|
high-frequency gravitational waves |
Outline of Lecture Delivered to
The Max Planck Institute for
Astrophysics (MPA)
(Unscheduled)
And
The National Institute for Nuclear
Physics (INFN)
(Robert M. L. Baker, Jr., PhD)
1. Introduction:
Good
Day. I’m
● today, we have the unique opportunity to study and utilize the
gravitational-wave phenomenon predicted by Poincaré and Einstein decades ago
because of recent advances in technology.
● today, we have the means to generate HFGW and to detect
HFGW in the laboratory because of the availability of two new HFGW detectors. And we now,
● today,
have the motivation to apply HFGW to
communication, space propulsion, imaging and, in general, the motivation for
the laboratory study of HFGW!
But first, allow me to tell you a bit about
myself and how my interest in HFGW developed:
In the 1950s, I co-authored a paper on
gravitational dynamics entitled “Satellite Librations”. I had just received my Ph.D. at UCLA in Engineering with specialization
in Astronomy (UCLA termed it an
“Aerospace” degree) and I was appointed to the faculty of the Astronomy
Department and later the Engineering Department as Lecturer and Assistant Professor. In the 1960s, I became the Head of a Lockheed
laboratory and a Dr. Robert Forward contacted me regarding my Satellite
Librations paper. He was interested in
something called “gravitational waves” and his Ph.D. thesis was the design of a
resonance device developed by a Joseph Weber called the “Weber Bar”. I invited Dr. Forward to deliver a lecture to
my staff and was intrigued with the possibility of sensing low-frequency (LF)
gravitational waves (GW) with frequencies on the order of a kHz or less using
the Weber Bar. I was also intrigued by the possibility of generating
high-frequency (HF) gravitational waves (GW) exhibiting frequencies of a GHz or
more. At the time, however, I saw no practical means to generate the HFGW.
Recently, my interest in HFGW has been rekindled and I presented a paper on the
subject in 2000 to the American Institute
of Aeronautics and Astronautics or
AIAA (included as Attachment 3 to
this lecture). I will commence my remarks with a literature survey.
2. Literature Survey:
I
preface my remarks by noting that in the 1960s to 1980s there was considerable
skepticism concerning the existence of gravitational waves and consequently
little attention was paid to the literature concerning the laboratory
generation of GW. In what follows, I list the various publications by date and
include several in the Attachments – it should be recognized, however, that
there may well be more publications than those that I have uncovered. There is
ample evidence, as seen below, that the laboratory generation of gravitational
waves has been thoroughly studied by dozens of scientists and many of the
devices suggested are both feasible and practical if we take advantage of
recently developed technology.
1960: Weber,
“Detection and generation of gravitational waves.” Suggests the use of
piezoelectric crystals to generate 1039
more GW power than could be generated by a rapidly spinning rod.
1962: Gertsenshtein, “Wave resonance of light and gravitational
waves.” This one-and-one half page note
suggests the conversion of light into HFGW-- “Gertsenshtein Waves”.
1964: Halpren and Laurent, “On the gravitational radiation
of microscopic systems.” The possibility of increasing HFGW flux by stimulated
emission (“gaser”) is discussed and “... the maximum of the gravitational
radiation occurs in a direction from
which the corresponding electromagnetic (EM) radiation is excluded.”
1966: Forward
and Miller, “Generation and detection of dynamic gravitational-gradient
fields.” Concerned with oscillating† gravitational gradients such as those that were the subject of Dr. Klemperer
and my earlier paper on satellite librations.
1968: Halpern and Jouvet, “On the stimulated
photon-graviton conversion by an electromagnetic field.” They questioned
whether gravitational forces can produce GW (only non-gravitational forces may
generate GW they thought), “... electromagnetic (EM) field enhances the
emission of gravitational bremsstrahlung photons ... such effects are however below the
threshold observability in all (using 1968 technology) empirically known
cases.” Attachment 4 to these lecture notes.
1969:
1974: Grishchuk
and Sazhin, “Emission of gravitational waves by an electromagnetic cavity.”
according to Weiss was “... only a factor of 100,000 from being feasible.” Thousands of “... such cavities” were ganged
together to produce GHz HFGW; but deemed too weak (using 1973 technology).
Attachment 5.
1975: Sekie, et al, “GW generation from an array of
Cds plates.” This paper was computationally flawed and the calculation and
design were significantly in error.
1978:
Rudenko and Braginsky, “Hertz-type gravitational wave generator.”
Suggested a possible GW laboratory experiment with 10 MHz HFGW. Calculated it
could generate 10-18 [watts].
