DIRD High-Frequency Gravitational Wave Communications

High-Frequency Gravitational Wave Communications

Defense Intelligence Reference Document, Acquisition Threat Support. DIA-08-1004-005, 6 April 2010 (ICOD: 1 December 2009).

Prepared by the Defense Intelligence Agency. This product is one of a series of advanced technology reports produced under the Defense Intelligence Agency Advanced Aerospace Weapon System Applications Program.

Summary

Fourteen laboratory high-frequency gravitational wave (HFGW) generators (or transmitters) have been proposed in the past 45 years in peer-reviewed journal articles.

The most promising laboratory HFGW generators are those that utilize very large numbers of sub-microscopic radiation elements.

The Piezoelectric Approach to HFGW generation is best for the proof-of-concept test and the proposed IR-excited Molecules Approach is best for an operational communications HFGW transmitter.

Ten different HFGW detectors (or receivers) have been proposed since 1978 and reported in peer-reviewed journal articles.

Several different HFGW receivers can be utilized for communication, but the proposed Li-Baker detector shows the most promise. The Li-effect, upon which the Li-Baker detector is based, is not so new that it is untested in the literature. At least nine peer-reviewed research publications concerning the theory have appeared following the initial peer-reviewed article by Li, Tang and Zhao (1992).

Because HFGW communications are carried on an extremely narrow beam directly through the Earth, there is a very low probability of interception.

Theoretical results confirm that the Li-Baker detector is photon-signal limited, not quantum-noise limited — that is, the Standard Quantum Limit is so low that a properly designed Li-Baker detector can have sufficient sensitivity to observe HFGWs of amplitude A of about 10⁻³² m/m.

Utilizing the IR-excited Molecules HFGW generator approach and the Li-Baker detector, the theoretical information-transfer rate over 7,000 km of distance, beamed directly through the Earth, is about 1.9 x 10⁶ bits per second.

A means of propagating a Frequency Time Standard may be one viable early low-bandwidth application for HFGW communications.

HFGW sources on the Earth, the Moon, and Mars may act as reference standards for interplanetary navigation, with the advantage that they cannot be shielded or shadowed by planetary masses. Plasma interference seen at planetary entry would be eliminated, and precise charting of Lagrangian points would be possible.

1.0 Introduction

1.1 Introduction

Of the applications of high-frequency gravitational waves (HFGWs), communication appears to be the most important and most immediate. Gravitational waves have a very low cross section for absorption by normal matter, so high-frequency waves could, in principle, carry significant information content with effectively no absorption, unlike electromagnetic (EM) waves. Multi-channel HFGW communications can be both point-to-point (for example, to deeply submerged submarines) and point-to-multipoint, like cell phones. HFGWs pass through all ordinary material things without attenuation and represent the ultimate wireless system. One could communicate directly through the Earth from Moscow in Russia to Caracas in Venezuela — without the need for fiber optic cables, microwave relays, or satellite transponders. Antennas, cables and phone lines would be things of the past. A timing standard alone, provided by HFGW stations around the globe, could result in a multi-billion dollar savings in conventional telecom systems over ten years, according to the recent analysis of Harper and Stephenson (2007). The communication and navigation needs of future magnetohydrodynamic (MHD) aerospace vehicles, such as the MHD aerodyne, which is high in electromagnetic interference, similar to plasma interference seen at reentry, would be another possible applications area for HFGW communications.

1.2 Definition of High-Frequency Gravitational Waves

Visualize the luffing of a sail as a sailboat comes about or tacks. The waves in the sail's fabric are similar in many ways to gravitational waves (GWs), but instead of sailcloth fabric, gravitational waves move through a fabric of space. Einstein called this fabric the space-time continuum in his 1915 work known as General Relativity (GR). Although his theory is very sophisticated, the concept is relatively simple. This fabric is four-dimensional: it has the three usual dimensions of space — east-west, north-south, and up-down — plus the fourth dimension of time. Here is an example: we define a location on this fabric as 5th Street and Third Avenue on the fourth floor at 9 AM. No one can see this fabric, just as no one can see wind, sound, or gravity. Nevertheless, those elements are real, and so is this fabric. If one could generate ripples in this space-time fabric, many applications would become available. Much like radio waves can be used to transmit information through space, gravitational waves could be used to perform analogous functions.

Gravitational waves are the subject of extensive current research, which so far has focused on low frequencies. High-frequency gravitational waves, as defined by physicists Douglass and Braginsky (1979), are gravitational waves having frequencies higher than 100 kHz. Low-frequency gravitational waves (LFGWs), such as those detectable by interferometric GW detectors — for example, the Laser Interferometer Gravitational Observatory, or LIGO — are not applicable to communications due to their very long wavelengths, often thousands of kilometers in length and, even more importantly, the inability to generate them effectively in the laboratory. Furthermore, LFGW detectors cannot detect HFGWs (Shawhan, 2004).

2.0 HFGW Communications

Consider the case of a single point-to-point two-station full duplex communication system. Such a system is often characterized as a single data link, and requires two transmitters, one at each end, and two receivers, one at each end. To avoid self-interference the link in one direction often uses a frequency of radiation different than the link in the opposite direction.

If one were to apply the emerging technology of gravitational wave control to such a link, one would use GW generators for the transmitters on each end, and GW sensors for the receivers at each end (Stephenson, 2009a). Station 1 would have a GW generator transmitting at a frequency of omega-1 and a GW sensor sensitive to a frequency of omega-2, without being sensitive to a frequency of omega-1. Likewise, station 2 would have a GW generator transmitting at a frequency of omega-2 and a GW sensor sensitive to a frequency of omega-1, without being sensitive to a frequency of omega-2. This is the minimum functionality required to constitute a communication link. Signal strengths of the respective GW generators would need to be sufficient to overcome link loss, coupling losses, and noise sources. Signal to noise considerations and link budgets are covered in further detail in Section 3.1.

2.1 HFGW Generators (Transmitters)

2.1.1 HFGW Generator Concepts

Several sources for HFGWs or means for their generation exist. The first generation means is the same for gravitational waves of all frequencies and is based upon the quadrupole equation first derived by Einstein in 1918. A formulation of the quadrupole that is easily related to the orbital motion of binary stars or black holes, rotating rods, laboratory HFGW generation, and so forth is based upon the jerk or shake of mass — the time rate of change of acceleration — and is derived by Baker (2006) as

P = 1.76 x 10⁻⁵² (2 r Δf / Δt)² watts (1)

where P is the power of the GWs in watts; r is the distance between two masses, in metres; Δf is a change in force, in newtons, over the time interval Δt in seconds — that is, the jerk or shake of the two masses, such as the change in centrifugal force vector with time, for example as masses move around each other on a circular orbit.

Please recognize, however, that Δf need NOT be a gravitational force (see Einstein, 1918; Infeld quoted by Weber 1964, p. 97; Grishchuk 1974). Electromagnetic forces are more than 10³⁵ larger than gravitational forces and should be employed in laboratory GW generation. As Weber (1964, p. 97) points out: "The non-gravitational forces play a decisive role in methods for detection and generation of gravitational waves." Equation (1) is also termed quadrupole formalism and holds in weak gravitational fields (well over 100 g's), for speeds of the generator components less than the speed of light and for r less than the GW wavelength. This last restriction may not really apply. Certainly there would be GW generated for r greater than the GW wavelength, but the quadrupole formalism might not apply exactly.

For very small Δt, the GW wavelength, which is approximately c times Δt, is very small and the GW frequency is high. As a numerical example, r is chosen to be 10 m (convenient laboratory size, though usually greater than the GW wavelength), Δf is about 4 x 10⁸ N — for example, the force produced by a large number of piezoelectric resonators — and Δt is 2 x 10⁻¹⁰ s, equivalent to about a 5 GHz jerk or shake frequency, so that the GW wavelength is 6 cm and P is about 2.8 x 10⁻¹³ W, or 0.28 picowatts. Clearly a very small HFGW power is generated.

One of the first suggested means for the laboratory generation of HFGWs was the so-called gaser, analogous to the laser for light. Simply described (Halpern and Laurent, 1964), the gaser consists of a long rod of a material, microscopic parts of which can be excited by a means such as electromagnetic radiation to emit HFGWs. They utilize linearized theory to treat the interaction of a gravitational field with matter: "Application is made to the emission of gravitons by microscopic systems such as molecules and nuclei."

