posted on Apr, 19 2006 @ 07:15 AM
Ah! Someone at last to discuss 4-dimensional physics and concepts!
I love the 4th dimension, and trying to envision it as well. I do a lot of drawing of tesseracts, trying to figure it all out. I actually was able to,
on my own, figure out how many sides, edges, and verticies a hyper-cube SHOULD have.
Drawing Hypercubes is probably the best thing for you to do to start extending your visualizations of them. The tricky part comes when you have to
realize that the cube inside the regular cube is the SAME SIZE as the regular cube (remember, in a cube, all sides are equal length). Also, even more
confusingly, the edges that move through the 4th dimension (or in the drawings, the ones that AREN'T at right-angles when conceptualized
3-dimensionally) are also the same length.
This leads to paradox that cannot be solved in 3-dimensions.
It's at that point that you start making your mind work in 4-dimensions.
Another important tool to understanding 4-dimensions is to try to understand General Relativity. Not just what it means, but how it works.
In truth, it's ALL 4-dimensional information. A body of mass (say the earth) creates a "dimple" in space-time. Space-time is 4-dimensional. If you
simplified it, it's a bend in the piece of rubber you always hear about, but now you have to take that (essentially 2-dimensional) rubber sheet with
a 3-dimensional warpage, and remember that it's now 3-d rubber (and it's everywhere in the universe), but that it warps into a 4th dimension.
Given that the 4th dimension is time, this is why it's space-time.
Imagine a grid in space now, a 3-d grid (so a bunch of cubes, hurray for cubes). If this is to be our rubber sheet, when you pass the earth through
the grid, what happens to the grid? It bends, and shifts, and you'll see the lines of the cubes become distorted as they bend INWARDS into the planet
earth (also note that this inwards is not unlike the attempted drawing of a 4-d object's inwards).
Back to the rubber sheet, we put something heavy in it, it doesn't just create a dimple, but a big pothole. So large that you can spin something (a
marble) around it. If you could throw it just right, and the rubber was frictionless, then the marble would circle forever inwards towards the
basketball in the middle.
Back to the grid, you have the earth. Throw the moon in there, and since the grid is "insubstantial", and so is without friction, the moon circles
the earth indefinitely, always falling inwards.
Now you're coming to understand how gravity is NOT a force, but rather an effect of the warpage of space-time!
Now you also can understand how light is affected by "gravity" even though it doesn't have mass - because the path that it's travelling along is
now warped and changed.
Fun stuff, eh?