How to Detect Extra Dimensions

Yes. In fact that this is the exact (very exciting and somewhat recent) experiment that proved that if gravity does propagate in higher dimensions, then the dimensions must be very thin. ▶ this video Edit: To be clear: the experiment I’m referring to was the observation of two neutron stars merging. Since there was no event horizon prior to the merger, we’d expect a lot of EM energy to be radiated away. This new observation is neat because we’d expect much less EM energy out of a black hole merger.

In a general case, yes. This happened recently with gravitational waves. The construction of multiple gravitational wave detectors across the planet allowed us to test a previously untestable hypothesis about the number of dimensions that gravity can act in. ▶ this video

The 5th dimension have already been experimentally conducted. ▶ this video I won't give away the spoiler but this article is written within a few months of the above video (oct vs dec). The paper in reference is: "Limits on the number of spacetime dimensions from GW170817" Pardo, Fishbach, Holz & Spergel 2018 link

For what it’s worth, evidence has come out (explained well by this PBS Space Time episode [1]) that makes the “gravity propagates over more than three spatial dimensions” theory a bit less likely. [1] ▶ this video

The problem is that gravity, like EM, follows an inverse-square rule. If gravity had a 4th dimensional component, we would expect to see an inverse-cube situation. The equation is: 1/(1-dimensions) Youtube video that explains this in depth: ▶ this video

Well, it has a gravitational effect, so it definitely exists inside of our normal spacetime. Scientists have explored alternative models of gravity or spacetime with additional spatial dimensions and things like that. As far as I know, none of them are very promising. There was an interesting PBS space time video about one example recently: ▶ this video Of course, it is definitely interesting to think about :)