I’m reading a book about string theory that is well outside of my area of expertise and find myself wondering about the consequences of motion in other dimensions.
Let’s say I, as an observer, am so small that the distances of the alleged extra spatial dimensions are no longer trivially “curled-up” as they are often described.
If an object remained motionless in the three macroscopic spatial dimensions, yet was displaced along one of the other dimensions, what would that look like to a tiny observer like me? Would it disappear from view altogether? I’m thinking of an analogy that as a 2-dimensional observer in a 2-dimensional world, if a particle suddenly moved perpendicular to the plane I live in, it would seem to disappear from my view.
It wouldn’t disappear from view.
One way to visualize this is to think of a two-dimensional world where one of the dimensions is curled up really small. Think of a really long garden hose where creatures live on the surface of the hose.
Big creatures can only slide back and forth along the hose. Small creatures notice that they can move around the hose as well.
Electromagnetic waves start out propagating in two dimensions on the surface of the hose. But as they wrap around they eventually turn into a ring-shaped wavefront moving linearly along the length of the hose. To the big creatures light appears to be one-dimensional on hoseworld, but at small scales it really is two-dimensional and the small creatures can see each other even if they’re on the other side of the hose.