# Is each succeeding dimension time? [closed]

I have been researching but I have found nothing on this topic (at least after basic google searching and some deeper searching on this site), I'm not sure if this is a common sense thing or it is wrong. I hear many people argue whether the fourth dimension is time or a spatial dimension, why is it not both? From my knowledge I believe that every dimension is spacial, but every dimension higher is time from the perspective of the previous dimension. If you connect the dots between two squares, you get a cube. And if you connect the dots from two cubes, you get a tesseract. So this would mean if I lived in two dimensions, then would the third dimension be time. And for me right now, the fourth dimension is time. Are the dots being connected just time?

## closed as unclear what you're asking by Bill N, John Rennie, user36790, Kyle Kanos, ACuriousMind♦Oct 21 '15 at 12:48

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• What do you mean by a "spatial dimension"? Why can you claim "if I lived in two dimensions the third dimension would be time"? What does it mean to be "time from the perspective of the previous dimension"? It's not at all clear what you are asking. – ACuriousMind Oct 21 '15 at 12:48
• @ACuriousMind If a two dimensional object was moved (x+2,y+2) and each vertex of the square connected, then it would form a 2D model of a cube. I was asking if the connecting vertices between two squares to form a cube were temporal in the second dimension. – Kyle Oct 21 '15 at 13:02

For physicists spacetime has a precise definition. It is a manifold equipped with a metric. At the risk of over-simplifying, a manifold is a thing that has dimensionality (four dimensions for spacetime) and a metric is a function that defines distances between points in the spacetime.

Whether a dimension is timelike or spacelike is determined by its sign in the metric. Relativity uses a metric in which three of the dimensions are spacelike and one is timelike. Extensions to higher dimensions, for example supergravity, may have varying numbers of spatial dimensions but only have one time dimension.

Your argument about calculating the length between vertices in a square, cube, tesseract etc is a good one because this is exactly what the metric tells us. That is, if you have an infinitesimally small four dimensional cube of size $dx$ by $dy$ by $dz$ by $dt$ the metric tells us the distance between opposite corners. However time is not a spatial dimension. In the metric we multiply $dt$ by the speed of light $c$ to turn it into a distance. For example the metric for flat spacetime is:

$$ds^2 = -c^2dt^2 + dx^2 + dy^2 + dz^2$$

In this equation $ds$ is the distance between the corners. Note that we have multiplied $dt$ by $c$ to convert it into a length, and note also that the $dt^2$ term has a minus sign unlike the spatial terms. This is what distinuishes time dimensions from spatial dimensions. That minus sign is also what gives us all the weird effects we see in relativity like time dilation and length contraction.

• If I was a fourth dimensional person, would the fifth dimension be time? Or is time just a separate dimension not numbered but applied the same way to every dimension? – Kyle Oct 21 '15 at 6:18
• @Kyle: If I were standing at the geographic center of a city, would there be a diner nearby? The answer depends on what city I'm in, and the answer to your question (insofar as one can parse the question at all) depends on what (generalized) spacetime you're in. If you don't specify your city, I can't tell you about its restaurants, and if you don't specify your spacetime, I can't tell you about its metric. – WillO Oct 21 '15 at 6:36
• @Kyle: Physicists normal label dimensions in an $n$ dimensional space by a number that runs from zero to $n-1$, and we conventionally label time as zero. So in four dimensions we label the dimensions as $x^0$, $x^1$, $x^2$, $x^3$ where $x^0$ is the timelike dimension (note that the superscript is just a label not an exponent). The phrase the fourth dimension to label time is not used outside of popular science articles. Labelling time as $x^0$ has the obvious advantage that you can tack on as many spatial dimensions $x^1$, $x^2$, etc as you want. – John Rennie Oct 21 '15 at 6:37