How to imagine the tenth dimension

[Alex K]

Absolutely, depending on what their properties are. First of all, if they are curled up (and that's the most common assumption to render them invisible to everyday experience), how and whether they can be detected experimentally depends on two factors:
1. which fields and particles can move in them
2. how large they are

If none of the known particles, but only gravity, can actually propagate through the extra dimensions, they must be relatively large to be noticed in experiments such as the LHC (for example, if there are two extra dimensions in which none of the known particles can move, they must be of micrometer size to be visible in next generation colliders)

If some of the known particles can move in the extra dimensions, possibly all of them, this means that everything including ourselves is spread out in the extra dimension(s) via quantum uncertainty. The fields which move in the extra dimensions can form resonances much like the acoustic standing waves you notice at certain frequencies in a small room. In particle physics, those resonances manifest as a repeating pattern of heavier copies of the existing particles, calles "Kaluza-Klein-Modes". Searches for such extra-dimensional resonances are ongoing at the LHC, but so far haven't yielded results.

Wow, thanks. This was actually really cool and interesting, is this theoretical physics?

Yes. Especially starting in the late 90s, there was a considerable section of the theoretical physics community working on these hypothetical models with extra dimensions. The trend was ignited by results in Superstring Theory which had indicated that extra dimensions might plausibly be large enough to be detectable, something that was previously considered impossible. By the time I did my Master's on some theoretical consistency issues in extra dimensions in '05, interest in the community was already starting to wane a bit because most plausible ideas had been worked out. Nowadays, people are mostly waiting for the experimental results.