v o l t s peak to peak, w i t h c u r r e n t s of the order of 2-4 - - PDF document

SLIDE 1

The P h y s i c s of the

T e s l a Magnifying T r a n s m i t t e r ,

and the T r a n s m i s s i o n of

E l e c t r i c a l Power Without Wires

by A n d r i j a P u h a r i c h , M.D., LLD.

SLIDE 2

ABSTRACT

1 . The T e s l a Magnifying T r a n s m i t t e r (TMT) i s an e l e c t r i c a l

• s c i l l a t o r

c o n s i s t i n g of a f l a t h o r i z o n t a l primary i n d u c t o ^ L on e a r t h coupled to a secondary, and a c a p a c i t o r b a l l C which l a t t e r i s e l e v a t e d above the e a r t h plane a t a d i s t a n c e which i szyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA h the wavelength of the resonant frequency of the system. 2. The LCR system i s resonant to the fundamental frequency of the e a r t h /

atmosphere which i s e s s e n t i a l l y a g i a n t c a p a c i t o r system.

3. The TMT generates e l e c t r i c a l p o t e n t i a l s of the order of 100,000,000 v o l t s peak to peak, w i t h c u r r e n t s of the order of 2-4 KAmps. 4. The TMT b r o a d c a s t s

e l e c t r i c a l power ( w i r e l e s s ) to the T e s l a Magnifying

R e c e i v e r (TMR) s t a t i o n s a t d i s t a n c e s of hundreds of m i l e s from the source. 5. T e s l a claimed the f o l l o w i n g e f f e c t s : a. The primary path of the w i r e l e s s power t r a n s m i s s i o n from TMT to the TMR i s through the e a r t h which becomes a conductor of

e l e c t r i c i t y .

' b. The secondary path of the w i r e l e s s power t r a n s m i s s i o n from TMT to TMR i s through the atmosphere to c l o s e the

c i r c u i t .

c . The

e l e c t r i c a l power i s t r a n s m i t t e d a t l e s s than 1 % l o s s .

d. He measured e l e c t r i c a l s t a t i o n a r y waves i n the e a r t h . e. He measured s i g n a l s t r a v e r s i n g the e a r t h a t v e l o c i t i e s 27 times the speed of l i g h t , c, f . The system as d e s c r i b e d , and the e f f e c t s claimed were a l l v e r i f i e d e x p e r i m e n t a l l y by T e s l a and h i s c o l l e a g u e s , i n 1904. No one has t r i e d to r e p e a t T e s l a ' s work s i n c e 1904. 6. There has been g r e a t r e l u c t a n c e on the p a r t of e n g i n e e r s and p h y s i c i s t s to accept T e s l a ' s data, l a r g e l y because such d a t a cannot be r e c o n c i l e d w i t h p h y s i c a l theory i n vogue between 1904 to 1976, and the experiments a r e not easy to r e p e a t . 7. A t h e o r e t i c a l e x p l a n a n t i o n

• f T e s l a ' s data on h i s TMT

i s g i v e n as f o l l o w s :

• 4 -

SLIDE 3

The L i e n a r d - W i e c h e r t s o l u t i o n of the Maxwell equations f o r electromagnetism

show t h a t the propagated EM wave i s a time d e r i v a t i v e of the v e l o c i t y , c, known as the r e t a r d e d

p o t e n t i a l . I n the TMT the r e t a r d e d p o t e n t i a l i s i d e n t i f i e d w i t h the atmospheric r a d i a t i o n of the EM s i g n a l from the e l e v a t e d c a p a c i t o r b a l l C. The L i e n a r d - W i e c h e r t s o l u t i o n a l s o shows the e x i s t e n c e

• f a wave f a s t e r than c known as the advance p o t e n t i a l .

S i n c e t h i s i s the imaginary s o l u t i o n , and does not have p h y s i c a l d e t e c t i b i l i t y , i t i s u s u a l l y ignored.

However, i f the advance p o t e n t i a l i s t r e a t e d by

the de B r o g l i e equation a s a phase v e l o c i t y wave we can v i s u a l i z e i t as a " h o l e "

• r t u b u l a r wave guide moving f a s t e r than c, f o r the r e t a r d e d

p o t e n t i a l which

i s slower than c, the two p o t e n t i a l s being ISO" out of phase.

