UNCLASSIFIED//FO R O FFICIAL USE O NLY Defense Intelligence Reference Document j^^^^^^JJ Acquisition Threat Support 6 April 2010 ICOD: 1 December 2009 DIA-08-1004-007 Concepts for Extracting Energy From the Quantum Vacuum UNCLASSIFIED//FO R O FFICIAL UO E O NLY UNCLASSIFIED //FO R O FFICIAL UG C O NL¥ Concepts for Extracting Energy From the Quantum Vacuum Prepared by: Acquisition Support Division (DW O -3) Defense W arning O ffice Directorate for Analysis Defense Intelligence Agency Author: AAP Person 58 Administrative Note COPYRIGHT WARNING: Further dissemination of the photographs in this publication is not authorized. This product is one in a series of advanced technology reports produced in FY 2009 under the Defense Intelligence Agency, Defense W arning Office's Advanced Aerospace W eapon System Applications (AAW SA ) Program, Com ments or questions pertaining to this document should be addressed to|AAP Person 1 |, AAW SA Program Manager, Defense Intelligence Agency, ATTN: CLAR/DW O-3, B ldg 6000, W ashington, DC 20340-5100. UNCI ACCTFTFn//FnP AFFTCTAI !■« nmv UNCLASSIFIED//FO R O FFICIAL USE O NLY Contents I. Summary........................................................................................... v II. Historical Concepts for Extracting Energy and Thermodynamic Considerations 1 III. O rigin of Zero-Point Field Energy........................................... 4 Elements of QED Theory.............................................................................................4 Elements of SED Theory............................................ 6 IV. Review of Selected Experiments..............................................................................7 Voltage Fluctuations in Coils Induced by ZPF at High Frequency...........................7 ZPF Energy Extraction by G round State Energy Reduction ...................................10 Tunable Casimir Effect.............................................................................................14 EV Phenomenon........................................................................................................17 V. Theoretical Considerations and Issues...................................................................22 QED Vacuum Revisited.............................................................................................22 QED Vacuum as a Plenum................................................. 22 QED Vacuum as a Mathematical "Placeholder" for Fluctuating Matter Fields 23 Casimir Effect Revisited...........................................................................................24 Casimir Effect in the Plenum Picture..................................................................24 Casimir Effect in the Fluctuating Matter Fields Picture....................................24 Type I (Transient) and Type II (Continuous) Machines.......................................25 Degradability of the Vacuum....................................................................................25 Alternatives to QED...................................................................................................26 Neoclassical Theories of QED Vacuum Fluctuation Effects...............................26 SED Model Revisited........................................................................................ 27 QED W ithout Second-Quantized Fields...............................................................28 Examples of Degradable of Decaying Vacuum.......................................................28 G ravitational Squeezing of the Vacuum........................................... 29 Redshifting the Vacuum ..................................................................... 29 Vacuum Field Stress: Negative Vacuum Energy from the Casimir Effect......30 iii UNCLASSIFIED / ^fiOB^UEIGIXUUJSMNWU UNCLASSIFIED//FO R O FFICIAL UO £ O NLY Squeezed Quantum Vacuum........................................................................... 32 Dirac Vacuum Decay: "Sparking the Vacuum"........................................... 33 Magnetically Induced Decay of the Dirac Vacuum............... 34 Melting the QCD Vacuum....................................... 35 Summary: ZPF Modes and Vacuum Field Energy................ 37 VI. Conclusion: The W ay Forward to 2050.................... 37 Acknowledgements.......................................................................................................41 Appendix: The QCD Bag Model...................................................................................42 References.....................................................................................................................44 Figures Figure 1. Illustration of the Casimir Effect................................................... 1 Figure 2. Vacuum-Fluctuation Battery................................................................. 1 Figure 3. ZPE Resonant Dielectric Spheres Electrical Power G eneration...................3 Figure 4. Theoretical Voltage Spectral Density of a Tungsten Coil.............................9 Figure 5. Energy Released from G round State Suppression of Hydrogenic Atom in a Microcavity........................................................ 11 Figure 6. Apparatus for G round State Energy Suppression: Casimir Segmented Tunnels...................................................... 13 Figure 7. Alternative Apparatus for G round State Energy Suppression: Casimir Strip and Spacer-Channels................................. 13 Figure 8. Experimental Apparatus for G round State Energy Reduction Tests.......14 Figure 9. Tunable Casimir Effect: Conductor vs. Dielectric............................... 15 Figure 10. Tunable Casimir Effect: Engine Cycle............... 16 Figure 11. Schematic of EV (Pulse Discharge Source) Device...................................18 Figure 12. SEM of EV Damage to Ceramic Plate.................................. 19 Figure 13. SEM of EV Damage to Palladium Target............................ 20 Figure 14. EV Moving at Downward Angle Away From Its Source...........................21 iv U N CLASSI FIE D / ^EaB-QEElG XAUUSfcANh* UNCLASSI FIED//FO R O FFICIAL USE O NLY Concepts for Extracting Energy From the Quantum Vacuum I. Summary Quantum theory predicts that the vacuum of space throughout the universe is filled with electromagnetic waves, random in phase and amplitude, propagating in all possible directions, and with a cubic frequency distribution. This differs from the cosmic microwave background radiation and is referred to as the electromagnetic quantum vacuum, which is the lowest energy state of otherwise empty space. W hen integrated over all frequency modes up to the Planck frequency, vP (~ 1043 Hertz [Hz]), it represents an energy density of as much as 10113 J/m3, which is far in excess of any other known energy source, even if only an infinitesimal fraction of it is accessible. Even if one is constrained to integrate over all frequency modes only up to the nucleon Compton frequency (~ 1023 Hz),1 this energy density is still enormous (~ 1035 J/m3). In addition, the electromagnetic quantum vacuum is not alone; it intimately couples to the charged particles in the Dirac sea of virtual fermion particle-antiparticle pairs (aka the Dirac vacuum) and thereby couples to the other interactions inherent in the Standard Model (weak and strong force vacua). However, in the Standard Model of particle physics, the weak force vacuum is essentially the electromagnetic vacuum, because photons serve as the massless eigenstates of (unified) electroweak theory with an "effective" coupling constant that is in fact electromagnetic in strength.2 And we can safely ignore any coupling of the quantum electromagnetic vacuum to the quantum chromodynamic vacuum in this paper because the latter coexists in two phases: (1) the ordinary vacuum exterior to the hadron, which is impenetrable to quark color, and (2) the vacuum interior of the hadron,3 in which the Yang-Mills fields that carry color (gluons) propagate freely. Both vacuum phases are separated by a boundary at the surface of the hadron on which the Yang-Mills and quark fields satisfy boundary conditions. 1 The characteristic frequency associated with the size of nucleons. 2 The weak force coupling constant is m erely the quantum electrodynamic/electrom agnetic coupling constant (i.e., the fine structure constant, a) that is "suppressed" by a sim ple inverse-quadratic ratio of the virtual weak force particle m ass to the proton m ass (a factor of IO4). 3 Hadrons are the class of strongly interacting elem entary particles which are a bound state of quarks. This class of particles has two subclasses: baryons (e.g., protons and neutrons com prised of three quarks) and m esons (com prised of two quarks). Even though this zero-point field (ZPF) energy seems to be an inescapable consequence of quantum field theory, its energy density is so enormous as to make it difficult to reconcile. Instead, many quantum calculations subtract the ZPF energy by ad hoc means (for example, renormalization). However, the effects of the quantum vacuum ZPF that are responsible for a variety of well- known physical effects are observed, such as: • Lamb shift. • Spontaneous atomic emission. v U N CLASSI FIE D //FAP HEFTC™! uccnM^ UNCLASSI FI ED//FO R O FFICIAL USE O NLY • Low-temperature van der W aals forces. • Casimir effect. • Source of photon shot and fluctuating radiation-pressure noise in lasers. • Astronomically observed cosmological constant (aka dark energy, a form of Casimir energy according to the Schwinger-DeW itt quantum ether prescription [Reference 1-4]). Rather than eliminate the ZPF energy from the equations, there is much left to be learned by exploring the possibility that it is a real energy. From this perspective, the ordinary world of matter and energy is like foam atop the quantum vacuum sea. If the ZPF is real, then there is the possibility that it can be tapped as a source of power or be harnessed to generate a propulsive force for space travel. This notion of exchanging energy with the quantum vacuum is the focus of this paper. An aircraft propeller or jet engine can push air backwards to propel the aircraft forward. A ship or boat propeller does the same thing in water. O n Earth there is air or water to push against. But a rocket in space has no material medium to push against, and so it needs to carry and eject propellant in order to provide momentum. A deep-space rocket must start out with all the propellant it will ever require, and this quickly results in the need to carry additional propellant just to propel the propellant. The breakthrough desired in space travel is to eliminate the need to carry propellant at all, that is, to generate a propulsive force without carrying and ejecting propellant? vi U NCLASSI FIED //FAP HEFTC™! mce^mi^ UNCLASSI FIED//FO R O FFICIAL USE O NLY II. Historical Concepts for Extracting Energy and Thermodynamic Considerations The Casim ir force is a force associated with the electromagnetic quantum vacuum (Reference 5). This force is an attraction between parallel uncharged m etallic plates that has now been well m easured and can be attributed to a m inute im balance in the ZPF energy (ZPE) density inside the cavity between the plates versus the region outside the plates as shown in Figure 1 (Reference 6-8). As shown in the figure, the vacuum is full of virtual photons (that is, zero-point vacuum fluctuations), but photons with wavelengths, X, m ore than twice the plate separation, d, are excluded from the space between them, which causes the im balance that pushes the plates together. The prim ary requirem ent for space travel is energy. It is som etimes assum ed that attem pting to extract energy from the vacuum ZPF would som ehow violate the laws of thermodynam ics. Fortunately, it turns out that this is not the case. A thought experim ent published by Forward (Reference 9, 10) dem onstrated how the Casim ir force could in principle be used to extract energy from the vacuum ZPF. Forward showed that any pair of conducting plates at close distance experiences an attractive Casim ir force that is due to the electrom agnetic ZPF of the vacuum . A "vacuum ­ fluctuation battery" can be constructed by using the Casim ir force to do work on a stack of charged conducting plates as shown in Figure 2. B y applying a charge of the sam e polarity to each conducting plate, a repulsive electrostatic force will be produced that opposes the Casim ir force. If the applied electrostatic force is adjusted to be always slightly less than the Casim ir force, the plates will m ove toward each other and the Casim ir force will add energy to the electric field between the plates. The battery can be recharged by m aking the electrical force slightly stronger than the Casim ir force to re­ expand the foliated conductor. Figure 1. Illustration of the Casimir Effect Electrostatic Repulsion t Vacuum Fluctuation Attraction Figure 2. Vacuum-Fluctuation Battery (Reference 9) Cole and Puthoff (Reference 11) verified that (generic) energy extraction schem es are not contradictory to the laws of therm odynam ics. For thermodynam ically reversible processes, no heat will flow at tem perature T = 0. However, for thermodynam ically 1 UNCLASSIFIED//Fnp nFFTr™» iiccnMiu UNCLASSIFIED//FO R O FFICIAL UO £ O NLY irreversible processes, heat can be produced and m ade to flow, either at 7" = 0 or at any other T > 0 situation, such as by taking a system out of m echanical equilibrium . Moreover, work can be done by or done on physical system s, either at T = 0 or T > 0 situations, whether for a reversible or irreversible process. However, if one is considering a net cyclical process on the basis of, say, the Casim ir effect, then energy would not be able to be continually extracted without a violation of the second law of thermodynam ics. Thus, Forward's process cannot be cycled to yield a continuous extraction of energy. Here, the recharging of the battery would, owing to frictional and other losses, require m ore energy than is gained from the ZPF. There is no useful engine cycle in this process; nonetheless, the plate-contraction phase of the cycle does dem onstrate the ability to cause "extraction" of energy from the ZPF. It does reflect work done by the ZPF on m atter. Another illustrative exam ple of an early schem e for extracting energy from the ZPF is described in a patent by Mead and Nacham kin (Reference 12). They propose that a set of resonant dielectric spheres be used to extract energy from the ZPF and convert it into electrical power. They consider the use of resonant dielectric spheres, slightly detuned from each other, to provide a beat-frequency downshift of the m ore energetic high-frequency com ponents of the ZPF to a m ore easily captured form . Figure 3 shows two em bodiments of the invention. The device includes a pair of dielectric structures (item s 12, 14, 112, 114 in the figure) that are positioned proxim al to each other and which intercept incident ZPE radiation (item s 16, 116 in the figure). The volum etric sizes of the structures are selected so that they resonate at a particular frequency of the incident radiation. B ut the volum etric sizes of the structures are chosen to be slightly different so that the secondary radiations em itted from them (item s 18, 20, 24, 118, 120, 124 in the figure) at resonance interfere with each other, thus producing a beat frequency radiation that is at a m uch lower frequency than that of the incident radiation, and that can be converted into electrical energy. A conventional m etallic antenna (loop or dipole type, or a RF cavity structure; item s 22, 122 in the figure) can then be used to collect the beat frequency radiation. This radiation is next transm itted from the antenna to a converter via an electrical conductor or waveguide (item s 26, 126 in the figure) and converted to electrical energy. The converter m ust include: 1) a tuning circuit or com parable device so that it can effectively receive the beat frequency radiation, 2) a transform er to convert the energy to electrical current having a desired voltage, and 3) a rectifier to convert the energy to electrical current having a desired waveform (item s 28, 30, 32, 34, 128, 130, 132 in the figure). 