EGM Electro-Gravi-Magnetics (EGM); Practical modelling methods of the polarizable vacuum - V

8/14/2019 EGM Electro-Gravi-Magnetics (EGM); Practical modelling methods of the polarizable vacuum - V

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Electro-Gravi-Magnetics (EGM)Practical modelling methods of the polarizable vacuum - V

Riccardo C. Storti 1, Todd J. Desiato

Abstract

An experimental prediction is developed considering gravitational acceleration g as a purelymathematical function across an elemental displacement utilising modified Complex Fourier Series.This is evaluated to illustrate that the contribution of low frequency harmonics is trivial relative to high frequency harmonics when considering g. Moreover, the formulation and development of the Critical

Boundary leading to the proposition that the dominant bandwidth arising from the formation of beatspectrums is several orders of magnitude above the Tera-Hertz (THz) range, terminating at the ZPF beat cut-off frequency is presented. In addition, it is proposed that the modification of g is dominated

by the magnitude of the applied magnetic field vector B A and that the Electro-Gravi-Magnetic(EGM) Spectrum is an extension of the classical Electro-Magnetic (EM) Spectrum.

1 [email protected] , [email protected] .


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1 I TRODUCTIO

1.1 GENERAL

The Polarizable Vacuum (PV) model provides a theoretical description of space-time that may be derived from the superposition of electromagnetic (EM) fields. It is conjectured that the space-timemetric might be engineered utilising Electro-Gravi-Magnetics 2 (EGM), where EM fields may be

applied to affect the state of the PV and thereby facilitate interactions with the local gravitationalenvironment. [1-4] This paper continues previous work leading to practical modelling methods of the PV based

on the assumption that dimensional similarity exists between the space-time geometric manifold andapplied EM fields. In accordance with Buckingham's Theory (BPT), experiments must be designedthat test the hypothesis stated in [2].

1.2 HARMONICS

The formulation herein advances the works [1-4] and facilitates the following additions to theglobal EGM construct,

i. Derivation of the fundamental harmonic beat frequency across an elemental displacement r,IFF r


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Therefore, the spectral modelling characteristics of the PV / ZPF may be articulated as follows,i. The free space harmonic mode bandwidth is - < n PV < + .

ii. The magnitude of the free space harmonic cut-off mode tends to infinity (n ).iii. The fundamental harmonic frequency of free space tends to zero [n PV = 1, PV(nPV ,r,M) 0Hz].iv. The presence of a planetary mass superimposed on the PV / ZPF alters the free space harmonic

mode spectrum, described by equation (1), to -n (r,M) nPV +n(r,M).v. The fundamental and cut-off harmonic frequencies of the PV / ZPF for a planetary mass

increases as r decreases according7

to:PV(1,r- r,M) > PV(1,r,M), (r-r,M) > (r,M) and n (r-r,M) < n (r,M)

(1,r,M) Hz (r,M) YHz n (r,M)

PV(1,R E,M0) 0 (R E,M0) < n(R E,M0) PV(1,R E,MM) 0.008 (R E,MM) 196 n (R E,MM) 2.4x10 28 PV(1,R E,ME) 0.0358 (R E,ME) 520 n (R E,ME) 1.5x10

28 PV(1,R E,M J) 0.2445 (R E,M J) 2x10 3 n(R E,M J) 7.6x10 27 PV(1,R E,MS) 2.4841 (R E,MS) 9x10

3 n(R E,MS) 3.5x1027

Table 1,Where,

Variable Description Unitsn(r,M) Harmonic cut-off mode of PV None

PV(nPV ,r,M) Harmonic field frequency of PV Hz(r,M) Harmonic cut-off frequency of PV HznPV Harmonic frequency modes of PV Noner Magnitude of position vector relative to

the centre of mass of a planetary bodym

r Magnitude of change of position vector mM Mass of the planetary body kgR E Radius of the Earth mM0 Zero mass condition of free space kgMM Mass of the Moon kgME Mass of the Earth kgMJ Mass of Jupiter kgMS Mass of the Sun kg

