Speed of Light in Rotating Frames

From: Jack Sarfatti (sarfatti_at_pacbell.net)
Date: 02/15/05 

Date: Tue, 15 Feb 2005 01:56:14 GMT

In a rotating non-inertial frame the speed of light does shift analogous
to a pseudo-scalar increasing in one sense of rotation and decreasing in
the opposite sense of rotation. This is in contrast to a spherically
symmetric compact source that is not rotating where the speed of light
remains at c for the fixed non-inertial observer although its direction
changes (bending of light - gravity lens). Gravimagnetic Lense-Thirring
frame drag, therefore, will be expected to shift the speed of light for
the non-inertial observers.

On Feb 14, 2005, at 3:04 PM, Jack Sarfatti wrote:

Metric engineering is the artificial warping of the fabric of space-time
using SMALL amounts of electrical power on board the "flying saucers" -
as small as a single AAA battery perhaps? ;-)

http://www.streetpeddler.com/cgi-bin/street/dynam.html?prod_group=toys&category=over_10&type=Energetic%20Bunny
http://stardrive.org/cartoon/dan.html
http://stardrive.org/cartoon/coffee.html
http://stardrive.org/cartoon/Saturn.html

The context here are Russian claims for torsion field-based advanced
weapons systems combined with a seeming glimmer of a confirmation from
an American physicist on a US Navy contract that subsequently went
"black" as well as http://americanantigravity.com/eric-davis.shtml for
the Rube Goldberg/Polish Joke version of metric engineering. :-)

When one reads Nick Cook's book "The Hunt For Zero Point" re:
Podkletnov, Ning Li and previous alleged Nazi experiments
http://www.findarticles.com/p/articles/mi_m2843/is_6_26/ai_94044223
rotation of a macro-quantum object seems to be important. Now we have
"supersolids" as well as superconductors. Is the flying saucer shell a
high Tc nano-smart super solid? (e.g. my 1969 paper "Destruction of
superflow in unsaturated 4He films and the prediction of a new
crystalline phase of 4He with Bose-Einstein condensation." Physics
Letters, Vol 30A, no 5 3 November 1969 pp 300-1).

Let's look at rotating frames in Einstein's theory. Start with a
non-rotating inertial frame K in Einstein's 1905 special relativity.
Direct warping of spacetime by real matter or by the virtual matter of
dark energy and dark matter will be neglected. Think of a Merry Go Round!

The space-time geometry in the global inertial frame K has the metric form

ds^2 - c^2dT^2 - dX^2 - dY^2 - dZ^2

Since kids are playing on the Merry Go Round we take it real slow and
gentle with a Galilean transformation to the rotating non-inertial frame
K about z axis at w RPM.

T = t i.e. ABSOLUTE COORDINATE TIME in this slow rotation limiting case.

X = xcoswt - ysinwt

Y = xsinwt + ycoswt

Z = z

Therefore, from Newton's calculus, the first-order differentials are

dX = dxcoswt - xwdtsinwt - dysinwt - ywdtcoswt

dY = dxsinwt + xwdtcoswt + dycoswt - ywctsinwt

Substitute dX & dY into INVARIANT ds^2 to get

ds^2 = [c^2 - w^2(x^2 + y^2)]dt^2 + 2wydxdt - 2wxdydt - dx^2 - dy^2 - dz^2

There is no real event horizon here like in a black hole because the
Galilean approximation here is

(w/c)^2(x^2 + y^2) << 1

The dimensionless gravimagnetic field is

Bi = goi

Bx = 2wy/c, By = 2wx/c, Bz = 0

What is the speed of light measured by an non-inertial observer fixed in
the rotating frame?

ds = 0 for a ray of light.

