> A minor niggly...
> When talking about the interval between two events in spacetime,
>
WikTionary.ORG defines the word " SpaceLike " as:
>
> " [ two events ] lying outside each other's light cone,
> so that no information can pass from one to the other. ".
>
> You wrote:
>
> " You may introduce more dimensions if you like,
> but what do you want with an 'energy-like' dimension ?
>
> I think about storing the energy into the rotations,
> so its enough to stay with four dimensions.
>
> The reason to think about this,
> is the possibility to describe spacetime by quaternions.
> Those have the intrinsic property of spin. ".
>
> Imagine 5 GPS-like birds shining well-regulated atom lasers at you.
>
> With 4, you know X, Y, Z and T but ( I imagine )
> the fifth would tell you the strength of your gravitational field,
> thus improving the accuracy.
Energy density is scalar, so appears in the hypercomplex scalar
dimension in quaternionic or octonionic representations. It
likewise shows up in the scalar dimension (albiet differentiated)
in the work-force form and conservation equations. There need be
no "added" dimension.
As to an earlier post in this discussion thread as to why
quaternions or my preference octonions, it is because the algebra
tells us how things must be, we are not left needing to guess. If
you would look at the pdf on my web site
www.octospace.com, you will
see how the full definition of octonion algebra and the simple and
painless acceptance that of the 16 ways the algebra can be rolled
out, there is no preferred selection, the electrodynamical fields,
forces, work, stress tensor, and conservation equations are mandated
by the algebra to be what we have accepted them to be.
The use of intrinsic curvature by Einstein to explain gravity was a
choice, not a requirement. GR, QED, QM, string theory, and my
octonion representation are all "generalized coordinate systems".
Remember when you studied classical mechanics and learned about
momentum space? Think about it, you did not rush out and say reality
is momentum space did you?
Math is robust, it allows multiple explanation paths. The true value
of any path is what insight it provides to us. The fact that one path
shows success does not in any way invalidate any other path. The fact
that any path has issues in some region of consideration, like GR with
particles, and QM with cosmology, does not invalidate either.
Using the mandates of octonion algebra, electrodynamics is covered,
and the additional degrees of freedom allow integration of gravity
without going to intrinsic curvature. All of the dynamical equations
are mandated by the algebra. Open your minds to the possibility.
Rick Lockyer
www.octospace.com
