Extraction of Zero-Point Energy from the Vacuum: Assessment of Stochastic Electrodynamics-Based Approach As Compared to Other Methods

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Article Extraction of Zero-Point Energy from the Vacuum: Assessment of Stochastic Electrodynamics-Based Approach as Compared to Other Methods

Garret Moddel * and Olga Dmitriyeva

Department of Electrical, Computer, and Energy Engineering, University of Colorado, Boulder, CO 80309-0425, USA; [email protected] * Correspondence: [email protected]; Tel.: +1-303-492-1889

Received: 16 February 2019; Accepted: 17 May 2019; Published: 23 May 2019

Abstract: In research articles and patents several methods have been proposed for the extraction of zero-point energy from the vacuum. None of the proposals have been reliably demonstrated, yet they remain largely unchallenged. In this paper the underlying thermodynamics principles of equilibrium, detailed balance, and conservation laws are presented for zero-point energy extraction. The proposed methods are separated into three classes: nonlinear processing of the zero-point ﬁeld, mechanical extraction using Casimir cavities, and the pumping of atoms through Casimir cavities. The ﬁrst two approaches are shown to violate thermodynamics principles, and therefore appear not to be feasible, no matter how innovative their execution. The third approach, based upon stochastic electrodynamics, does not appear to violate these principles, but may face other obstacles. Initial experimental results are tantalizing but, given the lower than expected power output, inconclusive.

Keywords: zero-point energy; quantum vacuum; vacuum energy; detailed balance; casimir cavity; stochastic electrodynamics

1. Introduction We present results from a set of experiments in which we attempted to extract quantum vacuum energy from a gas flow system based upon stochastic electrodynamics principles. To put this method in context we first outline other methods that have been proposed for harvesting this energy. The methods are divided into three classes, and the underlying principle of operation for each is assessed in terms of which would violate fundamental thermodynamics principles. Physical effects resulting from zero-point energy (ZPE) are well established ([1], Chapter 3). This has led to several proposals and reviews discussing the extraction of ZPE to use as a power source [2–9]. The ZPE extraction methods usually involve ZPE in the form of electromagnetic zero-point fields (ZPFs). The energy density of these ZPE vacuum fluctuations is ([1], p. 11): ! 8πν2 hν hν ρ(hν) = + , (1) c3 exp(hν/kT) 1 2 − where ν is the frequency, and k is Boltzmann’s constant. The first term in the large brackets describes Planck radiation from a black body at temperature T. At room temperature, at frequencies above 7 THz, the energy density is dominated by the second, temperature-independent term, which is due to zero-point energy. For high frequencies this energy density is large, but just how large depends upon the frequency at which the spectrum cuts off, a matter that is not yet resolved.

Atoms 2019, 7, 51; doi:10.3390/atoms7020051 www.mdpi.com/journal/atoms Atoms 2019, 7, 51 2 of 18

Two physical manifestations of the ZPF that will be discussed in this paper are zero-point noise fluctuations and the force between Casimir cavity plates. The available noise power in a resistance R per unit bandwidth is [10] ∆V2 hν hν = + , (2) 4R exp(hν/kT) 1 2 − The first term on the right-hand side is the thermal noise, which is approximated at low frequencies by the familiar Johnson noise formula. The second term, usually called quantum noise, is due to zero-point fluctuations. This physical manifestation of the ZPF dominates the noise at low temperatures and high frequencies. A second physical manifestation is evident with a Casimir cavity, which consists of two closely-spaced, parallel reflecting plates [11]. Because the tangential electric field is reduced (to zero for a perfect conductor) at the boundaries, limits are placed on the ZPF modes between the plates, and those modes having wavelengths longer than twice the gap spacing are suppressed to a degree determined by the plate reflectivity. This suppression is not imposed on the ZPF on the exterior side of the plats. The radiation pressure exerted on the exterior side of the plates is larger than on the interior, with the result that the plates are pushed together. The resulting attractive force between the plates is ([1], p. 58): π2}c F(d) = , (3) 240d4 where d is the gap spacing. For this force to be measurable with the currently available experimental techniques, d must be less than 1 µm. The benefits of tapping ZPE from the vacuum would be tremendous. Assuming even a conservative cutoff frequency in Equation (1), if just a small fraction of this energy were available for extraction, the vacuum could supply sufficient power to meet all of our needs for the foreseeable future. Cole and Puthoff [12] have shown that extracting energy from the vacuum would not, in principle, violate the second law of thermodynamics, but that is not equivalent to stating that extraction is feasible, nor do they attempt to describe how it could be accomplished. There is no verifiable evidence that any proposed method works [13], and there has been a continuing debate as to whether ZPE is fundamentally extractable [14]. In this article, we assess different methods that have been proposed to extract usable ZPE. We do not examine proposed methods to use ZPE forces as a means to enhance or catalyze the extraction of energy from other sources, such as chemical [15] or nuclear energy. We separate the different vacuum energy extraction approaches into three classes: nonlinear extraction, mechanical extraction, and pumping of gas. We analyze each to see if the underlying principles of operation are consistent with known equilibrium thermodynamics principles, and then draw conclusions about the feasibility of the ZPE extraction. Finally, we describe a method based on a stochastic electrodynamics picture of ZPE and present initial experimental results using the approach.