Grishchuk and Sazhin in early 1974 discussed the emission of gravitational waves by an electromagnetic cavity. In August of 1974 Chapline, Nuckolls and Woods suggested the generation of HFGWs by nuclear explosions. In this same regard Fontana suggested that the problem of efficient generation of HFGWs and pulses of gravitational radiation might find a reasonably simple solution by employing nuclear matter (Fontana and Baker, 2006; Fontana and Binder, 2009), especially isomers. A fissioning isomer not only rotates at extremely high frequency, about 3.03 x 10²⁴ per second according to the aforementioned references, but is also highly deformed in the first stages of fission — the nucleus is rotating and made asymmetric before fission. Thus one achieves significant impulsive forces, for example 3.67 x 10⁵ N, acting over extremely short time spans, for example 3.3 x 10⁻²² s. Alternatively, a pulsed particle beam, which could include antimatter, could trigger nuclear reactions and build up a coherent GW as the particles move through a target mass.

The usual difficulty with HFGWs generated by nuclear reactions is the small dimensions of their nuclear-reaction volumes — that is, the small moment of inertia and submicroscopic radii of gyration, for example 10⁻¹⁶ m, of the nuclear-mass system. Such a difficulty is overcome by utilizing small clusters of nuclear material whose nuclear reactions are in synchronization, for example through the use of a computer-controlled logic system. Such nuclear-energized HFGW generators are currently very theoretical.

Braginsky and Rudenko (1978) discussed the generation of gravitational waves in the laboratory and proposed a means utilizing small particles. In 1981 Romero and Dehnen analyzed the generation of gravitational radiation in the laboratory, also utilizing a linear array of piezoelectric crystals, which will be analyzed in more detail in Section 2.1.3. In 1988 Pinto and Rotoli presented a paper on the laboratory generation of gravitational waves at the Italian Conference on General Relativity and Gravitational Physics. Another Italian, Giorgio Fontana (1998), suggested the possibility of emission of high-frequency gravitational radiation from a junction between d-wave and s-wave superconductors. Kraus (1991) proposed that gravitational-wave communication might be possible, in the IEEE Antennas and Propagation magazine.

At the first HFGW Working Group Conference at the MITRE Corporation in 2003, Grishchuk analyzed electromagnetic generators and detectors of gravitational waves. At that same conference Valentin Rudenko presented a paper on the optimization of parameters of a coupled generator-receiver for a HFGW Hertz experiment. At the second HFGW Working Group Conference in Austin, Texas, in 2007, Kolosnitsyn and Rudenko presented another paper on the generation and detection of high-frequency gravitational radiation in a strong magnetic field. In 2007, and more recently this year, a new type of HFGW generator, detector and mirror system based on thin, type I superconducting films was proposed by R. Chiao, S. Minter, and K. Wegter-McNelly (2007; 2009a, b).

Therefore it is evident that a number of devices for the laboratory generation of HFGWs have been proposed, including the aforementioned gaser — as has been mentioned, first proposed by Halpern and Laurent in 1964, some 45 years ago — discussed by Fontana and Baker (2003), as well as an actual laser generator of HFGWs as discussed by Li and Li (2006). Finally, a rather practical laboratory HFGW generator, which may be appropriate for the initial proof-of-concept test, is one utilizing off-the-shelf components such as magnetron-energized piezoelectric crystals or Film Bulk Acoustic Resonators (FBARs), analyzed in Woods and Baker (2005) and Baker, Woods and Li (2006).

The figure of merit for a HFGW generator is given explicitly by Baker, Woods and Li (2006). This figure of merit can be extended by considering other effects, since in the laboratory the force change could not even approach those of the celestial sources. It would seem that the magnitude of any laboratory-generated GWs could be best increased (1) by utilizing electromagnetic forces rather than gravitational, (2) by increasing the distance between the gravitational radiators, (3) by increasing the GW frequency — that is, reducing Δt — and especially (4) by developing a large number of in-phase system elements. This last effect enters as the square of the number of elements, N, as proved using general relativity analyses by Dehnen and Romero-Borja (Romero and Dehnen, 1981; Dehnen and Romero, 2003). Such N-squared dependence also may be the key to successful laboratory generation of GWs, especially HFGWs.

In that regard, a recent proposal by Woods (Woods and Baker, 2009; Black and Baker, 2009) proposes the use of infrared-energized atomic nuclei, electrons and molecules, which have a very large N, contained in a stack of N waveguide rings. The distance between GW radiators may be proportional to the GW wavelength, in that it may have a limit that is less than or equal to a GW wavelength. The wavelength is inversely proportional to the GW frequency. Thus, given some value for the proportional constant — say unity, or the distance between radiators equal to one GW wavelength — the GW frequency cancels out.

As already noted, it is important to take advantage of the square of the number of in-phase elements for useful laboratory HFGW generation. If the elements are sliced in one dimension, the dimension along the axis of HFGW generation, in order to increase the number of elements, then the change in force per element will be inversely proportional to the number of elements. For example, if the elements are sliced into one hundred separate pieces, then each piece will have one hundredth of the force of the unsliced element. Essentially, f equals m a, and it is assumed that the acceleration of the element was the same after the split as before. This result also follows Equation (8), page 17 in Baker, Stephenson and Li (2008b): if there were 100 splits of an FBAR, then the power to an individual slice, P, and its mass, m, would both be one hundredth of their unsplit value and the square root of their product would again be one hundredth. The frequency of the split elements may be a higher value, but the attendant increase in GW power proportional to the square of the higher frequency and the decrease in power due to a smaller distance between tracks (assuming that the distance between tracks is one GW wavelength, which would be smaller) would cancel, and there would be no net effect on HFGW amplitude. It is concluded, therefore, that in this particular special situation the amplitude of the generated HFGWs is proportional to the number of in-phase elements, N, not the square. In any event, a large number of elements for a given HFGW-generator length can be best realized by reducing the size of the individual elements to submicroscopic size, as discussed in US Patent Number 6,784,591.

In the case of HFGW generation for communications applications, it is important to relate the amplitude of a GW, A, with the power, P, or more exactly with the GW flux in watts per square metre. For a viable communications link, the HFGW amplitude A must be large enough to be detected at the HFGW receiver. From Appendix B of Baker, Woods and Li (2006), A is proportional to the square root of the flux divided by the GW frequency, where A has the dimensionless value of spacetime strain, or metres per metre.

Following the preceding numerical example, we will concentrate the HFGW on a diffraction-limited area of 4 x 10⁻³ square metres, for a HFGW flux of about 7 x 10⁻¹¹ W per square metre. Thus A is about 2 x 10⁻³³. It is an extremely small HFGW amplitude, but possibly a detectable signal.

2.1.2 Alternative Approaches

There are several alternative approaches to the laboratory generation of HFGWs developed over the past 45 years, as discussed in the preceding section. They can be categorized as EM-cavity generated, nuclear-energy generated, superconductor-generated, laser-impact generated, and energized microscopic and submicroscopic-particle generated HFGWs. Of these categories the last appears to be the most promising for early deployment in HFGW communications systems. Furthermore, one embodiment of that category, the magnetron-energized FBAR generator utilizing off-the-shelf equipment, would seem the most useful for proof-of-concept tests. For a practical, operational communications system HFGW generator, the strong dependence of the generator's power on the number of radiating elements, N, recommends a system utilizing molecular elements as suggested by Braginsky and Rudenko (1978), or using infrared-energized pentane molecules in a stack of circular waveguides as proposed by Woods and Baker (2009). The magnetron-energized FBARs and the IR-energized pentane will be considered in the next sections.

2.1.3 Piezoelectric Approach

Let us consider the 1.8 x 10⁸ cell-phone film bulk acoustic resonator, 10,000 microwave-magnetron, proof-of-concept laboratory HFGW generator. Assuming a 10 micrometre distance or margin between the 100 micrometre square conventional FBARs, the overall length of the laboratory generator will be 110 x 10⁻⁶ m x 1.8 x 10⁸ elements, or 19.8 km. It will have a total HFGW power of 0.066 W, and for a distance out from the last in-line, in-phase FBAR element of one HFGW wavelength (6.1 cm) it will have a flux of 3.53 W per square metre, yielding a HFGW amplitude there of A equal to 4.9 x 10⁻²⁸ m/m. By the way, the in-line set of FBAR elements also produces a more needle-like radiation pattern of HFGWs, so that the flux and resulting A may even be larger.

