The notion of Extra Space Dimensions

[JK423]

Hello,
I want to understand if the 'extra space dimensions' is a realizable physical concept.
They are just an assumption made by some theories (string theory for example) but i can't understand it at all. Ofcourse, my 'baby' argument is:
-How can they exist since i can move my hand only in 3 directions?
The answer possibly is that they're so small that we cannot see them.
Then my next questions would be, 'Ok, what if they were large?'
I ask this because, if a dimension can exist in a 'small' version why couldn't it exist in a larger version? Or to put it another way, if the dimension is small then suppose i`m also small enough so that i can see it large.
So, if the extra space dimension is large relatively to me, how would that look? Theoretically i would be able to move along that dimensions but stay still in the ordinary three space dimensions.
This scenario simply isn't realizable in my understanding.. I can only move in 3 directions, not more, whatever the 'magnitude' of the extra direction is.

The above are the very first questions that every person (physicist or not) would ask when first hear about extra space dimensions. I got no understanding of the concept so i would be pleased if you give me some arguments that can make this scenario applicable in the real world.

Thanks a lot!

John

 

[DaveC426913]

Think of this:

It is assumed that the current 3 dimensions are of approximately similar scale, meaning the universe is approximately spherical. What if one or more of them were much, much smaller?

Let's say the Y and Z dimensions were only 1 light year across. The universe is an ellipsoid 14billion ly long and only 1 ly wide and 1 ly high.

If you traveled exactly in the Y direction, after 1 light year you would find yourself right back where you started. But you are free to set out in any direction you want. Say you headed at a random angle NorthWest by Up. You could travel a billion light light years through the X dimension with no trouble, but you would find yourself continually looping back to where you came from in the Y and Z dimensions. Your trip across the universe would trace out a helix. Think about an ant crawling along the surface of a garden hose at a slight angle. The ant likewise traces out a helix.

Now, what if the Y and Z dimensions were micrscopic? You are free to travel (or wave your arm) in your familiar X dimension as much as you want but you would be unaware that you are simultaneously moving through the tiny Y and Z dimensions all the while.


I've shrunk the number of dimensions for the above scenario, but it works with any number of dimensions. You are free to wave your arm through the 3 macroscopic dimensions that are familiar to you, to you are unaware that you are also looping helically through dimensions whose extent is far smaller than an atom.

Just like the ant that is free to wander along its macroscopic dimension of the garden hose, unware that it is actually traversing the garden hose's circumference at the same time. Its passage around the garden hose's girth (continually returning to the side where it started) does not impede its movement in the macroscopic dimension along the length of the hose.

 

[bcrowell]

I think DaveC has done a good job of answering question #1. This leaves question #2:

[...]if a dimension can exist in a 'small' version why couldn't it exist in a larger version? Or to put it another way, if the dimension is small then suppose i`m also small enough so that i can see it large.

I would take this as a separate question about what it is that sets the scale of the extra dimensions. Plain vanilla GR doesn't have any special scale, so there is no natural scale to pick for the scale of the extra dimensions. This is related to the fact that GR is background-independent.

String theory has a natural scale, which is the Planck length.

In theories with additional "large" dimensions, the natural scale is taken to be the TeV scale of electroweak unification, and this turns out to be the same as the Planck length in these theories (and therefore different from what we normally think of as the Planck length).

 

[JK423]

Thank you DaveC for the response.
I understand your argument in which, in order to understand higher dimensions, you reduce the problem to the "think what would happen if you lived in < 3 dimensions".
I cannot falsify it, but it's hard for me to convince myself that it could be true in this world.
It just that i cannot accept the fact that i would be able to stand still in the 3D world but still be moving at will in the extra dimensions.. (in the case these dimensions were large). Ok, and if i lived in 2D i would be able to do that in the 3rd dimension.. (your argument) but real world isn't 2D and there are no 2D beings either! Ofcourse this can neither falsify your argument (nothing i can think of can) but still.. hard to accept!
Anyway i have to think of it a little more, but such an assumption - the extra dimensions - seems so extreme and unnatural to me (this is not a serious argument ofcourse after studying modern physics! :P) that i don't think i would devote my life studying such a theory...
This story gives me the impression that theoriticians have accepted higher dimensions so much (20+ years of study) just because it 'seems' to solve many of the problems. That's acceptable.

bcrowell, thank you for your fine post as well!
Just a question, what do you mean 'background-independent"? What is string theory's background?

 

[DaveC426913]

I cannot falsify it, but it's hard for me to convince myself that it could be true in this world.
It just that i cannot accept the fact that i would be able to stand still in the 3D world but still be moving at will in the extra dimensions.. (in the case these dimensions were large). Ok, and if i lived in 2D i would be able to do that in the 3rd dimension.. (your argument) but real world isn't 2D and there are no 2D beings either! Ofcourse this can neither falsify your argument (nothing i can think of can) but still.. hard to accept!

Right. It's not meant to show that it exists, it's simply meant to show that, were it to exist, you would still move normally at not experience anything differently. It shows a way that it's not falsifiable simply with casual observation.

 

[bcrowell]

Just a question, what do you mean 'background-independent"? What is string theory's background?

String theory is done on the assumption that the geometry is a certain way: 11 dimensions tangled up in a certain topology. GR doesn't make any prior assumptions about the geometry.