T h i s " t u b u l a r wave guide" can be analyzed by means of the D i r a c equation ( f o r the e l e c t r o n ) which shows i t to be a r o t a t i n g f i e l d w i t h the p r o p e r t i e s

• f magnetism and

s p i n . At high v o l t a g e s , c a . 100 Mev., t h e r e i s an i n t e r - a c t i o n between the advance p o t e n t i a l wave guide f i e l d , and the r e t a r d e d p o t e n t i a l photonic f i e l d such that p a r t i c l e p a i r s ( e l e c t r o n - p o s i t r o n ) a r e c r e a t e d ,

• r the p a i r s a r e a n n i h i l a t e d to y i e l d photonic r a d i a t i o n .

I n dense m a t e r i a l s such a s that of the e a r t h t h i s r e a c t i o n i s augmented by the presence

• f atomic n u c l e i .

Thus t h e o r e t i c a l l y the TMT

can t r a n s f e r l a r g e amounts of c u r r e n t u s i n g the e a r t h as a conductor, and under a p p r o p r i a t e c o n d i t i o n s

• f

resonance (frequency and v o l t a g e ) g a i n (or m a g n i f i c a t i o n ) of power i s f e a s i b l e .

• 5"-

SLIDE 4

I n order to understand t h e workings of the T e s l a Magnifying T r a n s m i t t e r

(TMT), ,we w i l l p r e s e n t i n an elementary form some of the b a s i c concepts of

e l e c t r i c i t y as formulated by Maxwell (from E n c y c l o p a e d i a B r i t . , V.6,

• p. 660 f f ) . We r e l a t e e l e c t r o m a g n e t i c r a d i a t i o n to i t s source by means
• f the p o t e n t i a l s as g i v e n i n t h e two Maxwellian equations where:

B = Magnetic = Vector P o t e n t i a l (A) E = E l e c t r i c = S c a l a r P o t e n t i a l ((j)) B = c u r l A

(1)

9A

E = - grad ( j )

• —

( 2 )

9t The other two Maxwell equations become:

9A

V^(t) + d i vzyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

— = - p/e

( 3 )

zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA dt

"

1

9A 1 9 ( | ) V X (V x A) + +

grad —

= y j ( 4 )

"

" ' 9t " , 2

The d i v e r g e n c e of A and the time d e r i v a t i v e of ( J )

a r e not s p e c i f i e d by t h e i r

d e f i n i t i o n s i n terms of the f i e l d s , and may be chosen so t h a t ,

194.

d i v A +

= 0 ( 5 )

T h i s i s c a l l e d the L o r e n t z c o n d i t i o n

• n the p o t e n t i a l s .

I f the L o r e n t z

c o n d i t i o n i s s a t i s f i e d , the p o t e n t i a l s a r e s o l u t i o n s of the second-order

inhomogenous wave e q u a t i o n s ,

• 6-

SLIDE 5

1

a^cj)

• p/e

, (6)

1

a^A V^A

• (7)

The f i e l d s e x c i t e d by the charge P, and c u r r e n t j , source s a r e determined by d i f f e r e n t i a t i n g the p o t e n t i a l s , which a r e p a r t i c u l a r s o l u t i o n s of t h e s e e q u a t i o n s .

I t was f i r s t shown by Ludvig V a l e n t i n Lorenz,a Danish p h y s i c i s t , t h a t s o l u t i o n s

may be w r i t t e n f o r m a l l y as volume i n t e g r a l s over the source d i s t r i b u t i o n s e v a l u - ated at the r e t a r d e d time, equal to the time ( t ) f o r which the f i e l d i s d e s c r i b e d minus the d i s t a n c e t r a v e l l e d ( r ) d i v i d e d by the v e l o c i t y , or

t ' =

t - L , (8) c which would a l l o w the t r a n s m i s s i o n of the f i e l d s from the source w i t h v e l o c i t y c; t h a t i s .