2 U N CLASSI FI E D//mp nFFTr™i mce^mi^ UNCLASSI FIED//FO R O FFICIAL USE O NLY Figure 3. ZPE Resonant Dielectric Spheres Electrical Power Generation (Reference 12) The receiving structures are com posed of dielectric m aterial in order to diffract and scatter the incident ZPE radiation. The volum etric sizing requirements for the receiving structures are selected to enable them to resonate at a high frequency corresponding to the incident ZPE radiation, based on the param eters of frequency of the incident ZPE radiation, and the propagation characteristics of the m edium (vacuum or otherwise) and the receiving structures. Since the ZPE radiation energy density increases with increasing frequency, greater am ounts of electrom agnetic energy are potentially available at higher frequencies. Consequently, the size of the receiving structures m ust be m iniaturized in order to produce greater am ounts of energy from a system located within a space or volum e of a given size. Therefore, the sm aller the size of the receiving structures, the greater the am ount of energy that can in principle be produced by the system . Although a com puter m odel study perform ed at the Air Force Research Laboratory (Edwards AFB , CA) indicates that the invention could work, no experim ental study has been perform ed to validate this in the lab (F. B . Mead, private com m unication, 2002). Regarding critiques, it is not clear how the beat frequency can be picked up by the receiving loop antenna. There is no nonlinear m ethod in the invention showing that an electrom agnetic beat frequency can be generated and coupled to the loop. W ithout a nonlinear coupling m ethod there will be no sidebands, one of which would be frequency down-shifted and called the beat frequency. The coupling m ethod requires the generation of sidebands in the m ixing of two different frequencies via a nonlinear technique. However, an easy resolution to this potential deficiency is that the resonant dielectric spheres could be constructed of a nonlinear dielectric m aterial. Although several novel ZPF energy extraction m echanism s have been proposed in the popular and technical literature, no practicable technique has been successfully dem onstrated in the laboratory. To better understand how ZPE extraction m ethods 3 UNCLASSI FIED//EHR nFFTr™i iiccnMiu UNCLASSI FIED//FO R O FFICIAL USE O NLY m ight work, it is necessary to characterize the physics of the ZPF and proposed energy extraction techniques, and to evaluate their feasibility for application to space power and propulsion system s. In what follows, the physics of the ZPF and the experim ental investigations being pursued to address the question of extracting energy from the quantum vacuum are sum marized. III. Origin of Zero-Point Field Energy ELEMENTS O F QED THEO RY The basis of the ZPF is typically attributed to the Heisenberg Uncertainty Principle. According to this principle, A and B are any two conjugate observables that one is interested in m easuring, and they obey the com m utation relation [A,B] = ih4 Their corresponding uncertainty relation is MAS > h/2, where M is the variance (aka uncertainty) of observable A and AB is that of the conjugate observable B. This relation states that if one m easures observable A with very high precision (that is, its uncertainty M is very sm all), then a sim ultaneous m easurem ent of observable B will be less precise (that is, its uncertainty AB is very large), and vice versa. In other words, it is not possible to sim ultaneously m easure two conjugate observable quantities with infinite precision. This m inimum uncertainty is not due to any correctable flaws in m easurem ent, but rather reflects the intrinsic fuzziness in the quantum nature of energy and m atter. Substantial theoretical and experim ental work has shown that in m any quantum system s the lim its to m easurement precision is im posed by the quantum vacuum ZPF em bodied within the uncertainty principle. Nowadays one would rather see the Heisenberg Uncertainty Principle as a necessary consequence, and therefore, a derived result of the wave nature of quantum phenom ena. The uncertainties are just a consequence of the Fourier nature of conjugate pairs of quantities (observables). For exam ple, the two Fourier-wave-conjugates tim e and frequency becom e the pair of quantum -particle conjugates tim e and energy and the two Fourier-wave-conjugates displacem ent and wavenumber becom e the pair of quantum -particle conjugates position and m om entum . For m ore on this see, for exam ple, Reference 13. 4 / is the unit complex number, fl is Planck's reduced constant, 1.055 x 10 34 J s. 5 w is the mode or photon frequency and fio is the energy of a single mode or photon. Classically, electromagnetic radiation can be pictured as waves flowing through space at the speed of light. The waves are not waves of anything substantive, but are in fact ripples in the state of a field. These waves carry energy, and each wave has a specific direction, frequency and polarization state. This is called a "propagating m ode of the electromagnetic field." A useful tool for m odeling the propagating m ode of the electrom agnetic field in quantum m echanics is the ideal quantum m echanical harm onic oscillator: a hypothetical charged m ass on a perfect spring oscillating back and forth under the action of the spring's restoring force. The Heisenberg Uncertainty Principle dictates that a quantized harm onic oscillator (aka a photon state) can never com e entirely to rest, since that would be a state of exactly zero energy, which is forbidden by the com m utation relation outlined above. Instead, every m ode of the field has ha/2 as its average m inim um energy in the vacuum.5 (This is a sm all am ount of energy, but the num ber of m odes is enorm ous, and indeed increases as the square of the frequency. The product of this m inuscule energy per m ode, m ultiplied by the huge spatial density of m odes, yields a very high theoretical energy density per unit volum e.) 4 UNCLASSI FIED//EHR nFFTr™i iiccnMiu UNCLASSIFIED//FO R O FFICIAL UO £ O NLY This ZPE term is added to the classical blackbody spectral radiation energy density p(w)t/w (that is, the energy per unit volum e of radiation in the frequency interval (co, co + Jw)) (Reference 14): p((D))da) = (ka3/27t2c3)d<»r which integrates to an energy density, pe = hvp^/S^c3 a 10113 J/m 3. As large as the ZPE is, interactions with it are typically cut off at lower frequencies depending on the particle coupling constants or their structure. Nevertheless, the potential ZPF energy density predicted by quantum physics is enorm ous. Many experts have claimed that an enorm ous vacuum ZPF energy density would produce a corresponding enorm ous gravitational force of attraction (via Einstein's General Theory of Relativity) that would cause the im m ediate collapse of the entire universe. Thus they argue that such enorm ous vacuum energy cannot be real due to the fact that our universe is observed to be undergoing accelerated expansion. However, such argum ents are spurious because numerous studies in quantum field theory show that it is the low-frequency ZPF m odes that contribute significantly to the physical vacuum energy, because 1) only the low-frequency m odes are affected by the 5 UNCLASSI FIED//mp nFFTr™i iiccnMiu UNCLASSI FIED//TO R O FFICIAL USE O NLY presence of cosm ological spacetim e curvature, and 2) the high-frequency m odes are unaffected by the presence of cosm ological spacetim e curvature so they take the flat Minkowski spacetim e form ; that is, these m odes contribute nothing to the physical vacuum energy (Reference 4). This then enforces a very low-frequency cutoff that renorm alizes the total vacuum energy, leading to a m inute residual cosm ological vacuum energy density of 10 9 J/m 3, which has been observed. Also, investigators studying supersym m etric and superstring quantum gravity theories have proposed the lim ited cancellation of som e positive energy electromagnetic ZPF m odes by som e negative energy ferm ionic (Dirac vacuum ) ZPF m odes as an explanation for the observed m inute vacuum energy density. ELEMENTS O F SED THEO RY An alternative to QED, stochastic electrodynamics (SED) identifies the origin of the ZPF as a direct consequence of a classical ZPF background. SED begins with the ordinary classical electrodynam ics of Maxwell and Lorentz, but instead of assum ing the traditional hom ogeneous solution of the source-free differential wave equations for the electrom agnetic potentials, one instead considers that due to m ultiple charged particles m oving throughout the universe, there is always a random electromagnetic radiation background present that affects the particle(s) in any experiment. This new boundary condition (random radiation background) replaces the prior null background of traditional classical electrodynam ics. Moreover, the principle of relativity dictates that identical experiments performed in different inertial frames m ust yield the sam e result, and that this random classical electrom agnetic radiation m ust be isotropic in all inertial frames; it is invariant under scattering by a dipole oscillator, invariant under redshift (Doppler, cosm ological, gravitational, no Einstein-Hopf drag force), and m ust therefore have a Lorentz-invariant energy density spectrum . The only energy density spectrum that obeys such conditions is one that is proportional to the cubic power of the frequency. Interestingly, this is exactly the sam e frequency dependence as that of the QED spectral ZPF energy density described above, when the temperature Tis set to zero in Equation (1). Thus in SED, the random radiation assum es the role of the ZPE of QED, and is term ed the classical electromagnetic ZPE. Planck's constant appears then in SED as an adjustable param eter that sets the scale of the ZPE spectral density. The formulation of the SED m odel has evolved over tim e, beginning with the work of Nernst in 1916 and the later foundational work of Marshall and B oyer in the 1960s (Reference 14). The original Standard SED m odel was based on random phases with fixed electric-field m ode am plitudes. The m ore recent Modified SED m odel em ploys random phases with random electric-field m ode am plitudes and a full probability distribution for the ground state am plitude, in agreem ent with quantum theory (Reference 16). A com parison of SED with quantum theory shows that the first and second m om ents of the spectral energy distribution are identical, but beyond that, the distributions diverge widely. Nevertheless, several quantum theory results have been reproduced by m eans of the SED approach, such as (Reference 14, 17): • Quantum m echanical harm onic oscillator. • Lam b shift. • B lackbody radiation. 6 UNCLASSI FIED//EHR nFFTr™i iiccnMiu UNCLASSI FIED//FO R O mCIAL UDE O NLY • Van der W aals forces. • Casim ir forces. • Diam agnetism . • Davies-Unruh Effect. The strength of the SED m odel is that it is heuristically appealing, with transparent derivations, and it is applicable to linear system s. SED calculations have also been shown to be in one-to-one correspondence with the expectation values of the Heisenberg quantum equations of m otion for linear system s. B oth SED and QED will play a role in the discussions to follow. IV. Review of Selected Experiments In what follows, is an outline each of the proposed experim ental concepts that were selected for theoretical and laboratory investigation. A subset of our proposed concepts has undergone prelim inary evaluation by Lockheed-Martin review panels involving both internal R&D personnel and outside experts on theory and experim entation (V. Teofilo, private com m unication, 2005). VO LTAG E FLUCTUATIO NS IN CO ILS INDUCED BY ZPF AT HIG H FREQUENCY In a series of experiments, Koch et al. (Reference 18-20) m easured voltage fluctuations in resistive wire circuits that are induced by the ZPF. The Koch et al. result is striking corroboration of the reality of the ZPF and proves that the ZPF can do real work (cause m easurable currents). Although the Koch et al. experim ent detected m inuscule am ounts of ZPF energy, it shows the principle of ZPF energy circuitry to detect vacuum fluctuations and opens the door to consideration of m eans to extract useful am ounts of energy. The secondary consequences on other phenom ena, if energy can be successfully extracted, have not yet been investigated. B lanco et al. (Reference 21) have proposed a m ethod for enhancing the ZPF-induced voltage fluctuations in circuits. Theoretically treating a coil of wire as an antenna, they argue that the antenna-like radiation resistance of the coil should be included in the total resistance of the circuit, and suggest that this total resistance should be used in the theoretical com putation of ZPF-induced voltage fluctuations. B ecause of the strong dependence of the radiation resistance on the num ber of coil turns (quadratic scaling), coil radius (quartic scaling), and frequency (quartic scaling), any enhanced ZPF-induced voltage fluctuations should be m easurable in the laboratory at readily accessible frequencies (100 MHz com pared to the 100 GHz range necessary in the Koch et al. experim ents). In the theory of B lanco et al., random voltage fluctuations are conveniently described by their frequency spectrum . That is, given a sufficient tim e interval of m easured voltages, the m easurements are Fourier transform ed to the frequency domain to determ ine how the voltage fluctuations are distributed (for example, quantity of low- frequency, long duration fluctuations relative to high-frequency, short-duration 7 U N CLASSI FI E D//mp nFFTr™i mce^mi^ UNCLASSI FIED//FO R O FFICIAL USE O NLY fluctuations). Theoretically, the spectrum of voltage fluctuations, S(&,T), of a resistive circuit is given by (Reference 21): fl(®,T)hw 0(0, T) =-----------------coth K 2 ho ) 2kT J (2) where R(&,T) is the total resistance (ohm ic plus radiative), co is the (angular) frequency, and Tis the absolute temperature. The resistance R(®,T) is tem perature dependent through its ohmic contribution.6 Note the sim ilar hyperbolic cotangent functions appearing in Equation (2) and in the second line of Equation (1). The postulate of B lanco et al. is that the total resistance m ust include the radiation resistance of the circuit (Reference 21): 6 The radiation resistance depends only on frequency. ^T^^M+JUg-) (3) Under the assum ption that the wavelengths of the ZPF m odes of interest are larger than the dim ensions of the circuit, the radiation resistance of a coil is given by (Reference 21): ^(®) = 2 k 2N 2 ( aco ) 3 c \ c ) (4) where N is the num ber of coil turns, and a is the radius of the coil winding. According to B lanco et al., large enhancem ents in ZPF-induced voltage fluctuations are possible. B y reducing the tem perature to m inim ize ohmic resistance, m aking the coil of m any turns and large radius, and perform ing m easurements at high frequency, it should be possible to investigate this am plification effect. The predicted coil-enhanced voltage spectrum can readily be com puted. The result is shown in Figure 4 for a 1 cm diam eter coil of 2000 turns, m ade of 38 AW G tungsten wire, and kept at a tem perature of 3 K. In Figure 4, the upper (blue) curve represents the predicted voltage spectral density for the com bined ohm ic plus radiation resistance. The lower (red) curve is the predicted result when radiation resistance is ignored. If the postulate of B lanco et al. is correct, the enhancem ent in voltage fluctuations due to the antenna-like nature of the coil should be easily m easured at frequencies as low as 100 MHz (where the coil enhancem ent effect is ~ 100-fold for tungsten). 