Why does time only have one dimension

You're asking two separate questions. To take your second question first, the existance of seven extra spacelike dimensions is a requirement for the consistency of string theory and we have no experimental evidence that extra dimensions exist or that string theory is a good description of reality. So it's impossible to make any definitive comment about why we haven't observed the seven extra dimensions.

To get back to the question we can answer, modern physics treats spacetime as a four dimensional manifold equipped with a metric. Four dimensions just means we need four numbers to specify the location of a point in spacetime. Two points are identical if and only if all four numbers are the same. Note that so far we haven't said anything about time - only that there are four dimensions.

The metric is what gives a notion of distance to our manifold. It allows us to calculate the distance between any two points in our four dimensional spacetime along a curve. To do the calculation we need to choose a coordinate system, that is we choose four vectors that we use to mark out spacetime. For example these vectors could be $t$, $x$, $y$ and $z$, or polar coordinates $t$, $r$, $\phi$ and $\theta$, or even a coordinate system like Kruskal-Szekeres $u$, $v$, $\phi$ and $\theta$ that doesn't correspond to anything humans can observe.

The metric assigns a sign to each vector. The details are involved but basically one coordinate always has a negative sign while the other three have a positive sign. The vector with the negative sign is timelike while the ones with the positive signs are spacelike. NB I've used the word timelike not time because you can have coordinate systems where the timelike vector is not time is the sense we normally use the word. For example in Kruskal-Szekeres coordinates the ${\bf v}$ coordinate is the timelike one but is not simply time.

The point of all this is that what we think of as time is not a unique way to define coordinates for spacetime and it isn't special (well not mathematically - it's obviously special for humans). So there is no reason to treat the time coordinate differently from the three space coordinates. That's why we consider it a dimension like the other three dimensions.

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answered Jul 12 '14 at 9:49

John RennieJohn Rennie

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