual perspectives.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants propose that time is considered a scalar because it can be described in different frames, yet question how this holds true if time is relative.
  • One participant expresses a lack of understanding of fundamental physical concepts, indicating a struggle with the topic.
  • Another participant suggests that "time" is ambiguous, distinguishing between coordinate time and eigentime, and argues that the latter has a physical reality independent of coordinate systems.
  • A participant acknowledges being convinced by some points about time but admits to ongoing confusion regarding the concept, particularly in relation to relativity theory.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the nature of time as a scalar. There are competing views regarding the interpretation of time in different contexts, and the discussion remains unresolved.

Contextual Notes

Participants highlight the ambiguity of the term "time" and the importance of distinguishing between different interpretations, such as coordinate time and eigentime. There is an acknowledgment of the complexity involved in understanding these concepts, particularly in the context of relativity.

Who May Find This Useful

This discussion may be of interest to individuals exploring the foundational concepts of time in physics and mathematics, particularly those grappling with the implications of relativity and the nature of scalar quantities.

uiulic
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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?
 
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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.
 
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.
 
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).
 
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