8 U NCLASSI FIED//mp QESCIAI HccnMiu UNCLASSI FIED//FO R O mCIAL UDE O NLY Figure 4. Theoretical Voltage Spectral Density of a Tungsten Coil To successfully m easure the ZPF-induced voltage fluctuations, the requirem ents of low tem perature, large coil, and high frequency m ust be m et. The low-tem perature requirement is m et by perform ing the experim ent in a cooled dewar. Existing high- quality cryogenic dewars (pum ped down to 3 K) and sensitive laboratory instrum ents are suitable for the m easurements. The cold spot in one particular dewar under consideration is cylindrical, 2.5 cm in both diam eter and height. The largest coil that can be installed will thus have a coil radius of approxim ately a = 1 cm . To keep the linear dim ension of the coil sm all will require a sm all wire thicknesses, perhaps b = 0.01 cm (gauge 38 AW G). B y winding the coil in a num ber of layers (10 or 12 layers), a large num ber of turns can be accom m odated, perhaps N = 2,000 turns. To m inim ize ohmic resistance, wire m ade of tungsten (W ) is preferred; however, copper (Cu) is a suitable alternative. Voltage fluctuations in the 100 MHz range are easily detected using com m ercially available laboratory equipm ent; hence this experim ent could be perform ed using tungsten without resorting to the m ore sophisticated Josephson junction techniques required by Koch et al. for their higher frequency m easurements. For a copper wire coil, the m agnitude of the enhancem ent effect is reduced som ewhat com pared to the tungsten results shown in Figure 4. B ut for frequencies approaching the GHz regim e, the radiation resistance enhancem ent effect in copper wire is still predicted to be over 9 UNCLASSI FIED//mp nFFTr™i iiccnMiv UNCLASSI FIED//FO R O FFICIAL USE O NLY four orders of m agnitude larger. Com m ercial equipm ent readily allows m easurem ents of the voltage spectrum in the GHz regim e. Therefore, given a cost tradeoff of copper vs. tungsten coil fabrication, the use of copper coils m ay be preferred. Suitable coils can be fabricated by a custom coil-winding vendor. A second coil can be used in a control experim ent constructed with the sam e param eters as the first coil, but with half of its turns wound in the reverse direction. This will m ake the coil non-inductive so that its voltage spectral density should correspond to the lower red curve in Figure 4. ZPF ENERG Y EXTRACTIO N BY G RO UND STATE ENERG Y REDUCTIO N As first analyzed by B oyer (Reference 22), and later refined by Puthoff (Reference 23), the following paradox was addressed: even though atomic ground states involve electrons in accelerated m otion, such states are nonetheless radiationless in nature - even though it is well known from classical electrodynamics that charged particles undergoing acceleration m ust always em it radiation. For the standard B ohr ground state orbit of the hydrogen atom , this was interpreted as an equilibrium process in which radiation by the electron in its ground state orbit was com pensated by absorption of radiation from the background vacuum electrom agnetic ZPE. This interpretation has recently been strengthened by the analyses of Cole and Zou (Reference 24, 25) using a SED m odel for the vacuum ZPE. Since the balance between em itted orbital-acceleration radiation and absorbed ZPE radiation is m odeled as taking place primarily at the ground state orbital frequency, one can consider the possibility of using this feature in som e type of m echanism to extract energy from the ZPF. One fundam ental difference between the SED interpretation and that of quantum m echanics is that in quantum m echanics the Is state of the electron is regarded as having zero angular m om entum , whereas in the SED interpretation the electron has an angular m om entum of mecre /137 .7 7 me = electron mass (9.11 x IO-31 kg), re = electron radius, atomic fine structure (a.k.a. QED coupling) constant a = 1/137, and c/137 is the classical orbital velocity of the ground state electron. The B ohr radius of the hydrogen atom in the SED view is 0.529 A. This im plies that the wavelength (X) of zero-point radiation responsible for sustaining the orbit is 2n • 0.529 ■ 137 = 455 A (or 0.0455 gm ). It has been conjectured by Puthoff and Haisch (private com munication, 2004) that suppression of zero-point radiation at this wavelength (and at shorter wavelengths) inside a Casim ir m icrocavity could result in the decay of the electron to a lower energy state determ ined by a new balance between classical em ission of an accelerated charge and absorption of zero-point radiation at 1 < 455 A, where X depends on the m icrocavity plate separation (d). Since the frequency of this orbit is 6.6 x 1015 Hz, no m atter how quickly the atom were to be injected into a Casim ir m icrocavity, one would assum e that the decay process would be a slow one as experienced by the orbiting electron. Figure 5 shows a schematic representation of a hydrogenic atom in free space and inside a m icrocavity. 10 UNCLASSI FIED//EHR nFFTr™i iiccnMiu UNCLASSI FIED//TO R O FFICIAL USE O NLY Figure 5. Energy Released from Ground State Suppression of Hydrogenic Atom in a Microcavity, (fb = free-space Bohr orbit radius, ^ = suppressed Bohr orbit radius, X = resonant wavelength of Bohr orbit, and £w = released energy). Consider the possibility that the decay to a new sub-B ohr ground state would involve gradual release of energy in the form of heat, rather than a sudden optical radiation signature. Since the binding energy of the electron is 13.6 eV,8 it is estim ated that the am ount of energy released in this process could be on the order of 1 to 10 eV for injection of the hydrogen atom into a Casim ir cavity of d = 250 A. Furthermore, consider the possibility that when the electron exits the cavity it would reabsorb energy from the zero-point field and be re-excited to its norm al state. If these conjectures were to be verified by experiment, then the energy extracted in the process com es at the expense of the zero-point field, which in the SED interpretation propagates at the speed of light throughout the universe. In effect the energy would be extracted locally and replenished globally. The secondary consequences on other phenom ena, if this energy conversion were to succeed, have not yet been investigated. However, on a cautionary note, the conflicts between SED and QED theories (discussed in Section V) raise questions as to whether the conjectured approach discussed here is viable. This issue is perhaps best addressed by experim ent for its resolution. 8 1 eV = 1.602 x IO’19 J. In terms of an experim ental test, consider using m onatomic gases or liquids flowing in a block with Casim ir tunnels, which has the following attributes: 1) no dissociation process is required for m onatom ic gases or liquids, 2) heavier elem ent atom s are approxim ately two to four tim es larger than hydrogen and thus can utilize and be affected by a larger Casim ir cavity, 3) heavier elem ents have numerous outer shell electrons, several of which m ay be sim ultaneously affected by the reduction of zero­ point radiation in a Casim ir cavity. All of the noble gas elem ents contain ns electrons. He (Z = 2, r = 1.2 A) has two Is electrons. Ne (Z = 10, r = 1.3 A) has two each of Is and 2s electrons. Ar (Z = 18, r = 1.6 A) has two each of Is, 2s, and 3s electrons. Kr (Z = 36, r = 1.8 A) has two of each UNCLASSI FIED//fap nFFTr™i iiccnMiu UNCLASSIFIED//FO R O FFICIAL UO £ O NLY of Is, 2s, 3s, and 4s electrons. Xe (Z = 54, r = 2.05 A) has two of each of Is, 2s, 3s, 4s and 5s electrons. Larger Casim ir cavities would also be expected to have an effect on the energetics of the outer electron shells (at larger radii). One could therefore expect that a Casimir cavity having d = 0.1 gm could have an effect on reducing the energy levels of the outermost pair of s electrons, and possibly also p electrons and intermediate shell s electrons as well. Continuing with this m odel, it is reasonable to expect that a 0.1 gm Casim ir cavity could result in a release of 1 to 10 eV for each injection of a He, Ne, Ar, Kr or Xe atom into such a cavity. According to Maclay (Reference 26), a long cylindrical Casim ir cavity results in an inward force on the cavity walls due to the exclusion of interior ZPF m odes. In the "exclusion of m odes" interpretation of the Casim ir force, this im plies that a cylindrical cavity of diam eter 0.1 gm could yield the desired decay of outer shell electrons and subsequent release of energy. If one lets the length of the cylinder be 100 tim es the width, this results in X = 10 gm for the length of the Casim ir tunnel. Taking advantage of this effect, Puthoff (private com m unication, 2004) and Haisch and Moddel (Reference 27) propose a segm ented tunnel consisting of alternating conducting and non-conducting m aterials, each 10 gm in length. In a length of 1 cm , there could be 500 such pairs in segm ents, resulting in 500 energy releases (each yielding 1 to 10 eV) for each transit of an atom through the entire 1 cm -long Casim ir tunnel. Now consider a 1 cm 3 block that is built up of 10 gm thick alternating layers as described above (see Figure 6 for an illustration of this apparatus). Assum e that tunnels of 0.1 gm diam eter could be drilled through the cube perpendicular to the layers (this is not physically possible, of course; tunnel m anufacture m ust be done differently). If 10 percent of the cross section com prises entrance to som e 1.3 billion tunnels, then the am ount of energy released would be proportional to the flow rate of the gas through the tunnels (for the number of entrances and exits through Casim ir segm ents). A flow rate of 10 cm /s through a total cross sectional area of 0.1 cm 2 yields 1 cm 3 of gas per second flowing through the tunnels, which at STP would be 2.7 x 1019 atom s. A very sim ple sealed, closed-loop pum ping system could m aintain such a continuous gas flow. Since each atom interacts 500 tim es during its passage, there would be 1.3 x 1022 transitions per second in the entire cube of 1 cm 3. An energy release of 1 to 10 eV per transition corresponds to 2,150 to 21,500 W of power released from the entire Casim ir cube of tunnels. This can also be achieved by using a pair of plates with conducting strips creating Casim ir cavities (via 5000 strip pairs) that are separated by 0.1 gm spacers, through which Hg liquid or m onatomic gases (for exam ple, He, Ne, Ar, Kr, or Xe) flow (Reference 27). See Figure 7 for an illustration of this apparatus. However, again, all of this assumes that the chain of conjectures detailed above is correct. Fortunately, this can be experimentally tested. 12 U N CLASSI FI E D//EHR nFFTr™i mce^mi^ UNCLASSIFIED//rO R O FFICIAL USE O NLY Figure 6. Apparatus for Ground State Figure 7. Alternative Apparatus for Ground State Energy Energy Suppression: Casimir Segmented Suppression: Casimir Strip and Spacer-Channels Tunnels Microcavity fabrication to m atch the atomic ground states is daunting because there will potentially be fabrication irregularities that cause edge and surface effects which act upon the particles as they enter or exit the Casim ir region. And it is not possible to drill 1.3 billion tunnels having diam eters of 0.1 gm . However, it should be feasible to use m icrochip technology to etch holes into the individual layers first and then assem ble the stack. Extrem ely fine coregistration and alignm ent of stacks would be an issue, but a surm ountable one. A m uch sm aller num ber of layer pairs and tunnels would suffice for a m easurable dem onstration of release of ZPE by this process. If such a sm all-scale dem onstration succeeds, larger versions that convert m ore energy could be built that also take advantage of m ore efficient therm al-to-electrical energy conversion m ethods. Also if successful, such apparatuses could be used to explore for secondary effects of converting quantum vacuum energy into therm al, then electrical energy. Further investigation by Puthoff et al. (Reference 28) was based on the prem ise that the above principle is broadly applicable to other than just atomic ground states. In their experiment, H2 gas was passed through a 1 gm Casim ir cavity to suppress the ZPE radiation at the vibrational ground state of the Ha m olecule. The anticipated signature for such a process would be an increase in the dissociation energy of the m olecule. Initial experim ents, shown in Figure 8, were carried out at the Synchrotron Radiation Center at the University of W isconsin at Madison, where an intense UV beam is available to disassociate gas m olecules. Unfortunately, problem s with the synchrotron beam (unrelated to the experiment) prevented a definitive result from being obtained, so the efficacy of this ZPE-extraction approach rem ains undeterm ined at the present tim e. Further experim entation to investigate this hypothesis has yet to be com pleted. 13 UNCLASSI FIED//fap nFFTr™i hccomiu UNCLASSI FIED//FO R O mCIAL UDE O NLY Figure 8. Experimental Apparatus for Ground State Energy Reduction Tests TUNABLE CASIMIR EFFECT As previously discussed, the Casim ir Effect is a unique ZPF-driven quantum force that occurs between closely-spaced conductive cavity walls (or plates). If left unfettered, the plates will collapse together and energy is converted from the ZPF into heat (or other form s of energy) in accordance with the expression £ / A =-Tt3ht7 7207', where E/A is the energy per unit area of the plates and d is the plate separation. Investigation of this m echanism by Cole and Puthoff (Reference 11) showed that this process fully obeys energy conservation and thermodynam ic laws. Although the Casim ir force is conservative, and thus the Casim ir device m ight appear to be a one-shot device, the fact that the attractive Casim ir force is weaker for dielectric plates com pared to conductive plates raises the possibility of the use of thin-film switchable m irrors to obtain a recycling engine (Reference 29-31). Figure 9 shows a com parison of the strength of the Casimir force in a conductive cavity with that in a dielectric cavity. In such an application the plates are drawn together by the stronger force associated with the conducting state and withdrawn after switching to the dielectric state. The engine cycle for this concept is shown in Figure 10. Assum ing optim istic conditions for practical devices (negligible energy required for switching; plate separation oscillations between 30 nm and 15 nm for 1 cm 2 plates; driving circuit 14 U NCLASSI FIED//mp QESCIAI HccnMiu UNCLASSI FIED//FO R O FFICIAL USE O NLY « 10 tim es the weight of the Casim ir plates, and so forth), an estim ate of the achievable power m ight be obtained. B ased on the described param eters, and assuming a switching from a purely conductive state to a dielectric constant of K = 4, yields a figure of m erit of « 35 x f (MHz) W /kg (f = switching rate) for the power density (Reference 29). This can be com pared to the power density of « 5 W /kg achieved by current radioisotope therm oelectric generators. The predicted output power per unit area for this experim ental device is « IO-6 f (MHz)/4[J(pm )]3 W /cm 2. Spacing, d (pm ) Figure 9. Tunable Casimir Effect: Conductor vs. Dielectric 15 U NCLASSI FIED//mp QEEICIAI HccnMiu UNCLASSI FIED//FO R O FFICIAL USE O NLY Spacing, d (pm ) Another "tunable" conductive-type plate experim ent under consideration involves the use of plates consisting of three-dim ensional photonic crystals, with the bandgap of the photons that can transm it through the structure being a "tunable" value. Using m icroelectrom echanical processing m ethods, Sandia National Laboratory has produced such crystals and is researching m ethods of actively m odifying the structures while in use (Reference 32). The technology requirements for this concept are the nano­ fabrication of m icrocavities with thin-film deposited surfaces, RF-driven piezoelectric m ounts for cavity oscillation, m irror-switching m odality (for example, hydrogen pressure m odulation), and calorim etric m easurement of energy/heat production. An initial experim ent to explore this concept was recently performed by lannuzzi et al. (Reference 33). They investigated the effect of hydrogen switchable m irrors (HSMs) on the Casim ir force. HSMs are shiny m etals in their "as deposited" state. However, when they are exposed to a hydrogen-rich atm osphere, they becom e optically transparent. B ecause the electrom agnetic ZPF depends on the optical properties of the surfaces, the Casim ir force of attraction between two HSMs in air should be different than the attraction between the sam e HSMs im mersed in a hydrogen-rich atm osphere. That is because one expects that the Casim ir force will be m uch weaker when the HSM is in the 16 UNCLASSI FIED//mp nFFTr™i iiccnMiu UNCLASSI FIED//FO R O FFICIAL USE O NLY transparent state rather than in the reflective state. The experiment tested this for plate separations of 70 - 400 nm . lannuzzi et al.'s experim ental results showed that the Casim ir force did not noticeably decrease after filling the experim ental apparatus with hydrogen. This m ay have occurred for two reasons. First, the dielectric properties of the HSMs used in the experim ent are only known only in a lim ited