In the sense that physicists refer to when they discuss a 4th, 5th, 6th dimension:
– what does it mean to exist in another dimension?
– what kinds of things would you find in another dimension?
– what would said other dimension be made of?
– how many other dimensions are there?
– would this number differ between planets (could there be more dimensions on Jupiter than Earth, or is there a maximum possible number of dimensions across the universe?)
In: Physics
In the strictest mathematical sense, a “dimension” is just… a number. Some free parameter describing a measurable value that you can change. In the context of space, a space of *n*-dimensions (where *n* is some number) means you need at least *n* different numbers to describe where you are.
Say I had a string with some beads on it. You can grab some part of that string and say that’s going to be your “zero point”. Now, look at a bead on the string. *Where* is that bead, relative to your zero point? Some *X* number of whatever units, perhaps. That one number is all you need to define how far along the string the bead is. If you picked any other bead, the number will be different, assuming the beads can’t be literally on top of each other. Since you only needed one number to completely define where the bead is, the string is one-dimensional.
If you instead tried this on the surface of a sheet of paper, by drawing some “zero point” dot and drawing another dot somewhere else on the paper, where is that dot in relation to your zero point? You could say it’s X units away, just like last time, but… in which direction? I could draw another dot that’s the same distance away, but in some completely different place. Clearly one number isn’t enough to describe the location of the dot on the paper. You need another. You can do this in a couple different ways. The Cartesian coordinate system is the one most people would be familiar with, where you have to axes aligned perpendicular to one another (like graphing paper) and your two numbers are distances along those axes. Or you can use polar coordinates, where one number is the distance away, and the other is the angle you have to turn to face the correct direction. Either way, you need two numbers, thus, the sheet is two-dimensional space.
I think you should be able to see how three-dimensional space would follow from this.
So, to address your actual questions… what does it mean to exist in another dimension? Essentially, it means you have access to an extra number that defines your position. In three-dimensional space, you can describe where I am relative to any other point with just three measurements. But if you had access to the fourth dimension, you could be in the exact same position as me in those three dimensions, but still be somewhere else… because you have some *fourth* measurement that you can also be in. Our feeble minds can’t really comprehend this, since it’s not intuitive. I can’t just point in a direction and say “the fourth dimension is that way”. It’s impossible to picture. You can only really describe it in pure mathematics.
What would you find there? Well, *if* they’re real, the same stuff you’d find anywhere else, really. They might make some crazy shapes that would blow our minds, but it would presumably be the same boring particles we already know, just with some extra directions to wiggle in.
What would it be made of? Not really an answerable question. I guess you asked this from the perspective of “dimension” to mean something like a “parallel world”, like some popular media uses the word. It’s not really like that at all.
How many dimensions are there? Three, as far as anyone can tell. Four, if you count time, which in some ways you can think of like a dimension that everything is constantly moving through in a single one-way direction. There are some controversial theories out there that claim extra dimensions exist, but even if those theories are correct, those dimensions are more or less inaccessible except in the realm of the stupidly tiny. Like, the string example from earlier — to a big, bulky bead on the string, it can only move back or forth. But if you were a teeny tiny dust mite, you’d be so small that the string could be walked around like the outside of a cylindrical can. It’s effectively 1D to us, but 2D to a dust mite.
Would this differ between planets? Not really, again, as far as we can tell. Our universe, at least in all the parts we can see, seems to be three dimensional, everywhere.
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