Therefore

0 = [1 - (wr/c)^2](cdt)^2 - dL^2 - (Bxdx + Bydy)(cdt)

r^2 = x^2 + y^2 = distance from axis of rotation in cylindrical coordinates

dL^2 = dx^2 + dy^2 + dz^2

The physical time measured by a clock fixed to the rotating frame at r
will be, according to Einstein's SR time dilation and the GR principle
of equivalence

dT = [1 - (wr/c)^2]^1/2dt

The metric equation for the ray of light is then

0 = (cdT)^2 - dL^2 - (B.dr)(cdt) = (cdT)^2 - dL^2 - (B.dr)(cdT)(1 -
(wr/c)^2)^-1/2

Divide by dT^2

c^2 - (dL/dT)^2 - B.(dr/dT)c(1 - (wr/c)^2)^-1/2

dL/dT = c[1 - (B/c).(dr/dT)(1 - (wr/c)^2)^-1/2]^1/2

Obviously dL/dt = c is the speed of light in vacuum for the non-rotating
inertial frame. The rotation has changed the physical speed of light.
Note however that the speed of light does not change in a the vacuum
surrounding a nonrotating spherically symmetric mass.

Note that dr/dT = wr[1 - (wr/c)^2]^1/2

therefore, the vacuum speed of light in the rotating non-inertial frame is

dL/dT = c[1 - (B/c).(dr/dT)(1 - (wr/c)^2)^-1/2]^1/2

dL/dt = c[1 - Bwr/c]^1/2

where Bwr/c << 1

dL/dt ~ c(1 +- B|w|r/2c)

Note that when we change the sense of rotation w -> -w, the shift in the
speed of light reverses as well analogous to a pseudo-scalar violating
parity in the weak force of beta decay radioactivity.

The effective gravity here does not decay to zero at infinity like a
real gravity field from a compact source. See Landau & Lifshitz
"Classical Theory of Fields" Ch 10.

On Feb 14, 2005, at 2:01 PM, Jack Sarfatti wrote:

On Feb 14, 2005, at 1:14 PM, iksnileiz@earthlink.net wrote:

When I wrote "speed of light propagation", I meant the speed of light
propagation.

When O&R wrote "speed of light propagation", they meant the speed of
light propagation.

I am talking about the speed of light propagation.

  It's a tricky question in GR.

The time of delay in propagation of light in the Shapiro effect is not
due to a change in the physical speed of light in vacuum. It is due to
an INCREASE in the proper space length of the photon's path from the
Sun's curvature field. Wheeler & Ciufolini explain it in detail in
'Gravitation and Inertia". You do seem to get speed of light effects in
rotating frames like Sagnac effect and also gravimagnetism with rotating
sources, but you do not get it in Schwarzschild case where

ds^2 = c^2dT^2 - dR^2 - dL^2

ds = 0

(dR^2 + dL^2)^1/2/dT = c measured both by rest LNIF and coincident LIF
observers at same event P

dR = (1 - 2GM/c^2r)^-1/2dr = physically measured radial interval by
LNIF rods at rest relative to M source.

dT = (1 - 2GM/c^2r)^1/2dt = physically measured time interval by LNIF
clocks at rest relative to M source.

dL^2 = r^2(dtheta^2 + sin^2thetadphi^2)

Bending of light by gravity is

tan(chi) ~ dL/dR

gravity red shift is from

dt = dt'

i.e.

dT/(1 - 2GM/c^2r)^1/2 = dT'/(1 - 2GM/c^2r')^1/2

You do not understand elementary measurement theory in GR.

With gravimagnetism you do get new effect

ds^2 = c^2dT^2 - dR^2 - dL^2 - goi(cdt)dx^i = c^2dT^2 - dR^2 - dL^2 -
Bidx^i(cdt)

i = 1,2,3

Bi is the gravimagnetic field used by Ray Chiao in "gravity radio" for
submarine C^3.

Bi = g0i

for a light ray ds = 0

Therefore, I get the interesting formula (will work for Sagnac effect also!)

c^2 = (dR/dT)^2 + (dL/dT)^2 + cBi(dx^i/dT)(dt/dT)

dt/dT = 1/g00

Suspend summation convention

dX^i = (gii)^1/2dx^i

c^2 = (dR/dT)^2 + (dL/dT)^2 + c(gii)^-1Bi(dX^i/dT)goo^-1

i.e. (gii)^-1Bi(dX^i/dT) = (g11)^-1B1(dX^1/dT) + (g22)^-1B2(dX^2/dT) +
(g33)^-1B3(dX^3/dT)

Therefore, the measured speed of light for rotating sources and frames is

d(R^2 + L^2)^1/2/dT = c[1 - (gii)^-1(Bi/c)(dX^i/dT)goo^-1]^1/2

Eq 36 p. 17 of Brazilian paper mentions Moller's solution of this
problem using the Cartan tetrads that are a bridge between the two
complementary local gauge connection and tensor geometrodynamical
formulations of Einstein's 1916 GR before generalizations to additional
Shipov-type torsion dynamical compensating field and possibly others
from the hyperbolic boosts and the dilation parts of the Conformal
Group's Lie algebra.