range of wavelengths spanning 0.3 - 2.5 jim, while the experim ent m easured the transparency of the HSMs over a wavelength range of 0.5 - 3 pm . This narrower wavelength span excludes the rest of the electrom agnetic ZPF m odes having wavelengths shorter than 0.5 um and longer than 3 jim . The ZPF m odes lying outside this narrow wavelength span were not affected by the hydrogenation-induced transparency of the HSMs, hence their contribution to the total Casim ir force acting between the HSMs was not included. One would expect to see a significant decrease of the Casim ir force if the hydrogenation-induced transparency of the HSMs had affected all of the ZPF m ode wavelengths ranging from IR to UV (ZPF m odes with X >> 2.5 gm will not give rise to large contributions to the force). Second, the experim ent dem onstrated a property of the Lifshitz theory (see Reference 33 for m ore detail), that in order to significantly change the Casim ir force between surfaces at separations on the order of 100 nm it is not sufficient just to change their optical (IR and visible) reflectivity, but it is necessary to m odify their dielectric functions over a m uch wider spectral range. This com ports with the first reason, and indicates that m ore theoretical and experim ental work is needed to overcom e the shortcom ings of this experim ent, and allow for the design and testing of new experiments that can achieve Casim ir plate transparency over a wider spectral range. A notion sim ilar to the tunable Casim ir Effect involves changing the dim ensions of a rectangular "Casim ir box." Forward (Reference 34) proposed a paradox in which energy could be extracted by altering the aspect ratio of a conductive rectangular Casim ir cavity over a specific cycle of dim ension changes (for example, varying width while holding length constant). It was subsequently shown by Maclay (Reference 26, 35), that the Casim ir energy inside the box is not isotropic, varying in such a way that m ore work is expended in cycling the box dim ensions than can be extracted. It appears that no net gain of energy is theoretically possible in this schem e. W hether such considerations apply to the tunable Casim ir cavity concept rem ains to be assessed. EV PHENO MENO N Shoulders (Reference 36) developed an experim ental program to explore the physics of m icroscopic plasma vortices (aka force-free plasm oids), which are thought to be a form of ball lightning (Reference 37). This study was m otivated by the earlier experim ental work of W ells at the Princeton University Plasm a Physics Laboratory, B ostick and Nardi at the Stevens Inst, of Technology, and their collaborators (Reference 38-45). Shoulders became interested in the possibility of stable, quantized force-free structures that could be taken apart by som e process to yield a net energy gain for power generation. The foundation for this speculation was Nardi et al.'s (Reference 45) observation of strange electron concentrations they called vortex filam ents that formed in an electron beam m ade by plasma focus or relativistic electron beam m achines, which exhibited electron concentrations that appeared to violate the space charge law. Furtherm ore, Nardi et al. observed that the vortex filam ents were striking exposed m aterials (for exam ple, m etals, dielectrics, ceram ics, glass), boring sm ooth channels straight through them, and som etimes exploding with such a large force that they 17 U NCLASSI FIED//mp afftctai uccnMiu UNCLASSIFIED//FO R O FFICIAL UO £ O NLY created im pact craters or holes in the m aterials. Piestrup et al. (Reference 46) perform ed m ore recent experiments to investigate this unusual phenom enon. This discovery inspired Shoulders to consider vortex filam ents as a potential new source of energy, and hence he nam ed them electromagnetic vortices or "EVs." However, given that he could not experim entally verify the vortex nature of the phenom enon, he later redefined EV to m ean Electrum Validum (roughly translated as strong electron). B ostick and Shoulders began collaborating and realized that EVs were m uch easier to generate and observe using m icro-arc discharge devices because they are usually obscured by surrounding plasma in large high-power plasma m achines. This led Shoulders to design a series of low-voltage, low-power m icro-arc discharge (or condensed-charge em ission) devices to produce EVs in the lab. Figure 11 shows a schematic diagram for one em bodim ent of an EV (pulse discharge source) device. The EVs are generated at the cathode tip and then follow the path (dashed line above the dielectric) to the im pact site on the ground plane (in the figure, C = capacitor and V = voltage). The EVs generated by such devices were able to reproduce the m aterial dam age observed in Nardi et al.'s earlier experim ents. Figure 11. Schematic of EV (Pulse Discharge Source) Device (Reference 47) 18 U NCLASSI FIED//mp QEEICIAI .iccamiu UNCLASSI FIED//FO R O mCIAL UDE O NLY Figure 12 shows a scanning electron m icroscope (SEM) photograph of the dam age inflicted by a single EV burst fired along an alum inum -oxide ceram ic plate, The EV bored through the ceram ic form ing a sm ooth sym metrical channel along its path. Figure 12* SEM of EV Damage to Ceramic Plate (20 um scale) (Reference 36) 19 U N CLASSI FI E D/ /CEQJLQEElGIAUUfiMNWfr UNCLASSI FIED//FO R O FFICIAL UO £ O NLY Figure 13 shows a SEM photo of a single EV shot on a Palladium (Pd) target from a 40 pF capacitor charged to 3,000 Volts (containing 7.5 x 1011 electrons). At least 100 tiny craters were form ed in the target. The larger craters formed in the Pd target as seen in the photo suggest a very energetic im pact that m elted the Pd locally, m aking a sm all hole surrounded by a crater wall. Figure 13. SEM of EV Damage to Palladium Target (Reference 36) 20 U NCLASSI FIED//FnpnFFTn"i iiccnM^ UNCLASSI FIED//FO R O mCIAL UDE O NLY Figure 14 shows an exam ple of an EV m oving away from its source and shedding electrons while giving off light as it was decaying. Figure 14. EV (large blob at bottom) Moving at Downward Angle Away From Its Source (smaller blob near center of photo) (Reference 36) Shoulders' experim ental studies claim that EVs have physical characteristics corresponding to the phenomenon observed by Nardi et al. His conclusions were that EVs are com pact spherically shaped balls (diam eter » 1 - 20 pm ) of condensed high- density charge (~ 1030 electrons/m 3) with an internal electric field > 108 V/m , a charge- to-m ass ratio of 1.7588 x 1011 Coulom b/kg (= electron's charge-to-mass ratio), and a surface current density of 6 x 1015 Am ps/m 2 (Reference 36). Shoulders also reported that EVs are a source of (copious) X-rays; a single EV discharge gun can produce m ultiple EVs in which the coupling between adjacent EVs produces quasi-stable structures (chains); and EVs respond like an electron under deflection by external fields of known polarity. Since electrons would not be expected to bind together due to their m utual Coulom b repulsion, a speculative m odel based on the vacuum electrom agnetic ZPF was form ed 21 U NCLASSI FIED//mp QESCIAI HccnMiu UNCLASSIFIED//FO R O FFICIAL UO £ O NLY to explain the existence of EVs. The em erging laboratory evidence led investigators to consider the hypothesis that the Casim ir effect m ay be a m ajor contributing m echanism to the form ation of EVs in m icro-arc discharges. This conjecture is based on m odels by Casim ir (Reference 48) and Puthoff and Piestrup (Reference 49) suggesting that the generation of a relatively cold, dense, non-neutral (charged) plasma results in charge­ condensation effects that m ay be attributable to a Casim ir-type pinch effect (that is, ZPF-induced pressure forces) in which the inverse square-law Coulomb repulsion is overcom e by an attractive inverse fourth-law Casim ir force to yield a stable configuration of bound charges at sm all dim ensions. This is a derivative of Casim ir's sem i-classical m odel of the electron in which a dense shell-like distribution of charge m ight suppress vacuum fields in the interior of the shell (Reference 48). However, initial application of Casimir's m odel found that the vacuum field inside the m odeled electron was found to augm ent rather than offset the divergent Coulom b field thus rendering the electron's self-energy divergent. Puthoff (Reference 50) later resolved this problem by developing a self-consistent vacuum-fluctuation-based m odel in which the net contribution to the point-like electron's self-energy by its Coulomb and vacuum fields vanishes thus rendering a stable finite-m ass electron. Shoulders and collaborators subsequently investigated different approaches to extracting useful energy from the vacuum ZPF by way of exploiting EV phenom enon. Even though EVs can be easily produced in the lab, efforts to test this hypothesis have not m et with success due to technical problem s. However, this topic is ideal to pursue for future research. V. Theoretical Considerations and Issues QED VACUUM REVISITED QED Vacuum as a Plenum Continued theoretical and experim ental research has revealed that the vacuum constitutes an active agent that contributes to a host of phenom ena ranging from m icroscopic level shifts of atom ic states to possible connections to the cause of cosm ological expansion (Reference 14, 51). As m ore of its attributes are explored, the vacuum has been found to exhibit phenom ena characteristic of an optical m edium , such as induced birefringence in the presence of an applied m agnetic field (Reference 52), and breakdown (decay) in the presence of external electric fields (Reference 53-55). The current view is that the vacuum has structure, and can be considered m uch like a m edium of classical physics. However, the vacuum differs significantly from that of a classical m edium due to the existence of quantum fluctuations. A prim ary attribute of quantum theory is the concept of m atter and field fluctuations, rooted in Heisenberg's Uncertainty Principle. In second-quantized QED theory, the theory that applies to the electrom agnetic vacuum , the canonical approach to representing fluctuations of the free vacuum electromagnetic field is to express the field distribution in terms of standing- or traveling-wave norm al m odes. Section I suggested that the large value of the integrated ZPE density fuels the concept of potentially useful vacuum energy conversion to other form s, should even som e sm all part of the spectral energy distribution be accessible for conversion by technological m eans. 22 U N CLASSI FI E D//mp nFFTr™i mce^mi^ UNCLASSI FIED//TO R O FFICIAL USE O NLY QED Vacuum as a Mathematical "Placeholder" for Fluctuating Matter Fields The treatm ent of the QED vacuum as a fluctuating plenum with (form ally) infinite energy density has caused som e physicists to call into question the viability of the second-quantized QED form alism . Jaynes, for example, in considering the consequences for calculation of the Lam b shift of the 2s level of the hydrogen atom under the assumption of a m uch m ore m odest electron Com pton frequency cutoff (~ 1021 Hz), calculates a fluctuating power flow for the Poynting vector of 6 x 1020 MW /cm 2 - com parable in every square centim eter to the total power output of the sun - and states that "real radiation of that intensity would do a little m ore than just shift the 2s level by 4 m icrovolts" (Reference 56). However, despite alternatives to the form alism of QED that have been suggested (m ore on this later), second-quantized QED cannot be lightly dism issed; and this is so even though the infinities that m ust be dealt with by such procedures as renorm alization caused even one of its founders, Paul Dirac, to rem ark: "This is just not sensible m athematics. Sensible m athem atics involves neglecting a quantity when it turns out to be sm all - not neglecting it because it is infinitely great and you do not want it" (Reference 57). A second argum ent that can be raised against using the QED form alism to further explore vacuum fluctuation physics is that, despite the m agnitude of the energy density potentially associated with vacuum electrom agnetic fluctuations, observation of the cosm ological constant—a m easure of net vacuum energy density—has a value that is only on the order of the average energy density of (ordinary + dark) m atter in the universe ® IO9 J/m 3 (Reference 58, 59). This leads to what is often referred to as the 120 orders-of-m agnitude problem, or "cosm ological coincidence." In the m ainstream view, rather than the QED value being discounted, the resolution of this problem is thought to lie in the dom ain of infinity (or divergent integral) cancellations, requiring instead an accounting for the fine-tuning requirements of such cancellations (Reference 60, 61). Again, the root cause of the difficulties that accom pany second quantization of the vacuum field is that an unbounded plenum possesses an infinite num ber of degrees of freedom , each with its assigned ground-state fluctuation energy. In an attem pt to circumvent the difficulties associated with an unbounded, second-quantized plenum , alternative approaches to QED have been explored in the literature in som e detail, a few of which are discussed in Section V. A num ber of these alternative viewpoints interpret the second-quantized QED vacuum with its infinite degrees of freedom as sim ply an over-idealized m athem atical placeholder for "real" fields that originate in m atter fluctuations whose num ber of degrees of freedom is necessarily always lim ited. Nevertheless, though the alternative form alism s and associated interpretations differ significantly from the canonical approach, detailed calculations yield results identical to those generated by the second-quantized field formalism . As a result, even treated as a m athem atical placeholder for m atter fluctuation fields, at this point in our discussion the QED value m ust be taken seriously. The proposed corollary concerning the potentially significant conversion of QED vacuum energy to other forms is further evaluated in the sections that follow. 23 UNCLASSI FIED//fap nFFTr™i iiccnMiu UNCLASSI FIED//FO R O FFICIAL USE O NLY CASIMIR EFFECT REVISITED The m ost-quoted quintessential configuration for the conversion of vacuum energy to other form s of energy is the Casim ir effect. As previously discussed, when parallel conducting plates are placed in a vacuum , they attract one another by a very weak force that varies inversely as the fourth power of the distance between them . First com puted by Casim ir in terms of van dec W aals forces (a m atter-fields approach - see below), he soon realized that, because the force turns out to be independent of the m olecular details of the conductors, it could be com puted as a problem in vacuum energy, and that is the way it is now generally presented in the literature (the "plenum approach") (Reference 5, 62). Casimir Effect in the Plenum Picture One begins with the free quantum vacuum electrom agnetic field fluctuations, and then determ ines their m odification due to the insertion of two parallel plane conductors (that is, plates) as additional boundary conditions, which constrain a discrete set of intra­ cavity m odes of integer half-wavelengths. Aside from an unobservable, high-frequency­ cutoff-dependent, free-field term that rem ains from the m athem atical regularization procedure, the resulting (renorm alized) vacuum stress-energy tensor9 is given by (T^ J=(7i2hc/72OJ4)tZia^ (-l,l,l,-3), where the angular brackets denote the quantum (vacuum state) expectation value of the tensor 7^ ", d is the plate separation, and d/ag(-l,l,l,-3) denotes the diagonal elem ents of a 4x4 m atrix (Reference 1-3, 62).10 (t^ represents the real physical stress carried by the vacuum field fluctuations in the presence of the parallel plane conductors, and it encodes the Casim ir effect in terms of (1) an interaction energy per unit area, EM = -j?hc/720d3, and (2) a corresponding force per unit area, F / A =-n2hc7 240J4. If free to m ove in response to the attractive Casim ir force, the m otion of the plates toward each other is understood in the plenum approach to progressively elim inate intra-cavity m odes, converting their associated ground-state energies first into kinetic energy, and then, upon collision of the plates, into heat. Section II described the Casim ir-force-driven collapse of Forward's charged slinky as a Casimir-type configuration for building up an electric field to charge a battery, and how such processes were shown not to violate either conservation of energy or therm odynam ic constraints. 