Re: Octonian Wavefunctions -Still Any Research Today?

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 just have to add some information to my former posting, I feel:

Ok. here an explanation would be fine: I'm sorry, I thought that my
posting was to long already, so I didn't add the text about the
definitions with the octonions. -But another explanation will probably
be welcome, I hope..? -f you accept this posting, then here is the
long version:

Q: Why octonions, aren't they just 'out' after Einstein, even though
both Hamilton and Maxwell really liked them?

A: First of all, about modern physics: Both Hamilton and Maxwell very
remarkable persons in physics. -There shouldn't be any doubt, because
some of the most important concepts in physics still bear their names:
The Hamilton Equations and Maxwell Equations, If it wasn't for PAM
Dirac, and his remarkable accomplishments, then the Hamilton Equations
would still be the most fundamental known by man. (AFAIK). But
personally, I still believe in Hamilton and Maxwell, just let this be
said. Does their theroies look somehow strange today? - Honestly I
don't agree about this argument, and I will do my best to explain why
not...

Should everything important in physics (in this "Golden Age of
Physics"), have been done already; honestly, I don't think so! It's
like when somebody in the beginning of the 20th century said that
"everything important in theoretical physics already has been thought
out" or that "semiconductors are just a filthy mess, that no scientist
would like to have anything to do with". -We know a bit better
today...

Q: "Time or Proper Time, that's really the same stuff today, isn't
it?"

A: Well, a lot of people would really think so, but my answer is: No!.
-And honestly, i feel, that's it's hard to make the exclamation point
big enough on this one. One of the most important issues in PSR8,
which I shortly mentioned before, is the difference between "time" and
"proper time". Should the author of this article give somebody who are
studying (relativistic) physics a friendly advise, then this would
probably be the one: "Learn to see the difference between 'time' and
'proper time'".

It's a hard thing, but here are basically the difference in 'time' and
'proper time' in PSR8: First of all the concept of 'proper time' is
usually used. The usual concept of 'time' is used as a property
describing the LENGTH of a line in space-time. -Here is just a little
example of the property of 'time' which should really be seen as a
length in space-time: Should we really move a very long distance in a
few microseconds? - The distance could be so large, that we could be
talking about maybe a whole second! The quantity 'time' as usually
described, should (here in PSR8) be seen as an actual length in space-
time.

Q: But what is 'proper time'?

A: First of all, let's assume that you are living a normal human life
here on Earth: For example 1905 could have been the year, where you
were born, and maybe you would have made it until 2005. Shouldn't we
just say here, that we approximte a human lifetime with 100 years?
(sounds optimistic, but still somehow fair enough.)

In PSR8, here is a little diagram, that should show the conceptual
difference between 'proper time' (on the axis) and the usual time (a
length of a line in space-time): http://psr8-ha.googlegroups.com/web/PSR8-Diagrams.jpg,
the upper diagram with t=50y as an example.
[Sorry about the quality, I really don't know what's wrong with my
scanner this time: :-<) ! ]

Please notice, that in the general version, PSR8, then acceleration IS
actually allowed.

Q: Does your 'PSR8 Model' fit with the general theories of relativity?

A: Yes, there is no conflict at all. The transformations used in PSR8,
have actually been derived from normal relativity. The theory is
consistent with both SR and GR. However the conception is slightly
different:

* In the so-called R-Space: The unit vectors are expressing "proper
time" as well as spatial position.
* In the so-called P-Space: The unit vectors are expressing
"Mass" (and NOT energy) and momentum.

In PSR8, then it's specially important to notice:
*Time would be considered as the length of a "worldline".
*The same is somehow the case with "Energy".

Q: So aren't 'time' and 'energy' the main parameters on the axes?

A: No, actually not!

-The main parameters are 'proper time' and 'mass'. But both 'time' and
'energy' are still well-defined quantities.

Q: Paradoxes, -how many?

A: Basically none, but of course some really tricky problems can be
constructed; specially there can be a severe confusion about what is
'time' (using 't') and what is 'proper time' (using 'tau').

* 'Proper time' (tau) reminds very much about the usual Newtonian time
concept. This appears to be in best agreement with the usual human
intuition.
* 'Time' (t) in PSR8: That's a bit harder to describe! -But let's try:
It's actually a distance in space-time. It's really well-defined, but
we need a diagram to illustrate it: again http://psr8-ha.googlegroups.com/web/PSR8-Diagrams.jpg
(The upper drawing)

Please have a look at my new board on Google Groups: PSR8-HA. I will
do my best to illustrate the difference between time (t) and proper
time (tau), because this is really the clue to understanding my
socalled PSR8 Theory.

Q: Why Octonions; what's different in PSR8?

A: First what's different?. Here are the two main points:

First of all: We use different units than in SR/GR. Time and energy
does NOT make up the primary physical dimensions; however 'proper
time' and mass actually does.

Second: The usual idea of energy and momentum as a property of a
particle is exchanged with another slightly different idea: We are
talking about "intervals on dimensions" the same way as we are
thinking about space intervals and time intervals in the usual
physical space (Which I prefer to call the "R-Space").

I use 'quats' and octonions simply because I can. They just appear to
be very interesting, and I'm still fascinated by the ideas and
inventions by physicists like Hamilton and Maxwell. Personally, I
believe that the 'quats' (4D complex numbers) does actually reflect
the properties of the physical space-time. That's my believe (Maybe
you won't agree, but that's just my opinion.)

Hope, that this addition might add a bit of info, and maybe also clear
up a few things...

Otherwise, please visit my new forum on PSR8, which is still under
construction, however: http://Groups.Google.com/group/PSR8-HA (please
give me a month or two to add some relevant articles)

That will very soon include the definitions with the EQ's for the
octonian wavefunctions...

If you have a good question, then please just leave a note on my
board; I will do my best to answer within a few days...

Q: -And last but not least: Special versions of this "PSR8 Theory"?

A: Yes indeed. First there are PSR4, which will only handle a problem
that has 1 dimension in space. (Like 'flat spacetime' in SR). -And
both PSR4 and PSR8 exist in socalled 'delta-versions'.

PSR4-DELTA is basically intended for illustration and education. It
probably won't hold for many practical problems, but it's really good
to derive and illustrate the properties of the more general theory.
The delta-versions are like SR, which means, that accelerations can't
be included. 'Delta' means, that only intervals are handled, these
versions does NOT support partial derivatives in general. However, the
general model does...

Hope that I succeded to clear up a few of the things, which I just
felt was missing in the original article.

Rgds,
Peter Christensen
(CPH, DK)

.

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