Gravitational Radiation from Oscillating Gravitational Dipole

Transcription

1 Gavitational Radiation fom Oscillating Gavitational Dipole Fan De Aquino Maanhao State Univesity, Physics Depatment, S.Luis/MA, Bazil. Abstact. The concept of Gavitational Dipole is intoduced stating fom the ecent discovey of negative gavitational mass (g-qc/517 and physics/589). A simple expeiment, a gavitational wave tansmitte, to test this new concept of gavitational adiation souce is pesented. 1. INTRODUCTION When the gavitational field of an object changes, the changes ipple outwads though space and take a finite time to each othe objects. These ipples ae called gavitational adiation o gavitational waves. The existence of gavitational waves follows fom the Geneal Theoy of Relativity. In Einstein's theoy of gavity the gavitational waves popagate at the speed of light. Just as electomagnetic waves (EM), gavitational waves (GW) too cay enegy and momentum fom thei souces. Unlike EM waves, howeve, thee is no adiation in Einstein's theoy of gavity. The dominant channel of emission is quadupola. But the ecent expeimental discovey of negative gavitational mass 1, suggest the possibility of adiation. This fact is highly elevant because a gavitational wave tansmitte can be designed to geneate detectable levels of gavitational adiation in the laboatoy. Hee, we will study the theoy and design of the oscillating gavitational..theory Gavity is elated to gavitational mass of the paticles. The physical popety of mass has two distinct aspects, gavitational mass m and inetial mass m i. The inetial mass is the mass facto in Newton's nd Law of Motion( F mia), while the gavitational mass poduces and esponds to gavitational fields. It supplies the mass factos in Newton's famous invese-squae law of gavity ( F Gm m ; G is the Newton's 1 g1 g 1 gavitational constant). Accoding to the weak fom of Einstein s Geneal Relativity equivalence pinciple, the gavitational and inetial masses ae equivalent. Howeve ecent calculations have evealed that they ae coelated by an adimensional facto, which depends on the incident adiation upon the paticle. It was shown that thee is a diect coelation between the adiation absobed by the paticle and its gavitational mass, independently of the inetial mass. It was also shown that only in the absence of electomagnetic adiation this facto becomes equal to one and that, in specific electomagnetic conditions, it can be educed, nullified o made negative. This means that we can educe, nullify o make negative the gavitational mass of a body. This unexpected theoetical esult has been confimed by two expeiments using Extemely Low Fequency (ELF) adiation upon feomagnetic mateial 1,. g

2 The fact that negative gavitational mass to have been detected in both expeiments suggest that we now have available a plausible pocedue fo building an oscillating gavitational. The geneal equation of coelation between gavitational and inetial mass can be witten as : ad µσ mg mi 1 m i mic 4πf [ 1] whee D is the powe density of the incident( o emitted) adiation; f is the fequency of the adiation; a is the aea of the suface of the paticle of mass m i ; µ and σ ae espectively, the pemeability and the conductivity of the medium aound the paticle, in which the incident adiation is popagating. Fo an atom inside a body, the incident(o emitted) adiation upon the atom will be popagating inside the body, and consequently, σ σ body, µ µ body. Equation(1) shows that, elementay paticles (mainly electons ) can have thei gavitational masses stongly educed by means of Extemely-Low Fequency (ELF) adiation. Let us conside an electic cuent I though a conducto (annealed ion wie 99.98%Fe; 7 µ 5, µ ; σ 1. 1 S / m ) submitted to ELF electomagnetic adiation with powe density D and fequency f. Unde these cicumstances the gavitational mass m of the fee electons (electic cuent), accoding to Eq.(1), is given by aed µσ mge me 1 m e mec 4πf ge [ ] Hee, µ and σ ae espectively, the pemeability and the conductivity of the 1 annealed ion wie ; m e kg. If the ELF electomagnetic adiation come fom a half-wave electic encapsulated by an annealed ion (puified ion, with the same chaacteistics of the annealed ion wie), the adiation esistance of the antenna fo a fequency ω πf, can be witten as follows 4 ωµβ R z [ ] 6π whee z is the length of the and εµ β ω 1 + ( σ ωε ) + 1 ( σ ωε ) ω ε µ 1 1 c + + ω ω c ω c c v v whee c v [ 5] ε µ ( σ ωε ) 1 + is the velocity of the electomagnetic waves though the ion. ( µ µ µ ; ε ε ε ). Substituting (4) into () gives π µ R ( zf ) [ 6] v Note that when the medium suounding the is ai and ω >> σ ε, β ω ε µ, v c and R educes to the well-know expession R ( z ) 6 c ω πε. Fo σ >> ωε the Eq.(6) can be ewitten in the following fom ( n ) [ 4] π R σµ 9 ( z) f [ 7] The ohmic esistance of the is 5 z R R [ 8] ohmic S π whee is the adius of the coss