9 The stress-energy-momentum tensor, F"', is a matrix quantity that encodes the density and flux of a matter source's energy and momentum. Greek indices denote the matrix components over the spacetime coordinates. 10 For this derivation, the vacuum fluctuations of other quantum fields are essentially undisturbed by the presence of the conductors or are affected only in the immediate vicinity of the atomic nuclei that they contain. Casimir Effect in the Fluctuating Matter Fields Picture Com plem entary to the vacuum m ode description (plenum approach), the Casim ir effect can be described, like van der W aals attraction, as arising from correlations in the state of electrons in the two plates through the interm ediary of their coupled fields. From this standpoint (m atter-fields approach) there is no requirem ent for the high energy density vacuum field of the plenum approach to reside throughout all space. 24 UNn ASSIFIED/jtEQB HEFTCmi ■■« am. u UNCLASSI FIED//FO R O FFICIAL USE O NLY Unfortunately with regard to energy generation, though the Casim ir forces involved can be of significance for MEMS applications (Reference 63), the associated Casim ir energies involved are too sm all to be considered of significance for energy applications, so if the possibility for vacuum energy conversion exists, one m ust look elsewhere to other types of m atter-vacuum interactions. TYPE I (TRANSIENT) AND TYPE II (CO NTINUO US) MACHINES A key feature of the Casim ir process just described, regardless of viewpoint (plenum or m atter-fields), is that it is a "one-shot," transient, energy-producing m achine. That is, after delivering its energy, E, the m atter that com prises the m achine is in a "used" state (this used m atter is com monly referred to as "ash") and cannot be restored to the original state without an input of energy that is greater than or equal to E. This "one- shot" feature can be generalized to define a category of m achine called a Type I transient m achine, with the Casim ir m achine constituting the prototypical representative. Should gravitation eventually be traced to a vacuum ZPF origin as proposed by Sakharov (Reference 64), then the fall of an object of m ass m through a height h in a gravitational field (g = acceleration of gravity at Earth's surface), delivering its gravitational energy mgh upon im pact with the ground, would constitute another exam ple. In contrast, one can envision a Type II (continuous) m achine in which vacuum ZPF energy is converted to a useful form on a recycling basis without net alteration to its own m atter state. A hypothetical exam ple is the tunable Casim ir device that was reviewed in Section IV. The cycle of energy generation would consist of the collapse of conducting plates with delivery of energy, followed by separation of plates switched to insulating m ode for which the attractive force is considerably weaker, only to be switched back to conducting m ode for the next cycle, and so forth. Provided the input switching energy required per cycle is less than the output energy delivered per cycle, a continuous generation of energy without a net change in m atter configuration would result. A second example would be a nonlinear oscillator that continuously, on a steady­ state basis, down-shifted high-frequency com ponents of the vacuum ZPF spectrum to lower frequencies for convenient collection and application, without a net change in its own operation. Clearly a Type II m achine would be far m ore useful than a Type I m achine for energy extraction. Type II m achines would constitute a fuel-less energy source, with the am bient vacuum ZPF providing essentially unlim ited energy. For this to be the case, however, another requirem ent needs to be satisfied, which the next section will address. DEG RADABILITY O F THE VACUUM The possibility of continuous conversion of vacuum ZPE to other forms (that is, by a Type II m achine) requires that, in principle, vacuum energy m ust be degradable (that is, continuously consum able), not just that there be a surfeit of energy in place to harvest. This perspective leads to a rem arkable question for deeper explorations of QED. It turns out that the m athem atical structure of QED is based on a form alism in which the vacuum m ode structure and vacuum fluctuation energy per m ode are quantized in what could be called a "hard-wired" fashion; that is, they possess fixed im m utable values. Therefore, at the end of a cycle of a hypothetical Type II m achine, in 25 UNn ASSIFIED/jtEQR HEFTCmi ■■« am. u UNCLASSI FIED//FO R O FFICIAL USE O NLY which both m atter and vacuum m ode structure have been returned to their original states, the vacuum m odes m ust of necessity contain at a m inim um the sam e, "hard­ wired," energetic content as before the cycle. Therefore, assum ing local detailed- balance energy conservation, continuous conversion of vacuum ZPE to other form s via a Type II m achine is, from the QED viewpoint, forbidden in principle since the vacuum as described by the QED form alism is non-degradable. (Globally, vacuum energy is not conserved during cosm ological expansion, with work being done by the negative vacuum pressure to m aintain positive constant vacuum energy density and therefore increasing the vacuum energy (Reference 65) This outcom e of second-quantized QED theory perm its of but two interpretations with regard to continuous vacuum energy conversion: 1) QED theory, despite criticism s that can be leveled against it, is correct in its description of vacuum fluctuation dynam ics, and even though vacuum ZPE exists, it cannot be continuously converted to other form s, or 2) the axiom atic inconvertibility is an artifact of an over-idealized m athem atical structure, and therefore the possibility of conversion rem ains an open question.11 W hat is not in question, however, is that QED, as an axiom atic, quantum form alism based on the concept of an im m utable, non- degradable vacuum , does not support the concept of continuous vacuum energy conversion. 11 A number of publications by E. T. Jaynes, A. 0. Barut and their collaborators are based on the premise that second quantization is an unnecessary artifact of an over-idealized formalism. ALTERNATIVES TO QED As noted in Section V, despite its successes the second-quantized QED form alism with its infinite vacuum degrees of freedom and associated infinite energy density has been the subject of criticism and, as a result, alternatives have been proposed and investigated in the literature. The alternatives run the gam ut from neoclassical theories in which m atter is quantized but the fields are not (for example, the volum inous work of E. T. Jaynes), through classical theories where both m atter and fields are treated classically, with vacuum fluctuations fields taken to be real but of a classical nature (for exam ple, SED), to formalism s which elim inate the concept of vacuum fields altogether (for example, direct-action approaches investigated by A. 0. B arut and others; see the references cited below). Each of these will be exam ined briefly with regard to the possibility of useful "vacuum energy conversion." Neoclassical Theories of QED Vacuum Fluctuation Effects A m ajor proponent of the neoclassical approach has been E. T. Jaynes, who has questioned whether the quantized vacuum field is physically real or m erely an artifice of the second-quantized QED form alism . B ased on the fact that the QED formalism permits expression of effects in terms of quantized "self" or "source" fields as an alternative to expression in terms of quantized vacuum fluctuation fields, Jaynes advanced the hypothesis that QED effects can be attributed to the self-fields of quantized m atter without considering independent quantization of the vacuum fields, expressions in terms of the latter just being a placeholder for the form er. Pointedly, with regard to QED being "the jewel of physics because of its extrem ely accurate predictions," Jaynes' position is that "those accurate experim ental confirm ations of QED com e from the local source fields, which are coherent with the local state of m atter," and that "the quantized free field only tags along (Reference 66)." Jaynes nonetheless arrived at a conclusion that one m ight call Jaynes' Axiom , nam ely, "This com plete 26 UNCLASSI FIED//EHR nFFTr™i iiccnMiu UNCLASSI FIED//TO R O FFICIAL USE O NLY interchangeability of source-field effects and vacuum-fluctuation effects...shows that source-field effects are the sam e as if vacuum fluctuations were present." Applied to the case of a radiating atom , Jaynes provides a specific exam ple of his conclusion with the statem ent "The radiating atom is indeed interacting with an electrom agnetic field of the intensity predicted by the zero-point energy, but this is just the atom 's own radiation reaction field (Reference 67)." As a result, with the axiom atic second- quantized field form alism set aside, in the neoclassical approach any consideration of the conversion of vacuum ZPE for use m ust be displaced to consideration of the conversion and degradability of source or m atter-fields fluctuation energy for use, issues yet to be addressed in the literature. SED Model Revisited SED is a classical (that is, non-quantized) theory of particle-field interactions that assum es the existence of classical particles and a classical random background electromagnetic field distribution whose Lorentz-invariant spectral energy density is chosen to m atch that originally appearing in second-quantized QED. Given SED's heuristic value of classical-like m odeling and ease of calculation and its seem ing ability to address m any quantum m echanical problem s with success (as outlined in Section III), the SED approach has been em ployed in the literature to explore vacuum energy conversion. In the absence of a form alism for vacuum field quantization, there are no fundam ental im m utability constraints that would m itigate against vacuum energy degradability, so that issue is not testable under this form alism . Investigations to date have included the use of cavity-QED techniques to suppress atomic or m olecular ground states (Reference 28), and evaluation of the use of a nonlinear oscillator to continuously downshift high-frequency com ponents of the vacuum fluctuation spectrum to lower frequencies for convenient collection and use. W ith regard to the latter, the result of a nonrelativistic SED analysis is that the downshifting process acts to convert an initial hypothetical cubic-frequency vacuum fluctuation spectrum towards a Rayleigh-Jeans rather than a Planck heat spectrum (the former being a low energy approxim ation of the latter) (Reference 68, 69). Extension of the analysis to the relativistic regime does not alter this conclusion (Reference 70, 71). Though further work rem ains, these considerations lead one to conclude that SED in its present form is incom plete, and m ay not be useful for the assessm ent of the potential conversion of vacuum energy to other form s; its predictions concerning such m ust be treated with caution. Additional shortcom ings of the SED m odel include convoluted attem pts to derive interference effects or Schrodinger's equation, and the difficulty in explaining sharply- defined stationary states (that is, sharp atom ic spectra), though there have been m any attem pts (Reference 17). QED and SED do not in general yield the sam e results for nonlinear system s, although they are in agreem ent for the range of linear systems exam ined. The apparent disagreements between SED and QED are quite serious, and occur in areas in which QED is highly successful. Perhaps the source of these difficulties lies in accurately dealing with the nonlinear stochastic differential equations in SED for these problem s. Even still, it is likely that differences will rem ain, which should clearly be testable by experim ental m eans (Reference 72). For a very thorough, detailed and scholarly review of SED, see (Reference 17) and the corresponding review by Cole and Rueda (Reference 73). 27 UNCLASSI FIED//EHR nFFTr™i iiccnMiu UNCLASSI FIED//FO R O FFICIAL USE O NLY Given the heuristic value of certain aspects of SED m odeling, but with the shortcom ings outlined above noted, SED theorists de la Pena and Cetto have proposed a m odification to SED they call LSED (linear SED) (Reference 74). The m odification consists of the addition of three new constraining principles that result in a form of convergence with nonrelativistic quantum m echanics while retaining som e of the appealing attributes of standard SED (for exam ple, quantum states being stable on the basis of a dynam ic balance between absorption and em ission of background vacuum fluctuation fields). The added constraints (for example, an added constraint that invokes detailed energy balance for separate frequencies) result in correcting several known problem s with standard SED. For exam ple, now the equilibrium spectrum is Planck's, not Rayleigh­ Jeans, and wavelike behavior of m atter and nonlocality issues can be addressed, and so forth. The issue of continuous vacuum energy conversion has yet to be addressed in this new form alism , however, so that rem ains for the future. QED W ithout Second-Quantized Fields As yet another alternative to canonical second-quantized QED, B arut (Reference 75) has proposed that effects attributable to vacuum ZPF can be derived with a theory in which there are source (m atter) fluctuation fields but no vacuum fluctuation fields, and that even the form er can be elim inated. B arut's approach is developed in considerable detail as an independent, self-consistent, form ulation of QED in its own right. B arut argues that effects norm ally attributed to vacuum fluctuations in the second-quantized, linear theory of the radiation field can be equally well com puted within the fram ework of a non-second-quantized, nonlinear theory which is based entirely on m atter wave functions alone. His program is to assess how far one can go in understanding radiative processes without second quantization or vacua that fluctuate. B arut and his collaborators have successfully applied the theory to the Lam b shift and spontaneous em ission (Reference 76, 77), problem s of cavity QED (Reference 78), Casim ir-Polder and van der W aals forces (Reference 79), calculations of the electron's ge-2 factor (Reference 80-82),12 and the Davies-Unruh effect (Reference 83) am ong others. 12 g* is the electron's gyromagnetic ratio. Given that the form alism of second-quantized field operators are not used at all in the B arut approach, the seemingly quantized properties of fields are taken to sim ply reflect first quantization of the sources. Therefore, in the absence of the independent existence of second-quantized field fluctuations, the QED argum ents concerning im m utability and nondegradability of quantized vacuum fluctuation fields, and the corollary proscription against potential conversion of energy from such fields, do not apply. As in the neoclassical approach, the question of the conversion of quantum ZPE to other form s m ust be diverted to consideration of the global properties of m atter fluctuation interactions in the as-yet-incom plete developm ent of the B arut approach. EXAMPLES O F DEG RADABLE O F DECAYING VACUUM In closing, several exam ples of a degradable vacuum that are predicted by quantum field theory, quantum field theory in curved spacetim e, and the Standard Model of elementary particle physics will be reviewed. It turns out that the vacuum in QED theory is in fact degradable in spite of its "hardwired" ZPF m odes. 28 UNCLASSIFIED//Fnp nFFTr™» iiccnMiu UNCLASSI FIED//FO R O mCIAL UDE O NLY G ravitational Squeezing of the Vacuum In their study of traversable worm holes, Hochberg and Kephart (Reference 84) discovered that the gravitational field of any astronom ical body produces a zone of negative energy around it by "dragging" som e of the virtual quanta (a.k.a. vacuum ZPF) downward. They applied their discovery to the problem of creating and stabilizing traversable worm holes. Their quantum optics analysis showed that there is a distortion of the vacuum electromagnetic ZPF due to the interaction with a prescribed gravitational background, which results in "squeezed" vacuum states that possess a negative energy density. Squeezing of the vacuum is a quantum process that is roughly analogous to the com pression of an ordinary fluid. This m eans that as the vacuum field is continuously being squeezed by the gravitational field of a body, its energy is continuously being degraded with respect to the undisturbed rem ote vacuum field. The m agnitude of the gravitational squeezing of the vacuum can be estim ated from the quantum optics squeezing condition for given transverse (to the direction of gravitational acceleration) m om entum and (equivalent) energy eigenvalues, j = 8nrs/X,13 of two electromagnetic ZPF field m odes, subject to the squeezing condition j -^ 0, where X is the ZPF m ode wavelength and rs is the Schwarzschild radius of the astronom ical body under study (Reference 84).14 This condition sim ply states that substantial gravitational squeezing of the vacuum occurs for ZPF field m odes with X > 8nrs. The corresponding local vacuum state energy density that this effect produces is pE-gsvac = —Zlt^ c/X4. 