Decoding The Cipher of Genesis

Cartan Form GR

Let A^a^b^c be the Ricci rotation coefficients in the tangent space

Au^b^c = eu^aA^a^b^c

eu^a = Locally gauged T4 Cartan tetrad of Einstein's torsion-free 1916 GR.

eu^a = &u^a + Bu^a

&u^a = trivial globally flat Minkowski holonomic tetrad where the
tangent space and the base space are degenerate identical i.e. no
gravity, no inertia of the unstable Dirac Sea pre-inflationary false
warpless vacuum "before" the BIG BANG.

Casting "Oil" on the Stormy Waters of The Dirac Sea to create The Big
Bang from the binding energy of virtual electron-positron pairs in the
Vacuum Condensate of the Cosmic "multi-layered multi-colored" (Wilczek)
cosmic superconducting field.

Bu^a is the non-trivial part of the Cartan tetrad encoding the
post-inflationary emergent warps of gravity, inertia, dark energy and
dark matter in the Pacific Higgs Ocean. The anti-gravity dark energy
residual micro-quantum zero point fluctuations is the "fuel" of globally
superluminal weightless warp controlled geodesic drive and time travel
to the past through Star Gates.

The warp drive gauge potential field is

Bu = Bu^aPa/h = (Higgs Ocean Goldstone World Hologram Macro-Quantum Phase),u

h = Planck's constant

{Pa} = Lie algebra of the translation group T4 generated by John
Wheeler's total "mom-energy",

The Cartan 1-form for the connection of parallel transport in warped
spacetime is

A = Au^b^cSbcdx^u

{Sab} is the Lie algebra of the O(1,3) local Lorentz group in the
tangent space of Einstein's GR

The covariant exterior Cartan derivative D is then

D = d + A

d = ordinary flat space-time exterior derivative

d^2 = 0 in flat space-time sans gravity sans inertia (massless lepto-quarks)

D^2 = 0 in warped space-time with gravity and inertia as well as exotic
vacua domains.

The tidal stretch-squeeze curvature 2-form R is simply

R = DA = dA + AA

The tetrad 1-form is

e = eu^a(Pa/h)dx^u

The Gennady Shipov torsion 2-form T is then simply

T = De = de + Ae

On Feb 12, 2005, at 1:10 PM, Jack Sarfatti wrote:

Decoding The Cipher of Genesis

"quasi-local approach" ... "super-potential, which is a Hamiltonian
boundary term" "screen" of World Hologram i.e. local horizon on (anti)
De Sitter space-time with Hawking radiation? That is the gravity energy
only depends on the horizon surface not on local space volume elements!
3D Space is a holographic image! See p. 16 section E of Brazilian paper.
They go on to get a local representation in the complementary or dual
gauge-force picture that is physically equivalent to the nonlocal
geometrodynamic picture.

The Brazilians Arcos & Pereira (2005) discuss the nonlocality of the
gravity energy in Einstein's geometrodynamic representation with
curvature and no torsion that is Bohr complementary to the gauge force
representation with torsion and no curvature. However the Brazilian
"torsion" should not be confused with Gennady Shipov's torsion. They are
entirely different and different words should be used.

My own macro-quantum theory, for the emergence of Einstein's curvature
in the post-inflationary "Higgs Ocean" (Brian Greene) AKA "multi-layered
multi-colored" cosmic superconducting field (Frank Wilczek) AKA partial
cohering of the pre-inflationary random micro-quantum zero point false
vacuum fluctuations, is more naturally set in the Brazilian gauge force
representation initially although I immediately transform to Einstein's
orthodox geometrodynamical representation as more heuristic for getting
new insights.