Table 2,

3.2 PHENOMENA OF BEATS [5]

3.2.1 FREQUENCY

It was illustrated in [4] that it is convenient to model a gravitational field at a mathematical point utilising Complex Fourier Series obeying an odd number harmonic distribution. Subsequently, itfollows that a beat frequency r spectrum forms across r since n (r,M) n(r r,M). Hence,it is postulated that the change 8 in frequency across r may be usefully approximated as follows 9,

r n PV r , r , M, PV n PV r r , M, PV n PV r , M, (2)

The change 10 in harmonic cut-off frequency becomes,

r r , M,( ) r r M,( ) r M,( ) (3)

Where, represents the harmonic cut-off frequency of the PV. [4]

7 YHz = 10 24(Hz).8 Also termed a beat.9 The fundamental beat frequency occurs when n PV = 1 and may be expressed as r (1,r, r,M).10 Also been termed the beat bandwidth of the PV across r.


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3.2.2 WAVELENGTH

The change in harmonic wavelength r across r may be determined in a similar manner as follows,

r n PV r , r , M, PV n PV r r , M, PV n PV r , M, (4)

Where,

PV n PV r , M, c PV n PV r , M, (5)

Therefore, the change in harmonic cut-off wavelength may be given by,

r r , M,( ) c1

r r M,( )

1

r M,( ).

(6)

3.2.3 GROUP

3.2.3.1 VELOCITY

Group velocity is a term used to describe the resultant velocity of propagation of a set or

family of interacting wavefunctions. Within the bounds of this document, we consider two distinctscenarios by which to construct the mathematical model. The first scenario concerns itself withengineering representations at a mathematical point r.

At r, a spectrum of harmonic modes exists from -n nPV +n. Superposition of thesemodes produces the constant function g. Therefore, it follows that the group velocity at amathematical point is zero. Consequently, gravitational wavefunctions are not observed to radiate froma planetary body.

The second scenario considers group velocities over a differential element r. Recognisingthat the change in modal amplitude, across practical values of r at the surface of the Earth tends tozero, the group velocity vr at each harmonic frequency mode may be defined as follows,

v r n PV r , r , M, r n PV r , r , M, r n PV r , r , M,.

(7)

The terminating group velocity v is the group velocity induced by the change in

frequency at the highest harmonic mode n . Since the number of modes varies significantly with r,the group velocity terminates with respect to the induced beat across r at the highest common 11 mode number n (r,M). Subsequently, v occurs at the lower harmonic cut-off mode and may bedefined as follows,

v r r , M,( ) v r n r M,( ) r , r , M, (8)

3.2.3.2 ERROR

Evaluating equation (7,8) reveals incrementally non-zero magnitudes at low harmonicstending to zero ([ vr ],[v]) 0(m/s) as |nPV | n. However, the expected result is that the groupvelocity is exactly zero at all modes ([ vr ],[v]) = 0(m/s).

However, if r , then vr is non-trivial and a mathematical statement has been made predicting the radiation of gravitational waves from the centre of mass of a planetary body. Therefore,

we may consider the calculation of vr and v as being proportional measures of themathematical representation error R Error across r.It should be noted that the error revealed by equation (7,8) is introduced by the simplification

that the magnitude of the amplitude of n PV is constant across r. Typically, for practical values of r at the surface of the Earth 12, (R Error vr v)


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3.2.4 BEAT BANDWIDTH CHARACTERISTICS

3.2.4.1 FREQUENCY

Thus far, it has been illustrated in [4] that an amplitude and frequency spectrum exists at eachmathematical point over the domain 0 < |r | < . The preceding body of work has defined certaincharacteristics, including change over the domain r. However, the variation in spectral bandwidth

from r to r+ r requires further consideration.Assuming the ZPF energy across r is equal to the change in the magnitude of the rest mass

energy density influence |UPV(r,r,M) | yields,

U PV r r , M,( )h

2 c3. r r , M,( ) ZPF

4 r 1 r , r , M,( )

4.