1981: Romero and Dehnen, “Generation of gravitational
radiation in the laboratory.” A long row of piezoelectric crystal oscillators
(10,000) is utilized to produce coherent HFGW (up to GHz frequencies) in a 20
degree “.... needle radiation” forward beam without significant associated EM
emissions; but “... may be under the observational limit.” On the other hand,
from their equation (A.11) if utilized more and closer spaced crystals and THz
frequencies, then the radiated energy
climbs to much more than 10-9
[watts] and is probably observable! Attachment 6 to these lecture notes.
1988: Pinto and Rotoli, “Laboratory generation of gravitational
waves?” They suggested three classes of
HFGW generators: (1) EM stress-energy field, (2) HF electrical oscillations for
acoustical stress or mechanical stress energy, and (3) array (linear) of such
sources. 500 MHz and Germanium crystals
are utilized. They conclude that HFGW “... seems to be conceivable... but very
difficult to concretize....” They
predict little or no excessive EM to be generated.
1991: Pia Astone, et al., “Evaluation and
preliminary measurement of the interaction of dynamical gravitational near
field with a cryogenic gravitational-wave antenna.” High-rpm (approximately 30,000) rotor about 1
kHz. They couldn’t control the detector
frequency and the results were inconclusive.
Actually, they were not producing GW but rather an oscillatory
gravitational field†
– the generation of GW from rotors is not possible since for any significant GW
flux the rotor would break due to centrifugal force.
1991: John
D. Kraus, “Will gravity-wave communication be possible?” Describes a
gravitational –wave generator in which an electromagnetic pulse is introduced
into a toroidal cavity at its resonance frequency to produce a very small phase
shift that distorts the medium in the toroid i.e., the pulse causes “physical
motion of submicroscopic particles” or a jerk.
1997:
Argyris and Ciubotariu, “A proposal of new gravitational experiments.”
Their experiments concern the simulation of accelerations produced by a wave of
gravity, a source of HFGW, a direct-current gravitational machine, materials
with high gravitomagnetic permeability (the “gravitational superconductor”) and
the possibility of attenuation of gravitational attraction..
1998:
2000: Baker, AIAA
paper ... jerk formulation and many alternative means and devices for
generating HFGW are described. This
paper is Attachment 3 to these lecture notes. The more than one-watt-per-
square-meter HFGW flux generated (page 29 of the paper) should be sensed by
spacetime-curvature, piezoelectric-crystal-array, GW-to-EM conversion, and/or
gravity-modification detectors. The
devices discussed in the paper are protected under U. S. Patents 6,417,597 and
6,160,336 and patents pending.
2001: Portilla and Lapiedra, “Generation of high
frequency gravitational waves.” References
Gertsenshtein’s work and relies on an electric charge shaken (jerked) in a homogeneous
stationary magnetic field -- suggested that it is promising. Attachment 8 to
these lecture notes.
2002: Raymond
Chiao, “Superconductors as transducers and antennas for gravitational and
electromagnetic radiation.” Describes an experiment at UC Berkeley in which he
will try to convert electromagnetic waves into controlled gravitational waves
inside a device in which the circuit is poised to go from a normally conducting
state to a superconducting state. Electrons near the surface of the
superconductor move (are jerked) and generate the gravitational waves. He
indicates that the energy will be
divided evenly between GW and EM radiation. Attachment 9 to these lecture
notes.
________________
† Please note that a librating-mass-produced
oscillation (periodic, time-varying change) in a classical “gravitational field” (like tidal changes) is not a quadrupole-produced
“gravitational wave” in the spacetime
continuum. As an example, a rapidly rotating neutron star generates significant
gravitational waves, but no appreciable oscillations in its gravitational
field. On the other hand, a mass dipole generates no gravitational waves (please see, for example, Weber {1964}), but
does generate oscillations in its
gravitational field or “waves of gravity”, which perturb other masses and have
tidal influence. An electrically charged dipole will produce electromagnetic
(EM) waves, however.
3. Jerk Formulation of the Quadrupole
Equation (Sophomore Physics)
There is no new Physics here, simply a
different approach or formulation to render engineering applications more
apparent.