Recall that the pre-inflationary unstable false vacuum is a conformal
vacuum without gravitation or inertia admitting only massless
lepto-quark and boson gauge force special relativistic quantum fields.
U(1)SU(2)SU(3) is locally gauged in the false vacuum. No part of the 15
parameter conformal group is locally gauged pre-inflation.

Conformal Group C(4)

= Dilation*(Conformal Boosts to Uniformly Accelerating Hyperbolic
Motion)*(Translations)*(Space-Rotations)*(Inertial Frame Lorentz Boosts)

T4 = normal subgroup of translations generated by Wheeler's "mom-energy"
= Lie algebra {Pa}

O(1,3) = (Space-Rotations)*(Inertial Frame Lorentz Boosts) = Lorentz Group

Lorentz Boost = space-time rotation

real angles of rotation of an extended rigid body have imaginary
extensions that are equivalent to the "rapidities" of the Lorentz boosts.

Spontaneous breaking of O(3) rotation group symmetry in the ground state
of many spinning electrons is ferromagnetism. Ferromagnetism is a
preferred frame of orientation in space without explicit O(3) breaking
terms in the dynamical action.

Similarly, data like Cahill's and Consoli's claiming a preferred Lorentz
inertial frame would, if corroborated, merely mean spontaneous breakdown
of the O(1,3) group in the physical vacuum, particularly its boost
sector. The preferred frame of absolute rest means a set of rapidities
are chosen in a finite region of vacuum just like a set of rotation
angles (only latitude and longitude on the celestial sphere, twist
rotation (torsion field?) about the preferred space direction is another
issue using ALL THREE Euler angles, is chosen in a finite domain of the
ferromagnetic ground state.

Einstein, not knowing about spontaneous symmetry breakdown in 1905,
thought of the space of global inertial frames (pre-GR 1916) as an
affine space without a preferred origin. Lorentz thought of this space
of frames as a vector space with an origin. This is a real experimental
difference, but it is contingent not fundamental. The way the symmetry
breaks in a ferromagnetic domain is contingent like a pimple on one's
nose. Similarly, for Cahill's claim - a small blemish on Einstein's nose
for The Truth! :-)

All dynamics comes from the minimal coupling local gauge principle of
different symmetry groups both internal and external in 4D space-time.
Roger Penrose says extra space dimensions are unstable so let's see if
we can do without them. No supersymmetry needed as yet either since I
predict supersymmetry will not be found in the LHC and also that dark
matter detectors will never click with the right stuff, e.g.
on-mass-shell neutralinos et-al do not exist. These are falsifiable
predictions.

 From Stormy Dirac Sea to Calm Higgs Ocean (Oil upon The Waters of Creation)

Looking only, for now, at the low-energy tail of the false
pre-inflationary conformal vacuum sans gravity and inertia, both
emergent properties, the Dirac negative energy virtual Fermi energy is E
= 0 and the zero point PV virtual electron-positron pairs in a small
thickness of the Fermi surface form virtual bound states fusing into the
zero entropy BEC vacuum condensate "Higgs Ocean" that trigger the
inflation and the emergence of Einstein's gravity along with all rest
masses m and both dark energy and dark matter.

Post-inflation, the Cartan tetrad encoding the important part of the
equivalence principle (EEP) is

eu^a = (Kronecker Delta)u^a + Bu^a

Bu = Bu^aPa/h = (Higgs Ocean Goldstone Phase),u

{Pa} is Lie algebra of T4

i.e. the non-trivial curved intrinsic part - the actual or "real"
gravitational field that is locally equivalent to an inertial field in a
local non-inertial frame of reference, AKA "LNIF"

This is a spontaneous broken locally-gauged U(1)em vacuum symmetry
exactly like in the BCS superconductor where, instead of on-mass-shell
charged 2e electron pairs, we have neutral virtual electron-positron
pairs in an off-mass-shell "bound state". The result is a locally-gauged
T4 dynamical non-trivial tetrad field eu^a emergent from the spontaneous
broken U(1)em vacuum symmetry. The release of binding energy of the
virtual electron-positron pairs powers the Big Bang.