Why is time scalar, not vector?

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Discussion Overview

The discussion revolves around the nature of time as a scalar quantity versus a vector quantity. Participants explore the definitions and properties of vectors and scalars, particularly in the context of physics, including classical mechanics and special relativity.

Discussion Character

  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant suggests that a vector is a group of independent numbers, and questions why time, being independent of spatial coordinates, cannot be considered a vector.
  • Another participant notes that a real number can be viewed as an element of a one-dimensional vector space, but formal definitions may be unnecessary unless it is part of a higher-dimensional space.
  • A different viewpoint emphasizes that vectors have both magnitude and direction, while time lacks direction, thus supporting its classification as a scalar.
  • One participant proposes that in classical mechanics, time is independent of reference frames, which suggests it should not be treated as a vector. They also mention that in special relativity, time could be considered a component of a four-dimensional space-time vector.

Areas of Agreement / Disagreement

Participants express differing views on the classification of time, with some supporting its scalar nature and others suggesting it could be treated as a vector in certain contexts, particularly in relativity. The discussion remains unresolved regarding the broader implications of these classifications.

Contextual Notes

Participants highlight the dependence of definitions on context, such as classical mechanics versus special relativity, and the implications of coordinate transformations on the nature of time.

lowerlowerhk
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Let's see if I think correctly first: I think a vector is a group of numbers independent of each other. What we say 3D vector means "it takes three numbers to specify a position and these numbers are not (explicitly) dependent on each other. The so called 'direction' of a vector is a visualisation that reflects this property."

If the above is correct, and since time is also independent of spatial coordinates, then why can't time be a vector?
eg: in the definition of velocity as dx/dt, x is a vector while time is a scalar. Why so?
 
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You can think of a real number as an element of a one dimensional vector space. To formally make all the definitions and distinctions needed to define the one dimensional vector space is regarded as unnecessary bother unless the one dimensional space forms a subspace of a higher dimensional space.
 
Vector and scalar are physical quantities. And Vector has Magnitude and direction, satisfying the law of vector of addition. And Time doesn't have direction, this its scalar quality. And when a vector is multiplied, divided... with scalar, the quantity obtained is vector. So, when X, displacement is vector, when differentiating with time we obtain velocity,v which is also a vector quantity. Hope it helps...
 
I got an answer, not sure if it is the complete answer:

The reason to not define time as another vector is that, in classical mechanics, the value of time is independent of reference frame. In math terms, it means that the value of time does not change under a coordinate transform and thus the length of the resultant vector magnitude might change. This defeats the very purpose of creating the concept of vector - to get rid of coordinate dependency.

In special relativity, where time does change under coordinate transform, time could be formulated as a component of a 4D space-time vector. This vector's magnitude is defined to be conserved under coordinate transform.
 

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