Re: Octonian Wavefunctions -Still Any Research Today?
- From: Doug Sweetser <dougsweetser@xxxxxxxxx>
- Date: Tue, 29 Jan 2008 10:47:53 -0500 (EST)
+Hello Peter:
There simply is no better training that rewriting fundamental laws of
physics in your own nomenclature. I say this based on my own
experience at quaternions.com where I have done that for a substantial
number of laws, and should do it for more. That said, all such work,
great as it was for me, doesn't have a value to the larger physics
community. The only issue that can matter is if it changes something
fundamental.
Let me give you an example. I decided to take a class on special
relativity and solve all the problems assigned in two ways: one using
the global Lorentz group, or by using quaternions. I was able to
solve all 52 questions asked in the problem sets both ways. It was
only years after that I was able to see the full scope of that
project. A fellow named De Leo in the mid 90s figured out using
quaternion triple products how to represent the global Lorentz group.
That was good news. Yet I was not aware of his work at the time I
ground through those problems. Instead, what I did was develop a way
to solve all the problems locally. For many of the simple problems,
the solution was quasi-global, the local dependence disappearing
because the problem involved the origin or some other lucky break.
The more complicated problems had solutions that did dependent on the
events under discussion. While there are certainly reasons to enjoy
the power of global tools, the most important laws in physics are
local laws, the standard model and GR being the prime examples. That
issue - global versus local changes in inertial reference frames - is
worth bringing to a wider audience, not the details of how I solved
the problem sets.
Non-standard _usually_ does mean wrong. The reason is that standard
approaches are vetted through the process of writing books, editing
books, and then having said books be the basis of teaching classes in
the subject. Again, this does apply to my own work. One reason I try
to run my equations through Mathematica - despite its high cost in
dollars and time - is to catch my own mistakes. Beyond mere algebra
issues, there are conceptual issues that I paid no attention to, such
as the spin of a coupling J^u A_u which Feynman worked out. So there
is algebra and unconsidered issues to address. B. Adams question
brings up another trap: if you decide to get along with the
uncertainty principle and toss in another factor of i that commutes,
then you no longer have a division algebra.
You claim:
It is possible to use proper time and position in a coordinate system.
The details of this sound garbled to me. The Lorentz invariant proper
time is calculated from the Lorentz covariant measurements of time and
space. You need all 3 - covariant time, covariant space, and the
invariant interval - not two of three.
If you consider the numbers known as quaternions, then I will claim
that they are actually 4-Dimensional, the same way that I will say
that ordinary complex numbers are "2-Dimensional".
If I was a better math wonk, I would know how to say this right, but
here goes. One can work with complex numbers on the manifold C^1.
Complex functions then can depend on only one complex variable.
Complex numbers are usually introduced on the manifold R^2. There are
some folks who think the only way to think about complex numbers is on
the manifold R^2. Yet most of complex analysis happens in C^1 using z
and z*. If someone skilled in the jargon would like to clarify, I
would appreciate it.
The same goes for quaternions. People usually think about quaternions
on the manifold R^4. Yet one can work on the manifold H^1. This time
one needs the conjugates instead of one. I use q, q*, (iqi)* and
(jqj)* as the gang of four to cover anything that could be done on
R^4.
My point about "3" is that a quaternion is composed of 3 complex
numbers, not 4 complex numbers. The three complex numbers share the
same real and have 3 imaginary basis vectors, covering the four
degrees of freedom in a quaternion.
The 'trick' comment was directed as much at the field of study known
as string theory. I would prefer if professionals reserved the word
'theory' for a set of principles that can be used to make a great
number of calculations which have all been confirmed by peer-reviewed
physical experiments. That bar has not been passed for the work on
strings nor PSR8. The work on PSR8 is an area of study, and I do wish
you luck in your work. A testable hypothesis - where your proposal is
measurable different from the current theory - would justify studying
PSR8. I saw no such testable hypothesis. This is common condition.
Doug
.
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