Ferromagnetic Antenna and its Application to Generationand Detection of Gravitational Radiation

Fran De Aquino

Maranhao State University, Physics Department, S.Luis/MA, Brazil.deaquino@uema.br

A new type of antenna, which we have called Ferromagnetic Antenna, has been consideredfor Generation and Detection of Gravitational Radiation. A simple experiment, in whichgravitational radiation at 10 GHz can be emitted and received in laboratory, is presented.

1. INTRODUCTION

The gravitational mass, gm ,

produces and responds to gravitationalfields. It supplies the mass factors inNewton's famous inverse-square lawof Gravitation ( )2

122112 rmGmF gg= .

Inertial mass im is the mass factor in

Newton's 2nd Law of Motion ( )amF i= . Several experiments1-6, havebeen carried out since Newton to try toestablish a correlation betweengravitational mass and inertial mass. Some years ago J.F.Donoghueand B.R. Holstein7 have shown that therenormalized mass for temperature

0=T is expressed by 0mmmr δ+=where 0mδ is the temperature-independent mass shift. In addition, for

0>T , mass renormalization leadsto the following expressions forinertial and gravitational masses,respectively: βδδ mmmmi ++= 0 ;

βδδ mmmmg −+= 0 , where βδm is the

temperature-dependent mass shiftgiven by imTm 32παδ β = .

This means that a particle’sgravitational mass decreases with theincreasing temperature and that onlyin absolute zero ( )KT 0= aregravitational mass and inertial massequivalent.

The expression of βδm obtained

by Donoghue and Holstein referssolely to thermal radiation. The general equation ofcorrelation between gm and im will be

deduced here. Then we will show thatthe gravitational mass can be changedby means of Extreme-Low Frequency(ELF) electromagnetic radiation. Twoexperiments, using appropriated ELFradiation, has been carried out to testexperimentally this equation. Theexperimental results are in agreementwith the theoretical predictions. On theother hand, the detection of negativegravitational mass in both experimentssuggest the possibility of dipolegravitational radiation. This fact ishighly relevant because a gravitationalwave transmitter can be built togenerate detectable levels ofgravitational radiation in the laboratory. We have concluded from theexperiments that detectablegravitational radiation fluxes can beemitted from ferromagnetic materialsdipoles subjected to appropriated ELFelectromagnetic radiation. Here, we will present anexperiment which involves thegeneration and detection of high-frequency gravitational waves basedon this new technology.

22. THE CORRELATION ig mm .

In order to obtain the generalexpression of correlation between gm

and im , we will start with the definition

of inertial Hamiltonian, iH , and

gravitational Hamiltonian, gH , i.e.,

[ ]11

1

22

2222

22

2222

ϕϕ

ϕϕ

QcV

cmQcmpcH

QcV

cmQcmpcH

gggg

iiii

+−

=++=

+−

=++=

where im and gm are respectively,

the inertial and gravitational masses atrest. The momentum ip is given by :

221 cVVmp ii −= and 221 cVVmp gg −= ;

Q is the electric charge and ϕ is anelectromagnetic potential. The inertial Hamiltonian shift ,

Hδ , can be written in the followingform:

( )( ) ( )

[ ]211

2

2

2222

−

+=

=+−++=

=−+=

cm

pcm

QcmQcmpc

HHHH

i

i

ii

ii

δ

ϕϕδ

δδ

Note that the term inside the squarebracket is always positive. Thus,except for anti-matter ( 0<im ), the Hδis always positive. It is well known that the freeenergy of a system-F is related toinertial Hamiltonian, iH , by means of

[ ]3FHi =On the other hand, we can say that itsinternal energy U − which is given bythe component 00T of the energy-

momentum tensor µνT ,i.e., UT =00 ,

is related to gravitationalHamiltonian, gH , in similar fashion

[ ]4UH g =These energies are related byThermodynamics

( ) [ ]5TFTFU ∂∂−=or

[ ]6WFU −=where W can be interpreted (byanalogy to the 1st principle ofThermodynamics) as the work carriedout by the system. Note that Eq.[6] has a generalform(not only for thermal energy). Onthe other hand, the most generalrepresentation of W is obviously,given by means of the inertialHamiltonian shift Hδ . Therefore, wecan write Eq.[6] in the following form:

