Octonian Wavefunctions -The PSR8 Theory
PC
still don't know if it will be accepted in SPR, but there should be a
copy in new-theories no matter what, I think / Rgds, Peter C]
Hi,
I would like to describe a bit of my own field of research (years of
work, you know), and ask if somebody else are interested in the same
ideas (?!) -If it's the case, I would really like to make some
connections...
We always use complex numbers in physics, but why? -And even more
interesting, could there be an application for the complex numbers of
higher dimensions, as quaternions (4D) and octonions (8D)?
[Trying to write something to be accepted in sci.physics.research], -
it's hard because people always say, that octonions have been
completely out for almost houndred years, because they do not really
fit with Einsteins relativity (?) -People say so, but that's NOT my
opinion...
However, Hamilton was very interested, and the same was the case with
Maxwell. They were then considered as "fundamental physical
dimensions", or something as important like that. -But the interest
again then was lost, because these "dimensions" didn't fit with
Einsteins relativity. -Personally, I would say that something VERY
important was just forgotten, and I really hope that these quaternions
and octonians will be given a new chance in modern physics.
I'm working on a theory, which I call PSR8, and here is a bit about
it:
(I'm working on a forum on PSR8 (specially for the Hydrogen Atom at
the moment):
PSR8-HA: http://groups.google.com/group/psr8-ha )
First of all PSR8 means:
PS: Phase-Space
R: Relativity
8: 8 dimensional
However, it's not as 'bad' as it looks:
All these 'dimensions' are just well-known all ready:
* We have TIME (1D)
* We have POSITION (3D)
* We have ENERGY (1D)
* We have MOMENTUM (3D)
We need to know all these 8 parameters, that's known! -But I know,
that the idea of proper time or energy (or for a non-moving system
mass) as 'dimensions' is very unusual. However, I think that this
conception is actually working. It appears to do so in PSR8.
The most basic idea in PSR8 is to consider 'proper time' and momentum
as physical 'dimensions'. It's a bit hard to explain in a few lines,
but here I will try to do my best:
We know that a length of an object is physical. But we do NOT have to
specity where the object is located on the physical dimension POSITION
to know the length. It's the same with TIME: We know an interval, for
example a LIFETIME, but we do not have to specify when the object
existed. - I mean, was it in 1642 with Newton, or was it in 1905 with
Einstein? -A lifetime of a known physical object would always be the
same. -We all know that!
However, the new idea in the PSR8 theory is to consider ENERGY and
MOMENTUM the same way: As intervals on 'dimensions', I mean. The same
way as time and position are considered as dimensions, the same way
ENERGY and MOMENTUM should be considered as 'dimensions'. -Of course
an exact definition would require INTERVALS, and that's exactely the
idea in PSR8!
PSR8 is based on OCTONIAN wavefunctions, so here at least there is an
example on a theory, that dares to try to do so. -Are there anyone
else, then I would really love to hear about it! A concrete example on
PSR8 ( applied on a hydrogen atom as a test (PSR8-HA) again there is
my new forum: http://groups.google.com/group/psr8-ha (2008)
I'm interested in anything on quaternions and octonions, if applied in
math-phys, please notice! -If you are research'ing on something
similar, please just mail me...! (NOTE)
Now, what's these dimensions, and how do they associate to 'octonian
wavefunctions'?
* First Energy and momentum (totally 4D) make up their own quaternion
space
* The same is the case with time and space: 4D quaternion again
However the full space is 8D, because both are needed to specify a
physical state.
Totally 2*4 D = 8 D
Please notice that PSR8 is NOT in conflict with Einsteins theories
ANYWHERE. But somehow the conception is different on PSR8's 8
dimensions. To be very specific I use:
1: Proper time (tau)
j: x-position (x)
k: y-position (y)
l: z-position (z)
i: Mass (Closely related to ENERGY, but not the same!)
ij: p_x-momentum (p_x)
ik: p_y-momentum (p_y)
il: p_z-momentum (p_z)
-When i, j, k and i are used for the octonions.
Most essential in PSR8 is the equation, which I call the PSR8
Equation:
'E' = m c^2 + j p_x c + k p_y c + l p_z c
Or applied for the Hydrogen Atom (PSR8-HA) as a test of the theory:
http://psr8-ha.googlegroups.com/web/PSR8-HA-EQ.gif
-Where both m and n are determined by (real) physical constants. The
complex units are: i, j, k and l.
Hope to catch some interest for octonions, and alternative complex
wavefunctions
Best Rgds,
Peter Christensen
(Copenhagen, DK)