13 Note that j contains an extra factor of two (compared to the J derived in Reference 84) in order to account for the photon spin. 14 rs = 2GM/c2 is the critical radius at which a body of mass M collapses into a black hole. It is used here as a convenient distance parameter to simplify the inequality, but there is no actual black hole collapse involved in this mechanism. G is Newton's universal gravitation constant (6.673 x 10 11 Nm2/kg2). 15 A spacetime metric is a Lorentz-invariant distance function between any two points in spacetime, which is defined in terms of a metric tensor, ggv/ that encodes the geometry of spacetime (Greek indices g,v = 0...3 denote spacetime coordinates, x°.„x3, such that xL.-X3 = space coordinates and x° = time coordinate). It is not clear whether this m echanism can be exploited to extract energy from the vacuum . Conservation of energy suggests one of two possible outcom es: 1) the lost energy is injected into the gravitational energy of the body, or 2) the lost energy reappears as an accum ulation of positive energy density ZPF m odes elsewhere in the universe. Further research will be needed to address this question. Redshifting the Vacuum Calloni et al. (Reference 85, 86) explored the possibility of verifying the equivalence principle for the zero-point energy of QED. They used sem i-classical quantum gravity theory to evaluate the net force produced by the quantum vacuum ZPF acting on a rigid Casim ir cavity in a weak gravitational field which is m odeled using the standard Schwarzschild spacetim e m etric geom etry.15 They evaluated the regularized (or renorm alized) stress-energy tensor ^ Tv^ of the quantized vacuum electromagnetic field between two plane-parallel ideal m etallic plates lying in a horizontal plane. (rv^ encodes the Casim ir effect, which has a negative energy density and a negative pressure along the vertical (gravitational acceleration) axis between the plates. B im onte 29 U NCLASSI FIED//mp QESCIAI mce^mi^ UNCLASSI FI ED//FO R O FFICIAL USE O NLY et al. (Reference 87-89) also studied this problem using Green-function techniques in the Schwinger-DeW itt quantum ether prescription for (t^ in a curved spacetim e. The results from these studies agreed with the equivalence principle and showed that quantum vacuum ZPF does gravitate since the energy of each ZPF m ode is redshifted by the factor (-goo)1/2 = [1 - (2GM/c2r)]1/2 even though the m odes rem ain unchanged {M is the m ass of a gravitating body, r is the radial distance from the body, and goo is the tim e-tim e com ponent of the Schwarzschild m etric tensor). These studies suggest that cavity electrom agnetic vacuum states are continuously degrading inside a background gravitational field. The total energy (Ecascrav) stored in the Casim ir device is given by (Reference 87, 89): _ rAhcr 5 gd “ ~ " 72oM + 2 ~ where A is the area of the plates, d is their separation, and g is the acceleration of gravity at Earth's surface (9.81 m /s2). B ut can one extract energy from this m echanism ? The answer to this question is not known at present, but consideration of the conservation of energy suggests that the sam e two possible outcom es given in the previous section would seem to apply: 1) the lost energy is injected into the gravitational energy of the body, or 2) the lost energy reappears as positive energy density ZPF m odes elsewhere in the universe. Further research will be needed to address this question as well. Vacuum Field Stress: Negative Vacuum Energy from the Casimir Effect As this report has already discussed, the standard Casim ir effect (neglecting spacetim e curvature, a.k.a. background gravitational fields) is by far the easiest and m ost well known way to produce negative vacuum energy. Therefore, the vacuum within certain types of Casim ir cavity geom etries is degraded. It turns out that there are m any different types of Casim ir effects found in quantum field theory (Reference 1-3, 62, 90). For exam ple, if one introduces a single infinite plane conductor into the Minkowski (flat spacetim e) vacuum by bringing it adiabatically from infinity so that whatever quantum fields are present suffer no excitation but rem ain in their ground states, then the vacuum (electromagnetic) stresses induced by the presence of the infinite plane conductor produces a Casim ir effect. This result holds equally well when two parallel plane conductors (with separation distance d) are present, which gives rise to the fam iliar Casim ir effect inside a cavity. Note that in both cases, the spacetim e m anifold is m ade incom plete by the introduction of the plane conductor boundary condition(s). The vacuum region put under stress by the presence of the plane conductor(s) is called the "Casim ir vacuum." The generic expression for the energy density of the Casim ir vacuum is pCF =-A Dhcd"4, where A d = ^ (D)/8ti2 in spacetim es of arbitrary dim ension D (Reference 1-3). The appearance of the zeta-function ^ (D) is characteristic of expressions for vacuum stress-energy tensors, 7^ . In our familiar 4-dim ensional spacetim e (D = 4), A d = n2/720. To calculate T^ for a given quantum field is to calculate its associated Casim ir effect. U) (5) 30 UNCLASSI FIED//Fnp nFFTr™i iiccnMiu UNCLASSIFIED//FO R O FFICIAL UO £ O NLY W hen the plates in a Casim ir cavity are put into non-uniform accelerated m otion, it is possible in principle to create real photons out of the vacuum . This effect is referred to in the literature as the "dynam ical Casim ir effect," or m otion-induced radiation (Reference 62, 91). One version of the dynam ical Casim ir effect provides a way to degrade the vacuum whereby negative vacuum energy is produced by a single m oving reflecting (conducting) surface (a.k.a. a m oving m irror). A m irror m oving with increasing acceleration generates a flux of negative vacuum energy that em anates from its surface and flows out into the space ahead of the m irror (Reference 4, 92). This is essentially the sim ple case of an infinite plane conductor undergoing acceleration perpendicular to its surface. If the acceleration varies with tim e, the conductor will generally em it or absorb photons (that is, exchange energy with the vacuum ), even though it is neutral. This is an exam ple of the well-known quantum phenomenon of param etric excitation. The param eters of the electromagnetic field oscillators (for exam ple, their frequency distribution function) change with tim e owing to the acceleration of the m irror (Reference 93). Analogs of the Casimir effect also exist for fields other than the electromagnetic field. W hen considering the vacuum state of other fields, one m ust consider boundary conditions that are analogous to the perfect-conductor boundary conditions for the electromagnetic field at the surfaces of the plates (Reference 1-3, 62, 91). Other fields are not electromagnetic in nature; that is to say they are non-Maxwellian, and so the perfect-conductor boundary conditions do not apply to them . It turns out that com plete m anifolds exhibit what is called the "topological Casim ir effect" for any non-Maxwellian fields. In order to define boundary conditions for other fields replace the conductor boundary conditions and Minkowski spacetim e by a m anifold of the form 'Ji x z (that is, a product space), where 91 is the real line defining the tim e dim ension for this particular product space and S is a flat 3-dim ensional m anifold having any one of the following topologies: 9l2 x S1,91 x T2, T3, YR x K 2, and so forth, 91 being the real line that defines any linear space dim ension (for exam ple, 9? = line, SR2 = 2-dim ensional plane), Tn being the n-torus, K 2 the 2-dimensional Klein bottle, S1 the circle, and so forth. The case S = 9i2 x S1 has the closest resem blance to the electromagnetic Casim ir effect, the difference being that instead of im posing conductor boundary conditions, one im poses periodic boundary conditions on som e of the space coordinates in the 3­ dim ensional m anifold. W hen im posing this topological constraint on the field theoretic calculation of the topological Casim ir effect (for linear m assless fields), one finds that the generic expression for the energy density is also pCE = -A dfhaT4, where A l( = ±J((jr! /90), df is the number of degrees of freedom (for example, helicity states) per spatial point, the plus sign holds for boson fields (giving a negative energy density) and the negative sign for ferm ion fields (giving a positive energy density). If one were to adm it spin structure in the m anifolds described above and the field is spinorial, then there is another im portant subtlety that m ust be taken into account when evaluating T^ . However, this introduces an additional com plexity involving the relationship between the spin structure and the global structure (that is, the configuration space or fibre bundle) of the field in question whereby the topology not only of the base m anifold, but of the fibre bundle itself has an effect on T'"'. In addition to this, there are (compactified) extra-space dim ensional quantum field (that is, D- 31 UNCLASSI FIED//EHR nFFTr™i mce^mi^ UNCLASSI FIED//FO R O FFICIAL USE O NLY B rane or "brane world") analogs of the Casim ir effect yet to be explored. B ut a detailed consideration of these is beyond the scope of this report and will be left for future investigation. Squeezed Quantum Vacuum It was discovered in 1965 that quantum field theory has the rem arkable property of allowing states of m atter containing local regions of negative (vacuum state) energy density or negative fluxes (Reference 94). In general, the local (vacuum state) energy density in quantum field theory can be negative due to quantum coherence effects (Reference 94). A prim ary byproduct of this discovery is the "squeezed quantum vacuum," which later gave rise to new phenomenon such as the gravitationally squeezed vacuum discussed previously. Substantial theoretical and experim ental work has shown that in m any quantum systems the lim its to m easurement precision im posed by the quantum vacuum ZPF can be breached by decreasing the noise in one observable (or m easurable quantity) at the expense of increasing the noise in the conjugate observable; at the sam e tim e the variations in the first observable, say the energy, are reduced below the ZPF such that the energy becom es "negative." "Squeezing" is thus the control of quantum fluctuations and corresponding uncertainties, whereby one can squeeze/reduce the variance of one (physically im portant) observable quantity provided the variance in the (physically unim portant) conjugate variable is stretched/increased. The squeezed quantity possesses an unusually low variance, m eaning less variance than would be expected on the basis of the equipartition theorem . One can in principle exploit quantum squeezing to extract energy from one place in the ordinary vacuum at the expense of accumulating excess energy elsewhere. The squeezed state of the electrom agnetic field is a prim ary example of a quantum field that has negative energy density and negative energy flux. Such a state becam e a physical reality in the laboratory as a result of the nonlinear-optics technique of "squeezing"; that is, of m oving som e of the quantum -fluctuations of laser light out of the cos[m (t - z/c)] part of the beam and into the sin[m (t - z/c)] part (Reference 95­ 100).16 The observable that gets squeezed will have its fluctuations reduced below the vacuum ZPF. The act of squeezing transform s the phase space circular noise profile characteristic of the vacuum into an ellipse, whose sem imajor and sem im inor axes are given by unequal quadrature uncertainties (of the quantized electrom agnetic field harm onic oscillator operators). This applies to coherent states in general, and the usual vacuum is also a coherent state with eigenvalue zero. As this ellipse rotates about the origin with angular frequency, w, these unequal quadrature uncertainties m anifest themselves in the electromagnetic field oscillator energy by periodic occurrences, which are separated by one quarter cycle, of both sm aller and larger fluctuations com pared to the unsqueezed vacuum . 16 to is the angular frequency of light, t is time, and z denotes the z-axis direction of beam propagation. Caves (Reference 101) points out that if one squeezes the vacuum —that is, if one puts vacuum rather than laser light into the input port of a squeezing device—then one gets at the output an electromagnetic field with weaker fluctuations and thus less energy density than the vacuum at locations where cos2[g>(C — z/c)] ^ 1 and sin2[®(t- z/c)] « 1; but with greater fluctuations and thus greater energy density than the vacuum at locations where cos2[w(t - z/c)] << 1 and sin2[©(t - z/c)] = 1. Since the vacuum is 32 UNCLASSI FIED//mp nFFTHAi iiccnMiu UNCLASSIFIED//FO R O FFICIAL UO £ O NLY defined to have vanishing energy density, any region with less energy density than the vacuum actually has a negative (renorm alized) expectation value for the energy density - hence, this is a degradable vacuum . Therefore, a squeezed vacuum state consists of a traveling electrom agnetic wave that oscillates back and forth between negative energy density and positive energy density, but has positive tim e-averaged energy density. For the squeezed electromagnetic vacuum state, the energy density pe-sq^ is given by (Reference 102): Pfi-sqvacI —j— sinh^[sinh^+cosh^cos(2co(f-z/c) + 5)J (J/m1) (6) where L3 is the volum e of a large box with sides of length L (that is, put the quantum field in a box with periodic boundary conditions), £ is the squeezed state am plitude (giving a m easure of the m ean photon number in a squeezed state), and 5 is the phase of squeezing. Equation (6) shows that p&sqvac falls below zero once every cycle when the condition coshi > sinh^ is m et. It turns out that this is always true for every nonzero value of ^ , so pE-sqvac becom es negative at som e point in the cycle for a general squeezed vacuum state. On another note, when a quantum state is close to a squeezed vacuum state, there will alm ost always be som e negative vacuum energy densities present. Dirac Vacuum Decay: "Sparking the Vacuum" Fulcher et al. (Reference 53), Rafelski and Muller (Reference 54), and Rafelski (Reference 55) describe a phenomenon whereby the QED vacuum 17 behaves like a nonlinear dielectric m edium and undergoes breakdown (or decay) in the vicinity of super-heavy (supercritical) atomic nuclei18 or in the presence of externally applied electric or m agnetic fields of critical (or supercritical) strength.19 This decay results in the spontaneous production of electron-positron pairs from the vacuum . This phenom enon is known as the Heisenberg-Euler-Schwinger m echanism , which Rafelski and collaborators euphem istically call "sparking the vacuum." Ringwald (Reference 104) prefers to call it "boiling the vacuum." Supercritical atomic nuclei can be created by the slow collision of two uranium (or heavier) nuclei while critical/supercritical electric or m agnetic fields can be produced by ultrahigh intensity chirped-pulse am plification lasers (with power intensities on the order of 1019 to 1030 W /m 2). 17 For historical reasons, the QED vacuum is also called the "Dirac sea" or "Dirac vacuum" (Reference 103). 