[ ]7HFU δ−=Substitution of Eqs.[3] and [4] intoEq.[7] gives

( ) ( )( ) [ ]8

2

2

2212

21

cmm

QcmQcm

HHH

gi

gi

gi

−=

=+−+=

=−=

ϕϕ

δ

Comparison of Eqs.[2] and Eq. [8]shows that

[ ]9112

2

i

i

ig mcm

pmm

−

+−= δ

This is the general expression ofcorrelation between gravitational andinertial mass. We can look on this change inmomentum ( )pδ as due to theelectromagnetic energy absorbed oremitted by the particle ( by means ofradiation and/or by means of Lorentz'sforce upon the charge of the particle). In the case of radiation ( photonswith frequency πω 2=f ), if n is thenumber of incident (or radiated)photons on the particle of mass im , wecan write

[ ]10v/U

)dt/dz/(U)k//(nknp rr

===== ωωδ

Where rk is the real part

of the propagation vector k

;

ir ikk|k|k +==

; U is theelectromagnetic energy absorbed or

3emitted by the particle and v is thephase velocity of the electromagneticwaves, given by:

( )[ ]11

112

2

++===

ωεσµεκω

rrr

c

dt

dzv

ε , µ and σ, are the electromagneticcharacteristics of the medium in whichthe incident (or emitted) radiation ispropagating ( 0εεε r= where rεis the relative electric permittivity and

mF /10854.8 120

−×=ε ; 0µµµ r= where

rµ is the relative magnetic permeability

and m/H70 104 −×= πµ ). For an atom

inside a body , the incident(or emitted)radiation on this atom will bepropagating inside the body , andconsequently , σ = σbody , ε = εbody,µ =µbody. From the Eq.[10] follows that

[ ]12rnc

U

v

c

c

U

v

Up =

==δ

where rn is the index of refraction,given by

( ) [ ]13112

2

++== ωεσµε rrr

v

cn

c is the speed in a vacuum and v isthe speed in the medium. By the substitution of Eq.[12]into Eq.[9], we obtain

[ ]141121

2

2 ir

i

g mncm

Um

î

−

+−=

Substitution of nhfnU == ω

intoEq.[14], gives

[ ]15112

2

2mn

cm

nhfmm r

i

ig

−

î

î

+−=

Light can be substantially sloweddown or frozen completely by opticallyinducing a quantum interference in aBose-Einstein condensate 8 .Thismeans an enormous index of refractionat ~1014Hz. If t he speed of light isreduced to <0.1m/s, the Eq.[15] tell usthat the gravitational masses of the

atoms of the Bose-Einsteincondensate become negative. Let us now consider theparticular macroscopic case in whichall the particles inside a body have thesame mass im . If SN is the averagedensity of incident (or emitted)photons upon the body (number ofphotons across the area unit), and ais the area of the surface of eachparticle of mass im , then accordingto the Statistical Mechanics, thecalculation of n can be made basedon the well-known method ofProbability of a Distribution . The resultis

[ ]16aS

Nn =

Obviously the power P of theincident radiation ( photons withfrequency f ), must be

2/ NhftNhfP =∆= , thus we can write2hf/PN = . Substitution of N into

Eq.[16] gives

[ ]1722

Dhf

a

S

P

hf

an =

=

where D is the power density of theincident( or emitted) radiation. ThusEq.[15] can be rewritten in thefollowing form:

[ ]18112

2

mcvfm

aDmm

iig

−

î

î

+−=

For ωεσ >> Eq.[11] reduces to

[ ]194

µσπf

v =

By substitution of Eq.[19] into Eq.[18]we obtain

[ ]2014

12

2

3 i

i

ig mfcm

aDmm

−

î

î

+−=πµσ

4 This equation shows that,elementary particles (mainly electrons),atoms or molecules can have theirgravitational masses stronglyreduced by means of ELF radiation. It is important to note that in theequation above, ferromagneticmaterials with very-high µ requestsmaller value of D .

