# What do I need to read to understand dimensions and spacetime?

The concept of dimension seems to be:

In physics and mathematics, the dimension of a space or object is informally defined as the minimum number of coordinates needed to specify any point within it.

According to wikipedia. But the fourth dimension seems to have also some kind of connection with spacetime which seems to be related to Minkowski spaces. I want to understand dimensionality and also learn about these issues about spacetime.

I'm searching for references on what I should read in order to understand this, I'm searching for a serious way (no pop-science) to understand it, I'm searching for a list of topics and also some recomendations on textbooks for it.

I hope I'm not asking too much, but I'm very curious to grasp this subject. I'm also realistic on this, I do not think it's something easy of fast to learn.

EDIT: I've found some books on Minkowski spaces, I guess I'll be able to understand from those in the near future.

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There are two different concepts of the fourth dimension in what you talk about. Four dimensional Euclidean space, $\mathbb R^4$ has four equivalent coordinates. To find the distance between two points, you sum the squares of the differences of coordinates and take the square root. Many things are similar to your experience in $\mathbb R^3$
Spacetime is a different creature. The time axis is fundamentally different from the three space axes. Your normal experience should tell you this and it doesn't lie. Mathematically it is because the "metric" has a minus sign on the difference in time-$d^2=\Delta x^2+\Delta y^2+\Delta z^2 -c^2\Delta t^2$ This means "distances" are not positive definite. Anywhere a light ray goes is zero distance. If the distance between two points is greater than zero, they can't influence each other and there is a reference frame where they happen at the same time. If the distance is less than zero, one precedes the other and does in all reference frames.
 Distance between two points less than zero? Is it possible? How? I intuitively thought that the distance between two points could always be a positive number. – Gustavo Bandeira Feb 19 at 5:44 Oh sorry, I guess you're saying something like: $D>0=$ something in my front and $D<0=$ something in my back. Is this it? – Gustavo Bandeira Feb 19 at 5:50 Actually, what can be negative is the square of the distance, this is because in Minkowski space the time axis is imaginary, so the distance itself can be an imaginary number. But Gustavo, from my point of view, it is just a math trick that extends the intuitive definition of distance in real space to other physical system. I dont think there are many physicists that think that an imaginary axis is "real" (but I might be wrong) – julian fernandez Feb 19 at 5:58 @julianfernandez: In fact, there is a discussion in Wheeler's gravitation about how you can call the time axis imaginary (in that the coordinates are $ict$) in special relativity and make things work, but not in general relativity. You have to view the minus sign as coming from the metric. I don't remember the details. – Ross Millikan Feb 19 at 13:59 @Ross thanks, I wasn't aware of that!! – julian fernandez Feb 19 at 14:26