18 Supercritical atomic nuclei have an electric charge (proton number) of Z > 173, which produces supercritical electric fields. 19 The critical QED vacuum breakdown electric field strength is Ec = 2mt2c3/r\e ® 1018 Wm, where e is the electron charge (1.602 x 10 19 C). This quantity is defined by the total rest-energy of an electron-positron pair created from the vacuum divided by the electron's Compton wavelength. And the critical QED vacuum breakdown magnetic field strength is Bc = EJc = 1010 Tesla. Supercritical fields have strengths greater than Ec or Bc. To be m ore precise, when an electric field is m ade sufficiently strong so that the vacuum polarization (that is, virtual electron-positron pairs, aka ZPF) becom es real, then, due to charge conservation, the balancing charge m ust be elim inated, and so during the process of changing the vacuum from a neutral to a charged state, som e charge m ust be em itted. And if in the vicinity of the electric field of a super-heavy nucleus or of an externally applied electric or m agnetic field, the vacuum carries the charge of an electron, the em itted particle m ust always be a positron. Studies have 33 UNCLASSI FIED//EHR nFFTr™i mce^mi^ UNCLASSI FIED//FO R O FFICIAL USE O NLY shown that this positron m ust have a very well defined energy. The applied electric field determ ines how large this energy will be. If the electric/m agnetic field is increased above critical strength, then m ore electron-positron pairs will be produced from the vacuum . Clearly, the charged vacuum is a new ground state of space and m atter. The normal, undercritical, electrically neutral vacuum is no longer stable in supercritical fields: it decays spontaneously into the new stable but charged vacuum . Thus the standard definition of the vacuum , as a region of space devoid of real elem entary particles, is no longer valid in very strong external fields. The vacuum is better defined as the energetically deepest and m ost stable state that a region of space can have while being penetrated by certain fields. Magnetically Induced Decay of the Dirac Vacuum Xue (Reference 105, 106) developed a Dirac vacuum decay m echanism that is different from the Heisenberg-Euler-Schwinger m echanism and proposed that energy could be continuously extracted from it. He m odeled his decay m echanism after the (vacuum electrom agnetic) Casim ir effect wherein the vacuum state is m odified by boundary conditions. From an energetic point of view, the Casim ir effect can be physically understood as the following: 1) the continuous energy spectrum of vacuum electromagnetic fields is m odified by boundary conditions to be discrete; 2) the vacuum energy of the "final" vacuum state, com puted from the discrete energy spectrum in a given finite volum e, is sm aller than the vacuum energy of the "initial" vacuum state, com puted from the continuous energy spectrum in the sam e volum e; 3) as a result, the vacuum gains energy and becom es energetically unstable and has to decay from the "initial" vacuum state to the "final" vacuum state by quantum field fluctuations. This difference of vacuum energies between two vacuum states m ust be released, and this leads to the attractive and m acroscopic force observed in the Casim ir effect. Xue suggests that instead of m odifying the energy spectrum of virtual photons by boundary conditions as in the Casim ir effect, one should attem pt to vary the vacuum energy by m odifying the negative energy spectrum of virtual ferm ions (in the Dirac vacuum ) by an externally applied m agnetic field (of strength 8). In this case, the externally applied m agnetic field acts as a boundary condition on the Dirac vacuum . Xue defines the vacuum state with 8 = 0 as the "initial" vacuum state and the vacuum state with 8 * 0 as the "final" vacuum state. The negative energy spectrum 20 of the initial vacuum state is m odified to the negative energy spectrum 21 of the final vacuum state, due to the external m agnetic field. If the vacuum energy of the final 8*0 vacuum state m ade by virtual fermions fully filling its negative energy spectrum is 20 The negative and nondegenerate energy spectrum of free virtual charged fermions in the Dirac vacuum is: ef (Id) = “(d + Py + Pi + ^ ) ' where p is the magnitude of the fermion's momentum, (pKf py, pz) are the spatial momentum components, and m is the fermion's mass. This spectral energy density is integrated over all possible momentum states of the quantum field fluctuations in order to give the total (negative) Dirac vacuum energy. 21 The energy spectrum of virtual charged fermions in the presence of an external constant magnetic field (a.k.a. the Landau levels) is: el (^,«,/i) = “(/^2 + w‘+|e| ^(2« + l)-^/i) , where e is the fermion's bare charge, h = ±1 is the fermion's helicity, n = 0,1,2,3,..., and the magnetic field 8 is along the z-axis. This negative energy spectrum is degenerate in the phase space of (pX/ py). This spectral energy density is integrated over all possible momentum states of the quantum field fluctuations in order to give the total (negative) Dirac vacuum energy. 34 UNCLASSI FIED//fap nFFTr™i iiccnMiu UNCLASSIFIED//FO R O FFICIAL UO £ O NLY sm aller than that of the initial 8 = 0 vacuum state m ade by virtual ferm ions fully filling its negative energy spectrum, then the vacuum state gains energy and m ust decay from the initial vacuum state to the final vacuum state by quantum field fluctuations. The difference in vacuum energies between the two vacuum states m ust be released. Xue m akes all the usual vacuum expectation value renorm alization calculations upon ef and el, and found that the energetic difference between the vacuum states B = 0 and B * 0 is negative, indicating that the vacuum energy of the 8*0 state is sm aller than the vacuum energy of the 8 = 0 state; that is, the vacuum state gains energy when the external m agnetic field is applied to it. He shows that this effect occurs because in a finite volum e of space and with a finite m om entum cutoff at the Planck scale Ap, the total num ber of ferm ion states in the vacua of negative energy spectra ef and el are finite and all these ferm ion states of negative energy levels from -Ap to -me2 are fully filled. The negative energy spectrum ef is not degenerate, while the negative energy spectrum el is degenerate, and the total num bers of fermion states in both cases are the sam e. On the basis of quantum field fluctuations toward the lowest energy state and the Pauli principle, when the external m agnetic field is applied upon the vacuum, the vacuum reorganizes itself by fully filling all fermion states according to the degenerate negative energy spectrum el, instead of the nondegenerate ef. As a consequence, the vacuum m akes its total energy lower. The energy released by this decay process is: AE =-8aB 2V/3n, where 1/is the volum e of space occupied by the external m agnetic field, and a is the electromagnetic fine structure constant. In principle, this effect can occur for any value of the applied m agnetic field, and in this particular decay process a non-critical m agnetic field is required. Xue predicts possibly observable effects such as the vacuum acting like a param agnetic m edium that effectively screens the strength of the external m agnetic field to a sm aller m agnitude; the associated ZPF could lead to the em ission of neutrino-antineutrino pairs from the vacuum ; and photons will be spontaneously em itted. He estim ated that the released vacuum energy (ae) will be about 1 percent of the total energy stored in the external m agnetic field, so it is not yet clear whether this vacuum decay m echanism will lead to any beneficial energy extraction. Melting the QCD Vacuum The idea of supercriticality as discussed in Section V also has applications in other field theories, such as those of pion fields, gluon fields (quantum chromodynam ics or QCD), and gravitational fields (general relativity). Static fields that are strong enough to cause the norm al vacuum , which is devoid of real particles, to break down into a new vacuum in which real particles exist is also predicted for these fields. A review a vacuum decay concept that is different from supercriticality in QCD theory follows. In their study of the structured vacuum , Rafelski and Muller (Reference 54) and Rafelski (Reference 55) analyze the nature of the strongly interacting (QCD) vacuum and elucidate its character from the Standard Model of particle physics and high energy particle accelerator data. They concluded that in addition to the electroweak vacuum (that is, the unified electromagnetic and weak force vacua) there exists a dual QCD vacuum structure: one vacuum structure that is everywhere in space and consists of a com plicated soup of interacting gluons which confine the quarks - this is called the ordinary or "frozen" vacuum ; and another vacuum structure that is found inside 35 UNCLASSI FIED//mp nFFTr™i mce^mi^ UNCLASSI FI ED//FO R O FFICIAL USE O NLY elem entary particles (for exam ple, hadrons), and which behaves like the dielectric vacuum of electrodynam ics. In this second vacuum structure, particles that have a strong charge (such as quarks or gluons) can m ove freely, but are confined by the frozen vacuum that is everywhere else. This is called the perturbative, or gluon, or "m elted" vacuum, which can also be pictured as a quark-gluon plasm a. They estim ate that there is a "latent heat" of ~ 1 GeV/fm 3 (or 1035 J/m 3)22 associated with the phase change of transforming from one vacuum structure to another when the gluonic structures of the perturbative vacuum are m elted. It is im portant to point out here that this is a degradable vacuum structure. 221 GeV = 109 eV; 1 fm = 10 15 m. 23 In quantum field theory, the vacuum expectation value (of a quantum operator) is also called a "condensate," and this is denoted by placing angular brackets around the quantum operator. 24 See Appendix A for a detailed explanation of the QCD bag model. This unusual dual vacuum structure led Rafelski and Muller to speculate on a m echanism for the "burning of m atter" as the ultim ate source of energy in which it m ight be possible that the energy contained within baryons could be converted into useful energy. Their idea is to rem ove or destroy the three quarks residing inside a baryon in order to gain energy, the latent heat, from the m elted vacuum inside the baryon. This process also entails the decay of the quarks via lepton-quark interactions, which is a topic that is beyond the scope of this chapter. They suggest that it m ight be possible that producing a quark-gluon plasma in high energy nuclear collisions could be a very efficient source of energy. In this process atomic nuclei would be collided at high energy in order to form a com pressed high density zone in the region where the two nuclei overlap. This would lead to the m elting of the vacuum and the subsequent direct conversion of m atter into radiation, thus releasing ~ 1035 J/m 3 of energy density. This m agnitude of energy density would be very useful as a source of energy for space propulsion applications. Rafelski and Muller point out that the com m only held view that the centers of neutron stars are dead and cold, due to their nuclear fuel having burnt out and the energy of gravitational collapse having been expended for the conversion of the collapsed star into a gigantic atom ic nucleus, is not the com plete story. They hold open the possibility that the entire rest-mass of all the baryons inside neutron stars m ight becom e available and converted into heat. In their scenario, the core of a neutron star is actually com posed of condensed quark m atter, and the rest-mass of baryons is burnt up into radiation inside the quark core. They also point out that supernovae explosions, gam ma ray bursts, positron em ission from the center of our galaxy, quasars, and galactic nuclei have been observed to em it extrem e am ounts of thermal energy, the m echanism s of which are still not understood today. Gogohia (Reference 107, 108) m odeled Rafelski and Muller's idea by using an effective potential approach for com posite condensate23 operators to formulate a general m ethod of calculating the non-perturbative (NPC) Yang-Mills vacuum energy density (aka the QCD bag m odel constant, B g)24 in the covariant gauge QCD vacuum -ground state. His result that B g = 1.84 GeV/fm 3 (or 2.95 x 1035 J/m 3) found very good agreem ent with its phenom enological value and with Rafelski and Muller's naive estim ate. Gogohia also calculated the contribution of the gluon condensate energy density to B g: (asf2/n> = 1.82 GeV/fm 3 (or 2.92 x 1035 J/m 3), where as is the strong 36 UNCLASSI FIED//Fnp nFFTr™i iiccnMiu UNCLASSI FIED//FO R O FFICIAL USE O NLY coupling strength (aka quark-gluon coupling) and r is the gluon field strength tensor (tensor indices suppressed). The quark condensate energy density contribution to B g is down by two orders of m agnitude from this estimate. Gogohia argues that the bag constant determ ines the energy which can be released from the NPC vacuum , which he considers to be a "perpetuum source of infinite energy." He did not propose a detailed physical m echanism that specifies how to release a finite portion of the bag constant energy or whether one could introduce som e type of cyclic process to extract energy. This requires further research in order to resolve this question. Summary: ZPF Modes and Vacuum Field Energy The previous exam ples illustrate how the vacuum becom es degradable or can decay when perturbed under certain conditions. In each of the exam ples, the vacuum ZPF m odes were perturbed by boundary conditions, quantum optics effects, or interacting/externally applied fields in such a way as to drive the QED field's vacuum state energy below zero, or the QED vacuum undergoes decay along with the spontaneous production of particle-antiparticle pairs, or the vacuum undergoes a phase change and releases energy as in the QCD case. The (electromagnetic) Casim ir effect is an exam ple in which certain ZPF m odes are excluded by physical boundary conditions that perturb the free-space vacuum ZPF m odes, thus driving the vacuum electromagnetic field energy below zero inside a Casim ir cavity. In accordance with the discussion in Sections III and V, the ZPF m odes serve only as a placeholder for a quantum field's vacuum state calculations. Therefore, the "hardwired" ZPF m odes cannot be driven below the ground state. It is only a quantum field's overall (renormalized) vacuum state energy that can be driven down to or below the ground state. The QED vacuum (in both of its incarnations: virtual bosonic electrom agnetic vacuum and virtual ferm ionic Dirac vacuum ) and the QCD vacua are degradable while both can also undergo decay via numerous m echanism s. Energy release is predicted for som e of the decay m echanism s while it has already been observed via the Casim ir effect and the inflationary expansion of the universe. Therefore, one can conjecture that the key to exploring the possibility of extracting energy from the vacuum is to invent new boundary conditions or new com binations of boundary conditions as well as new m ethods of m odifying the quantum vacuum boundary conditions that perturb the ZPF m odes of any quantum field under study. Quantum vacuum boundary conditions can take m any different form s: they can be physical boundaries like the conductor or dielectric plates used in Casim ir cavities, which can also involve com plex cavity geom etries; they can be topological—that is, complex spacetim e geom etries with special coordinate constraints; or they can be in the form of interacting or externally applied fields such as gravitational, electrom agnetic, electroweak, scalar, QCD, m assive fields or dense, m oving nuclear m atter on the quantum vacuum , and so forth. This is a topic that is in need of dedicated theoretical and experim ental research (Reference 62, 91, 103). VI. Conclusion: The Way Forward W hat are the conclusions that can be drawn from the considerations presented in this report regarding the concept of continuous conversion of energy from the quantum electromagnetic vacuum , the Dirac vacuum , or even the QCD vacua? UNri ACCTFTFD/yFnP HEFTCmi ■■« am. u 37 UNCLASSI FIED//FO R O FFICIAL USE O NLY First, one sees that although the original inspiration for the concept of continuous vacuum energy extraction cam e from