3. EXPERIMENTAL TESTS

In order to check Eq.[20]experimentally, it was built anapparatus ( System H ) presented inFig.1. Basically, a 9.9mHz Transmittercoupled to a special antenna. The antenna in Fig.1 is a half-wave dipole, encapsulated by a ironsphere (purified iron, 99.95% Fe;

00005 µµ ,i = ; m/S.i710031 ×=σ ). We

will check the effects of the ELFradiation upon the gravitational massof the ferromagnetic material (ironsphere) surrounding the antenna. The radiation resistance of theantenna for a frequency fπω 2= , canbe written as follows 9

[ ]216

2zR iir ∆

πβωµ=

where z∆ is the length of the dipoleand

( )

( )

( ) [ ]22

112

112

2

2

ii

r

iiriri

iiii

i

vv

c

cn

c

c

ωωω

ωεσµεω

ωεσµεωβ

=

==

=

++=

=

++=

where iv is the velocity of the radiationthrough the iron. Substituting [22] into [21] gives

( ) [ ]233

2 2zfv

Ri

ir ∆µπ

=

Note that when the mediumsurrounding the dipole is air and

εσω >> , 00µεωβ ≅ , cv ≅ and rR

reduces to the well-know expression( ) 3

02 6 czRr πεω∆≅ .

Here, due to ii ωεσ >> , iv isgiven by the Eq.[19]. Then Eq.[23] canbe rewritten in the following form

( ) [ ]249

332 fzR iir µσπ∆

=

The ohmic resistance of the dipole is 10

[ ]252 0

Sohmic Rr

zR

π∆≅

where 0r is the radius of the cross

section of the dipole, and SR is thesurface resistance ,

[ ]262 dipole

dipoleSR

σωµ

=

Thus,

[ ]2740 dipole

dipoleohmic

f

r

zR

πσµ∆≅

Where 0µµµ ≅= copperdipole and

m/S.copperdipole71085 ×==σσ .

The radiated power for aneffective (rms) current I is then

2IRP r= and consequently

( ) [ ]289

332

fS

zI

S

PD iiµσπ∆

==

where S is the effective area. It can beeasily shown that S is the outerarea of the iron sphere ( Fig.1), i.e.,

22 1904 m.rS outer == π . The iron surrounding the dipoleincreases its inductance L . However,for series RLC circuit the resonancefrequency is LCfr π21= , then when

rff = ,

.C

L

C

L

CfLfXX

r

rCL 02

12 =−=−=−

ππ

Consequently, the impedance of theantenna, antZ , becomes purelyresistive, i.e.,

5

( ) .RRRXXRZ ohmicrantCLantant +==−+= 22

For mHz.ff r 99== the lengthof the dipole is

mmm.ffvz ii 70070022 ===== σµπλ∆ .

Consequently, the radiation resistance

rR , according to Eq.[24], isΩµ564.Rr = and the ohmic

resistance, for mmr 130 = , according to

Eq.[27], is Ωµ020.Rohmic ≅ . Thus,

Ωµ584.RRZ ohmicrant =+= and theefficiency of the antenna is

( )%..RRRe ohmicrr 569999560=+= . The radiation of frequency

mHz.f 99= is totally absorbed bythe iron along a critical thickness

mmm.fz ii 11011055 =≅== σµπδ .

Therefore, from the Fig.1 we concludethat the iron sphere will absorbpractically all radiation emitted from thedipole. Indeed, the sphere has beendesigned with this purpose, and insuch a manner that all their atomsshould be reached by the radiation. Inthis way, the radiation outside of thesphere is practically negligible. When the ELF radiation strikesthe iron atoms their gravitationalmasses, gim , are changed and,

according to Eq.[20], become

[ ]2914

12 2

2

32 i

i

iiiigi mD

m

a

fcmm

î

−

+−=

πσµ

Substitution of [28] into [29] yields

( ) [ ]3016

12 4

222

i

i

iiiigi mzI

m

a

cSmm

î

−

+−= ∆σµ

Note that the equation abovedoesn't depends on f . Thus, assuming that theradius of the iron atom is

