Re: Imaginary reality

[Daniel Schroeder <DSCHROEDER@CC.WEBER.EDU>]

> > Given that the wavefunction has to be a two-component object, why
> > is it so convenient to use complex numbers to encode the two
> > components?  Beats me.  Always seemed a little spooky, to tell
> > the truth.
>
> Why spooky?  There are lots of cases where we do similar things, e.g.
> bundling 3 or 4 scalar equations into one vector equation.  Whenever there
> are N solutions to the same equation, it is just a matter of time before
> somebody contrives a formalism that allows us to bundle them together.

But with complex numbers, it seems a little too lucky that the rule for
multiplication, "derived" using the crazy formula i^2 = -1, would turn
out to be just what we need.  This issue, of course, is not unique
to quantum mechanics; I find it a bit spooky wherever it comes up in
physics.  Probably I just don't understand the math deeply enough.

Dan