(9)

Where, the ZPF beat cut-off frequency ZPF becomes,

r r , M,( )ZPF

42 c3.

h U PV r r , M,( )

. r 1 r , r , M,( )4

(10)

Therefore, the ZPF beat bandwidth ZPF may be defined as,

ZPF r r , M,( ) r r , M,( )ZPF

r 1 r , r , M,( ) (11)

3.2.4.2 MODES

The ZPF beat cut-off mode n ZPF corresponding to ZPF may be determined utilisingequation (12) developed previously in [4] as follows,

PV n PV r , M,n PV

r

3 2 c. G. M.

r .. e

G M.

r c2.

.

(12)

Where, PV(n ZPF ,r,M) = (r,r,M) ZPF and |nPV | = n (r, r,M) ZPF

n r r , M,( )ZPF

r r , M,( ) ZPF

PV 1 r , M,( ) (13)

3.2.4.3 CRITICAL RATIO

K R is defined as the ratio of the applied fields to the background13 field by any suitable

measure. [3] Consequently, K R in terms of the ratio of energy densities may be defined as thefollowing simplification,

K R U ZPF

U ZPFK R

r r , M,( ) ZPF4

4

r r , M,( )ZPF4

r 1 r , r , M,( )4

,

(14)

3.3 CRITICAL BOUNDARY

3.3.1 FREQUENCY

The Critical Boundary represents the lower boundary of the ZPF spectrum yielding aspecific proportional similarity value as follows,

13 Refers to the conditions of the space-time manifold at the surface of the Earth, prior to successfulexperimentation.


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r r , M, K R ,4

r r , M,( ) ZPF4

K R r r , M,( ) ZPF4

r 1 r , r , M,( )4.

(15)

Therefore, the similarity bandwidth S is given by,

S r r , M, K R , r r , M,( ) ZPF r r , M, K R ,

(16)

3.3.2 MODE

The mode number of may be calculated by re-use of equation (12) as follows,

n r r , M, K R , r r , M, K R ,

PV 1 r , M,( ) (17)

Consequently, the change in the number of modes as a function of K R may be given by,

n S r r , M, K R , n r r , M,( ) ZPFn r r , M, K R ,

(18)

3.4 BANDWIDTH RATIO

A bandwidth ratio R may be defined relating ZPF to . This represents the ratioof the bandwidth of the ZPF spectrum to the Fourier spectrum . R provides a useful conversionrelationship between forms over practical bench-top values of r and may be defined as follows,

R r r , M,( ) ZPF r r , M,( )

r r , M,( ) (19)

Change in Radial Displacement

B a n

d w

i d t h R a t

i o

R R E r , M E,

r

Figure 1,

4 PHYSICAL MODELLI G

4.1 GENERAL SIMILARITY EQUATIONS

4.1.1 OVERVIEW

It was illustrated in [2] that acceleration may be represented by the superposition of wavefunctions. The Primary Precipitant was decomposed to form General Modelling EquationsGME x. Therefore, for applied 14 experimental fields, the change in GME x is equal to the requiredchange of the magnitude of the gravitational acceleration vector g.

Storti et. al. stated in [2] that GME 1 is proportional to a solution of the Poisson equationapplied to Newtonian gravity, where the resulting acceleration is a function of the geometry of theenergy densities. GME 2 is proportional to a solution of the Lagrange equation where the resulting

14 Artificial fields commencing from zero strength.


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acceleration is a function of the Lagrangian densities of the EM field harmonics in a vacuum.Assuming proportional 15 similarity ( |K R | 1) between the Experimental Prototype

16 (EP) andthe mathematical model, a family of General Similarity Equations GSE x may be defined whereGME 1 GME 2 for all r as |nPV | n ZPF and +n ZPF < +.

4.1.2 GSE x

GSE 1,2 may be formed utilising the energy balancing equations as follows: GME x g 0 (20)

GME x g 2 g.

(21)Where,

GME x K 0 X,( )

2 r .