3 section of the, and suface esistance, R S Thus, R ohmic ωµ σ z µ 4πσ f Whee µ µ coppe µ 7 σ σ S / m. coppe R S is the [ 9] [ 1] and The adiated powe fo an effective (ms) cuent I is then P R I and consequently, the powe density, D, of the emitted ELF adiation, is ( zi ) P π D σµ S S 9 f [ 11] whee S is the aea suound of the. Fo f 69. 4µ Hz, the length of the is z λ v f π µ σ f. 1m Substitution of (11) into () yields 4 a e 4 mge me ( µ σ ) ( zi) 1 me [ 1] 6mcS e Note that the equation above doesn't depends on f. Thus, assuming that the adius of the electon 6 (egion which electon is "concentated") is 15 e ( 1 4πε )( e me c ). 8 1 m, 9 e 4π e m then the Eq.(1) a becomes mge me I 1 m e S Thus, fo S. 1m and I 1A ( cuent tough the ELF antenna) the gavitational mass of the fee-electons becomes m 4. 5 ge m e [ 1] This means that they becomes "heavy" electons. Gavitational effects poduced by ELF electomagnetic adiation upon the electic cuent in a conducto was ecently studied 7. An appaatus has been constucted to test the behavio of cuent subjected to ELF adiation. The expeimental esults show that gavitational mass of the fee-electons can becomes stongly negative. The oscillation of the gavitational masses of the feeelectons though the wie poduces gavitational adiation, but too weak due to the gavitational mass of the electons to be vey small. Howeve when the electons become "heavy", the gavitational adiation flux can be vey lage. Conside a half-wave electic whose elements ae two cylindes of annealed ion (99.98%Fe; 7 µ 5, µ ; σ 1. 1 S / m ) subjected to ELF adiation with fequency f 69. 4µ Hz (see Fig.1). The enegy flux caied by the emitted gavitational waves can be estimated by analogy to the oscillating electic. As we know, the intensity of the emitted electomagnetic adiation fom an oscillating electic ( i.e., the enegy acoss the aea unit by time unit in the diection of popagation) is given by 8 4 π Π f F ( φ ) sin φ [ 14] c ε The electic moment, Π Π sinωt, can be witten as qz, whee q is the oscillating electic chage, and z z sinωt ; thus, one can substitute Π by qz, whee z is the amplitude of the oscillations of z. Thee ae seveal ways to obtain the equivalent equation fo the intensity of the emitted gavitational adiation fom an oscillating

