I just posted a brief, informal paper The Lorentz Force Equation and
Geodesic Motion at
which I actually wrote a week ago and did not post. This paper will help to
illustrate how I got from http://arxiv.org/abs/gr-qc/0511050 to
http://home.nycap.rr.com/jry/Papers/Uncertainty%20and%20GR.pdf, which is
attempting to show that Heisenberg uncertainty derives from general
relativity. And it will help to show how the present effort on HUP really
is part of an effort to solve the two problems in
http://arxiv.org/abs/gr-qc/0511050, discussed below.
In addressing the issues of the gravitational pseudo tensor t^u_v and
integrating energy densities in general, I came to realize that the only
gravitational t^u_v which could be separated from T^u_v was the one for
RomanT^u_v because of the special property that RomanT^u_v = scalar
Kronecker^u_v. I was able show in
how the Lorentz force, in differential form, is the equation for geodesic
motion in an adiabatic fluid. But, when I wanted to integrate back up to a
finite region of spacetime (last page) to reconstruct the usual expression
for Lorentz force (7), (24), I started to mull what happens when one
integrates in curved spacetime, picked up the first sense that the
uncertainty principle might be lurking nearby, and started on the present
The two main problems in the paper at http://arxiv.org/abs/gr-qc/0511050 are
1) the t^u_v pseudo tensor is just that; I need to correct its treatment.
The various energy tensors remain intact, however. Second, in light of what
I am doing now with HUP, I'd have to say that the earlier paper drew a
connection between General Relativity and Yang-Mills gauge theory, but that
the direct connection to HUP and QM is the one I am developing at present in
http://home.nycap.rr.com/jry/Papers/Uncertainty%20and%20GR.pdf. I have
posted a number of replies today that summarize my current thinking on this,
which has changed significantly in the last 48 hours.
As I have said in some other posts, I now believe that the tensor density
integration problem in GR is HUP in disguise.