Although the frequencies may be different, one can extrapolate approximately from the results of Dehnen and Romero-Borja's analyses (2003), in which the angle of the needle-like radiation pattern is inversely proportional to the square root of the product of the distance between the radiators (the width between FBAR bands or tracks) and N. The distance for the system discussed here is 6.1 cm and for Dehnen's system 0.00001 m, for a factor of 6,100; and N differs by 1.8 x 10⁸ divided by 5 x 10⁷, about 3.6, for a product of 2.2 x 10⁴, and the inverse of the square root is 6.7 x 10⁻³. Using the result from Dehnen's paper of a needle half angle of 1.7 degrees, we would extrapolate to 0.0115 degrees, or very approximately 2 x 10⁻⁴ radians.

Since there is no longer the constraint to the use of rudimentary off-the-shelf components as there was for the proof-of-concept apparatus, the specially designed submicroscopic elements can be manipulated. First, they will be staggered into two bands or tracks of 100 rows each, or 110 x 100 micrometre, giving 1.1 cm wide bands of FBARs a wavelength, or 6.1 cm, apart. The rows will be staggered by displacing adjacent rows in the bands by 1.1 micrometres. Thus the overall length will be reduced to 198 m. Second, the 100 micrometre length of each FBAR element can be sliced, along the direction of travel of the HFGW build-up, into one hundred 1 micrometre wide slices exhibiting 0.1 micrometre margins. The staggered row displacements are now reduced to 11 nanometres. The overall length will be reduced to about 198 cm.

Concentrating the 10 MW power to each of these 1.1 cm wide bands may prove to be difficult. Thus, as an example, the continuous-wave magnetrons will be replaced by a pulsed microwave source having one-microsecond-long pulses one second apart. The required average power for each FBAR band will now be 10 W. As a practical nanotechnology limit, the slice width can be reduced by two orders of magnitude to 10 nanometres. This would also require that the row displacements would be 110 picometres — we are now into atomic if not sub-atomic dimensional changes. The overall length could be reduced to about 2 cm, or the amplitude of the HFGWs could be increased to A equal to 4.9 x 10⁻²⁶. In this latter case the average energizing microwave power applied to each band would need to be increased to 1 kW. A preferred compromise at this apparent nanotechnology limit might be to reduce the HFGW generator's length to about 20 cm and increase the HFGW amplitude A to 4 x 10⁻²⁷ m/m.

The complementary approach to optimizing a practical HFGW generator is to increase the force produced by each element without increasing the required power — that is, increasing element efficiency. This was initially done using the modern lightweight piezoelectric FBARs rather than the heavy 10-gram crystals of 1981 vintage considered by Dehnen and Romero-Borja. Special designs of FBAR-like elements for optimum force-generation efficiency will improve the HFGW generator performance beyond that for the usual cell-phone FBAR designs. Another approach to element design is to utilize nano-size lasers whose targets are the force-generating elements (Li and Li, 2006). Utilization of myriads of nano-size lasers would generate high-frequency HFGW pulses, as noted in US Patent Number 6,784,591. Thus there are a number of opportunities to enhance HFGW generation performance, utilizing special element designs, either by reducing the generator size or increasing the generated HFGW amplitude, or both.

2.1.4 Infrared-Excited Molecules Approach

The very theoretical IR-generated HFGWs suggested by Woods and Baker (2009) have significant promise. If one has a standing wave in a waveguide ring and excites it properly, then one will have a GW source at its center. The GW flux produced at its center is proportional to the n submicroscopic particle pairs — in this case pentane molecule pairs — in each ring. There is no n-squared buildup, but there is an n buildup. If one has a stack of N plates of rings, which are excited in sequence at light speed as a GW passes by, then one has an n times N-squared buildup in GW flux.

Next consider a number N of orbit planes stacked one on top of another, with the gravitational-wave radiation growing in flux proportional to N-squared as the GW moves up the axis of the N orbit planes. The stack of orbital planes is now replaced by a stack of N plates, each containing n molecules in each waveguide ring. Now there is a HFGW wave moving up the axis of the rings, normal to the waveguide plates, and increasing in strength according to the product n times N-squared.

One should consider the IR rings in more detail. As calculated, the IR wavelength is about 2.5 x 10⁻⁶ m. The IR waveguide has a cross-sectional area radius of one quarter of the wavelength in order for it to be a monomode, lowest-order-mode, waveguide, so that the phase does not change across the waveguide. Thus the cross-sectional area of each IR ring is pi times the square of 2.5 x 10⁻⁶ m divided by four, or 1.23 x 10⁻¹² square metres, and its diameter is 1.25 x 10⁻⁶ m. The volume of each 100-metre-radius nano-size toroidal ring is 2 pi x 100 x 1.23 x 10⁻¹², or 7.7 x 10⁻¹² cubic metres. The mass density of pentane is divided by its molecular mass, and that gives the density of jerkable masses of 6.3 x 10²⁸ per cubic metre. Thus the number of jerkable mass pairs, n, in a 100-metre-radius circular waveguide is 6.3 x 10²⁸ times 7.7 x 10⁻¹², or 4.85 x 10¹⁷ submicroscopic particles or potentially jerkable masses, so that n equals 2.45 x 10¹⁷ mass pairs.

According to Table 1 of Woods and Baker (2009), for pentane the power per pair is 4.62 x 10⁻¹⁶ W. Thus the flux at one metre distance for all of the mass pairs in a single ring, from Equation (8) of Black and Baker (2009), is n times 0.01146 times that power, or 1.29 W per square metre. It should be recognized that the axes of the opposite pentane molecules' jerk, in response to the EM wave, may not be anti-parallel and tangential to the circular waveguides. On the other hand, the radiation pattern for the HFGW exhibits some omni-directional form, so significant HFGW radiation will be directed along the axis of the stack of circular waveguides, normal to the plates, and the HFGW will build up.

Next consider a more convenient laboratory arrangement for the rings. The ring radius is reduced to one metre, but 100 rings are set up concentrically — side-by-side concentric rings in the same plane or plate — with an average radius of one metre. The reduced radius drops the power per ring by a factor of 100 squared, to 4.62 x 10⁻²⁰, but because of the 100 concentric rings the value of n remains the same. Thus the flux for a single plate of concentric rings is only reduced by 10⁴, to 1.29 x 10⁻⁴ W per square metre. Now stack some 10⁶ of these 1.25 x 10⁻⁵ m thick plates on top of one another. Thus a 1.25 m high stack, barrel or cylinder, as described in Baker (2001), is created. In this case N equals 10⁶ and the N-squared law can be applied. Thus a HFGW total flux of 1.29 x 10⁸ W per square metre in a very narrow beam will be generated by the stack.

Of course, as pointed out in Woods and Baker (2009), caution needs to be taken on how much power is fed to each ring. One possible arrangement is to feed the output of one ring to the input of the next. The problem here is that the source will not have a long enough coherence length, even if the attenuation of the IR does not kill the power after a ring or two. To avoid this, from one source the available energizing power could be divided equally between all the rings and fed to them up the stack or cylinder at the speed of light. The practical difficulty would be how to drive them all in correct phase, but it is a challenge for future research in the IR-ring approach.

For an operational 50,000 angstrom infrared, 12.5 metre long, 10-metre radius cylindrical HFGW generator — 10⁴ concentric rings per plate, so that the per-plate flux is 1.29 x 10² W per square metre, and 10⁷ plates (Woods and Baker, 2009) — the flux at a one-metre distance from the generator is, according to Table 1 of Black and Baker (2009) for N equal to 10⁷, 1.146 x 10¹² times 1.29 x 10², or 1.48 x 10¹⁴ W per square metre. This is very large, but with a very narrow 2.3 x 10⁻⁴ radian half-power-point needle beam. The required generator power can be reduced by utilizing pulsed HFGWs.

Suppose that the distance between the generating or transmitting device and the detecting or receiving device is a little more than an Earth's equatorial radius, or about 7 x 10⁶ metres. At this distance, 7,000 km, the flux of the received signal S is 1.48 x 10¹⁴ divided by the square of 7 x 10⁶, or about 3 W per square metre — more than adequate for an effective communication system.