N

N

n A

E A k A n A, t,2

=

N

N

nA

B A k A n A, t,2

=

c2.

(22)

K 0 X,( )G M.

r c2.K R

.

(23)

Where, K 0(,X) is the engineered relationship function 17 as derived in [3] , k A denotes the appliedwave vector and the permittivity and permeability of free space, 0 and 0 respectively, act as theimpedance function 18.

Substituting equations (22,23) into (20,21) and solving for K R yields the Critical Ratioexplicitly in terms of applied fields as |nA| n ZPF such that |K R | 1 as follows,

K R

2 c2.

N

N

nA

B A k A n A, t,2

=

.

N

N

n A

E A k A n A, t,2

=

c2

N

N

n A

B A k A n A, t,2

=

.

(24)

Subsequently, proportional 19 representations of similarity over the domain 1< |nA|


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GSE E A B A, k A, n A, t, 1 2,

2 c2.

N

N

n A

B A k A n A, t,2

=

.

N

N

n A

E A k A n A, t,2

=

c2

N

N

n A

B A k A n A, t,2

=

.

(25)

Similarly, it follows that GSE 3 may be written utilising the following equation,

K R K C K 1 K 2,

U PV r r , M,( )

0

0

.

(26)Where,

K C K 1 K 2,2 K 1 r , E, D, X,( )

K 2 r , B, D, X,( )

1

K PV2

N

N

n A

E A k A n A, t,2

=

.

N

N

n A

B A k A n A, t,2

=

.

(27)

Substituting equations (27) into (26) when |K R | = 1 yields GSE 3 as follows,

GSEE A B A, k A, n A, t, r , r , M,3

1

K PV r M,( ) U PV r r , M,( ).

0

0 N

N

n A

E A k A n A, t,2

=

.

N

N

n A

B A k A n A, t,2

=

..

(28)

Such that,

K PV r M,( ) e

2G M.

r c2.

.

(29)

GSE 4,5 may be formed by combining GSE 1,2 with GSE 3, as follows,

GSE E A B A, k A, n A, t, r , r , M, 4 5,

GSE E A B A, k A, n A, t, r , r , M, 3

GSE E A B A, k A, n A, t, 1 2, (30)Where,

Variable Description UnitsGME x Change in applied acceleration vector m/s

2 g Magnitude of gravitational acceleration vector m/s 2 EA(k A,nA,t) Magnitude of applied electric field vector in complex form V/mBA(k A,nA,t) Magnitude of applied magnetic field vector in complex form TK C(K 1,K 2) Critical Factor Pac Velocity of light in a vacuum m/sG Gravitational constant m 3kg -1s-2

Table 3,

4.2 QUALITATIVE LIMITS

Theoretical qualitative behaviour may be obtained for GSE 1,2 by taking the limits of theRHS 20 of equation (25) with respect to applied EM fields. By performing the appropriate substitutions 21 the following results were obtained utilising the limit function within the MathCad 8 Professionalenvironment.

E A 0B A

GSE E A B A, k A, n A, t, 1 2,lim

+lim

- 0 (31)

20 Right Hand Side.21 Where |K R | 1 as [ |nPV |,|nA|] n ZPF .


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B A 0E A

GSE E A B A, k A, n A, t, 1 2,lim

+lim

- 2 (32)

GSE 1,2(EA,BA,k A,nA,t) qualitatively imply that achieving complete dynamic, kinematic andgeometric similarity between the applied EM fields and g, is facilitated by maximising B A whilstminimising E A. This suggests the proposition that B A dominates the local modification of g.

The result, |lim GSE 1,2(EA,BA,k A,nA,t)| 2 as E A 0+ and B A -, arises from the finalenergy density state of the PV after successful experimentation being twice the initial state. This resultsin a net magnitude of acceleration of 2g and may be represented by the following equations, wheref denotes the final state of the PV for complete similarity:

n PV k PV,

E f k PV n PV, t,2 2

N

N

n A

E A k A n A, t,2

=

.

