# 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?

• If it was a vector, what would its direction be? – Martin Ender Apr 2 '13 at 10:54
• @Martin forward, obviously! – rubenvb Jun 18 '15 at 12:22

## 3 Answers

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.

• 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.

• 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 '14 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 '14 at 12:04

A vector is a scalar with direction. So Time can be a vector, but what it means depends on the context. In 1D it has only 2 directions, positive and negative with zero being positive. In 2D it can be an angle between ÷/-Pi radians. And so on.

Time can be a single dimension attached to the familiar 3 Euclidian spacial dimensions and in this case it is arbitrarily deemed to be a scalar until people wonder why time doesn't go backwards. The answer to that annoying inane question is that relativistic Time is a 3D vector property of 3D space, not a scalar attached to it. And vectors do not sensibly take on negative values. For example look outside at a flag pole and tell me if the flag is blowing backward or forward or not at all? It's a nonsense question right? Because the wind blows or it doesn't, and it blows in a direction with a positive value.

The terms backwards and forwards cannot be used to describe the wind. Neither does real time go backward or forward, but merely faster or slower.

And so when you move in space relativisticly, the passage of time in each frame of reference of nearby objects will vary according to the various directions of motion (time vectors) and their various instantaneous locations in relation to each other.

## protected by Qmechanic♦Mar 16 '14 at 10:47

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