With this configuration, the width of the needle-like, narrow HFGW beam at the receive end is 2.3 x 10⁻⁴ times 7 x 10⁶, or 1.6 km, and multiple HFGW carrier frequencies can be used, so the signal is very difficult to intercept and is therefore useful as a low-probability-of-intercept signal, even with widespread adoption of the technology. The amplitude A of the HFGW at 7,000 km, with the HFGW frequency twice the IR frequency at 1.2 x 10¹⁴ per second, is A equal to 1.28 x 10⁻¹⁸ times the square root of S divided by the GW frequency, or 1.8 x 10⁻³² in dimensionless units, which would be detectable by the currently designed Li-Baker HFGW detector. Since the exact frequency and phase of the HFGW signal is known — unlike the stochastic relic HFGWs, for which the Li-Baker detector was designed — a much more sensitive, optimized HFGW detector will likely be developed.

As shown by Grishchuk (2008), there will be negligible relic HFGW noise at the IR HFGW generator's frequency of 1.2 x 10¹⁴ per second, and no other cosmic sources at these frequencies are currently hypothesized. Prior to the proof-of-concept test, one can assume a noise figure at the Li-Baker detector of 10⁻⁸ W per square metre.

2.2 HFGW Detectors (Receivers)

2.2.1 Alternative Approaches

One of the first suggested means for the detection of HFGWs concerns electromagnetic detectors (Braginsky et al. 1974; Braginsky and Rudenko, 1978). Then Pegoraro et al. (1978) suggested the use of tuned resonant chamber HFGW detectors. Rudenko and Sazhin in 1980 proposed a laser interferometer as a gravitational wave detector, somewhat similar to the current Japanese approach. In 1995 Tobar characterized multi-mode resonant-mass HFGW detectors, and three years later in 1998 Ottaway et al. proposed a compact injection-locked Nd:YAG laser for HFGW detection. And in 1999 Tobar suggested microwave parametric transducers for the next generation of resonant-mass gravitational wave HFGW detectors.

In the past few years HFGW detectors have been fabricated at Birmingham University, England; INFN Genoa, Italy; and in Japan. These types of detectors may be promising for the detection of HFGWs in the GHz band (MHz band for the Japanese) in the future, but currently their sensitivities are orders of magnitude less than what is required for the detection of high-frequency relic gravitational waves from the big bang. Such a detection capability is to be expected utilizing the Li-Baker detector. Nevertheless, all four candidate detectors, plus possibly the use of superconductors (Li and Baker, 2007), should be analyzed for possible military applications.

The Li-Baker HFGW detector was invented by R. M L Baker, Jr., of Transportation Sciences Corporation, California, and patented in the People's Republic of China (Baker, 2001). Based upon the theory of Li, Tang and Zhao (1992), termed the Li-effect, the detector was proposed by Baker during the period 1999 to 2000, a patent for it was filed in 2001 and subsequently granted, and preliminary details were published later by Baker, Stephenson and Li (2008a). This detector was conceived to be sensitive to relic HFGWs having amplitudes as small as 10⁻³² to 10⁻³⁰.

The Birmingham University HFGW detector measures changes in the polarization state of a microwave beam, indicating the presence of a GW, moving in a waveguide about one metre across. See also Cruise (2000), Ingley and Cruise (2001) and Cruise and Ingley (2005). It is expected to be sensitive to HFGWs having spacetime strains of about 2 x 10⁻¹³ per square root hertz, where A is as usual a measure of the strain or fractional deformation in the spacetime continuum, dimensionless in metres per metre.

The INFN Genoa HFGW resonant antenna consists of two coupled superconducting spherical harmonic oscillators a few centimetres in diameter. The oscillators are designed to have, when uncoupled, almost equal resonant frequencies. In theory, the system is expected to have a sensitivity to HFGWs with fractional deformations of about 2 x 10⁻¹⁷ per square root hertz, with an expectation to reach a sensitivity of about 2 x 10⁻²⁰ per square root hertz (Bernard, Gemme, Parodi and Picasso, 2001; Chincarini and Gemme, 2003). As of this date, however, there is no further development of the INFN Genoa HFGW detector.

The Kawamura 100 MHz HFGW detector has been built by the National Astronomical Observatory of Japan. It consists of two synchronous interferometers exhibiting an arm length of 75 cm. Its sensitivity is now about 10⁻¹⁶ per square root hertz. According to Cruise (2008) of Birmingham University, its frequency is limited to 100 MHz, and at higher frequencies its sensitivity diminishes. In the case of the infrared-excited molecules approach, one might employ a variant of the Robinson Gravitational Wave Background Telescope for the receiver or detector (Yoon et al., 2006). It is a bolometric large-angular-scale cosmic microwave background polarimeter, but might possibly be modifiable for direct HFGW detection.

2.2.2 Concept (Li-Effect)

The Li-effect was first published in 1992, and subsequently some nine peer-reviewed papers have been published concerning it, including a capstone paper, Li et al. (2008). The Li-effect is very different from the classical inverse Gertsenshtein effect. With the Li-effect, a gravitational wave transfers energy to a separately generated electromagnetic wave in the presence of a static magnetic field. That EM wave has the same frequency as the GW and moves in the same direction. This is the synchro-resonance condition, in which the EM and GW waves are synchronized — move in the same direction and have the same frequency — and is unlike the Gertsenshtein effect.

The result of the intersection of the parallel and superimposed EM and GW beams, according to the Li-effect, is new EM photons moving off in a direction perpendicular to the beams and the magnetic field directions. Thus these new photons occupy a separate region of space that can be made essentially noise-free, and the synchro-resonance EM beam itself, in this case a Gaussian beam, is not sensed there, so it does not interfere with detection of the photons. This Li-effect was utilized by Baker (2001) in the design of the Li-Baker HFGW detector and the Chinese patent of a device to detect HFGWs.

The synchro-resonance solution of Einstein's field equations (Li et al., 2008, pp. 411 to 413) is radically different from the Gertsenshtein (1962) effect. The newer Li-effect solution utilizes a coupling between EM and gravitational waves (Li, Tang and Zhao, 1992) that arises according to the theory of relativity. A strong static magnetic field in the y-direction, B, is superimposed upon a GW propagating in the z-direction, as in the inverse Gertsenshtein effect. However, with the Li-effect there is an additional focused microwave beam, a Gaussian beam, at the expected frequency, phase and bandwidth of the HFGWs, in the same z-direction as the GW.

Unlike the Gertsenshtein effect, a first-order perturbative photon flux (PPF), comprising the detection photons, will be generated in the x-direction. Since there is a 90-degree shift in direction, there is little crosstalk between the PPF and the superimposed EM wave, so the PPF signal can be isolated and distinguished from the effects of the Gaussian beam, enabling detection of the GW.

Here is how it works. The perturbative photon flux, which signals the detection of a passing gravitational wave, is generated when the two waves, EM and GW, have the same frequency, direction and phase. This situation is termed synchro-resonance. These PPF detection photons are generated as the EM wave propagates along its z-axis path, which is also the path of the GWs. The magnetic field is in the y-direction. According to the Li-effect, the PPF detection photon flux, also called the Poynting vector, moves out along the x-axis in both directions.

The signal, the PPF, and the noise, or background photon flux (BPF) from the Gaussian beam, have very different physical behaviors. The BPF background noise photons are from the synchro-resonant EM Gaussian beam and move in the z-direction, whereas the PPF signal photons move out in the x-direction along the x-axis. The PPF signal can be intercepted by electromagnetic-interference-shielded microwave receivers located on the x-axis, isolated from the synchro-resonance Gaussian EM field, which is along the z-axis. In addition, isolation is further improved by cooling the microwave receiver apparatus to greatly reduce thermal noise background (Baker, Stephenson and Li, 2008a).

The resultant efficiency of detection of HFGWs is very much greater than from the inverse Gertsenshtein effect, which has been exploited in some previously proposed HFGW detectors and found to have insufficient sensitivity to HFGWs (Eardley et al., 2008). The amplitude of the PPF has space accumulation dependence — that is, it is proportional to the length of the wave overlap. This is because the GWs (gravitons) and EM waves (photons) have identical propagation velocities, so that the two waves overlap synchronously and coherently throughout and their interaction is cumulative (Boccaletti et al., 1970; DeLogi and Mickelson, 1977). This is the synchro-resonant condition, or Li-effect. This means that for maximum signal, the interaction overlap coupling must be as long as possible.

