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geometric algebra (was: Re: Flatland is not dark (was: Photons in other dimensions))



At 1:04 AM -0400 4/16/04, John Denker wrote:
In particular, what some people call a magnetic field vector
in the Z direction can be represented at least as well by
a *bivector* in the XY plane. That is, when I look through
the telescope I borrowed from William Clifford and Hermann
Grassmann, I see a different and grander truth: I see a
version of electromagnetism that does not require any
cross products and does not require any right-hand rule.
Whereas the cross-product machinery only makes sense in
D=3+1 (three space dimensions plus time), the geometric-
algebra machinery makes perfect sense in D=2+1, D=3+1,
and indeed D=N+1 for all N>=2.

John,

Do you posit that this is true for _any_ physics application of the cross
product, i.e., that there is a "different and grander truth" in GA?
(Another re-wording of the question is: "Are there any cases where the
cross product is better than GA?")

Thanks,
Larry