(33)

n PV k PV,

B f k PV n PV, t,2 2

N

N

n A

B A k A n A, t,2

=

.

(34)

As |nA| n ZPF , the superposition of applied wavefunctions describes the magnitudes of theelectric and magnetic field vectors as constant (steady state) functions. Therefore, Maxwells Equations(in MKS units) may define the system characteristics as follows ( is the charge density and J isthe vector current density), [6]

E A.

0E A 0, B A

. 0, B A 0 J.,

(35)Consequently as |nA| n ZPF , optimal similarity occurs when:

1. The divergence of E A is maximised.2. The magnitude and curl of E A is minimised.3. The magnitude and curl of B A is maximised.

As the square root of the ratio of the sum of the applied fields approach c, GSE 1 approachesunity as follows,

N

N

n A

E A k A n A, t,2

=

N

N

n A

B A k A n A, t,2

=

c

GSE E A B A, k A, n A, t, 1lim

1 (36)

Similarly, the square root of the ratio of the sum of the applied fields influence on GSE 2 may beexpressed as follows,

N

N

n A

E A k A n A, t,2

=

N

N

n A

B A k A n A, t,2

=

c

GSE EA

BA

, k A

, nA

, t,2

lim

|Undefined | (37)


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Consequently, characteristics of equations (31-37) are such that:4. GSE 1(EA,BA,k A,nA,t) qualitatively implies |K R | = 1 when |EA2/BA2| c as |nA| n ZPF 5. GSE 1(EA,BA,k A,nA,t) qualitatively implies use over the range 0 |GSE 1(EA,BA,k A,nA,t)| < 26. GSE 2(EA,BA,k A,nA,t) qualitatively implies use over the range:

0 |GSE 2(EA,BA,k A,nA,t)| < 1 1 < |GSE 2(EA,BA,k A,nA,t)| < 2The results presented above should not be taken as definitive mathematical solutions or

experimental predictions. However, deeper consideration may suggest that GSE 1 represents an

expression biasing constructive EGM interference, whilst GSE 2 biases destructive EGM interferencewith g. The undefined result indicated by equation (37) may suggest that the local space-timemanifold cannot be totally flattened in the presence of applied EM fields. The applied fields representenergy contributions that inherently modify the geometry of the local space-time manifold.

5 METRIC E GI EERI G

5.1 POLARIZABLE VACUUM

Utilising GSE 3, we may write22 the exponential metric tensor line element for the PV model

representation of GR in the weak field limit analogous to the form specified in [3] as follows,

ds 2 g dx. dx.

c2 dt 2.

K EGMK EGM dr

2 r 2 d2. r 2 sin ( )

2. d2..

(38)

g 001

K EGM (39)

g 11 g 22 g 33 K EGM (40)

Where,

K EGM e

2G M.

r c2.

. 11

2GSE 3

..

K PV3 e

K 0 X,( ). (41)

Note:i. K EGM is a function of the applied fields and constituent characteristics (E A,BA,k A,nA,t).

ii. |nA| >> 1

5.2 DESIGN CONSIDERATIONS

5.2.1 RANGE FACTOR

The range factor St (r,r,M) is the product of UPV(r, r,M) and the impedance functionZ. It is a useful at-a-glance design tool that indicates the boundaries 23 of the applied energyrequirements for experiments and may be represented as follows,

St r r , M,( ) U PV r r , M,( ) 0

0

.

(42)

We may determine specific limiting characteristics of the range factor for an idealexperimental solution, where the upper limiting value is defined by,

0 r St r 0, M,( )

3 M. c2.

4 .1

r r ( )3

1

r 3.

0

0

.lim+

St r 0, M,( ) 0

(43)

The lower limiting value is defined by,

22 In terms of the applied Poynting Vector.23 The greater the magnitude of the range factor, the greater the magnitude of applied energy requiredfor complete dynamic, kinematic and geometric similarity with the EP.


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r St r , M,( )

3 M. c2.

4 .1

r r ( )3

1

r 3.

0

0

.lim-

St r , M,( )3

4M. c2.