(})(x, y, z, t )

= p(x', y', z', t - r / c )

47Te

dV , (9)

1

j ( x ' , y', z', t - r / c ) A(x, y, z, t ) =

_ dV

4iT r (10)

i n which r i s the d i s t a n c e from a source point (primed c o o r d i n a t e s ) to the f i e l d point ( p l a i n c o o r d i n a t e s ) .

These a r e the r e t a r d e d p o t e n t i a l s ; mathema-

t i c a l l y the advanced p o t e n t i a l s , w i t h the i n t e g r a l s e v a l u a t e d a t

t + r / c , a r e e q u a l l y v a l i d , but i n the c l a s s i c a l r a d i a t i o n theory p h y s i c a l s i g n i f i c a n c e

i s not a t t a c h e d to such s o l u t i o n s .

The reason f o r t h i s l a c k of n o t i c e of the

advanced p o t e n t i a l s i s t h a t they move a t speeds g r e a t e r than c and

t h e r e f o r e

• 7 -

SLIDE 6

cannot be d e t e c t e d by p h y s i c a l i n s t r u m e n t s a l l of which o p e r a t e e i t h e r

a t , or below, the

v e l o c i t y of l i g h t , c . The Lorenz advanced p o t e n t i a l s o l u t i o n i s

t h e key to understanding the

T e s l a Magnifying T r a n s m i t t e r

(TMT).

The TMT has

two components where the

p h y s i c a l c a p a c i t o r C, i s

the source

f o r the s c a l a r p o t e n t i a lzyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA (p; and the p h y s i c a l i n d u c t o r L, i s

the

source

f o r

the v e c t o r p o t e n t i a l A. The two s o u r c e s a r e coupled a s a s e r i e s LC r e s o n a t o r .

Resonance i s achieved w i t h r e s p e c t to t h e e a r t h / a i r c a p a c i t o r C' a s the load which has

a r e s i s t i v e component R. For the TMT t o operate and e f f i c i e n t l y

c a r r y out w i r e l e s s t r a n s m i s s i o n of e l e c t r i c a l energy two c o n d i t i o n s must be s a t i s f i e d :

1) The p o t e n t i a l of the TMT must exceed 100,000,000 v o l t s a t a

resonant frequency f o r

the

system L C R . 2)

A T e s l a Magnifying

R e c e i v e r (TMR) s h a r p l y tuned to the

L C R resonant frequency must be p l a c e d somewhere

• n t h e e a r t h to r e c e i v e t h e e l e c t r i c a l power o f the

TMT.

The v e c t o r p o t e n t i a l A a s s o c i a t e d w i t h L then takes the

form of the advanced

p o t e n t i a l which propagates through the e a r t h a t v e l o c i t y g r e a t e r than c . The

advanced p o t e n t i a l propagates a s

a r o t a t i n g "magnetic" f i e l d

( t a n g e n t i a l to l i n e of propagation) which c r e a t e s a t u n n e l e f f e c t "wormhole" from the

TMT

to t h e

TMR. The " h o l e " thus c r e a t e d i n

advance of the a r r i v a l of the r e t a r d e d

p o t e n t i a l from the source (j), i n f a c t , " d i r e c t s " the e l e c t r o m a g n e t i c r a d i a t i o n to t h e

TMR where maximum power t r a n s f e r

• c c u r s .

A simple example w i l l show t h a t the r e t a r d a t i o n i s r e s p o n s i b l e f o r t h e e x i s t e n c e of t h e p h y s i c a l e l e c t r o m a g n e t i c f i e l d s , which must f a l l o f f

a s the

i n v e r s e

f i r s t power of the

d i s t a n c e . L i k e w i s e , the

advance p o t e n t i a l i s

r e s p o n s i b l e f o r " t u b u l e " or "wormhole" e f f e c t s i n

any media which a r e i n

e f f e c t r o t a t i n g "magnetic" f i e l d s propagating f a s t e r than the speed of l i g h t and which i n c r e a s e a s the f i r s t power of the d i s t a n c e .