2. Analysis

2.1. Nonlinear Processing of the Zero-Point Field

2.1.1. Rectification of Zero-Point Fluctuations in a Diode Several suggested approaches to extracting energy from the vacuum involve nonlinear processing of the ZPF. One particular nonlinear process is electrical rectification, in which an alternating (AC) waveform is transformed into a direct (DC) one. Valone [9] describes the electrical noise in resistors and diodes that results from zero-point fluctuations. He discusses the use of diodes to extract power from these ambient fluctuations, and compares this to diodes used for thermal energy conversion. For example, in thermophotovoltaics radiation from a heated emitter is converted to electricity. In Valone’s case, however, the source is under Atoms 2019, 7, 51 3 of 18 ambient conditions. In support of Valone’s approach, a straightforward analysis of diode rectification Atoms 2019, 7, x FOR PEER REVIEW 3 of 18 in the presence of thermal noise does appear to produce a rectified output from that noise unless aunless compensating a compensating current current is added is added to the to system the system [16]. [16]. Valone Valone is particularly is particularly interested interested in thein the use use of zero-biasof zero-bias diodes diodes for for zero-point zero-point energy energy harvesting, harvesting so, so as as to to rectify rectify the theambient ambient fluctuationsfluctuations withoutwithout having to supply power in providingproviding aa voltagevoltage biasbias toto thethe diodes.diodes. This nonlinear extraction represents aa sortsort ofof Maxwell’s demondemon [[17].17]. In 1871 Maxwell developed a thought experiment in which a tiny demon operates a trapdoor to separate gas in equilibrium into two compartments, one holding more energetic mole moleculescules and the other holding holding less less energetic energetic ones. ones. Once separated, the resulting temperature didifferencefference could be usedused toto dodo work.work. This is a sort of nonlinear processing, in which the system, consistingconsisting of the demon and the compartments, operates didifferentlyfferently on a moleculemolecule depending upon its thermalthermal energy. In the nearly fifteenfifteen decades since its creation, innovativeinnovative variations variations on on the the original original demon demon have have been been proposed proposed and then and found then tofound be invalid. to be Despiteinvalid. theDespite best ethefforts best of Maxwell’sefforts of Maxwell’s demon and demon his scrutineers and his [scrutineers18,19] there [18,19] still is nothere corroborated still is no experimentalcorroborated evidenceexperimental for the evidence demon’s for viability the demon’s [20], and viability for the [20], current and analysesfor the current I will assumeanalyses that I will he cannotassume assist that he us cannot in extracting assist us energy in extrac fromting a system energy in from equilibrium. a system in equilibrium. In the absenceabsence ofof suchsuch aa demon,demon, thermalthermal noisenoise fluctuationsfluctuations cannotcannot be extractedextracted without the expenditure of additional energy, becausebecause suchsuch fluctuationsfluctuations areare inin aa state of thermal equilibrium with their surroundings [[21].21]. These thermal fluctuations fluctuations ar aree described by the firstfirst term on the right-hand side of EquationEquation (2).(2). In equilibrium, the second law of thermodynamicsthermodynamics applies and no system can extract power continuously.continuously. All processes in such aa systemsystem areare thermodynamicallythermodynamically reversible.reversible. A detailed balance description of the kinetics of such a situation was developed by Einstein to explain the relationship between the emission and absorptionabsorption spectra of atoms [[22],22], and discussed as a manifestation of equilibrium by Bridgman [[23].23]. If thethe equilibriumequilibrium is is altered, altered, for for example example by by the th additione addition of aof non-equilibrium a non-equilibrium radiation radiation field, field, then thethen detailed the detailed balance balance is replaced is replaced by a less by restrictivea less restrictive steady statesteady condition state condition and it becomes and it becomes possible topossible extract to power. extract power. The diff Theerence difference between between detailed detailed balance balance and steady and steady state state is illustrated is illustrated with with the three-statethe three-state system system shown shown in Figure in Figure1. Each 1. Each arrow arro representsw represents a unit a ofunit energy of energy flux. Influx. the In steady-state the steady- casestate showncase shown in Figure in 1Figurea, the total1a, the flux total into anyflux stateinto equalsany state the equals total flux the out total of it.flux Under out equilibrium,of it. Under however,equilibrium, a more however, restrictive a more detailed restrictive balance detailed must be observed,balance must in which be observed, the flux between in which any the pair flux of statesbetween must any be pair balanced. of states This must is depictedbe balanced. in Figure This 1isb. depicted in Figure 1b.

