selfAdjoint said:
Superstring theory has 10 dimensions. One of them is time and the other nine are spacelike. Three of the nine are our visible three and the other six are hidden from us, perhaps by being compacted into tiny sizes, much smaller than a subatomic particle.
Although on the surface of Earth it's easy to distinguish height from the other two visible dimensions, in zero gravity that's not so, and anyone of them can be transformed into any other by a rotation. So it's really meaningless to contemplate naming all nine, when even the three traditional names don't work in general.
In the Zen-like interest of meaningless contemplation, I offer the following.
Front-back
Right-left
up-down
future-past
in-out
We see that the idea of dimension involves a seperation. This separation can be made into a gradient by choosing a discrete unit and applying it along a line according to some rule for summation. The easiest rule for summation is that all units are equal, no units can overlap, and there is no defined space between units. This corresponds to Euclidean geometry.
SelfAdjoint is correct in that these separations are not universal, but depend upon the imposition of an observer with an implied pre-existing basis. What does right-left mean to a jellyfish? What is up-down in freefall?
Classical spacetime therefore relies on the idea that the basis is orthagonal, that is, that there is a ninety degree rotation between basis lines. We then find that the spatial dimensions are limited to x, y, and z. There also must be a time dimension, and as Wizardblade has shown, the common idea is that the time dimension is added to the others, making x, y, z and t, four in total.
Mathematicians prefer to use more general terms which can be manipulated algebraically. So they say x_1, x_2, and x_3 instead of x, y, and z, where the notation x_1 would be read "x sub one". This leaves them free to generalize further to x_n where n takes on the values in the set (1,2,3). Then why not go further and talk about the set n=(1,2,3...), where the triple period means that the numbers go on and on, presumably to infinity.
But that is math and not physics. Not yet, anyway.
Observable, measurable, experimental results seem to defy explanation under the classical spacetime model, which is that there are three spacelike dimensions and one timelike dimension. We can explain these results by invoking additional dimensions. You can get a good introduction to this idea by reading the book, "Flatland". Basically, in two dimensions, as on a sheet of paper, you can draw a circle and label the inside of the circle A and the outside of the circle B. Logically, the circle separates A from B. There is no point in A which is also in B.
If you draw the circle on a sphere, the problem changes. Again, label the inside of the circle with some mark, A if you like. Now expand the circle to the equator of the sphere and beyond. Make the circle smaller again as it enters the opposite hemisphere from where you marked the A. Now you see that your mark, A, is no longer inside the circle, but has gone to the outside. What happened? In three dimensions, the two dimensional notion of inside and outside has been lost. The mark, A, is not inside the circle or outside the circle, but it is both.
So we find that electrons can be contained inside a quantum well. The quantum well is a device which has walls that the electron cannot penetrate, nor does the electron have enough energy to leap up over the top to escape the well. Yet it can be demonstrated that an electron trapped inside a quantum well can and will escape, no matter how tall or thick the walls. If the well is three dimensional, and the electron escapes, we can explain this behavior by invoking a fourth dimension. As in the circle on the sphere, the A, or electron, is neither inside nor outside the well, so it can escape through the next higher dimension.
But does this solution have any physical meaning? Can we find a rational explanation for the quantum behavior of the electron without invoking a fourth spatial dimension? I don't know. String and M use ten dimensions to explain observable parameters of physical behaviors of particles. Is there a simpler explanation? I don't know.
It does seem to me that Wizardblade and many others have made an error in counting time as the fourth dimension. The rules of measurement demand that time be present in any separation. Einstein pointed out that space and time are the same thing. We need to overcome the idea that time should be counted apart from space. It is clear from first principles that time and space overlap. We cannot therefore make a rational mathematics, or physics, by simply adding time to space. We have to address the question of spacetime equivalence if we are to make any progress.
R.