This is another popular
explanation of just what the “imaginary” numbers are doing in the wave equation: they’re accounting for the difference, in spacetime, between the three spatial dimensions and the ‘fourth’ dimension of time. You really can treat it as a graphable dimension — we used to draw the graphs as an exercise in understanding special relativity— but the fourth dimension has different qualities than the first three. It turns out that the nature of the imaginary number aligns with these.
I realize James doesn’t really like the connotations of “imaginary,” but it’s what they’re called. I didn’t make that up. You can call them something else.
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