0

0

1

2

r 3..

(44)

The range of |St (r,r,M) | over the domain 0< |r |> 1 ( ZPF >> Ce) as it would imply that the beat bandwidth of ZPF frequencies, over practical

benchtop values of r, is much larger that the Compton frequency of an Electron, contradicting contemporary belief.

Similarly, if St 0, then Ce >> ZPF and would seem to imply that, assuming Ce isrepresentative of a natural gravitational boundary condition, proportional similarity ( |K R | 1) byartificial means is not experimentally practical and the mathematical model derived to achievesimilarity is inappropriate. Therefore, it follows that we might expect that 0 the Fourier cut-off change).

St r r , M,( ) r r , M,( )

Ce (47)

The 3 rd Sense Check St may be defined as the ratio of the harmonic cut-off modes acrossr (expected to be: 1).

St r r , M,( )n r r M,( )

n r M,( ) (48)Therefore it follows that,

R r r , M,( )St r r , M,( )St r r , M,( ) (49)

The 4 th Sense Check St may be defined in terms of R Error across r as follows (expectedto be: 1),

St n PV r , r , M, v r n PV r , r , M,

v r r , M,( ) (50)


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Hence,

Radial Distance

S e n s e

C h e c

k

St R E r , M E,

St R E r , M E,St r r , M E,

St r r , M E,

R E

r

Figure 24 2,

Harmonic

S e n s e

C h e c

k

St n PV R E, r , M E,

N N

n PV

Figure 3,

6 E GI EERI G CHARACTERISTICS

6.1 BEAT SPECTRUM

Characteristics of the beat PV / ZPF spectrum, over r = 1(mm), at the surface of the Earthmay be approximated according 25 to the following table,

Characteristic Evaluated ApproximationWavelength PV(1,R E,ME) 8.4x10 6 (km)Change in Wavelength r (1,R E,r,M E) 1.8 (m) Change in Cut-Off Wavelength (R E,r,M E) 0 (m)Group Velocity vr (1,R E,r,M E) 1.3x10

-11 (m/s)

Terminating Group Velocity v(R E,r,M E) 1.3x10-11

(m/s) Representation Error R Error 1.3x10 -9 (%) Fundamental Beat Frequency r (1,R E,r,M E) 7.5x10

-12 (Hz)Change in Cut-Off Frequency (R E,r,M E) 45 (PHz)Beat Cut-Off Frequency (R E,r,M E)ZPF 371 (PHz)Beat Cut-Off Mode n(R E,r,M E)ZPF 1x10

19 Beat Bandwidth ZPF (R E,r,M E) 371 (PHz)

24 Y-Axis is logarithmic scale.25 PHz = 10 15(Hz).


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Critical Boundary Frequency (R E,r,M E,50%) 312 (PHz)Critical Boundary Mode n(R E,r,M E,50%) 8.7x10

18 Similarity Bandwidth S(R E,r,M E,50%) 59 (PHz)Similarity Modes nS(R E,r,M E,50%) 1.7x10

18 Bandwidth Ratio R (R E,r,M E) 8.2Bandwidth Ratio ( r = 17mm) R (R E,r,M E) 1Range Factor

|St (R E,r,M E)| 88 (MPa M )Range Factor Upper Limit |St (R E,,ME)| 2x10 5 (GPa G ) 1st Sense Check St(R E,r,M E) 4.8x10

-4 2nd Sense Check St (R E,r,M E) 5.8x10

-5 3rd Sense Check St(R E,r,M E) 14th Sense Check St(nPV ,R E,r,M E) 1

Table 4,

6.2 CONSIDERATIONS

Some of the factors to be considered in experimental design configurations may be articulatedas follows:

1. The experimental design should attempt to maximise the applied energy density with thehighest frequency conditions possible.

2. Optimal conditions occur approaching the ZPF beat cut-off mode n ZPF.3. EM modes within an experimental volume are subject to normal physical influences. The

fundamental frequency mode will not exist within a Casimir experiment, as the pseudo-wavelength is too large. Hence, the equivalent gravitational acceleration harmonic cannotexist.

