APPENDIX B.

Surface Area of a Sphere Spinning Such That its Circumferential Velocity is Equal to the Velocity of Light.


Repeating (2.4)


DL* = Ge2 sinq cosq dq df
(B.1)

Integrating, first with respect to f yields


L* = 4pGe2 ó
õ 		p/2

0 
 sinq cosq dq
(B.2)

where advantage of symmetry with regard to q has been incorporated. Evaluation of (B.2) is simple and gives


L * = 2pGe2
(B.3)


This is exactly half the surface area of the sphere when at rest, the reduction being caused by the Lorentz - Fitzgerald contraction of circumferential dimensions.




APPENDIX C.


Derivation of the Lorentz - Fitzgerald Contracted Dimensions l5 and l6 in Section 2.1.


Consider Fig. C.1 below. This is a plan view of a cross-section of Fig. 2.1 taken at the plane of the elemental.


Picture 4


Fig. C.1 - Plan View at Electron Elemental.


From the Figure


l =Ge sinq cosf secj
(C.1)

So that


l dj = Ge sinq cosf secj dj
(C.2)

and therefore the Lorentz - Fitzgerald contracted element of l5 is given by


dl5 = Ge sinq cosf sec2j æ
è 		1 -   e wsp2 l 2
c 2
 ö
ø 		1/2

 
 dj
(C.3)


Because, by far, the greater part of the contraction takes place at the perimeter, this process can be greatly simplified by the approximation


dl5 = Ge sinq cosf sec2j æ
è 		1 - e wsp2 Ge2 sin2q
c 2
 ö
ø 		1/2

 
 dj
(C.4)


The small error that this approximation introduces will be compensated out by way of the process that determines the value of Ge.

When ewspGe = c, (C.4) becomes


dl5 = Ge sinq cosq cosf sec2j dj
(C.5)

Integrating


l5 = Ge sinq cosq cosf ó
õ 		f

0 
 sec2j dj
(C.6)

which evaluates to


l5 = Ge sinq cosq sinf
(C.7)

Consequently, in Fig. 2.1,


l6 = l5 cotf    = Ge sinq cosq cosf
(C.8)


P5 Version 1.1.2
Ó P.G.Bass, August 2011

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