m.riron1010401 −×= ; 2192 104624 m.ra ironi

−×== πand ( ) kg.kg..mi

2627 10279106618555 −− ×=×=then the Eq.[30] can be rewritten asfollows

( ) [ ]3111038212 44iigi mI.mm −×+−= −

The equation above shows thatthe gravitational masses of the ironatoms can be nullified for A.I 518≅ .Above this critical current, gim

becomes negative. The Table 1 presents theexperimental results obtained from theSystem H for the gravitational mass ofthe iron sphere, ( )sphereirongm , as a

function of the current I , forkg.m sphereiron 5060= ( inertial mass

of the iron sphere ). The values for

( )sphereirongm , calculated by means of

Eq.[31], are on that Table to becompared with those supplied by theexperiment. The experiment showed that thegravitational mass can be reduced,nullified or made negative by means ofappropriated ELF electromagneticradiation. The experimental results arein agreement with the theoreticalpredictions, calculated by means ofEq.[20]. In another previous experiment 11

we have built a system (calledsystem-G) to test the Eq.[20]. In thesystem-G, a spiral antenna (half-wavedipole) was encapsulated by ironpowder and the iron powder by aannealed iron toroid. We havechecked the effects of the ELFelectromagnetic radiation upon thegravitational mass of ferromagnetictoroid surrounding the ELF antenna,the results have been similar.However, the system-G works with

6very high electric currents(up to 300A)while the system-H, just up to 10A. From the technical point of view,there are several applications to thisdiscovery. Now we can buildgravitational binaries, and to extractenergy from any site of a gravitationalfield. The gravity control will be alsovery important to systems of Transport,and for Telecommunication too, aswe will see soon after.

4.GRAVITATIONAL RADIATION

When the gravitational field of anobject changes, the changes rippleoutwards through space and take afinite time to reach other objects.These ripples are called gravitationalradiation or gravitational waves . The existence of gravitationalwaves follows from the General Theoryof Relativity. In Einstein's theory ofgravity the gravitational wavespropagate at the speed of light. Just as electromagnetic waves(EM), gravitational waves (GW) toocarry energy and momentum from theirsources. Unlike EM waves, however,there is no dipole radiation in Einstein'stheory of gravity. The dominantchannel of emission is quadrupolar.But the detection of negativegravitational mass suggest thepossibility of dipole gravitationalradiation. This fact is highly relevantbecause now we can build agravitational wave transmitter togenerate detectable levels ofgravitational radiation in the laboratory. Let us consider an electriccurrent IC through a conductor(annealed iron wire 99.98%Fe;

m/S.;, 70 10031000350 ×== σµµ )

submitted to ELF electromagneticradiation with power density D andfrequency f . If the ELF electromagneticradiation come from a half-wave

electric dipole ( copper )encapsulated by an annealed iron(purified iron, with the samecharacteristics of the annealed ironwire), the radiation resistance of theantenna for ωεσ >> , according toEq.[23], can be written as follows

( ) [ ]329

332 fzRr σµπ∆

=

The ohmic resistance is

[ ]3340 dipole

dipoleohmic

f

r

zR

πσµ∆≅

The radiated power for aneffective (rms) current I is then

2IRP r= and consequently, the powerdensity, D , of the emitted ELFradiation, is

( ) [ ]349

332

fS

zI

S

PD σµπ∆

==

where S is the area surround of thedipole. For Hz.f µ469= , the length ofthe dipole is

m.ffvz 10022 ==== σµπλ∆ The gravitational mass of thefree-electrons into the wire ( electriccurrent IC ) can be obtained by meansof the substitution of [34] into [20],i.e.,

( ) ( ) [ ]3516

12 4

2

24e

e

eege mzI

cSm

amm

î

−

+−= ∆σµ

Substitution of numerical valuesinto Eq.[35] leads to the followingequation

[ ]36110

12 42

6

eege mIS

~mm

î

−+−=−

Thus, for 210 m.S ≅ and AI 100≅(current trough the ELF antenna) thegravitational mass of the free-electronsbecomes

ege mm 200−≅This means that they becomes"heavy" electrons.