It should be noted that the identification of this coupling, or Li-effect, upon which the Li-Baker HFGW detector is based, is not so new that it is untested in the literature. At least nine peer-reviewed research publications concerning the theory have appeared following Li, Tang and Zhao (1992), including those by Li and Tang (1997), Li et al. (2000), Li, Tang and Shi (2003), Li and Yang (2004), Li and Li (2006), Li and Baker (2007), Li, Baker and Fang (2007), Baker, Stephenson and Li (2008a), and Li et al. (2008).

2.2.3 Quantum Back-Action Limit

The Standard Quantum Limit (SQL) will be introduced and reviewed in this section (Stephenson, 2009b), and the design of the Li-Baker HFGW detection system will also be reviewed to understand how the SQL might limit the sensitivity of this new type of GW detector.

Review of the Standard Quantum Limit. The Standard Quantum Limit is often defined as the limit on measurement accuracy at quantum scales due to back-action effects. But what is back-action? (See Kippenberg and Vahala, 2008.) From Clerk (2008), the Heisenberg uncertainty principle is that the product of the position uncertainty and the momentum uncertainty is greater than one half of Planck's reduced constant. Thus measuring x disturbs p, which in turn disturbs future measurements of x: the position uncertainty at a later time equals the initial position uncertainty plus the elapsed time multiplied by the initial momentum uncertainty divided by the mass of the system under measurement. The energy divided by the square of the speed of light may be substituted for mass in an energy-only system.

To summarize, the quantum effect of measurements on future measurements is quantum back-action. Therefore the Standard Quantum Limit defines the lower sensitivity limit for all measurement instruments, including gravitational-wave detectors, according to the Heisenberg uncertainty principle. Detectors cannot avoid quantum back-action; however, the use of higher energies in the detection process can change the relative scale and impact of back-action, and the use of squeezed states can shift the relative distribution of back-action into states not involved in measurement.

Coherent versus stochastic SQL. The question under consideration is whether or not the Li-Baker detector is quantum-limited when detecting relic HFGWs. In other words, does the Standard Quantum Limit interfere with the sensitivity of the Li-Baker detector design? The answer will be negative if the SQL is less than 10⁻³² m/m. Grishchuk (1977, 2007) has calculated the SQL for GW detectors in general, which for a coherent GW is the square root of the quantity one over Q, multiplied by the square root of Planck's reduced constant times the frequency divided by the energy; and there is a corresponding expression for a stochastic GW.

Here the detection limit is the metric strain detection limit in metres per metre; the frequency is that of the sensed gravitational waves, typically around 10 GHz in the Li-Baker detector; the energy is the effective energy contained within the detector cavity summed over the detection averaging time; and Q is the quality factor or selectivity of the signal over noise. The SQL depends on the values of these parameters. For the remainder of this section we will consider the SQL of only the stochastic signal detection case.

Impact of contained energy levels on the SQL. First we estimate a realistic best case for the energy contained within the detection process. Typically it is expected that for a refrigerated microwave resonant cavity the best possible electrical quality factor will be around 2 pi x 10⁵. Assuming a best-efforts value of 1000 W for the power of the Gaussian beam in a laboratory installation, the effective total radio-frequency energy stored in the microwave resonant cavity of the Li-Baker detector, summed over the system averaging time, is estimated (Grishchuk, 2007) over a typical 1000-second averaging time. Both the Li-Baker detector and a detector using the Gertsenshtein effect use a large static magnetic field B. For the present suggested outline design for the Li-Baker detector the nominal value of B is 3 tesla, which sets the magnetic energy density. The interaction volume in a practical laboratory-based detector is likely to be a maximum of around 1 cubic metre, so the effective total stored energy from the Gaussian beam is much greater than the stored magnetic field energy, and it follows that the energy E is approximately the radio-frequency energy, 10¹¹ joules, to a reasonable approximation.

Sources of quality factor and effect on the SQL. To calculate the detection limit we also need the value of the detector quality factor Q, which is not the same as the cavity quality factor. Anything that concentrates or enhances the signal preferentially over noise, in any measurement dimension, can be considered a contributor to the quality factor. The quality factor can therefore be understood as the signal selectivity in each dimension, so that the total Q is the product of the radial, solid-angle and temporal quality factors.

The temporal quality factor in the Li-Baker detector arises from averaging the signal over time, so that at 10 GHz it is 10 x 10⁹ Hz multiplied by 1000 seconds, or 10¹³. There is a contribution to Q arising from the fractal membranes that focus and concentrate the signal photon energy — but not the background photons — along the radial dimension. The radial selectivity arising from the general relativity solution, in conjunction with fractal membranes, is calculated by Li et al. (2008); their table III gives a radial quality factor of 3.4 x 10²¹.

This is mostly due to the effective Q contribution arising from the synchro-resonance solution to the Einstein field equations, which limits the PPF signal to a radiation pattern in certain directions, whereas noise is distributed uniformly. By utilizing directional antennas, the Li-Baker detector can capitalize upon this gain due to the focusing power of fractal membranes as a contribution to Q in angular space as well. This is calculated in detail, octant by octant, by Li et al. (2008). A non-directional antenna corresponds roughly to a solid angle of 2 pi steradians, one hemisphere, so that the effective antenna gain is estimated as 2 pi steradians divided by 10⁻⁴ steradians, or 6.3 x 10⁴. Therefore the predicted maximum quality factor will be about 2.1 x 10³⁹. This finally gives the Standard Quantum Limit for stochastic GW detection at 10 GHz:

detection limit = 1.8 x 10⁻³⁷ m/m (10)

Comparison of the SQL with predicted sensitivity. A detection limit of 1.8 x 10⁻³⁷ m/m represents the lowest possible GW amplitude detectable by each radio-frequency receiver in the Li-Baker HFGW detector, limited by quantum back-action. An additional factor of one over the square root of two applies if the separate outputs from the two receivers are averaged, rather than used independently for false-alarm reduction, resulting in a minimum detection limit of 1.2 x 10⁻³⁷. Since the predicted best sensitivity of the Li-Baker detector in its currently proposed configuration is about 10⁻³² m/m, these results confirm that the Li-Baker detector is photon-signal limited, not quantum-noise limited; that is, the Standard Quantum Limit is so low that a properly designed Li-Baker detector can have sufficient sensitivity to observe relic HFGWs of amplitude about 10⁻³² m/m.

2.2.4 Li-Baker HFGW Detector

The detector has five major components.

1. A Gaussian, focused, minimal-side-lobe microwave beam is aimed along the plus-z-axis at the same frequency as the intended HFGW signal to be detected (Yariv, 1975), typically in the GHz band, and also aligned in the same direction as the HFGW to be detected. The microwave transmitter's horn antenna would be located on the minus-z-axis.

2. A static magnetic field B, generated by two powerful magnets, typically using powerful superconductor magnets such as those found in a conventional MRI medical body scanner, is directed along the y-axis.

3. Two paraboloid-shaped reflectors, formed from fractal membranes (Wen et al., 2002; Zhou et al., 2003; Hou et al., 2005), are located in the y-z plane at the origin of the coordinate system to aim and focus the detection photons at diffraction-limited spot antennas connected to two microwave receivers. These reflectors are segmented, similar to a Fresnel lens, and located back to back in the y-z plane. They are thin enough — less than a centimetre thick in the x-direction — not to block the z-directed Gaussian beam. These microwave reflectors reflect the x-directed detection photons and reject the z-directed Gaussian-beam photons, which move parallel to the surface of the reflectors in the y-z plane.

4. High-sensitivity shielded microwave receivers are located at each end of the x-axis, each about one metre distant from the origin.

5. Interior noise from thermal photon generation is eliminated by cooling the Li-Baker detection apparatus to below about 48 millikelvin. Thus there are effectively no thermal photons at 10 GHz. Noise from the interior background photon flux from the EM Gaussian beam is reduced to a negligible level by moving the receivers out to the side about a metre away from the EM beam and by a series of superconductor or microwave-absorbent baffles to shade the receivers. Stray EM resulting from scattering of particulate matter near the apparatus and possible dielectric dissipation can be effectively suppressed by evacuating the apparatus to about 7.5 x 10⁻⁷ torr, a rather high vacuum. External noise is eliminated by the use of a steel and titanium cryogenic containment vessel surrounding the low-temperature Li-Baker detection apparatus.