I f a charge

e, i s

r e s t r i c t e d to a s m a l l r e g i o n of space near t h e o r i g i n

• f c o o r d i n a t e s ,

then, to

a f i r s t approximation, t h e

v e c t o r p o t e n t i a l a t

a

l a r g e d i s t a n c e

r , i s simply

y e v ( t - r / c ) A(x, y, 2, t ) = _ ^ 4zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

T T

r (11)

The.-relation

B = c u r l A

r e q u i r e s t a k i n g the space d e r i v a t i v e s , each term of

which would behave a s 1/r^ a t b e s t , except f o r

the f a c t t h a t t h e d i s t a n c e

r , i s

a l s o i n v o l v e d i n

the r e t a r d e d time. The r a d i a t i o n f i e l d i s

thus pro- p o r t i o n a l to the time d e r i v a t i v e of the v e l o c i t y . When we s o l v e the equation i n t e g r a l s a t t + r / c ,

the r a d i a t i o n power w i l l i n c r e a s e p r o p o r t i o n a t e l y

w i t h d i s t a n c e and v e l o c i t y a s r ^ . The l a t t e r s o l u t i o n s must be a r r i v e d a t r e l a -

t i v i s t i c a l l y .

With r e s p e c t to the r e t a r d e d

p o t e n t i a l , i f

the

motion of

the

SLIDE 7

charge i s c o n f i n e d to the z

a x i s , the magnetic f i e l d i s a z i m u t h a l , and

g i v e n by

4>

qv 1 — s i nzyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

0 = —

qv s i n 0

4lTC

4TTe

(12)

r c " I n t h i s simple approximation

0 i s the angle between the z a x i s and the

l i n e

r from s o u r c e to o b s e r v e r . The corresponding e l e c t r i c v e c t o r i s along the d i r e c t i o n of change i n angle and equal i n magnitude to cB

i n t h e s e u n i t s .

The e x a c t p o t e n t i a l s corresponding to a p o i n t charge, i n c o n t r a s t to t h i s approximation a r e not obtained by s u b s t i t u t i n g the t o t a l charge f o r the volume i n t e g r a l i n d i c a t e d i n the r e t a r d e d p o t e n t i a l s . The problem a r i s e s because of the f i n i t e v e l o c i t y of f i e l d propagation, so t h a t the i n t e g r a l of the r e t a r d e d charge d e n s i t y over space i s not i n g e n e r a l equal to the t o t a l charge. C o n v e r s e l y , the advance p o t e n t i a l charge d e n s i t y

w i l l i n g e n e r a l be g r e a t e r than the t o t a l charge, hence the

"magnifying" c h a r a c t e r of the T e s l a T r a n s m i t t e r . The c o r r e c t p o t e n t i a l s f o r an e l e c t r o n

• f charge

e, a r e 4 ' n

• e

R -zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

R" v / c

A = - 1

4zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA T T

ev

R - R* v / c (13) (14)

i n which

R i s the r a d i u s v e c t o r from the e l e c t r o n to the f i e l d p o i n t , v

i s the v e l o c i t y of the e l e c t r o n , and the square b r a c k e t i s used to denote the

f a c t t h a t a l l q u a n t i t i e s a r e to be e v a l u a t e d a t the r e t a r d e d time, not the

time of o b s e r v a t i o n . These a r e known as the L i e n a r d - W i e c h e r t p o t e n t i a l s . Before the advent of r e l a t i v i t y theory they could not be j u s t i f i e d f o r h i g h - v e l o c i t y e l e c t r o n s , because i t was n e c e s s a r y to assume t h a t Maxwell's equations

were v a l i d o n l y i n the r e f e r e n c e frame of the o b s e r v e r .

But the L i e n a r d - Wiechert p o t e n t i a l s a r e r e l a t i v i s t i c a l l y c o r r e c t , and a r e a l s o v a l i d f o r the e n t i r e range of c l a s s i c a l e l e c t r o d y n a m i c s . The g e n e r a l formula f o r the r a t e

• f r a d i a t i o n from a moving charge, as d e r i v e d from the L i e n a r d - W i e c h e r t

p o t e n t i a l s , depends on the v e l o c i t y as w e l l as the a c c e l e r a t i o n . T h i s e x p l a i n s why the TMT i s only e f f e c t i v e i f i t o p e r a t e s at a p o t e n t i a l above 100,000,000 v o l t s which imparts a r e l a t i v i s t i c v e l o c i t y (and energy) to e l e c t r o n s .