7 Now consider a half-waveelectric dipole whose elements are twocylinders of annealed iron (99.98%Fe;

m/S.;, 70 10031000350 ×== σµµ )

subjected to ELF radiation withfrequency Hz.f µ469= (see Fig.2). Theoscillation of the gravitational massesof the "heavy" electrons through thisferromagnetic antenna will generate agravitational radiation flux very greaterthan the flux which is generated bythe electrons at the "normal " state( eg mm ≅ ).The energy flux carried by

the emitted gravitational waves can beestimated by analogy to the oscillatingelectric dipole. As we know, the intensity of theemitted electromagnetic radiation froman oscillating electric dipole ( i.e., theenergy across the area unit by timeunit in the direction of propagation) isgiven by 12

( ) [ ]372

223

420

2

φε

Ππφ sinrc

fF =

The electric dipole moment ,tsinωΠΠ 0= , can be written as qz ,

where q is the oscillating electriccharge, and tsinzz ω0= ; thus, one can

substitute 0Π by 0qz , where 0z is theamplitude of the oscillations of z . There are several ways to obtainthe equivalent equation for theintensity of the emitted gravitationalradiation from an oscillatinggravitational dipole. The simplest wayis merely the substitution ofε (electric permittivity) by GG πε 161=(gravitoelectric permittivity 13,14,15 ) andq by gm (by analogy with

electrodynamics, the gravitoelectricdipole moment can be written as zmg ,

where gm is the oscillating

gravitational mass). Thus the intensityof the emitted gravitational radiationfrom an oscillating gravitational dipole,

( )φgwF , can be written as follows:

( ) [ ]388 2

23

420

23

φπ

φ sinrc

fzGmF gwg

gw =

where gwf is the frequency of the

gravitational radiation (equal to thefrequency of the electric currentthrough the ferromagnetic dipole). Similarly to the electric dipole,the intensity of the emitted radiationfrom a gravitational dipole is maximumat the equatorial plane ( 2

πφ = ) andzero at the oscillation direction( 0=φ ). The gravitational mass gm in

Eq.[38] refers to the total gravitationalmass of the "heavy" electrons, givenby

( ) geantg mVm/electronsfreem 32910 −=where antV is the volume of theantenna. For the microwave ferromagneticantenna in Fig.2, 381047 m.Vant

−×= and

ege mm 200−≅ . This gives kgmg610−≅ .

The amplitude of oscillations ofthe half-wave gravitational dipole is

gwgw

f

cz

220 == λ

This means that to producegravitational waves with frequency

GHzfgw 10= , the length of the

ferromagnetic dipole, 0z , must beequal to 1.5cm. By substitution ofthese values and kgmg

610−−≅ into

Eq.[38] we obtain

( ) [ ]39102

29

r

sinFgw

φφ −≅

At a distance mr 1= from the dipolethe maximum value of ( )φgwF is

( ) 292 10 m/WFgw

−≅π

For comparison, a gravitationalradiation flux from astronomicalsource with frequency 1Hz andamplitude 2210−≅h ( the dimensionlessamplitude h of the gravitational wavesof astronomical origin that could bedetected on earth and with a

8frequency of about 1 kHz is between10-17 and 10-22 ) has 16,

29

2

22

2

5

23

1010100

1061

32

1

m/Wh

Hz

f.

dt

dh

G

cFgw

−−

− ≅

×=

=

=

π

As concerns detection of thegravitational radiation from dipole,there are many options. A similargravitational dipole can also absorbenergy from an incident gravitationalwave. If a gravitational wave is incidenton the gravitational dipole(receiver) inFig.2(b) the masses of the "heavy"electrons will be driven into oscillation.The amplitude of the oscillations willbe the same of the emitter, i.e., 1.5cm,and there will be an induced electriccurrent I ' through the ferromagneticantenna of the receiver (see Fig.2(b)). The weakness with whichgravitational waves interact with matteris well-known. There is no significantscattering or absorption. It means thatgravitational waves carry uncorruptedinformation even if they come from themost distant parts of the Universe.Consequently , a gravitational wavestransceiver, based on the experimentpresented in Fig.2, would allow us tocommunicate through the Earth, which,like all matter of the Universe, istransparent to gravitational waves.Furthermore, the receiver would allowus to directly observe for the first timethe Cosmic Microwave Background inGravitational Radiation, which wouldpicture the Universe, just at thebeginning of the Big Bang.

