On Feb 13, 11:49*pm, Edward Green wrote:
[...]

How is information of the sense of rotation communicated to the field,
when apparently nothing in the source term admits it!?


Consider the solid ball in R3 of radius ð (that is,
all points of R3 of distance ð or less from the origin).
Given the above, for every point in this ball there is
a rotation, with axis through the point and rotation
angle equal to the distance of the point from the origin.
The identity rotation corresponds to the point at the
center of the ball. Rotation through angles between
0 and -ð correspond to the point on the same axis
and distance from the origin but on the opposite
side of the origin. The one remaining issue is that
the two rotations through ð and through -ð are the
same. So we identify (or "glue together") antipodal
points on the surface of the ball. After this
identification, we arrive at a topological space
homeomorphic to the rotation group.
http://en.wikipedia.org/wiki/Rotation_group

consider a closed Universe, that is, we take omega
= 1+å and either identify the antipodes after a
parity reversal, or consider a tunneling over the
extent of the hypersphere at a given time. In
either case, it is the red-shifted radiative
image of the local matter that appears spread
here in the far infrared while the tunneling
is assumed to be instantaneous from here to
here, through a distance. In other words, the
energy borrowed from the vacuum by virtual
photons of energy ~ mc2 is entirely returned
by their cosmological redshift, the process being
coherent. The scalar Riemannian curvature R thus
appears in the one-loop diagrams of QFT while
the Newtonian force emerges only at the two-loop
level. Now the range of the near field of our
coupled oscillators reaches to the Universe, within
which coherent modes can arise in which the local
oscillators fully partake if they are assumed to
lie entirely within their coherence domain. The
equivalence principle also emerges naturally
http://arxiv.org/abs/physics/0107015

IOW... "over all space" is code-speak for
the notions for of that nut E. Mach.


Sue...






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