SLIDE 8

• dU

d t '

6TTe (y' -

(V X v ) V c 2 )

1 - V'

(15)

Where

U i s the t o t a l energy of the source, and

r e l a t i v i s t i c a l l y , the v e l o c i t y i s i n t e r p r e t e d a s the r e l a t i v e v e l o c i t y of the charge

e, w i t h r e s p e c t to the o b s e r v e r , but t ' i s the r e t a r d e d time, w i t h r e s p e c t to which the v e l o c i t y and a c c e l e r a t i o n of the source a r e to be e v a l u a t e d . L i k e w i s e , f o r the advanced p o t e n t i a l s o l u t i o n t '

becomes the advanced

time, and the r e l a t i v i s t i c s o l u t i o n i s given a t 1 + V ^ / c ^ . The e x p r e s s i o n s f o r the e l e c t r i c and magnetic f i e l d s a r e complicated except f o r simple motions, but i n a l l c i r c u m s t a n c e s B = r X r / c

(16)

so t h a t the magnetic f i e l d i s always p e r p e n d i c u l a r to the e l e c t r i c

f i e l d ,

and to the r e t a r d e d r a d i u s v e c t o r from the charge to the f i e l d p o i n t . For the advanced p o t e n t i a l the magnetic f i e l d i s always 180° to the

e l e c t r i c f i e l d , and to the r a d i u s v e c t o r from the f i e l d p o i n t to the charge.

These

r e l a t i o n s h i p s can be more p r e c i s e l y s t a t e d by working more d i r e c t l y w i t h the time d e r i v a t i v e of the v e l o c i t i e s — b o t h l e s s , and g r e a t e r than c . I n accord w i t h the p r i n c i p l e s of F o u r i e r a n a l y s i s , the s o l u t i o n s of the

inhomogeneous wave equation may be c o n s t r u c t e d from components t h a t a r e harmonic i n time, so t h a t the time dependence may be r e p r e s e n t e d by the

e x p o n e n t i a l c o e f f i c i e n t

p - i o j t

(17)

Here w = 2iTv i s the a n g u l a r frequency, and i , i s the imaginary number

I n t r o d u c i n g the f a c t o r

• ioj i s e q u i v a l e n t to t a k i n g the time d e r i v a t i v e
• f the v e l o c i t y .

T h i s f a c t o r can be broken down by E u l e r ' s formula i n t o the sum of two terms,

• ne the r e a l p a r t , and the other the complex p a r t , so c a l l e d because i t

c o n t a i n s the imaginary f a c t o r i .

• /o -

SLIDE 9

The a c t u a l f i e l d s a r e to be i d e n t i f i e d w i t h the r e a l p a r t of the complex

f i e l d e x p r e s s i o n s , as obtained by use of the E u l e r formula

j - i t u t

= cos cot - i s i n cot (18) together w i t h the r e a l p a r t of the corresponding formula f o r the complex f a c t o r i n the s p a t i a l c o o r d i n a t e s . To o b t a i n i n s t a n t a n e o u s v a l u e s of the energy d e n s i t y and o t h e r q u a n t i t i e s t h a t depend on the product of

f i e l d

s t r e n g t h s , i t i s n e c e s s a r y to w r i t e the r e a l f i e l d s b e f o r e m u l t i p l y i n g , but i t i s simple enough to f i n d the time average of such p r o d u c t s . The r o l e of advanced p o t e n t i a l waves w i t h v e l o c i t y g r e a t e r than c was p o r t r a y e d from a d i f f e r e n t approach by L o u i s de B r o g l i e i n 1923. He proposed t h a t p a r t i c l e s , such a s the e l e c t r o n , should have wave p r o p e r t i e s . He suggested t h a t a p a r t i c l e of mass m^ a t r e s t and thus having an energy

( r e l a t i v i s t i c )zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA

m^c a l s o has a s s o c i a t e d w i t h i t a p e r i o d i c phenomenon of a

s p e c i f i c frequency

VQ = E/h =zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA moC^/h. (19)