4 gavitational. The simplest way is meely the substitution of ε (electic pemittivity) by εg 1 16πG (gavitoelectic pemittivity 9 ) and q by m g (by analogy with electodynamics, the gavitoelectic moment can be witten as m g z, whee m g is the oscillating gavitational mass). Thus the intensity of the emitted gavitational adiation fom an oscillating F φ, can be gavitational, ( ) witten as follows: F π Gm g gw ( φ ) sin φ [ 15] gw 4 8 gw c z f whee f gw is the fequency of the gavitational adiation (equal to the fequency of the electic cuent though the ). Similaly to the electic, the intensity of the emitted adiation fom a gavitational is maximum at the equatoial plane ( φ π ) and zeo at the oscillation diection( φ ). The gavitational mass m g in Eq.(15) efes to the total gavitational mass of the "heavy" electons, given by m g 9 ( 1 fee electons/ m ) Vantmge whee V ant is the volume of the antenna. Fo the micowave antenna in Fig.1, m and mge 4. 5me. V ant This gives 6 m g 1 kg. The amplitude of oscillations of the half-wave gavitational is c z λgw f gw This means that to poduce gavitational waves with fequency f gw 1GHz, the length of the, z, must be equal to 1.5cm. By 4 substitution of these values and m 6 g 1 kg into Eq.(15) we obtain sin φ F gw 1 At a distance 1m fom the F φ is 9 ( φ) [ 16] the maximum value of ( ) F gw π 9 ( ) W / 1 m Fo compaison, a gavitational adiation flux fom astonomical souce with fequency 1Hz and amplitude h 1 ( the dimensionless amplitude h of the gavitational waves of astonomical oigin that could be detected on eath and with a fequency of about 1 khz is between 1-17 and 1 - ) has 1, F gw 1 c dh π G dt 5 f h W / m 1Hz 1 As concens detection of the gavitational adiation fom, thee ae many options. A simila gavitational can also absob enegy fom an incident gavitational wave. If a gavitational wave is incident on the gavitational (eceive) in Fig.1(b) the masses of the "heavy" electons will be diven into oscillation. The amplitude of the oscillations will be the same of the emitte, i.e., 1.5cm. Recently supeconductos have been consideed as macoscopic quantum gavitational antennas and tansduces 11, which can diectly convet a beam of gavitational adiation into electomagnetic adiation and vice vesa. In shot, now thee is a stong evidence that will be possible to geneate and detect gavitational adiation in laboatoy. gw

5 5 REFERENCES 1. De Aquino, F.() " Possibility of Contol of the Gavitational Mass by means of Exteme-Low Fequencies Radiation ", Los Alamos National Laboatoy, pepint no.g-qc/517.. De Aquino, F.() Coelation between Gavitational and Inetial Mass: Theoy and Expeimental Test, Los Alamos National Laboatoy, pepint no.physics/589.. De Aquino, F.() Gavitation and Electomagnetism: Coelation and Gand Unification, Jounal of New Enegy, vol.5, no, pp Los Alamos National Laboatoy pepint no.g-qc/ Chiao, R. Y. () "Supeconductos as quantum tansduces and antennas fo gavitational and electomagnetic adiation", Los Alamos National Laboatoy, pepint no.g-qc/41 p Schultz, B.F. () "Gavitational Radiation", Los Alamos National Laboatoy, pepint no.g-qc/69, p Chiao, R. Y. ()"Supeconductos as quantum tansduces and antennas fo gavitational and electomagnetic adiation", Los Alamos National Laboatoy, pepint no.g-qc/41. 4.Stutzman, W. L, Thiele, G.A, Antenna Theoy and Design. John Wiley & Sons, p Stutzman, W. L, Thiele, G.A, Antenna Theoy and Design. John Wiley & Sons, p Alonso, M., Finn, E.J.(197) Física, Ed. Edgad Blüche, p.149. Tanslation of the edition published by Addison-Wesley (1967). 7. De Aquino, F.() " Behavio of Electic Cuent Subjected to ELF Electomagnetic Radiation", Los Alamos National Laboatoy pepint no.physics/ Alonso, M., Finn, E.J.(197) Física, Ed. Edgad Blüche, p.97. Tanslation of the edition published by Addison-Wesley (1967).

6 6 ELF antenna coppe encapsulted by annealed ion 1cm 69.4µHz Micowave Antenna annealed ion 1.5cm Gavitational Radiation 1GHz (a) 69.4µHz 69.4µHz Tansmitte Gavitational Waves 1.5cm 1GHz 1.5cm I ' Induced Electic Cuent Emitte Faaday Cages Receive (b) Fig.1 - Schematic diagam of the antennas to poduce and eceive gavitational adiation..