In summary, several different HFGW receivers can be utilized for communication; but the proposed Li-Baker detector shows the most promise.

3.0 Operational Concerns

3.1 Link Budget

3.1.1 Signal-to-Noise Ratio

Signal-to-noise ratio (SNR) is an important figure of merit in communication systems because it is an indicator of whether or not a transmitted signal will be useful upon arrival at its destination, the receiver. Without processing gain, an SNR greater than one will be required to maintain a link budget. On the transmitter's end, the signal-to-noise is determined by the useful signal that is produced by the transmitter after it is already in its transmission mode — such as the GW power at the output of the GW generator antenna — divided by the root sum square of the uncorrelated noise sources referred to the same spot in the signal chain, that is, the output-referred noise equivalent power.

The components of the transmitter's noise equivalent power may be sorted by the source of the noise. First, before the signal is converted to GW it is in the realm of EM or photon radiation. Photons themselves make noise, and this component goes as the square root of the total number of photons. Then there is thermal noise, that is, the photons generated by blackbody radiation of the transmitter components themselves. Other electronic and semiconductor components providing the source signal generate their own photon noise due to carrier activity. All these noise sources are carried along with the original EM signal and may be converted just as faithfully as if they were signals, should they fall within the transmission bandwidth. All of this is just for the EM noise component.

The generation process itself may also be a source of noise, and will vary widely depending upon the generator method used. For example, the generation process noise created in the gaser would be significantly different than that created in a tuned resonant EM toroid cavity. This of course would be an important consideration in selecting a generator type.

Finally, it is expected that there are a variety of GW noise sources. Background sources from space are predicted, in low levels, across the entire frequency spectrum. Also, in a GW generator situation, parasitic vibrations may also have quadrupole moments — such as the walls of a generation cavity, or an unwanted vibration within a slab of superconductor — and these could also generate GW noise.

Then there is link loss to contend with. While it is expected that the attenuation of GW due to absorption and scatter will be quite low, geometry alone will dictate that a spherically uniform radiating source will fall off as one over the square of the range. This link loss will affect both the transmitted signal and the transmitted noise.

In the receiver all these same noise sources are duplicated in reverse. Referring power now to the input, there will be a received power, and noise created by the receiver that was not created at the transmitter, also GW-to-EM conversion noise, and EM receiver noise of the same types as received propagated transmit noise. Added to this will be GW noise admitted as outlined for transmitters. When all these noise components are referred to the input of the receiver, the total noise equivalent power, which is the root sum square of all the noise components, must be less than the signal present at the input of the receiver to qualify as a useful link.

A few comments are in order regarding the Q-factor of the receiver. One way to increase Q is to narrow bandwidth. However, this has limited value. At some point, shrinking the bandwidth will shrink the signal received as quickly as the noise received, and some receiver noise components remain constant, resulting in a net drop in SNR. Another way to increase Q is to arbitrarily increase sample times of the signal. This technique will, relatively speaking, shrink receiver-end noise components as referred to the input of the receiver, but it will not have any impact on the noise generated at the transmitter. Therefore in this case the SNR will approach a constant. However, both of these approaches for improving sensitivity will have an adverse effect on the information capacity of the channel, which is important for a communication application.

3.1.2 Link Budget Considerations

Now consider the signal side of the communication challenge. The central question is: how do we close the link? That is, how much signal is necessary at the input of a communication channel to have a useful signal at the other end? In general, an EM signal will be used to actuate some type of GW generation device, and this device will have a conversion efficiency, which represents the ratio of power of the EM input signal to power of the GW signal generated. Not all of the GW generated will be constructively used to radiate in the desired direction; some of the GW power will be lost to destructive interference, and some will not be radiated through the antenna aperture. Thus the transmitter will have a less-than-unity radiated power efficiency.

Then there will be propagation link loss, or transmission loss, which will be the antenna pattern integrated across the solid angle of the receiver antenna aperture as seen from the source. The receiver may have a GW antenna that aids in focusing an otherwise wider solid angle into a narrower detection aperture, and if this is true, then there will be an efficiency associated with this receiver antenna.

At the receiver's detector there is another conversion factor to account for: the conversion efficiency of GW signal power to EM signal power, which would be much less than unity, except that the Q factor enters the equation as a component of it. Of course Q may also impact the bandwidth range over which the signal is collected. There is also a hidden integral here which occurs over the sample time, which is understood.

All of these terms will have to be defined and well understood before a communication system can be successfully designed. Many of these parameters have been predicted for the components reviewed in prior sections; however, they will not be verified until a successful experiment can be performed.

3.2 Bandwidth

An estimate of the bandwidth that a HFGW transglobal communication system might achieve, after a proof-of-concept test is successfully completed, based on a technical paper by Black and Baker (2009), is as follows. For a 50,000 angstrom infrared, 12.5 metre long, 10-metre radius cylindrical HFGW generator — 10⁴ concentric rings per plate and 10⁷ plates (Woods and Baker, 2009) — the flux at a one-metre distance from the generator is 1.48 x 10¹⁴ W per square metre, very large, and with a very narrow 2.3 x 10⁻⁴ radian half-power-point needle beam. The required generator power can be reduced by utilizing pulsed HFGWs. Suppose that the distance between the transmitting device and the receiving device is a little more than an Earth equatorial radius, about 7 x 10⁶ metres. At this distance, 7,000 km, the flux of the received signal S is about 3 W per square metre, more than adequate for an effective communication system.

With this configuration, the width of the needle-like, narrow HFGW beam at the receive end is 1.6 km, and multiple HFGW carrier frequencies can be used, so the signal is very difficult to intercept, and is therefore useful as a low-probability-of-intercept signal, even with widespread adoption of the technology. From the amplitude relation derived in the appendix of Baker, Stephenson and Li (2008a), the amplitude A of the HFGW at 7,000 km, with the HFGW frequency twice the IR frequency of 1.2 x 10¹⁴ per second, is 1.8 x 10⁻³² in dimensionless units, which would be detectable by the currently designed Li-Baker HFGW detector. Since the exact frequency and phase of the HFGW signal is known, unlike big-bang relic HFGWs for which the detector was designed, a much more sensitive, optimized HFGW detector will likely be developed.

Grishchuk (2008) indicates that there will be negligible relic HFGW noise at the IR HFGW generator's frequency of 1.2 x 10¹⁴ per second, and no other cosmic sources at these frequencies are currently hypothesized. Prior to the proof-of-concept test, we will assume a noise figure at the Li-Baker detector of 10⁻⁸ W per square metre.

Using C. E. Shannon's classical equation (1948), the maximum rate of information transfer, C, is given by the bandwidth B multiplied by the base-two logarithm of one plus the signal-to-noise ratio. With a signal of 3.0 W per square metre and noise of 10⁻⁸ W per square metre, C is about 1.9 x 10⁶ bits per second. The bandwidth B here is arbitrarily taken to be 100 kHz for a future advanced system. The necessity for large temporal Q factors, of order 10⁹, currently precludes bandwidths larger than a few hertz for early systems, but the use of coherent signals will represent an easing of sensitivity requirements significantly, improving bandwidth. Note that it is based on a single carrier chopping frequency, whereas in practice one can spread the information over an entire band of HFGW frequencies.

3.3 Frequency and Time Standard

The first application of HFGW to the distribution of frequency and time standard (FTS) data would be to assist otherwise conventional communications equipment. A typical near-Earth distribution system could conceivably result in a number and configuration of ground stations positioned around the globe.

The large transmitter ground stations would provide the signals used as both the frequency and time standards. All FTS ground stations would be synchronized such that they emit signals exactly in phase with each other, all tied to a common frequency time source, such as the US Naval Observatory. Each station would use a different frequency such that the remote terminal user set could easily differentiate signals, and any phase or time difference observed would be due to either the relative position of the remote terminal with respect to each ground station, or the relative velocity of the remote terminal with respect to each ground station. Each ground station would transmit both a carrier wave signal for a frequency reference and a periodic pulse signal for a time reference. At least three ground stations would be needed for self-triangulation by the remote terminals, at least four with redundancy. HFGWs will propagate through the Earth with little modification, but very slight HFGW phase modification may be observed in surveillance applications (Baker, 2007).

