It's not Hestene's technique

Newsgroups: sci.physics.research
Subject: Re: Solving problems in special relativity w/quate
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Sender: Doug Sweetser<sweetser@alum.mit.edu>
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Mark Hopkins wrote:

>What you're doing [by solving problems in special relativity using
>quaternions] is essentially redeveloping the Spacetime Algebra
>formalism of Hestenes.

In my post, I described Hestenes' method explicitly but not in as
much technical detail as Hopkins provided. I argued that my
approach was different because I used only real-valued quaternions.
An event, represented as a quaternion, multiplied by an element of
the Lorentz group, represented as a unit complex quaternion, is not a
quaternion, it is a complex-valued quaternion. The distinction
matters because quaternions are a mathematical field and complex-
valued quaternions are an algebra but not a field. I work with the
former, Hestenes worked with the latter. That clear distinction
means the two approaches are different.

Perhaps Hopkins is arguing that "essentially" there is no significant
difference between the two approaches. I know that practically
there is a considerable difference due to the power and elegance of
working with a true mathematical field instead of a closely related
algebra. I can easily track the four numbers that make up every
quaternion I work with. I get thoroughly bamboozled by the 16
elements of the spacetime algebra involving scalars, vectors,
bivectors, pseudovectors and pseudoscalars. Simplicity and power
are worth working toward.


Doug Sweetser
http://world.std.com/~sweetser

Bringing the power of the calculus back
to the events themselves