REFERENCES

1. Eötvos, R. v. (1890), Math. Natur. Ber.Ungarn, 8,65.

2. Zeeman, P. (1917), Proc. Ned. Akad. Wet.,20,542.

3. Eötvos, R. v., Pékar, D., Fekete, E. (1922)Ann. Phys., 68,11.

4. Dicke, R.H. (1963) ExperimentalRelativity in “Relativity, Groups andTopology” (Les Houches Lectures), p. 185.

5. Roppl, P.G et. al. (1964) Ann. Phys (N.Y),26,442.

6. Braginskii, V.B, Panov, V.I (1971) Zh.Eksp. Teor. Fiz, 61,873.

7. Donoghue, J.F, Holstein, B.R (1987)European J. of Physics, 8,105.

8. M. M. Kash, V. A. Sautenkov, A.S. Zibrov, L. Hollberg, H. Welch, M. D.Lukin, Y. Rostovsev, E. S. Fry, and M. O.Scully, (1999) Phys. Rev. Lett. 82, 5229 ; Z.Dutton, M. Budde, Ch. Slowe, and L. V.Hau, (2001) Science 293, 663.

9. Stutzman, W.L, Thiele, G.A, AntennaTheory and Design. John Wiley & Sons,p.48.

10. Stutzman, W.L, Thiele, G.A, AntennaTheory and Design. John Wiley & Sons,p.49.

11. De Aquino, F. (2000) " Possibility of Control of the Gravitational Mass by means of Extra-Low Frequencies Radiation", Los Alamos National Laboratory, preprint gr-qc/0005107.

12. Alonso, M., Finn, E.J.(1972) Física, Ed.Edgard Blücher, p.297. Translation of theedition published by Addison-Wesley(1967).

13. Chiao, R. Y. (2002) "Superconductors as quantum transducers and antennas for gravitational and electromagnetic radiation", Los Alamos National Laboratory, preprint gr-qc/0204012 p.18.

14.Kraus,J.D. (1991) IEEE Antennas and Propagation Magazine, 33, 21.

15.Landau, L. D. and Lifshitz, E.M. (1951) The Classical Theory of Fields, 1st edition, (Addison-Wesley) p..328 ; Forward, R. L. (1961) Proc. IRE, 49, 892 ; Ciufolini, I. et al., (1998) Science, 279, 2100.

16. Schultz, B.F. (2000) " Gravitational Radiation", Los Alamos National Laboratory, preprint gr-qc/0003069, p.5.

9

Cross section

Front view

Fig.1 - Schematic diagram of the System H

coiled spring

counterweight (dipole + wires)

encapsulated antenna

r=123mmii σµiron

26mm

70mm

Transmitter 9.9mHz

scale

ferromagnetic sphere

counterweight

10

( )sphereirongm

I ( kg ) (A) theory experimental

0.00 60.50 60.5

1.00 60.48 60.(4)

2.00 60.27 60.(3)

3.00 59.34 59.(4)

4.00 56.87 56.(9)

5.00 51.81 51.(9)

6.00 43.09 43.(1)

7.00 29.82 29.(8)

8.00 11.46 11.(5)

8.51 0.0 0.(0)

9.00 -12.16 -12.(1)

10.00 -40.95 -40.(9)

Table 1

Note: The inertial mass of the iron sphere is kg.m sphereiron 5060=

11

(a)

Emitter Faraday Cages Receiver (b) Fig.2 - Schematic diagram of the ferromagnetic antennas to produce and receive gravitational radiation.

1.5cm

Gravitational Radiation

ELF antenna copper dipole encapsulted by annealed iron

10cm

MicrowaveFerromagnetic Antenna (annealed iron dipole)

1.5cm

69.4µHz

10GHz

Transmitter

69.4µHz69.4µHz

1.5cm 10GHz

Gravitational Waves Induced Electric CurrentI '