I f i t moves r e l a t i v e to an o b s e r v e r w i t h a c e r t a i n v e l o c i t y

'V, the o b s e r v e r

w i l l see the frequency s h i f t e d (by the r e l a t i v i s t i c time d i l a t i o n d e f i n e d by

the theory of r e l a t i v i t y ) to a v a l u e

V = Vo (1 - vVc^)

(20) On the o t h e r hand, the energy of the moving p a r t i c l e i s such t h a t i t would correspond to a frequency v = V o ( l - v V c ^ ) (21) De B r o g l i e proved t h a t t h e s e two waves moved so as to be always i n phase: the former a t the same speed a s the p a r t i c l e , i . e . , <c, and the second a t a d i f f e r e n t speed V. Because V i s g r e a t e r than c (advanced

p o t e n t i a l ) ,

i t cannot, a c c o r d i n g to the theory of r e l a t i v i t y , r e p r e s e n t a t r a n s p o r t of

energy, and De B r o g l i e c a l l e d i t the phase wave. He r e c o g n i z e d the analogy to a phenomenon of o r d i n a r y wave motion i n a d i s p e r s i v e medium, t h a t , when a group of waves of s l i g h t l y d i f f e r e n t f r e q u e n c i e s t r a v e l a t s l i g h t l y

d i f f e r e n t

speeds, they produce by i n t e r f e r e n c e a group wave t h a t t r a v e l s a t a speed

s i g n i f i c a n t l y d i f f e r e n t from a l l

• f them, and i t i s the group v e l o c i t y t h a t

r e p r e s e n t s the speed of t r a n s p o r t of energy by the waves.

SLIDE 10

Making use

• f t h i s p a r a l l e l , de B r o g l i e deduced the

wavelength,

A,

• f

the matter waves; P p = momentum of p a r t i c l e h = P l a n c k ' s c o n s t a n t J u s t a s P l a n c k ' s equation E = hv

(23)

i s t h e

fundamental r e l a t i o n s h i p f o r

l i g h t quanta, so the

equation h A =

(24)

i s the

fundamental equation f o r matter waves. Given the e x i s t e n c e of the advance p o t e n t i a l , and i t s

r e l a t i o n s h i p to the

phase wave, as r e l a t e d to

the

t r a n s p o r t of energy ( r e t a r d e d p o t e n t i a l , and

group wave) we a s k

how the

high p o t e n t i a l s of the

TMT e x p l a i n power con-

d u c t i o n through the e a r t h ? P a i r p r o d u c t i o n i s a p r o c e s s i n which a h i g h energy wave (gamma wave f r e - q u e n c i e s ) i s converted i n t o an e l e c t r o n and

a p o s i t r o n . The p r o c e s s i s

d e s c r i b e d i n

an e l e c t r o n theory proposed by P. A. M. D i r a c through a method

• f approximation. He envisaged the

p r o c e s s a s

the t r a n s i t i o n of an e l e c t r o n

from a n e g a t i v e to

a p o s i t i v e energy s t a t e .

There i s

a f r a c t i o n of r e s i d u a l

energy i n

p a i r p r o d u c t i o n , symbolized by the

Greek l e t t e r a l p h a ,

a, unex-

pended i n c o n v e r s i o n

• f energy to mass, t h a t appears i n

any

• ne p a r t i c l e

(e.g., the e l e c t r o n ) . T h i s i s g i v e n by the k i n e t i c energy of t h a t e l e c t r o n Eg

minus i t s

r e s t energy, mc^, d i v i d e d by the

energy of the

gamma r a y

hv, minus t w i c e the r e s t energy o f the

e l e c t r o n

2 mc^,

• r .

SLIDE 11

( EzyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Q - mc')

a =

— .

(hv - 2

mc^)

(25) Because the

same equation a p p l i e s to each of the two e l e c t r o n s t h a t a r e formed, i t must be symmetric about the

c o n d i t i o n t h a t each o f the p a r t i c l e s has h a l f t h e r e s i d u a l energy, symbolized by a ( i n e x c e s s of t h a t conveyed to a " t h i r d body", such a s

the

atomic n u c l e u s ) ; i . e . , t h a t

a = 0.5.

