29.01.2008

(Quotations from Evans' papers are displayed in **black**.)

With the introduction to his paper #100 [1.1]. Evans announces a review of major themes of his ECE theory. Evans Section 7 [1.7] deals with the Sagnac effect. In contrast to Evans' opinion that effect is best understood for a long time in the scope of Relativity. The reader is kindly requested to have a look at the literature [12],[13],[14].

We consider a light fibre placed in the x,y-plane along a circle of radius R around the centre.

Let (t,x,y,z) be the coordinates of a Minkowskian inertial-frame with its origin centered at the axis of rotation of the fibre-device with rotation around the z-axis. Then the metric of the frame is given by:

ds² = dx² + dy² + dz² − c² dt² .

We introduce cylindrical coordinates (r,θ) instead of (x,y) by x = r cos θ, y = r sin θ, and restrict our consideration to the submanifold r=R, z=0 (given by the light fibre) to obtain the metric of the submanifold:

ds² = c²dt² − R²dθ² .

Relative to this coordinate frame S the points of the fibre are travelling with the (constant) velocity

v = R dθ/dt = R ω .

We introduce a new coordinate frame S'(t',θ') where the points of the fibre are at rest:

θ' = γ(θ − ωt) ,
t' = γ(t − ^{R²ω}/_{c²} θ)
where
γ = (1 − ^{R²ω²}/_{c²})^{−½}

to obtain the corresponding metric by transforming ds². This yields

ds² = c²dt'² − R²dθ'² .

The invariance of the line element yields that the circular travelling
θ'(t') = __+__ ct'/R of the two light beams travelling along
x² + y² = R² with velocity c is seen from S' as two light beams travelling
along x'² + y'² = R² with the same velocities c as well in clockwise or
counter-clockwise sense respectively. However, **the distances to be covered
until the beams meet the world-lines of their initial point are different**:

Let L' denote the distance measured in S' once around the circular light fibre.
Then the time T_{-}' of the clockwise running signal to return to its initial point
is given by

L' = c T_{-}' + v T_{-}' ,
hence
T_{-}' =
^{L'} / _{c+v} ,

while the counter-clockwise signal needs the time T_{+}' given by

L' = c T_{+}' − v T_{+}' ,
hence
T_{+}' =
^{L'} / _{c−v} .

The time difference is (with v=Rω, L'=2πR)

Δt = ^{2πR} / _{c−v} −
^{2πR} / _{c+v} = 2πR (^{1} / _{c−v}
− ^{1} / _{c+v}) =
^{4πRv} / _{c²−v²} .

The result of that measurement in S' is transmitted to the non-rotating inertial system S and gives information about the angular velocity ω of S' relative to S.

That's the whole story in the simple case of a rotating circular light fibre. The reader will find more general configurations considered in the literature, e.g. in [12], [13], [14].

[1.1] M.W. Evans, *A Review of Einstein-Cartan-Evans (ECE) Field Theory
(Introduction of Paper #100)*,

http://www.atomicprecision.com/blog/2007/12/27/introduction-to-paper-100/wp-filez/a100thpaperintroduction.pdf .

[1.2] M.W. Evans, *Geometrical Principles (Section 2 of Paper #100:
A Review of Einstein-Cartan-Evans (ECE) Field Theory*,

http://www.atomicprecision.com/blog/wp-filez/a100thpapersection2.pdf .

[1.3] M.W. Evans, *The Field (Section 3 of Paper #100:
A Review of Einstein-Cartan-Evans (ECE) Field Theory*,

http://www.atomicprecision.com/blog/wp-filez/a100thpapersection3.pdf .

[1.4] M.W. Evans, *Aharonov Bohm and Phase Effects in ECE Theory (Section 4 of Paper #100:
A Review of Einstein-Cartan-Evans (ECE) Field Theory*,

http://www.atomicprecision.com/blog/wp-filez/a100thpapersection4.pdf .