The counterpart to the fixed ground infrastructure would be the remote terminal side, or user side, of the FTS infrastructure. Each remote terminal would need to be equipped with a small HFGW receiver, which could pick up all three or four ground stations simultaneously. The arrival times of the received pulse signals could be compared via time difference of arrival, and used to develop a position estimate. The carrier-wave signal phases could be compared to determine the Doppler velocity of the remote terminal with respect to an Earth-centred inertial coordinate system. Thus the HFGW FTS system could be used as a navigational aid, akin to the GPS system. This end of the infrastructure would be receive-only and could therefore be a very low power device. Therefore mobile devices, such as portable remote spaceborne terminals, could be typical users of such a navigational service.

The navigational sensitivity of the HFGW receiver would depend on the frequencies used in the HFGW FTS system, as the received carrier-wave HFGW signal would act as the remote terminal's built-in frequency standard, replacing the need for internal crystal oscillators or caesium or rubidium standards. An HFGW FTS carrier wave with a frequency of 300 GHz, with a wavelength of 1 mm, would result in three-picosecond-type time accuracy. The use of time difference of arrival with these accuracies would allow for arbitrarily small navigational errors.

3.3.1 Improvements Accruing from a HFGW Time Standard

The cost of the FTS infrastructure must be more than balanced by the benefit resulting from that infrastructure if the cost is to be justified. Given that GPS already provides adequate navigation services for most applications, navigational benefits alone would not justify the cost of an HFGW FTS system. However, in the case of a universal HFGW FTS, there are additional benefits associated with applying the frequency and time standards to standard telecommunications problems. The universal nature of the HFGW frequency and time standards is especially helpful. The following telecommunication benefits of an HFGW FTS system will be described: improvement in acquisition time from search space improvements, improvements in modulation and coding efficiency from phase noise improvements, and improvements in bandwidth efficiency from frequency noise improvements.

3.3.2 Search Space Improvement Accruing from HFGW FTS

The following points are relevant with respect to the universal use of HFGW FTS among all remote terminals, including for instance cell phone handsets and their associated cellular towers.

During signal acquisition the receiving terminal must perform a search of the search space of frequency, phase, and code to acquire the transmitting terminal signal. If there is less noise in these parameters the search space is reduced, speeding acquisition. Ultra-fast acquisition allows more efficient Time Domain Multiple Access style operations, such as transmit on demand, that use bandwidth more efficiently.

An equation for acquisition search space time is the product of the number of phase space cases to check for acquisition, the number of frequency cases to check, the number of code sync possibilities to check, and the acquisition test time per test case.

In a typical example, if 30 MHz chipping is used with a 5-microsecond error, there will be 150 code sync possibilities to check. If a frequency error of 1 Hz within the acquisition window would cause a missed acquisition, and the worst-case frequency error is 150 Hz, then the number of frequencies that must be checked is also 150. Finally, we must check each possible phase possibility, say 16 different options for 16-PSK. PSK stands for phase shift keying and is the encoding of data bits using incremental phase modulation. For a 5-microsecond acquire test time, the result is an acquisition time of 150 x 150 x 16 x 5 microseconds, or 1.8 seconds.

However, with effectively perfect knowledge of time, frequency, and hence also phase, there will only be one case to check, so the result is an acquisition time of 5 microseconds. This is essentially instantaneous for applications such as TCP/IP or VoIP. This will favorably impact the overall Time Domain Multiple Access efficiency in that it speeds the claiming process to the point where an always-on link can be replaced by a link on demand. This is a saving of 25 to 50 percent in channel usage for VoIP and TCP/IP sessions over always-on.

3.3.3 The Impact of Phase Noise Improvements on Phase Shift Encoding

The use of a universal HFGW FTS would also benefit the relative phase noise of all terminals, allowing for finer phase encoding. Phase noise limits the type of modulation and manner of encoding that can be performed in phase space, commonly used for over-the-air telecommunication systems. An HFGW FTS system could reduce phase noise by providing a frequency reference with outstanding stability. For example, moving from QPSK to 8PSK or 16-PSK improves bandwidth efficiency by a factor of 2 to 4.

Where nominal performance allows only QPSK, improved phase noise would allow higher-density phase encoding. Data rate will scale linearly with encoding efficiency: the data rate is half the bandwidth, multiplied by the coding efficiency and the forward-error-correction rate, divided by the pseudo-noise spreading factor. Coding efficiency will be a factor of 2 better when moving from QPSK to 8PSK, or a factor of 4 better when moving from QPSK to 16-PSK. This will translate directly into a linear increase in the allowable data rate that a given bandwidth can support. Put another way, a universal frequency time standard could quadruple over-the-air bandwidth efficiencies just by improving phase noise alone. Phase noise improvements would be limited only by the slight variations induced in the HFGW signal passing through the Earth as described in Baker (2007).

3.3.4 The Impact of Frequency Noise Improvements on FDMA and FHSS

The very low noise frequency standard that would be supplied by an HFGW FTS system would allow for much more efficient use of reserved frequency bandwidth. Frequency noise limits the type of modulation and manner of encoding that can be performed in frequency space, such as Frequency Division Multiple Access (FDMA) or Frequency Hopping Spread Spectrum (FHSS). HFGW can reduce frequency noise by providing a frequency reference with outstanding stability. For example, guard bands can be shrunk in FDMA, and frequency slices can be smaller and more stable in FHSS.

Guard band bandwidth efficiency can be defined as the total bandwidth minus the sum of the guard bandwidths, divided by the total bandwidth. Guard bands often consume 30 to 50 percent of assigned frequency space. While guard bands would still be required to allow for the side lobes of signals, the frequency error component would be eliminated. Similar efficiencies may be gained in the FHSS approach. A better knowledge of absolute frequency allows better frequency coding efficiencies.

3.4 Possible Future Upgrades to the FTS Devices

Per the 9 February 2009 issue of New Scientist, optical lattice clocks are under development that will lead to a dramatic improvement over the current standard caesium atomic oscillation clocks that now provide frequency time standard references. Optical lattice clocks vibrate at optical frequencies rather than microwave frequencies, with the reference frequency mixed down via frequency combs to allow measurements back down in the microwave regime. Strontium lattice clocks are already operating with measurement precisions of 1 part in 10¹⁶, and theoretical performance approaches 1 part in 10¹⁸. At this precision one could measure the time delay caused by changing one centimetre in height in the Earth's gravitational field.

3.4.1 Propagating Signals From Optical Lattice Clocks for Timing

The 1 part in 10¹⁸ measurement precision of optical lattice clocks will be affected by general relativity effects — in other words, propagation delays due to gravitational field gradients will be readily measurable. "It will make us think a little harder about what we really mean by time," Kleppner (2008). In effect, measuring the propagation delays at this level allows very fine measurement of the geoids, or surfaces of constant gravity, surrounding planets and inhabiting interplanetary and interstellar space. The delay experienced by radio-frequency waves could therefore be precisely compared with the propagation delay experienced by gravitational waves, which are not as strongly affected by the presence of mass. Such a differential propagation delay comparison could lead to an important new technology in the mapping of geoids, which could for instance be applied to the problem of mapping the positions of the Lagrangian points, which vary slightly over time.

3.4.2 In Navigating and Mapping Interplanetary Geoids

The importance of locating and navigating to Lagrangian points is well established (Baker, 1967). The Earth and Sun's gravitational fields balance at five Lagrangian points, L1 to L5. L1 is an ideal location for solar monitoring, whereas L2 is permanently shielded from the Sun.

4.0 Future Potential

4.1 Developmental Roadmap

A development roadmap is suggested here for the application of high-frequency gravitational waves in the field of communications. The development roadmap should be twofold:

• Theoretical work should continue on HFGW transmitters (generators) and receivers (detectors).
• Experimental devices should be built and tested in the laboratory and then transitioned over to a practical communications system.

Theoretical research is always an ongoing enterprise, but it is especially important to encourage work in the development of experimental approaches aimed at demonstrating laboratory generation and sensing of gravitational waves for the next few years. This is the kind of academic work that is best done in a research university setting, at least for the next ten years or so, until laboratory experiments can verify laboratory generation. Without early confirmation the technology will not gain widespread acceptance and move forward.