Below an energy of about 10,000,000 e l e c t r o n v o l t s f o r

the gamma r a y , t h e

p r o b a b i l i t y f o r p a i r p r o d u c t i o n i s almost independent of the atomic number

• f t h e

m a t e r i a l ; and,

up t o about 100,000,000 e l e c t r o n v o l t s of energy,

i t i s almost independent of the

q u a n t i t y a . At higher e n e r g i e s , approx- i m a t e l y equal to

• r g r e a t e r than 100,000,000 e l e c t r o n v o l t s , p a i r p r o d u c t i o n

i s the

dominant mechanism o f r a d i a t i o n i n t e r a c t i o n w i t h m a t t e r . According to D i r a c ' s " h o l e " theory a l l n e g a t i v e energy s t a t e s a r e o r d i n a r i l y

f i l l e d w i t h e l e c t r o n s , a u n i f o r m i t y t h a t i s

i m p o s s i b l e to d e t e c t and which

i s

sometimes c a l l e d the

e l e c t r o n vacuum, A hole i n

the

d i s t r i b u t i o n of n e g a t i v e energy s t a t e s c o n s t i t u t e s the a n t i - e l e c t r o n , w i t h p o s i t i v e charge and p o s i t i v e energy.

The t r a n s i t i o n of an e l e c t r o n from a n e g a t i v e energy s t a t e to one of

p o s i t i v e energy r e s u l t s i n

the

c r e a t i o n of a p a i r .

The r e v e r s e t r a n s i t i o n

r e s u l t s i n

the

a n n i h i l a t i o n of

a p a i r .

C o m p l i c a t i o n s a r i s e from such a

quantum theory of the pure r a d i a t i o n f i e l d , e x c l u d i n g charges and other

s o u r c e s . Such c o m p l i c a t i o n s have no c o u n t e r p a r t i n c l a s s i c a l theory, but

i t i s p o s s i b l e t o d e s c r i b e a vacuum r a d i a t i o n f i e l d i n

terms of q u a n t i z e d normal modes i n such a way t h a t Maxwell's equations a r e

s a t i s f i e d i n

t h e l i m i t

• f P l a n c k ' s c o n s t a n t approaching zero

(h ^ 0) i n

a d d i t i o n to L o r e n t z co- v a r i a n c e a s r e q u i r e d by s p e c i a l r e l a t i v i t y . These normal modes correspond to photons, which i n d i v i d u a l l y c a r r y energy, momentum, and angular momentum.

I n a c t u a l p h y s i c a l world p a r t i c l e s s e r v e a s s o u r c e s and a b s o r b e r s f o r

photons. As an example o f the c o m p l i c a t i o n s , the n e g a t i v e energy s t a t e s of the D i r a c theory a r e

a f f e c t e d by the e x i s t e n c e o f

an e l e c t r o m a g n e t i c f i e l d (such a s

h i g h v o l t a g e ) , r e s u l t i n g i n

what i s

c a l l e d the p o l a r i z a t i o n of the

vacuum.

A c o n s t a n t f i e l d produces a c o n s t a n t p o l a r i z a t i o n which would be unobservable; and s t r a i g h t forward attempts to compute i t s magnitude have l e d to the

embar-

r a s s i n g r e s u l t t h a t the e f f e c t i s i n f i n i t e .

Inhomogeneous f i e l d s produce

f i n i t e and o b s e r v a b l e e f f e c t s t h a t can c a l c u l a t e d .

These c o m p l i c a t i o n s a r o s e

• ut of the

attempt to s o l v e some o f the d e f e c t s of p r i n c i p l e i n

the Schrodinger

equation f o r wave mechanics.

