Grand secret between Einsteinians

**John C. Polasek**

On Sat, 03 Sep 2005 21:11:36 GMT, Tom Roberts
wrote:

Mike wrote:
Tom Roberts wrote:
Conservation of energy is indeed a "murky subject" when one considers
non-local measurements. Locally there's no doubt that energy is
conserved. This is a non-local example.

I suppose you understand the ramifications of your statements on the
nature of physical reality.

Somehow I don't think my statements are going to affect nature or how
she operates the universe. (:-))

If you do understand what non-local
non-conservation of energy implies, why do you still deal with GR and
not going back to your drawing board for a better theory?

Because GR _IS_ the best theory we have right now for such phenomena. By
a considerable margin. Non-local non-conservation of energy is not a
problem, and GR itself agrees with all experiments within its domain of
applicability[#]. Experiment is the touchstone for physics, not the
nebulous ideas you seem to think imply there is a "better theory" out
there....

[#] But there are some tantalizing intimations of new
phenomena and/or possible violations of GR: dark matter
and energy, and the anomalous accelerations of Pioneer
and other spacecraft.

Just for the purpose or being a little more explicit without crashing
the ongoing party, do you believe Dr. Roberts there is some process
that non-locally pumps or drains energy so that the world is
maintained?

Huh? There is no "pump or drain" involved in the non-local
non-conservation of energy, it's just that in general there is no
self-consistent definition of "energy" over a finite region, and if
there is no well-defined notion of "energy", how could it possibly be
"conserved"?

Take a non-local region. Divide it into N local regions. In
each local region energy is conserved.

No. In GR energy is conserved only approximately in any finite region;
it is exactly conserved only in the limit as the 4-volume of the region
goes to zero. That is, conservation of energy is expressed as a
differential equation, and in general it is not integrable.

But that may not be the case in
the union of these non-local regions according to your heterology.

I have no "heterology", I merely point out that you cannot generalize
this property that holds only in the limit as 4-volume = 0 to a finite
region. shrug

I do not see anything that happens according
to GR in between these local regions that can result in a non-local
non-conservation of energy.

Clearly you do not understand the issues involved. There are thorns when
attempting to union an infinite number of infinitesimal regions into a
finite-sized region. This is called "integration" and for the integrals
we are concerned with, the general integrability condition is that the
Riemann curvature tensor be zero (i.e. the manifold be flat throughout
the region of interest). That is sufficient but not necessary, and there
are some special cases for which Riemann is nonzero but a meaningful
global definition of energy can be made.

Tom Roberts
All of this debate is due to the fact that relativity has no strong
model. It's all done with Schwarzschild and it contains errors. I can
see that nearly everyone believes gravity reduces the frequency of
light. And that clocks run slow in gravity. And that, generally
speaking the velocity of light is constant. Er, except for Shapiro.
Lots of debate about how energy can't be conserved.

Dual Space theory has it right: a clock in gravity will run slower and
its emitted frequency will be lower than out of gravity. But, energy E
= hf never changes after that. Likewise the speed of light is reduced
at the origin in gravity. Therefore right at the source (with the
clock in gravity) the clock is X% low, its emitted frequency is X%
low, and the WL is normal = 1.

But on rising out of the gravity field, the energy hf remains the
same, but c increases by X% so the WL stretches by X%. That's the red
shift-increase in wavelength. The frequency remains as manufactured
and with its original energy never more or less.

But in relativity, the Pound and Rebka ("Possible Weight of Photons")
experiment talks as if the frequency is reduced on the way out of a
gravity well due to energy loss % = gh/c^2. So if it loses X% in
frequency on the way out, and is now measured for frequency by a clock
outside that is thereby running X% faster, the difference in frequency
will be 2X% double the ideal value.

The cause for the Shapiro effect should be derivable from the
Schwarzschild metric but I haven't seen it done.

In Dual Space, c reduces X% with gravity (in place of "time dilation")
and also the underlying space cells dilate by X%, because gravity is a
sign of a weakened underlying Espace. With DS you can get all of
relativity in a Cartesian model, besides which DS can explain the
Pioneer anomaly. I am finishing up a paper on it for the arxiv's.

John Polasek
http://www.dualspace.net

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