4. Optimal experimental conditions occur when the ratio of the applied Poynting Vector to theImpedance Function approaches unity. [2]

5. Numerical solutions 26 to equation (15) indicate that greater than 99.99 (%) of the EGM beatspectrum occurs in the PHz range 27.

6.3 EGM WAVE PROPAGATION

The gravitational effect generated by a specifically applied EM field harmonic may beconceptualised as a modified EM wave. Figure (5) and (6) depict the manner in which pseudo-wave

propagation occurs. This has been termed EGM Wave Propagation and has 5 components as follows,i. The Electric Field Wave (magenta).

ii. The Magnetic Field Wave (blue).iii. The Electro-Gravitic Coupling Wave (green).iv. The Magneto-Gravitic Coupling Wave (Red).v. The Poynting Vector indicated in Figure (5) and (6) as the wave propagation arrow.

Figure 28 5,

26 Numerical approximations were performed using MathCad 8 Professional at default convergence,constraint and precision tolerance settings, to a display accuracy of 15 decimal places.27 K R 1 when (R E,r,M E,99.99999999999999%) 312 (PHz) and ZPF (R E,r,M E) 371(PHz).28 Figure not to scale.


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Figure 28 6,

6.4 DOMINANT & SUBORDINATE BANDWIDTHS

The EGM spectrum is fictitious and is derived from the concept of similarity. However, practical benefits to facilitate understanding of the concepts presented herein may be realised by thearticulation, in terms of applied experimental fields of the conventional representation of the EMspectrum. [8,9]

The EGM spectrum represents all frequencies within the EM spectrum but may be simplifiedinto two regimes. These have been termed the dominant and subordinate gravitational bandwidths( EGM and EGM respectively) as indicated in Figure (7).

Figure 31 7,

At the surface of the Earth, over practical benchtop values of r, EGM is responsiblefor significantly more than 99.99(%) of the spectral composition of g. Therefore, utilising table (1)we may speculatively re-define 29 the classical EM spectral representation for frequencies of GammaRays at a mathematical point with displacement r as follows 30,

i. 105(PHz) > > 1(YHz)ii. g > 1(YHz)

Where g represents the gravitational frequency of the applied experimental fields for completedynamic, kinematic and geometric similarity with the background gravitational field at the surface of the Earth.

6.5 KINETIC & POTENTIAL

The EGM Spectrum may be considered a hybrid function of an amplitude and frequencydistribution. The harmonic behaviour across an element r has been described in terms of:

i. The Fourier Spectrum termed the Potential Spectrum and is non-physical.ii. The ZPF Spectrum termed the Kinetic Spectrum and is physical.

Properties of the Fourier spectrum are such that wavefunction amplitude decreases asfrequency increases, whereas properties of the ZPF spectrum dictate constant amplitude with increasingfrequency. Consequently, merging the two distributions, as defined by equation (14), producesengineering properties and boundaries seemingly consistent with common-sense expectations.

The Potential Spectrum has the advantage of being able to fictitiously represent ZPF behaviour at a mathematical point in addition to r. This is otherwise not possible due to the ZPF

29 By approximation for illustration purposes at the surface of the Earth.30 YHz = 10 24(Hz)


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being a physical manifestation of g and the constituent wavefunctions possess finite wavelengths.Appendix (A) contains visualisation of physical modelling characteristics of the ZPF Spectrum.