The most benefit would come from a coordinated effort spread over a number of different universities. Wherever possible, pre-existing assets should be utilized to stretch funding as far as possible. For example, if synchrotron light is needed to verify the Gertsenshtein effect and the Li-effect, a survey of existing national synchrotron light facilities should be part of the funded effort to find an appropriate host facility. The funding activity — that is, the National Science Foundation — would have the overall responsibility to coordinate this activity in an ongoing manner, through proposal review, contract awards, and progress reviews, and the approach should be flexible enough to allow the redirection of funding should a particularly promising new technology or invention move to the forefront.

Assuming that positive laboratory results can be achieved and peer reviewed in a 10 to 12 year timeframe, the next step would call for a period of prototype development, in which the device physics and engineering needed to support the technology could be matured. As prototypes show promise they could be transitioned to device development, the first time that industry would likely enter the field. Once the individual devices required to support GW communication technology — for example, GW generators and GW sensors — are in place, at that point it will be possible to begin full-scale development of systems applications. This is a conservative timeline, based on scaling from the development of previous technologies. If breakthroughs materialize, or if the pace of technological development quickens, progress may certainly occur more quickly than this.

4.2 HFGW Communications Predictions to 2050

In what follows, with an eye to the future, extrapolations are made concerning the development of an HFGW communications technology into the far future, for example 2050 and beyond. It is difficult to predict even ten years in advance, to the time when we expect to have the results of the proof-of-concept test — the Bell-Watson experiment — and the immediate applications to HFGW communications completed. Speculation beyond that time will be contingent upon advanced development of FBAR crystals, new materials within the toroidal waveguides, and so forth, or even entirely new approaches such as those proposed by G. Fontana, V. Rudenko, R. Chiao and others.

No doubt the Li-Baker detector performance can also be greatly improved with stronger magnetic fields, more intense Gaussian beams, and better baffles, as well as new detector designs yet to be developed, possibly based upon theories developed at Birmingham University, INFN Genoa and the National Astronomical Observatory of Japan. Optimum designs of communication channels, bands and modulation are also anticipated. Many of these advanced concepts were discussed at the third HFGW Workshop in Huntsville in February 2009.

Nanotechnology advances will allow for the fabrication of smaller and smaller HFGW transceivers having millimetre dimensions and milliwatt power requirements by 2050, and radio-ID, or rather HFGW-ID, nanochip tags may be ubiquitous. Gravitational wave transmissions would also have the advantage of being able to pierce the protective plasma shielding that may in the future be routinely used to protect the crew aboard manned vessels — that is, communications through artificial magnetospherics, a technological limit of radio-frequency communications.

4.3 Interplanetary Navigation and Geoid Mapping to 2050

While there is no doubt that stellar tracking will remain the primary source of navigation for space missions in the foreseeable future, HFGW may also prove useful in conjunction with radio frequency in providing a navigation aid for interplanetary missions, with no planetary shielding, by mapping geoids in interplanetary space via long baseline navigation. For instance, if there were one GW source on Earth and one GW source on the Moon, such a pair of GW sources would provide relative beacons for missions to Mars that could serve multiple roles as navigation beacons, communication relays, and, in conjunction with radio-frequency signals, map geoids via relative time difference of arrival signals. Very long baseline navigation could be achieved by placing a source on Earth and one GW source on Mars for a baseline that would most often be very widely spread with respect to the outer planets, for outer planetary missions.

4.4 Other Possible HFGW Applications

The most stunning advances in HFGW applications will probably not be in communications, but in remotely HFGW-generated nuclear fusion, HFGW propulsion and HFGW surveillance. If an ultra-high-intensity HFGW flux impinges on a nucleus, it is possible that it could initiate nuclear fusion at a remote location, or mass disruption. Also it may be possible to create radioactive-waste-free nuclear reactions and energy reactions (Fontana and Baker, 2007). As they suggest:

"At high amplitudes, gravitational radiation is nonlinear, thus we might expect a departure from geometric optics. Fortunately, the problem has already been theoretically examined and the resulting effects are found to be advantageous. Nonlinearity improves the focusing process and h goes to one in finite time, producing a singularity regardless of the starting, non-focused amplitude of the impinging gravitational wave (Corkill and Stewart, 1983; Ferrari, 1988a; Ferrari 1988b; Ferrari, Pendenza and Veneziano, 1988; Veneziano, 1987; Szekeres, 1992). The effect of a 0.995 pulse of HFGWs on the couple formed by a deuterium nucleus and its electron is the reduction of their relative distance by a factor of 200. If this distance reduction is effective for a few picoseconds, then the two nuclei of a deuterium molecule can fuse and give an He atom plus energy, which is the usual nuclear-fusion process in a star."

HFGWs could theoretically be used for propulsion and control of the motion of objects such as missiles, missile warheads, spacecraft, and asteroids, and remote control of clouds of hazardous vapors. Gravitational field changes by one or more HFGW generators could urge a spacecraft in a given direction, causing a lower static gravitational field in front of a vehicle, so that it falls forward, and a higher one behind, providing a push. The concept is that the mass essentially rolls down a hill produced by the static gravitational field; that is, the potential energy increase of a mass is provided by the energetic HFGWs. The magnitude of the static gravitational field is proportional to the square of the HFGW frequency (Landau and Lifshitz, 1975, section 108, page 349). Specifically:

"Since it has definite energy, the gravitational wave is itself the source of some additional gravitational field (static g-field). Like the energy producing it, this field is a second-order effect in the h-i-k. But in the case of high-frequency gravitational waves the effect is significantly strengthened: the fact that the pseudotensor t-i-k is quadratic in the derivatives of the h-i-k introduces the large factor lambda to the minus two. In such a case we may say that the wave itself produces the background field (static g-field) on which it propagates. This field is conveniently treated by carrying out the averaging described above over regions of four-space with dimensions large compared to lambda. Such an averaging smooths out the short-wave ripple and leaves the slowly varying background metric (static g-field)."

Such an application must also await the future development of very high-intensity HFGW generators.

A novel means of imaging or HFGW surveillance might be developed in future to establish a system to allow for observing activities and materials in three dimensions, within and below structures and within the Earth and its oceans. Gravitational waves, including HFGWs, pass through most material with little or no attenuation; but although they are not absorbed, their polarization (Li and Nan, 2009), phase velocity (causing refraction or bending of gravitational rays), backscatter, and other characteristics can be modified by a material object's texture and internal structure. For example, the change in polarization of a GW passing through a material object is discussed in Misner, Thorne, and Wheeler (1973):

"In the real universe there are spacetime curvatures due not only to the energy of gravitational waves, but also more importantly to the material content of the universe ... its wavelength changes and the gravitational wave backscatters off the curvature to some extent. If the wave is a pulse, then the backscatter will cause its shape and polarization to change."

It is difficult to theoretically establish the actual magnitude of the changes, especially at very high frequencies, 10¹⁴ Hz and higher, and to quantify them prior to HFGW generation and detection laboratory experiments.

4.5 2050 and Beyond

The phases of human space exploration may be divided into the following phases:

• Epoch 1: interplanetary exploration
• Epoch 2: interstellar exploration
• Epoch 3: intergalactic exploration
• Epoch 4: universal exploration

Each phase will have its own challenges and opportunities, but one can certainly speculate that the human need for connectedness and communication knows no bounds. So any scope of expansion beyond Epoch 1 will have enormous challenges in the area of communication. The vast distances involved will require some form of communication that entails faster-than-light propagation. While this is a highly speculative area, such schemes have been proposed for faster-than-light HFGW. Both Fontana and Meholic, in unpublished reports, have proposed models of the universe, such as the trispace model, in which subluminal or luminal gravitational waves may couple into a super-luminal parallel universe inside which faster-than-light speeds are possible. Such a scheme would be required to communicate between star systems and galaxies if humankind is to maintain any type of cohesive civilization. Without communications we have a history of fractured civilization, and we slip into becoming our own worst enemy. Universal communication holds the lofty promise of universal peace.

5.0 Acknowledgements

The research published in technical papers authored by Gary Stephenson, chief investigator for Seculine Consulting — Stephenson (2009a), Harper and Stephenson (2007) and Stephenson (2009b) — was crucial in the preparation of this study and is gratefully acknowledged.

(The numbered reference list, Appendix A on nomenclature, Appendix B on the detailed Li-Baker detector design plan, and Appendix C, a reprinted paper on perturbative photon fluxes generated by high-frequency gravitational waves, are omitted for length; the complete text is at the source.)