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[Phys-L] The Rigid Rotating Disk in Relativity

Technical points:

It has been pretty common since the discovery of dark energy to finger the
Higg's vacuum residue energy. It fits the bill nicely as it has positive
energy density and negative pressure of virtually the same magnitude. And my
thinking for a while has been that some slight asymmetry between the pos and neg
energy Higg's particles would lead to something other than zero as a sum of
the two. The math doesn't work out though - at least where I am now. The
Higg's residue energy, since it comes from a (phi)^4 term in the Lagrangian
(and Hamiltonian) results in postive energy from both the trads and the suppls.
From the (phi)^2 contributions we get i times i = -1 for the suppls, 1 times
1 = +1 for the trads. But from the (phi)^4 terms we get i^4 = +1 for both.
So both types of particles yield positive energy residues from Higgs sym
breaking.

Regarding the rotating disk: I would have liked to have been a part of the
conversation on AVOID, as this is really my specialty. There are really only
at best 20 or so experts in the world right now who really appreciate the
issues on this one. Virtually all of the other discussions either rehash stuff
that is already well discussed/researched, or more commonly, contain
misunderstandings and misconceptions.

For one: Any accelerating system (rectilinear accel or rotational motion)
is flat. This is a point that save for one obscure text, never seems to be
covered in GR texts/courses. I think the reason is that most physicists are
confused by it and don't understand the differences between grav and accel. I
have even seen a popular level book written by a physicist that says
accelerating frames are curved.

The basic principle is this. If the Riemann curvature tensor for a given
space is zero in one coordinate system, it is zero in all coordinate systems.
Accelerating frames are transformations of coordinates in 4D from an inertial
(flat) coordinate system to a non-inertial (accelerating) 4D coord system.
Thus, the curvature tensor is zero in the new coords.

the equivalence principle is only true locally (at a point.) No acclerating
system is everywhere equiv to a gravitational system, and vice versa. The
key here is that there is no transformation that can take us from an inertial
system to a gravitational system (but there are transformations from inertial
to accelerating.) Both accel and grav systems are non-inertial, but only
grav systems are curved. Both accel and grav systems can have time dilation
effects. It is not time dilation per se (or for that matter length
contraction) that gives rise to curvature. Consider a flat piece of rubber. Stretch
it. It is still flat, even though coordinate length measurements may have
changed.

The rotating disk circumference issue hinges on there being a curved 2D
surface (the disk surface) buried in a 4D flat space. The 4D space on the
rotating disk is flat, just like the 4D space of the lab. Those who claim length
contraction in the circumferential direction admit this, but argue that like a
sphere in a flat 3D space, the 2D space of the disk surface can be curved in
a flat 4D space.

The whole issue hinges on simulatneity definition. The SR length
contraction is a direct result of lack of simultaneity. If two frames have the same
simultaneity, there can be no length contraction between them. (Explained in
my first Found Phys Lett article - as background, as anyone knowing SR well
should know this). If you have the same simuitaneity on the disk (even though
clock speeds are different) as in the lab, there can be no length
contraction. If you don't have the same simultaneity on the disk, then it turns out
that there is a time discontinuity on the disk. Thus, if you think time is
continuous (pretty fundamental), then there is no length contraction on the disk
and the disk is flat. This is my position.

Please forward these comments to the AVOID list. Thanks.

Got to go. We have a friend visiting from Australia we haven't seen in 33
years, and we are taking him to see some sights.

Wishing you inner peace,
Bob




----- Original Message -----
From: _RBZannelli@aol.com_ (mailto:RBZannelli@aol.com)
To: _klauber@iowatelecom.net_ (mailto:klauber@iowatelecom.net)
Sent: Monday, September 12, 2005 11:26 AM
Subject: Fwd: The Rigid Rotating Disk in Relativity


Bob I sent this off to Dr Kaku. I have also been thinking about the Higg's
field contribution to vacuum energy. If I am correct that the only interaction
between positive and negative energy states is via their contribution to
space time curvature, then a supplemental higgs vev might nicely cancel the
traditional Higg's field contribution to vacuum energy or perhaps almost cancels
the Higg's contribution making this the source of dark energy without
affecting yukawa couplings. The Higg's relationship is intimately tied to the weak
force where we have CP hence TS violation. Of course this is just a hand
waving argument I know but maybe worth thinking about perhaps.

Bob Z
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