second-quantized QED theory, it m ust be acknowledged that QED, as an axiomatic, quantized form alism based on the concept of an im m utable, non-degradable vacuum, does not support the concept of continuous vacuum energy conversion. Given that second-quantized QED is our m ost com prehensive quantum theory to date, its lack of support for continuous vacuum energy conversion m ust be given serious consideration. Second, SED as an alternative theory, whose form alism has been taken to support the concept of continuous vacuum energy conversion, has enough shortcom ings in its current state of developm ent that one m ust conclude that it is not at present an adequate tool for the assessm ent of potential vacuum energy conversion. SED predictions m ust thus rem ain suspect in the absence of experim ental confirm ation. The purpose of the experim ental program outlined in Section IV is m eant to address this need. Third, the concept of the conversion of energy from vacuum fluctuations is in principle not falsifiable, given the unknowns which present theory has yet to resolve (for exam ple, cosm ological dark energy, m ultiple vacuum structures), and the num erous approaches currently being brought to bear in the developm ent of quantum theory. Finally, even though experimental efforts at energy extraction from the vacuum have been proposed or are already under way at various laboratories, definitive theoretical support underpinning the concept of useful extraction of energy from quantum fluctuations is not yet in place. Such support awaits theoretical developm ents that either posits a plenum that (unlike second-quantized QED) can be shown to be degradable, or posit conversion of energy associated with m atter fluctuations, also in a degradable fashion. Since the quantum fluctuations of interest are associated with quantum ground states, what is m inim ally required are particle-vacuum or particle­ particle interactions that result in the form ation of alternate lower-energy, ground states of m atter/field configurations. Suggested approaches to be explored are those which are known to yield results consistent with the existence of vacuum fluctuation fields, but without the form alism of independently postulated second-quantized vacuum fields. W hether useful conversion of energy from quantum fluctuations can be accom plished, and identifying the unequivocal conditions under which this can be achieved, are yet to be determ ined. It has been shown that the QED vacuum is in fact degradable under the action of a variety of Casim ir effects, quantum optical vacuum squeezing, gravitation-induced vacuum squeezing, or gravitational redshifting. There is also QED vacuum decay via the critical/supercritical electric fields of superheavy atom ic nuclei, X-ray free-electron lasers, or externally applied (non-critical) m agnetic fields. However, it is not known whether these effects can be exploited for the continuous extraction of useful energy from the vacuum . The concept of a dual, degradable vacuum structure in QCD can possibly lead to the generation of useful energy via the release of latent heat from m elting the QCD vacuum . A gam e changer m ay appear that could dram atically accelerate or alter the direction of theoretical and experim ental program s. Such a gam e changer could entail a com plete, com prehensive unified field theory (that is, a finalized quantum superstring theory, or som e other theory that replaces it), or a com pletely new theory for the quantum 38 UNCLASSI FIED//EHR nFFTr™i iiccnMiu UNCLASSIFIED//FO R O FFICIAL UO £ O NLY vacuum and its related spacetim e physics (for exam ple, "em ergent" spacetim e/gravity theories (Reference 109-111)). New m aterials or com binations of m aterials, such as condensed m atter (superconductors), sem iconductors or m etam aterials, would also be an im portant gam e changer because of the unique ways that quantum fields would interact with them to produce phenom ena of interest. In going forward to the potential dem onstration of continuous energy extraction from the vacuum , one should consider the following additional action item s for further R&D: • The quantum vacuum electromagnetic effects outlined in Section IV were com puted to scale with Planck's constant and are therefore very sm all. In order to have a practical device based on quantum vacuum properties, it would be preferable that the vacuum effects the scale, m eaning that the effects are essentially independent of Plank's constant and consequently m ay be m uch larger. B y itself this requirem ent does not guarantee a large enough m agnitude, but it certainly helps. Electromagnetic Casim ir effects are typically sm all and difficult to m easure. In fact, m easurem ents have only been m ade for sim ple geom etries such as the parallel plate or the sphere-plate geometries. This fact raises a question: Is it possible to am plify these effects and bring them into a useful range? This is certainly one of the challenges of vacuum engineering. The experim ent described in Section IV could address this question. • Experim ents are needed to explore som e of the issues that are beyond the present com putational ability of QED; for exam ple, the effect of com plex geom etries on vacuum forces, or the effect of interacting or externally applied fields or dense, m oving nuclear m atter on the quantum vacuum . Is it possible to m ake a stable vacuum field that has a large variation in energy density? Can energy density gradients be found on a length scale that is useful for technological applications? One needs to greatly increase our knowledge of the quantum vacuum . The developm ent of a very sensitive sm all probe that provides a frequency decom position of the local vacuum energy density would very useful. - A first step in this direction was recently proposed by Marecki (Reference 112) who generalized the analysis of the output of balanced hom odyne detectors (B HDs). The m ost im portant feature of these devices is their ability to quantify the quantum vacuum fluctuations of the electric field because the output of B HDs provides inform ation on the one- and two-point functions of arbitrary states of quantum fields. Marecki com puted the two-point function and the associated spectral density for the ground state of the quantum electric field in Casim ir geom etries, and predicts a position- and frequency-dependent pattern of B HD responses if a device of this type is placed inside a Casim ir cavity. The proposed device allows for the direct detection of quantum vacuum fluctuations and provides a spatial m apping of the vacuum energy contained inside the cavity. This offers a potential new characterization of ground states in Casim ir geom etries, which would provide an understanding of the vacuum energy densities present in som e regions in these geometries. • From the status of current research in Casim ir forces, it is clear that one is at the cusp of describing the properties of the quantum vacuum for real system s with real m aterial properties. For exam ple, there is no general agreem ent regarding the calculations of static vacuum forces for geom etries other than infinite parallel plates 39 U N CLASSI FI E D//mp nFFTr™i mce^mi^ UNCLASSI FIED//FO R O FFICIAL USE O NLY of ideal or real m etals at a temperature of absolute zero. Non-zero tem perature corrections for flat, real m etals are uncertain. There are fundam ental disagreem ents about the com putation of vacuum forces for spheres or rectangular cavities, and about how to handle real m aterial properties and curvature in these and other geom etries. Indeed, it is very difficult to calculate Casim ir forces for these sim ple geom etries and to relate the calculations to an experiment. Calculations have yet to be done for m ore com plex geometries. The usual problem s in QED (for exam ple, divergences due to unrealistic boundary conditions, to curvature, to interfaces with different dielectric coefficients) abound. These problem s require theoretical and experim ental resolution. • As stated in Section V, there is need to find new boundary conditions for the vacuum that can alter the vacuum energy density by orders of m agnitude m ore than with the current boundary conditions, which are primarily m etallic or dielectric surfaces. Perhaps the use of new m aterials (for exam ple, those with a negative index of refraction, or an ultra-high electrical carrier density, either steady state or transient), or novel condensed m atter (superconducting) m aterials m ay open the door to new Casim ir phenom ena. Recently the use of (negative index) metamaterials was proposed to m ake a repulsive Casim ir force (Reference 113). W ith significantly increased funding for research, som e breakthroughs in this area m ight be possible. • There are several im portant experim ents that can aid our understanding of vacuum energy and Casim ir forces that m ay lead to significant im provem ents in our engineering capability: - Experim ents m easuring the Casim ir forces for sem iconductor surfaces would be helpful in the developm ent of new applications of vacuum forces and to dem onstrate that it is possible to alter the Casim ir force by altering the carrier density. - The m easurem ent of Casim ir forces and energies for different geom etry and com position objects, such as rectangular cavities or spheres, would provide data for theoretical m odeling. Measurements of Casim ir forces between separate, nonplanar surfaces are also needed. There m ay be surfaces that have larger forces than the classic parallel plates. - New boundary conditions or new m ethods of m odifying the known quantum vacuum boundary conditions m ay be needed to generate the large changes in free-field vacuum energy required if "vacuum engineering" as proposed in this report is ever to becom e practical. For example, the vacuum energy density difference between parallel plates and the region outside them in free space is sim ply not large enough in m agnitude for large-scale engineering purposes. Energy densities, positive or negative, that are orders of m agnitude greater are required. Such energy density regions m ay be possible, at least in som e cases. For exam ple, a region appeared in the one-dim ensional dynamic system in which the energy density was below that of the Casim ir parallel plate region (Reference 114). - Experim ents to verify the adiabatic Casim ir effect have been suggested in the literature. This is an im portant theoretical issue that has ram ifications in different 40 UNCLASSI FIED//EHR nFFTr™i iiccnMiu UNCLASSIFIED//FO R O FFICIAL UO £ O NLY fields, including astrophysics and elementary particle physics. Clever experim ental approaches should be developed to explore the adiabatic Casim ir effect. • There are num erous potential ways in which the ground state of the vacuum electromagnetic field m ight be engineered for use in MEMS and NEMS applications. • Dirac vacuum decay via external (non-critical) m agnetic fields requires further evaluation, and it should becom e possible to experim entally test this in the laboratory within two to five years. • Theoretical and laboratory studies of the dual QCD vacuum have been underway for over 20 years. The progress in experim ental particle physics is such that one gains an order of m agnitude in the resolution (that is, energy) of elementary particle structures roughly every decade. It is hoped that the com m issioning of the Large Hadron Collider will lead to higher resolution probing of the dual QCD vacuum structure, and help to determ ine whether there are deeper grand unified and/or Higgs vacuum structures residing within quarks. Future accelerator experim ents should be designed to explore Rafelski and Muller's and Gogohia's proposal to extract energy from the "m elted" QCD vacuum . Acknowledgements The author wishes to thank colleagues H. E. Puthoff (EarthTech, Int'l), V. Teofilo (Lockheed Martin), B . Haisch (ManyOne Networks), L. J. Nickisch (Northwest Research Assoc.), A. Rueda (California State University-Long B each), D. C. Cole (B oston University), M. Ibison (Inst, for Advanced Studies at Austin), S. Little (EarthTech Int'l), and M. Little (EarthTech Int'l), for their technical contributions to this report. W e also thank J. Newm eyer (Lockheed Martin), E. H. Allen (Lockheed Martin), T. W . Kephart (Vanderbilt Univ.), and P. C. W . Davies (Arizona State Univ.) fortheir very useful input. 41 U N CLASSI FI E D//mp nFFTr™i ..ccamiu UNCLASSI FIED//FO R O FFICIAL USE O NLY Appendix: The QCD Bag Model W hen considering the effective m asses of quarks bound within hadrons, it is com m on to think of the constituent m asses of the quark and antiquark pair as their zero-point energy (ZPE) when they are bound by the confining potential25 (acting between a quark and an antiquark) with an energy spectrum that corresponds to the m asses of the observed m esons. For charm , and heavier quarks, it appears that the total ZPE is not m uch different from the m asses of the lowest-lying m eson states. This picture also holds true for baryons. The quark-gluon m odel for hadrons is called "the bag m odel." 25 Quarks carry "color charge" as well as electric charge. Color charge is considered to be the "true" charge of strong interactions. Gluons are the "photons" of strong interactions, and color is exchanged by eight bicolored gluons, which are massless and have spin 1. Color interactions are assumed to be a copy of electromagnetic interactions. Theoretical and phenomenological studies found that the confining potential U(r) lies between a Coulomb and a harmonic oscillator potential: V(r) = -(4a5 /3r) + kr, where r is the radial distance between confined quarks, k is a constant parameter, and f is the color factor associated with as for the case of quark- antiquark pair confinement in mesons. For the case of baryons (qqq), the color factor in U(r) is replaced by f . Even in an "em pty" bag—that is, one containing no quarks—there will be nonzero fields present because of quantum zero-point fluctuations (ZPF). This gives rise to a zero­ point (ZP) or Casim ir energy inside the em pty bag. The estim ated total ZP/Casimir energy of the confined gluon field inside a spherical bag is Ezp ~ +0.7/a (or +0.7Ac/a in MKS units), where a is the radius of the bag in GeV 1 units. Ezp is num erically the entire story because the ZPE contribution of the confined ferm ion (quark) field is far sm aller than Ezp (the leading approximation per degree of freedom is down by two orders of m agnitude). A typical em pty bag has an estim ated radius a « 2.6 GeV-1 (0.5 fm ), so Ezp ~ 10 1 GeV (or 10-11 J), and this result rem ains approxim ately true if one uses a = 5.07 GeV-1 (1 fm ) for a nucleon-sized bag. If the bag contains quarks, then this result does not change because the quarks don't affect the ongoing quantum ZPF inside the bag due to asym ptotic freedom . The inventor of the em pty bag m odel (Ken Johnson) proposed that space is filled with closely packed em pty bags, and that the energy of space filled with contiguous bags is sim ply the sum of the field energies contained within each bag. B ut this is not widely accepted since the phenom enologically preferred m odel for the exterior "ordinary" vacuum is given as follows. QCD color confinem ent in hadrons is approxim ated by the phenom enologically successful "bag m odel." In this m odel, the "ordinary" vacuum external to hadrons is a perfect color m agnetic (or chrom omagnetic) conductor; that is, the chrom om agnetic perm eability p is infinite, while the chromom agnetic vacuum in the interior of the bag is characterized by p = 1. This im plies that the color electric (B qcd) and m agnetic (B qcd) fields are confined to the interior of the bag, and that they satisfy the following boundary conditions on its surface S: n ■ B qcdIs = 0, n x B qcdIs = 0, where n is a unit norm al vector to S. In other words, this m odel defines QCD vacua that coexist in two phases: 1) an ordinary vacuum exterior to the bag, im penetrable to color; and 2) a vacuum interior of the bag, in which the Yang-Mills fields that carry color (gluons) propagate freely. B oth phases are separated by the surface boundary of the bag upon which the Yang-Mills and ferm ion (quark) field satisfy the aforem entioned boundary 42 U N CLASSI FI E D/ ^EQ&AEEIG MUUSMNW ^ UNCLASSIFIED//FO R O FFICIAL UO £ O NLY conditions. 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