For

• ne t h i n g , the

s p i n of the e l e c t r o n was i n t r o d u c e d i n t o the equation by Schrodinger on an

ad_ hoc b a s i s ; and f o r

another the equation i s not

i n

harmony w i t h the

theory of r e l a t i v i t y . The

d i f f i c u l t y a r i s e s from the f a c t t h a t the r e l a t i v i s t i c e x p r e s s i o n f o r

t h e

energy,

E , of a f r e e p a r t i c l e i s

E = + (cp)2 + (mc^)-

(26)

• /3

SLIDE 12

Where m and p a r e the mass and momentum, r e s p e c t i v e l y of the f r e e

p a r t i c l e , and

c i s the

v e l o c i t y of l i g h t . T h i s cannot be used d i r e c t l y , as the square root has

no c l e a r meaning once the t r a n s i t i o n i s made to the

• p e r a t o r s

( e i t h e r S c h r o d i n g e r ' s d e r i v a t i v e s , or Heisenberg's m a t r i c e s )

• f quantum t h e o r y .

The problem was s o l v e d by D i r a c i n

1928 by the

expedient of s e t t i n g E = c (o^Px + a p + a^Pz) + 3

mc^ ( 2 7 )

i n which p^^, py,

pg., a r e the

t h r e e mutually p e r p e n d i c u l a r components of

momentum, s a t i s f y i n g p^^ + Py^ + p^^ = p^. Here a ^ ^ , tty,zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA a^, and 3 a r e

determined by the requirements t h a t they be independent of p o s i t i o n

and

time and t h a t E^ = (cp)2 + (mc2)2 ,

(28)

the same r e s u l t s t h a t would be obtained by s q u a r i n g both s i d e s of equation (26) above. The

a ' s and 3 cannot be o r d i n a r y numbers, a s the

r e s t r i c t i o n s on them

show; a t y p i c a l one i s a^S

+ 3

• t

x

~ ^*

Rather they t u r n out

to be o p e r a t o r s

themselves. Moreover, whereas f o r a

c l a s s i c a l f r e e p a r t i c l e t h e

• r b i t a l angular momentum L i s

a c o n s t a n t of

the motion, t h i s i s not t r u e f o r

a p a r t i c l e the

energy of which i s

• f t h e

form of equation ( 2 7 ) ; i n s t e a d to L must be added a combination of

the

a's and 3. T h i s combination must r e p r e s e n t an a n g u l a r momentum, which

does not depend on t h e motion o f

the

p a r t i c l e , and i s t h e r e f o r e an i n t r i n s i c

angular momentum, or s p i n . T h i s c a n

be v i s u a l i z e d a s T e s l a ' s r o t a t i n g mag-

n e t i c f i e l d (as an advanced p o t e n t i a l ) i n

the

n e g a t i v e energy s t a t e

• f

D i r a c behaving l i k e de B r o g l i e ' s phase wave w i t h r e s p e c t to the p a r t i c l e s t a t e . When t h e e f f e c t of an e l e c t r o m a g n e t i c

f i e l d i s

i n c l u d e d i n the equation, the " s p i n " i s

found to have a s s o c i a t e d w i t h i t a magnetic moment

(as proposed by Uhlenbeck and Goudsmit).

Thus D i r a c ' s p r o p o s a l s o l v e d the

• two

d i f f i c u l t i e s , and

• f course h i s t o r i c a l l y implied the e x i s t e n c e of the

e l e c t r o n a n t i - p a r t i c l e — t h e p o s i t r o n — w h i c h was d i s c o v e r e d i n 1931. But the d e s c r i p t i o n of p a r t i c l e s and r a d i a t i o n i s f a r from complete. The f a c t remains t h a t no one y e t (1976) knows how to w r i t e down e x a c t l y ,

i n

compact form, an equation d e s c r i b i n g the complete i n t e r a c t i o n between a proton and an e l e c t r o n , l e t a l o n e s o l v e i t . Thus when we t r y to e x p l a i n

• /4

SLIDE 13

the o p e r a t i o n of the TMT i n terms of advance p o t e n t i a l theory, phase wave theory, and n e g a t i v e energy s t a t e theory, we can only suggest t h a t T e s l a ' s i d e a s a r e f e a s i b l e . T h e i r v a l i d i t y can only be proved i n w e l l - d e s i g n e d experiments.

I t i s c l e a r t h a t t h e r e i s no c o n t r a d i c t i o n between

T e s l a ' s data and c l a i m s , and t h a t of modern theory.

• iS

SLIDE 14

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SLIDE 15

SLIDE 16

SLIDE 17