As is well known and
noted specifically in a letter to me from Dr. Geoff Burdge, Deputy Director for
Technology and Systems of the National Security Agency, “Because
of symmetry, the quadrupole moment can be related to a principal moment of
inertia, I, of a three-dimensional tensor of the system and … can be
approximated by
-dE/dt » -G/5c5
(d3I/dt3)2
= - 5.5x10-54 (d3I/dt3)2.” (1)
In which k in Burdge’s notation is G
(not, however, the Einstein tensor) and the units are in the MKS system [watts]
not the cgs and the two sides of the equation are essentially the same. In this case, for a collection of masses like
a rim around a pivot,
I
= dm r2 [kg-m2], (2)
where
dm = mass of an individual magnetic sites around
the rim [kg], and
r = the distance from
a pivot out to any single dm on the rim [m] (or more exactly, the radius of
gyration of the rim). Thus
d3I/dt3 = dm d3r2/dt3 = 2rdmd3r/dt3 +… (3)
and d3r/dt3 is
computed by noting that by
2rdm d2r/dt2 = 2rfr [N-m] (4)
where fr = radial force on
dm . The derivative is approximated by
d3I/dt3 @ 2r Dfr/Dt , (5)
in which Dfr is the nearly instantaneous increase in the force on magnetic sites,
dm, caused by the magnetic field of current-carrying coils when they are
turned on and off or pulsed by transistors or ultra-fast switches, that is, a
jerk. In this regard, the coils on any
given rim segment are sequenced radially outward (at the local GW speed, say
the speed of light) in order to generate or build up the train of coherent HF
gravitational waves as they move through the energizable magnetic sites. In order not to build up acceleration the
jerks are reciprocating; but due to the square in the kernel of the quadrupole equation, the GW radiates in
both directions along the axis of the jerk no matter which direction the masses
are jerked. In summary
P = - 1.76x10-52
(2rDfr/Dt)2
[watts]. (6)
Alternately, from Eq.
(1), p. 90 of Joseph Weber, one has for Einstein's formulation of the
gravitational-wave (GW) radiated power of a rod spinning about an axis through
its midpoint having a moment of inertia, I [kg-m2], and an angular
rate, w [radians/s] (please also see, for example, pp. 979 and 980 of Misner,
Thorne, and Wheeler, in which I in the kernel of the quadrupole equation also
takes on its classical-physics meaning of an ordinary moment of inertia):
P
= 32GI2 w6 /5c5 =
G(Iw3)2/5(c/2)5
[watts] (7)
or
P
= 1.76x10-52(Iw3)2
= 1.76x10-52(r[rmw2]w)2 [watts] (8)
where [rmw2]2
can be associated with the square of the magnitude of the rod’s
centrifugal-force vector, fcf, for a rod of mass, m,
and radius of gyration, r. This vector reverses every half period at twice the
angular rate of the rod (and a component’s magnitude squared completes one
complete period in half the rod’s period). Thus the GW frequency is 2w and the time-rate-of-change of the magnitude of,
say, the x-component of the centrifugal force, fcfx is
Dfcfx/Dt µ 2fcfxw. (9)
(Note that frequency, u = w/2p.) The
change in the centrifugal-force vector itself (which we call a “jerk” when
divided by a time interval) is a differential vector at right angles to fcf
and directed tangentially along the arc that the dumbbell or rod moves through.
Equation (6), like Eqs. (7) and (8), are approximations and only hold
accurately for r << lGW and for speeds of the GW generator components far less than c. Please see, for example, Pais, p. 280.
Equation
(8) is the same equation as that given for two bodies on a circular orbit
on p. 356 of Landau and Lifshitz (I=mr2 in their notation) where w = n, the orbital mean motion.
Equation (9)
substituted into Eq. (8) with rmw2 associated with Dfcf yields
P
= 1.76x10-52 (2rDfcf /Dt)2, (10)
where (2rDfcf /Dt)2 is the kernel of the quadrupole
approximation equation.
As
a validation of Eq. (10), that is a validation of the use of a jerk to estimate
gravitational-wave power, let us utilize the approach for computing the
gravitational-radiation power of PSR1913+16. From section 3, Eq. (2) of my AIAA paper (Attachment 3) we computed
that each of the components of force change, Dfcfx,y = 5.77x1032 [N]
(multiplied by two since the centrifugal force reverses its direction each half
period) and Dt = (1/2)(7.75hrx60minx60sec) = 1.395x104 [s]. Thus using the
jerk approach:
P = 1.76x10-52{(2rDfcfx/Dt)2 + (2rDfcfy/Dt)2} =
1.76x10-52(2x2.05x109x5.77x1032/1.395x104)2x2
= 10.1x1024
[watts]
(11)
versus the result of 9.296x1024
[watts] using Landau and Lifshitz’s more exact two-body-orbit formulation given
by Eqs. (1.1) and (1.2) of my AIAA
paper integrated using the mean anomaly not the true anomaly. The most stunning
closeness of the agreement is, of course, fortuitous since due to orbital
eccentricity there is no symmetry among the Dfcfx,y components around the orbit
and, as will be shown, there are errors inherent in the approximations of Eqs.
(18) and (20) of my AIAA paper
leading to Eq. (10). Nevertheless, since the results for GW power are so close,
orbital-mechanic formulation compared to the utilization of a jerk, the
correctness of the jerk formulation is well demonstrated!