[1.5] M.W. Evans, *Tensor and Vector Laws of Classical Dynamics and Electrodynamics
(Section 5 of Paper #100)
*,

http://www.atomicprecision.com/blog/wp-filez/a100thpapersection5.pdf .

[1.6] M.W. Evans, *Spin Connection Resonance (Section 6 of Paper #100)
*,

http://www.atomicprecision.com/blog/wp-filez/a100thpapersection6.pdf .

[1a] M.W. Evans, *Development of the Einstein Hilbert Field Equation . . .*,

http://www.aias.us/documents/uft/a103rdpaper.pdf .

[1b] M.W. Evans, *Proof of the Hodge Dual Relation*,

http://www.atomicprecision.com/blog/wp-filez/a100thpapernotes16.pdf .

[1c] M.W. Evans, *Some Proofs of the Lemma*,

http://www.atomicprecision.com/blog/wp-filez/acheckpriortocoding5.pdf .

[1d] M.W. Evans, *Geodesics and the Aharonov Bohm Effects in ECE Theory*,

http://www.aias.us/documents/uft/a56thpaper.pdf .

[2] S.M. Carroll, *Lecture Notes on General Relativity*,

http://xxx.lanl.gov/PS_cache/gr-qc/pdf/9712/9712019v1.pdf, 1997.

[3] S.M. Carroll, *Spacetime and Geometry*,

http://xxx.lanl.gov/PS_cache/gr-qc/pdf/9712/9712019v1.pdf, 1997.

[4] F.W. Hehl and Y.N. Obukhov, *Foundations of Classical Electrodynamics*,
Birkhäuser 2003

[5] G.W. Bruhn, *Consequences of Evans' Torsion Hypothesis*,

ECEcontradictions.html .

[6] G.W. Bruhn, *Remarks on Evans' paper #100 - Section 2*,

onMwesPaper100-2.html .

[7] M.R. Spiegel, *Vector Analysis*,

in Schaum's Outline Series, McGraw-Hill.

[8] G.W. Bruhn, *Evans' "3-index Î-tensor"
*,

Evans3indEtensor.html .

[9] G.W. Bruhn, *Comments on Evans' Duality*,

EvansDuality.html .

[10] G.W. Bruhn, F.W. Hehl, A. Jadczyk , *Comments on ``Spin Connection Resonance
in Gravitational General Relativity''
*, ACTA PHYSICA POLONICA B Vol. 39/1 (2008)

pdf . html

[11] G.W. Bruhn,
*Remarks on Evans/Eckardt’sWeb-Note on Coulomb Resonance,*,

RemarkEvans61.html .

[12] WIKIPEDIA, *Sagnac effect / Calculations*

http://en.wikipedia.org/wiki/Sagnac_effect#Calculations

[13] N.N. , *Reflections on Relativity, Sect. 7.2:
The Sagnac Effect*,

http://www.mathpages.com/rr/s2-07/2-07.htm

[14] O. Wuckwitz , *Sagnac effect, twin paradox and space-time topology ...*,

arXiv 2004

(08.01.2008)
**An Editorial Note by G. 't Hooft in Found. Phys.
**

(29.01.2008)
**Remarks on Evans' Web Note #100-Section 7: The Sagnac Effect
**

(25.01.2008)
**Remarks on Evans' Web Note #100-Section 6: SCR
**

(16.01.2008)
**Remarks on Evans' Web Note #100-Section 5: EM field
**

(08.01.2008)
**Remarks on Evans' Web Note #100-Section 4: The Aharonov Bohm effect
**

(05.01.2008)
**Remarks on Evans' Web Note #100-Section 3: Field and Wave equation
**

(01.01.2008)
**Remarks on Evans' Web Note #100-Section 2: Torsion and Bianchi identity
**

(27.12.2007)
**Remarks on Evans' Web Note #103
**

(19.12.2007)
**Myron now completely confused
**

(14.12.2007)
**Evans' Central Claim in his Paper #100
**

(10.12.2007)
**How Dr. Evans refutes the whole EH Theory
**