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 Puharich, M.D., LLD.

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 o 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 s 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 at 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 repeat 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 engineers 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 data 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 explanantion of T e s l a ' s data on h i s TMT i s given as f o l l o w s :

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The Lienard-Wiechert s o l u t i o n of the Maxwell equations for 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 Lienard-Wiechert s o l u t i o n a l s o shows the e x i s t e n c e of a wave f a s t e r than c known as the advance p o t e n t i a l . Since 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 as 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 "hole" or t u b u l a r wave guide moving f a s t e r than c, for 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 of 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 retarded 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 ) are c r e a t e d , or 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 as 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 of 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 of resonance (frequency and v o l t a g e ) gain (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"-

I n order to understand the 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 present 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 Encyclopaedia B r i t . , V.6, p. 660 f f ) . We r e l a t e electromagnetic r a d i a t i o n to i t s source by means of the p o t e n t i a l s as given i n the 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 v — = - p/e (3)

dt "

1 9A 1 9(|) V X (V x A) + + grad — = y j (4)

" " ' 9t " ,2

The divergence 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 Lorentz c o n d i t i o n on the p o t e n t i a l s . I f the Lorentz 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 equations,

-6-

1 a^cj) - p/e ,

0 (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 , sources 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 these equations.

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 ; mathema­t 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 evaluated a t t + r / c , are 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 attached 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 that they move a t speeds g r e a t e r than c and t h e r e f o r e

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cannot be detected by p h y s i c a l instruments a l l of which operate 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 the 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 l (p; and the p h y s i c a l inductor 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 sources are 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 the e a r t h / a i r c a p a c i t o r C' as the load which has a r e s i s t i v e component R. For the TMT to 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 placed somewhere on the e a r t h to r e c e i v e the e l e c t r i c a l power of 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 tunnel e f f e c t "wormhole" from the TMT to the TMR. The "hole" thus c r e a t e d i n advance of the a r r i v a l of the retar 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 electromagnetic r a d i a t i o n to the TMR where maximum power t r a n s f e r o 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 the e x i s t e n c e of the p h y s i c a l electromagnetic f i e l d s , which must f a l l o f f as 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 as 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 region of space near the o r i g i n of c o o r d i n a t e s , then, to a f i r s t approximation, the 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 ) = _ ^

4TT 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 as 1/r^ at b e s t , except f o r the f a c t t h a t the d i s t a n c e r , i s a l s o involved i n the re 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 pro­p 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 as 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 ret a r d e d p o t e n t i a l , i f the motion of the

charge i s confined to the z a x i s , the magnetic f i e l d i s azimuthal, and given by

4>

qv 1 — s i n 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 source to observer. 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 0 and equal i n magnitude to cB i n these u n i t s . The exact 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 are 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. Conversely, 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 general 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 of charge e, a r e

4'n-e R - R" v / c

A = - 1 4TT

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 oint, 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 bracket i s used to denote the f a c t that a l l q u a n t i t i e s a r e to be evaluated 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 Lienard-Wiechert 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 th a t Maxwell's equations were v a l i d only 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 for the e n t i r e range of c l a s s i c a l electrodynamics. The g e n e r a l formula f o r the r a t e of r a d i a t i o n from a moving charge, as d e r i v e d from the Lienard-Wiechert 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 operates 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 .

- dU

dt' 6TTe 0

(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 as 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 observer, 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 circumstances

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 int 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 th a t a re harmonic i n time, so t h a t the time dependence may be represented by the exponential c o e f f i c i e n t

p - i o j t (17)

Here w = 2iTv i s the angular frequency, and i , i s the imaginary number Intro 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

of 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, one 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 -

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 instantaneous v a l u e s of the energy d e n s i t y and other 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 before 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 products.

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 portrayed 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 as 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 ) 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 = moC^/h. (19) I f i t moves r e l a t i v e to an observer w i t h a c e r t a i n v e l o c i t y 'V , the observer 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 defined 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 other hand, the energy of the moving p a r t i c l e i s such that 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 these two waves moved so as to be always i n phase: the former a t the same speed as 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 recognized 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 of 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.

Making use of t h i s p a r a l l e l , de B r o g l i e deduced the wavelength, A, of the matter waves;

P

p = momentum of p a r t i c l e

h = Pla n c k ' s constant

J u s t as Plan c k ' s equation

E = hv (23)

i s the 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 (re t a r d e d p o t e n t i a l , and group wave) we ask how the high p o t e n t i a l s of the TMT e x p l a i n power con­duction through the ear t h ?

P a i r production i s a process i n which a high energy wave (gamma wave f r e ­quencies) 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 process i s des 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 of approximation. He envisaged the process as 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 production, symbolized by the Greek l e t t e r alpha, a, unex­pended i n conversion of energy to mass, t h a t appears i n any one 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 given by the k i n e t i c energy of that 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 ray hv, minus twice the r e s t energy of the e l e c t r o n 2 mc^, or.

( E 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 of the p a r t i c l e s has h a l f the r e s i d u a l energy, symbolized by a ( i n excess of that conveyed to a " t h i r d body", such as 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 ray, the p r o b a b i l i t y f o r p a i r production i s almost independent of the atomic number of the m a t e r i a l ; and, up to 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 qu a n t i t y a. At higher e n e r g i e s , approx­imately equal to or gr 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 production i s the dominant mechanism of r a d i a t i o n i n t e r a c t i o n w i t h matter.

According to D i r a c ' s "hole" theory a l l negative 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 un i f o r m i t y t h a t i s impossible to de 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 negative 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 negative 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 . Complications 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 complications have no counterpart 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 to 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 quantized normal modes i n such a way tha t Maxwell's equations a r e s a t i s f i e d i n the l i m i t of Planck's constant approaching zero (h 0) i n a d d i t i o n to Lorentz co-v a r i a n c e as 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 rve as sources and absorbers for photons. As an example of the complications, the negative 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 of an electromagnetic f i e l d (such as high 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 constant f i e l d produces a constant 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 embar­r 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 observable 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 arose out of the attempt to s o l v e some of 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 one th i n g , the s p i n of the e l e c t r o n was introduced 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 the energy, E , of a f r e e p a r t i c l e i s

E = + (cp)2 + (mc^)- (26)

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Where m and p are 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 operators ( e i t h e r Schrodinger's d e r i v a t i v e s , or Heisenberg's m a t r i c e s ) of quantum theory.

The problem was solved 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^ (27)

i n which p , py, pg., a r e the thre 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, 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 squaring 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, as 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 + 3otx ~ *

Rather they t u r n out to be operators 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 the o r b i t a l angular momentum L i s a constant of the motion, t h i s i s not tr u e f o r a p a r t i c l e the energy of which i s of the 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 angular momentum, which does not depend on the 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 can be v i s u a l i z e d as T e s l a ' s r o t a t i n g mag­n e t i c f i e l d (as an advanced p o t e n t i a l ) i n the negative energy s t a t e of 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 the e f f e c t of an electromagnetic f i e l d i s inc 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 proposal solved the

-two d i f f i c u l t i e s , and of 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 discovered 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 that no one yet (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 alone s o l v e i t . Thus when we t r y to e x p l a i n

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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 negative energy s t a t e theory, we can only suggest that 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 well-designed experiments. I t i s c l e a r t h a t there 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 th a t of modern theory.

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