Waves in 4D

  • #1

Summary:

Is there any research on "waves" in a three dimensional solid caused by said solid propagating through a fourth dimension?
I am uncertain if this belongs in the differential geometry thread because I don't know what area of mathematics my question belongs in to begin with, but of the math threads on physics forums, this one seems like the most likely to be relevant.
I recently watched a video by PBS infinite series called "Can We Hear Shapes?" about waves propagating through 2 dimensional surfaces, linked here: This got me wondering though. Waves propagate through a 1D line by making the line oscillate through a second dimension and a wave propagates through a 2D surface by making said surface oscillate through a third dimension. There is no real-world analogue to 3D solids, but it should be possible to at least model or abstractly analyze waves propagating through a 3D solid by making it oscillate through a fourth dimension.
What I want to know is if anyone has done any research on this before. Is there anywhere I can go to read about this sort of thing? Or, if there hasn't been any actual research on it, has the topic ever at least been mentioned in passing in a mathematical context?
 

Answers and Replies

  • #2
martinbn
Science Advisor
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Not sure what you are asking, but you can study the wave equations in any number of space dimension. You can find a lot of literature on subject, just do a web search.
 
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