Travel and locate extra dimensions

Question

I'm a newbie to String Theory.

String Theory says there are extra dimensions apart from the 4 known ones (space and time).

1. Even if the extra dimensions are very small, what makes the theory say they can't be located in a room saying their coordinates are $(x, y, z)$ at this $t$ time? Any analogies, since this is beyond my imagination.

2. If there are dimensions, shouldn't we / anything else be able to travel in them without even touching the other coordinates like $x, y, z$ and time?

EDIT :

Thanks for the answers ! But i would like further clarity . The main point of asking this question was the following :

The extra dimensions are extremely small, which i can imagine with no issues. But i would like to know why they (extra dimensions) cannot be just expressed as say infitesimally small 'pockets' at say (x,y,z) in space.

For example, I have a very small object at (7,0,0); anywhere this object moves in x axis; we can never use y and z axis to point it's location; making x axis 'unique'. Similarly for y and z axis. They are 'unique'.

So if the other space dimensions exist in our 3D space , they should be somewhere in (x,y,z) , which doesn't make them unique, right ?

Answer 1

I have only a vague understanding of string theory, but I believe there are several variants of it, so there may be more than one answer to your question. However, one explanation is that the additional dimensions are very tightly curled, so although they exist at every point in our 3d space they are too small to be viewed at our scale. You would, however, exist in them, in the sense that your body is made up of tiny strings that are so small that they can extend into the extra dimensions.

It is impossible to visualise ten dimensions in three. However, to get an idea, think of the tiny hooks on a piece of Velcro. If you were to shrink the hooks progressively you would reach a point at which you could no longer see them, and the Velcro would feel smooth to the touch. Conversely, if you were a giant, normal Velcro might seem smooth to the touch, so scale plays a role in determining whether a physical feature is detectable. The hooks of the shrunken Velcro, which are everywhere on its surface but impossible to see, are analogous to the tightly curled additional dimensions everywhere in our 3D space.

Answer 2

OK, first up, there are a few other answers on the stack, like this relating to compactified dimensions...and Marco is right also, but anyhow:

1) They are located in your room, all around you. Just very small. Like a sheet of paper (3D just its thickness is v small) looks 2D, and then if you scrunched it up into a minuscule point it looks 1D you have 'compactified' 3D into 1D...thats a pop-sci answer.

2) Because they are v small (Planck scale) you would also need to be that size to even consider that...again, think of the sheet of paper, only something quite small can 'travel' its 'third' dimension only. This again is a pop-sci level answer...see the ref for deeper understanding if you care to