There are
some very sophisticated and exact computer simulations of the generation of
gravitational waves (please see, for example, S. F. Ashby, Ian Foster, James M.
Lattimer, Norman, Manish Parashar, Paul Saylor, Schutz,
A word about the
word quadrupole: the basic physical process for generating a gravitational wave
is the third time derivative of the motion of a mass, termed a "jerk"
or Δf/Δt, where Δf is an increase in force, f, on the mass carried
out over a small time interval, Δt.
As noted in Attachment 3, that physical process produces a gravitational
wave with a power given by, for example, the quadrupole approximation
(as originally derived by Einstein) or it could be determined directly from the
special and general relativity equations (using a computer- implemented numerical integration as, for example,
discussed in.
Ashby, et al (2000)). That is, the quadrupole itself is not the
physical process at all, but only one means of establishing the power of the
gravitational wave. This situation is
similar to
. Applications
4.1
Propulsion:
Landau
and Lifshitz (1975), in The Classical Theory
of Fields, on page 349 state: “Since it has definite energy, the
gravitational wave is itself the source of some additional gravitational
field... its field is a second-order effect ... But in the case of high-frequency gravitational waves the effect is
significantly strengthened ...” Thus it is possible to change the
gravitational field near an inanimate object by means of HFGW and move it.
Bonner
and Piper (1997), in their paper entitled “The gravitational wave a rocket”
state: “Loss of mass and gain in
momentum arises ... because of the emission of quadrupole or octupole GW.” Thus, according to them, one has the
potential of propelling a craft by means of GW.
4.2
Communication:
At
least two HFGW detectors or “receivers” are now functional {Cruise and Ingley
(2001) Attachment 1 and Gemme, Parodi, and Chincarini (2001-2002) Attachment 2}
together with HFGW generators or “transmitters” (many of them have been
identified earlier in this lecture) can be linked in order to carry information
at high frequencies/bandwidths (THz to QHz and above – the higher the frequency the more efficient is the HFSC generation). And,
like the gravitational field itself, GW passes unattenuated through all material things and can, for
example, reach deeply submerged submarines. As Thomas Prince (Chief Scientist, NASA/JPL and Professor of Physics
at Caltech) recently commented: “Of the applications (of HFGW), communication
would seem to be the most important. Gravitational waves have a very low cross
section for absorption by normal matter and therefore high-frequency waves
could, in principle, carry significant information content with effectively no
absorption unlike any electromagnetic waves.” Such a HFGW communication system
would represent the ultimate wireless
system -- point-to-multipoint QHz communication without the need for expensive enabling infrastructure, that is,
no need for fiber-optic cable, satellite transponders, microwave relays, etc. Antennas, cables, and phone lines
would be a thing of the past!
.
4.3
Imaging:
Lower
diffraction for HFGW allows for imaging using the refractive properties of HTSC
for use in communications and propulsion. {Such refractive properties were
found by
Refractive
properties of HTSC also open up the possibility of a HFGW Telescope. It may be
possible to intensify any anisotropic relic cosmic background features that may
exist (MHz to THz) and possibly image HFGW celestial point sources such as:
rapid stellar compression shock waves (jerks) and even very speculative, nearer,
relic mini black holes – a candidate for Dark
Matter. Dr.
If intervening matter between the HFGW
generator and detector causes a change (even a very slight one) in HFGW polarization,
diffraction, dispersion or results in extremely slight scattering or
absorption, then it may be possible to develop a HFGW “X-ray” like system. It
may, in fact, be possible to image directly through the Earth and view
subterranean features, such as geological ones, to a sub-millimeter resolution
for THz HFGW.
5. Recommendations:
5.1
Organize and schedule an International HFGW
Working Group meeting this year (2002) in order to trade ideas, stimulate
thinking, and define experimental parameters.
5.2
Promote an experiment utilizing a three GHz HFGW (or higher frequency) generator
from the list presented in the Literature Survey Section, for example a HTSC
under a three GHz (or higher frequency) magnetic field, a linear array of the
piezoelectric crystals under computer control, one of the devices discussed in
Baker’s AIAA paper (Attachment 3), such as the oscillatory
spindle, etc. The generator should be appropriately shielded in order to
prevent the emission of EM radiation from the energizing elements of the
generator. In order to assure reliable and non-controversial results, two
detectors, utilizing different techniques should be utilized: one being the
University of Birmingham’s HFGW detector (Attachment 1) and the other being the
INFN, Genoa’s HFGW detector (Attachment 2) – both tuned to 3 GHz (a frequency
selected for a practical-sized HFGW detector and a one-HFGW-wavelength, 10 to
20 cm, dimensioned HTSC disk generator).
The time is
right, carpe diem... seize the
moment!