7 CO CLUSIO S

The construct herein suggests that the delivery of EM radiation to a solid spherical test objectmay be used to modify its weight. Specifically, at high energy density and frequency, the gravitational

spectral signature of the test object may undergo constructive or destructive interference. However, thefrequency dependent conditions for gravitational similarity at the surface of the Earth are enormous:[ 312(PHz) and

30 ZPF 371(PHz)].Summarising yields:

i. The ZPF spectrum of free space is composed of an infinite number of modes n PV, withfrequencies tending to 0(Hz), as illustrated in table (1).

ii. The group velocity produced by the PV at a mathematical point and across practicalvalues of r at the surface of the Earth is 0(m/s). Consequently, gravitationalwavefunctions are not observed to propagate from the centre of a planetary body.

iii. |UPV(r,r,M) | is proportional to ZPF (r,r,M).iv. g exists (at practical bench-top experimental conditions / dimensions) as a relatively

narrow band of beat frequencies in the PHz Range. Spectral frequency compositions below this range 31 are negligible [similarity 0(%)].

v. General Similarity Equations (GSE x) facilitate the construction of computational models

to assist in designing optimal experiments. Moreover, they can readily be coded intooff-the-shelf 3D-EM simulation tools to facilitate the experimental investigation process.

vi. A solution for optimal experimental similarity utilising EM configurations exists whenMaxwells Equations at steady state conditions are observed such that:1. The divergence of E A is maximised.2. The magnitude and curl of E A is minimised.3. The magnitude and curl of B A is maximised.

References

[1] R. C. Storti, T. J. Desiato, Electro-Gravi-Magnetics (EGM) - Practical modelling methods of the polarizable vacuum I, http://www.deltagroupengineering.com/Docs/EGM_1.pdf [2] R. C. Storti, T. J. Desiato, Electro-Gravi-Magnetics (EGM) - Practical modelling methods of the

polarizable vacuum II, http://www.deltagroupengineering.com/Docs/EGM_2.pdf [3] R. C. Storti, T. J. Desiato, Electro-Gravi-Magnetics (EGM) - Practical modelling methods of the polarizable vacuum III, http://www.deltagroupengineering.com/Docs/EGM_3.pdf [4] R. C. Storti, T. J. Desiato, Electro-Gravi-Magnetics (EGM) - Practical modelling methods of the

polarizable vacuum IV, http://www.deltagroupengineering.com/Docs/EGM_4.pdf [5] Wolfram Research: http://scienceworld.wolfram.com/physics/BeatFrequency.html [6] Wolfram Research: http://scienceworld.wolfram.com/physics/MaxwellEquationsSteadyState.html [7] MathCad 8 Professional Reference Tables by MathSoft: http://www.mathcad.com/ [8] Wolfram Research: http://scienceworld.wolfram.com/physics/ElectromagneticRadiation.html [9] Georgia State University: http://hyperphysics.phy-astr.gsu.edu/hbase/ems1.html - c1

31 Approximately less than 42(THz).


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16

APPE DIX A

PHYSICAL MODELLING CHARACTERISTICS

For r


17/18

17

0 0.5 1 1.5 2

Critical Ratio

S R E r , M E, 50 %.,

Re S R E r , M E, K R ,

Im S R E r , M E, K R ,

50 %. 100 %.

K R

Figure A4,

0 0.5 1 1.5 2

Critical Ratio

S

R E

r , ME

, 50 %.,

S R E r , M E, K R ,

50 %. 100 %.

K R

Figure A5,

0 0.5 1 1.5 2

Critical Ratio

n R E r , M E, 50 %.,

Re n R E r , M E, K R ,

50 %. 100 %.

K R

Figure A6,

0 0.5 1 1.5 2

Critical Ratio

n R E r , M E, 50 %.,

Im n R E r , M E, K R ,

50 %. 100 %.

K R

Figure A7,


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0 0.5 1 1.5 2

Critical Ratio

n R E r , M E, 50 %.,

n R E r , M E, K R ,

50 %. 100 %.

K R

Figure A8,

0 0.5 1 1.5 2

Critical Ratio

n S R E r , M E, 50 %.,

Re n S R E r , M E, K R ,

Im n S R E r , M E, K R ,

50 %. 100 %.

K R

Figure A9,

0 0.5 1 1.5 2

Critical Ratio

n S R E r , M E, 50 %.,

n S R E r , M E, K R ,

50 %. 100 %.

K R

Figure A10,

Documents

EGM Electro-Gravi-Magnetics (EGM); Practical modelling methods of the polarizable vacuum - V