Trying to wrap my head around dimensions

[Green Zach]

As far as i know, a dimension is basically spatial parameters in which "stuff" can move. I think that what bugs me the most about physics is that we know the what but not always the why... obviously this is not anyone's fault especially because finding out why things are the way they are is much harder than figuring out what they are/do. So my question about dimensions is do they actually exist? or are they produced by other laws? i.e. you have time, objects, and forces so thus velocity is born. velocity isn't really a thing you can "touch"... its just what happens when other laws are taken into consideration. So to explain the question and where it comes from... imagine that their is a universe in which forces only pushed on a flat plain... not because they couldn't push in a Z direction... just that they didn't. If no laws (such as the ones in our universe) forced the objects inhabiting this theoretical universe to move in the Z direction then would this universe technically be considered 2D? let's say one day for some reason a force comes along and pushes one of the objects in the 2D universe into the Z direction... the 2D universe would now be transformed into a 3D universe. So if this is true then dimensions should not really be "things" but just an effect of the directions that forces push. So this being said... our universe has the potential to be 20D but no forces "push" in thows directions so we are stuck in our mundane 4D (11D if you like). I am not sure if what i said is how dimensions work and would like to know if it is because it seems to make sense to me... thou i can already sort of spot some problems with it... So are dimensions based on the direction forces in a universe? or is it something else?

 

[Nabeshin]

This is an interesting point you bring up.

I suppose you're right, we say our universe has three spatial dimensions because we observe things to move in those three dimensions. There would be no evidence for a fourth unless it was somehow detectable and influenced these three, but we do not see this. Thus we conclude (prima facie) that there are only three dimensions. The question of whether there are 20 dimensions seems rather moot if we cannot know whether or not they exist.
This is all rather abstract, but if no natural phenomena produces any translation through a fourth (or fifth, etc) dimension, it seems dubious that we would devise such a means. If we are to accept your analogy with the 2D plane, surely we, being higher order beings, would observe the 3-D nature of their universe. However, if as you say forces simply never act along the Z-axis and thus they are stuck in the X-Y plane, the Z-axis would remain undetectable. This is of course a significant alteration of physical laws, but assuming this were the case I see no reason to suspect the existence of additional dimensions.

Occam's razor would seem to prefer the explanation that there are three spatial and one time dimension, over the statement that there are 3+N spatial and 1+M time dimensions, which we simply cannot observe.

 

[granpa]

particles don't have to move in that dimension to be able to detect it. if the fields they create spread out in x dimensions then the force will follow a 1/x-1 law. so all we have to do is look for a force that doesn't follow an inverse square law.

I would suggest that thinking in terms of fields would be more productive than thinking in terms of motion.

 

[atyy]

How do we even know we need 3 dimensions of space as in Newton's theory or special relativity? How do we know our world is not really 2D? The answer is simply that if we use 2D in Newton's theory, it doesn't seem describe the experimental results too well, but if we use 3D it does. Newton's theory is wrong at high speeds, and presumably all our theories are wrong at some level. Maybe a better theory will be discovered in the future requiring only 2D or 20D, but for the moment, we can only go with our best current theories.