Ken S. Tucker wrote: Ken S. Tucker wrote: Jay R. Yablon wrote:
Jay R. Yablon wrote: Hannu wrote:
I have understood that the total energy is ill defined concept in
General Relativity ?

Well, total energy is defined mathematically as an energy for which
T^uv_;u=0, and the zero must be ensured identically.

T^uv is local energy-momentum _density_, not _total_energy_.

T^uv is NOT *arithmetically RELATED* to E^2 = m^2 + p^2, in GR.!!

Agreed.

To obtain
total energy you need to integrate the local density over the region of
interest, and that's the problem: in general for a curved manifold such an
integral is not well defined.

Tom,

Are you speaking of a curved spacetime problem or a quantum problem?

NATURE doesn"t care if MKSA (meter)^2 is "curved", "quantum" or BOTH.!!

-- For curvature, so long as we have g^uv defined at each point,

Try just THREE points ..HERE.!!

and the scalar sqrt(-g), we can in principle take a volume integral
"Integral sqrt(-g) T^00 d^3X" that will relate observed physics to
choice of coordinates. To Ken Tucker: Is that right?

No.!! "Observed physics" (i.e. mass) does NOT (CANNOT or will NOT)
*arithmetically* RELATE to the GR "Integral sqrt(-g) T^00 d^3X".!!

Oops I was lurking...
I think so. The T^00 define a static situation, like two
distant observers A and B at relative rest relating by
radar. --

Let T^00 define a static situation, like THREE distant observers
A, B and C, at relative rest relating by radar, E^2 = m^2 + p^2.
Most folks may be better able to grasp Euclid's a^2 = b^2 + c^2.
Most folks might BEST be able to grasp capitals A^2 = B^2 + C^2.!!

-- They will have a non-ambiguous result in their
distances, although there would be differences since
their clocks may be at different potentials and that
establishes the delta of the sqrt(-g) that occurs between
them.

I'd like to add, as a radio technician, that a standing
wave can always be created in a circuit, so a standing
radio wave could always be created between A and B,
with each observer A and B agreeing to a fixed number
of cycles separating their respective locations, (although
differ on the frequency depending upon their relative
potentials).

The problem seems to be, for ANY tesnor defined at
a "local," i.e., theoretically infinitesmal point in spacetime, how do we
carry out integration over a finite region when "points" in physics are not
infinitesmal. It seems almost a problem with using calculus, where delta
x -- dx -- 0, and it suggests that in physics, the best we can do is delta
x where delta is small but finite.
Jay.

The PoR can be clarified by defining it by

U_i =0 , i = 1,2,3.

For example an invariant, (Planck's)

h = p_u x^u = p_0 x^0 = rest energy * rest time

Planck's, h = k*c*{e}
= 2*#*{e}
= 2*(Magnetic Flux quantum)*(Electric charge)
..in MKSA - 2*(Webers - Volt*seconds)*(Ampere*seconds)
..in MKSA - 2*(Volts)^2*(seconds)^2 / (Ohms)
..in MKSA - 2*(Ohms)*(Amperes)^2*(seconds)^2
..in MKSA - 2*(Volts)*(Amperes)*(seconds)^2
..in MKSA - 2*(Watts)*(seconds)^2
..in MKSA - 2*(Joules)*(seconds)
..in MKSA - Angular momentum.

NO Angular momentum expression in GR (i.e. E^2 = m^2 + p^2).

Note MKSA is the OLD SI GiORGi MKSA SYSTEM of standard MEASURE.
Note MKSA is NOW finished; Outdone by: NEW SI GUESS STANDARD.!!

= 6.626*10^-27 ergs.seconds
= 6.626*10^-34 Joules.seconds
Note that you are mixing up your STANDARds, there, dooOP.
Planck's h = 6.535457053*10^-34 NEW SI Joule*seconds, iSS.
PLANCK's h = SLiGHTLY different number in NEW SI GUESS iSS.
Planck's h = a transcendental mathematical constant, like c.
Planck's h = a transcendental mathematical constant, like pi.

when p_i = p*U_i =0.

The U_i =0 leads directly to Minkowski's ds^2 = dt^2 - dr^2.

$ Euclidian PROOF
So RiGHT back to PYTHAGORAS THEOREM: p^2 = e^2 - m^2
..or in non-Ph.Tivity Euclidian: c^2 = b^2 - a^2
..or in general, SiMPLiFYs to .. z^2 = y^2 - x^2
..U_i =0 leads to Minkowski's ds^2 = dt^2 - dr^2.

GR "Integral sqrt(-g) T^00 d^3X" does not RELATE GR m^2, at all.!!

brian a m stuckless


Regards Ken S. Tucker
New Paper: General Relativity, Maxwell's Electrodynamics, and the
Foundations of the Quantum Theory of Gravitation and Matter
(gr-qc/0511050).