# Is time a Scalar or a Vector?

In Wikipedia it's said that time is a scalar quantity. But its hard to understand that how? As stated that we consider only the magnitude of time then its a scalar. But on basis of time we define yesterday, today and tomorrow then what it will be?

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If it was a vector, what would its direction be? –  Martin Büttner Apr 2 '13 at 10:54

To pick up on twistor59's point, time is not a vector but a time interval is.

The confusion arises because you have to define carefully what you mean by the word time. In special relativity we label spacetime points by their co-ordinates $(t, x, y, z)$, where $t$ is the time co-ordinate. The numbers $t$, $x$, etc are not themselves vectors because they just label positions in spacetime. So in this sense the time co-ordinate, $t$, is not a vector any more than the spatial co-ordinates are.

But we often use the word time to mean a time interval, and in this sense the time is the vector joining the spacetime points $(t, x, y, z)$ and $(t + t', x, y, z)$, where $t'$ is the time interval you measure with your stopwatch between the two points. The interval between the two points is $(t', 0, 0, 0)$ and this is a vector.

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Yep good point. Wiki could do with a little bit of caveating of their sentence in order to avoid these confusions. –  twistor59 Apr 2 '13 at 13:30

In physics101, scalar quantities are defined to be ones which have magnitude only, and no direction, where "direction" in this context means a direction in three dimensional space. Time clearly has no such direction.

However, in slightly more advanced physics, where special relativity is applied "scalar" is used as a shorthand for "Lorentz scalar" - a quantity which does not change under Lorentz transformations. Time most certainly does change under Lorentz transformations, so is not a scalar in this context.

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twistor59, If you imagine time to be one dimensional and therefore linear, then time can be a vector quantity. Even if it only has two possible directions that it can go. However, I think personally that time should be classified as a pseudo-vector, as it can be measured both as a scalar and as a vector. –  user42646 Mar 16 at 10:19
Well, numbers are vectors too.Since they belong to the vector space $\mathbb{R}^1$. Pseudo-vector is a misleading term, becuase it has an specific meaning (axial vector). –  jinawee Mar 16 at 12:04

## protected by Qmechanic♦Mar 16 at 10:47

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