Figure 1. IllustrationIllustration of of detailed detailed balance. balance. In In this this three- three-statestate system system each each arrow arrow represents represents one one unit unit of ofenergy energy flux. flux. The The system system in ( ina) is (a )in is steady in steady state, state, such such that thatthe tota thel total flux fluxinto intoeach eachstate stateequals equals the total the totalflux out flux of out it; of In it; system In system (b) (notb) notonly only does does the the steady-state steady-state condition condition apply, apply, but but the the more more restrictive detailed balance also applies, in which thethe fluxflux betweenbetween eacheach pairpair ofof statesstates isis balanced.balanced.

This concept of detailed balance can be applied to the extraction of thermal noise from a resistor at ambientambient (equilibrium)(equilibrium) temperature. temperature. To To optimally optimally transfer transfer power power from from a source, a source, in this incase this thecase noisy the resistor,noisy resistor, to a load to thea load load the resistance load resistance should beshould adjusted be adjusted to match to that match of the that source. of the In source. that case, In that the loadcase, generatesthe load generates an equal noisean equal power noise to power that of to the that source, of the and source, an equal and poweran equal is power transferred is transferred from the from the load to the source as was transferred from the source to the load. Because of this detailed balance, no net power can be extracted from a noisy resistor. To analyze the case of extracting energy from thermal noise fluctuations in a diode, consider the energy band diagram for a diode shown in Figure 2, where transitions among three different states Atoms 2019, 7, 51 4 of 18 load to the source as was transferred from the source to the load. Because of this detailed balance, no net power can be extracted from a noisy resistor. AtomsTo 2019 analyze, 7, x FORthe PEER case REVIEW of extracting energy from thermal noise fluctuations in a diode, consider4 of 18 the energy band diagram for a diode shown in Figure2, where transitions among three di fferent are shown. For simplicity, five other pairs of transitions are not shown and are assumed to have states are shown. For simplicity, five other pairs of transitions are not shown and are assumed to negligible rates. (Not shown are (i) direct transitions between the p-type region valence band and the have negligible rates. (Not shown are (i) direct transitions between the p-type region valence band n-type region conduction band; (ii) transport of valence-band charge carriers (holes) through the and the n-type region conduction band; (ii) transport of valence-band charge carriers (holes) through junction region; (iii) generation and recombination in the n-type region; (iv) direct transitions the junction region; (iii) generation and recombination in the n-type region; (iv) direct transitions between the n-type region valence band and the p-type region conduction band; and (v) generation between the n-type region valence band and the p-type region conduction band; and (v) generation and recombination in the junction region. A completely parallel set of processes could be added for and recombination in the junction region. A completely parallel set of processes could be added for these transitions, and would not change the physical principles involved, or the conclusions drawn.) these transitions, and would not change the physical principles involved, or the conclusions drawn.)

Figure 2. Diode energy band diagram. Shown are electron transitions between the conduction and valenceFigure 2. bands Diode in energy the p-type band region, diagram. corresponding Shown are to electr generationon transitions rate g, and between recombination the conduction rate r. Alsoand shownvalence arebands electron in the transitions p-type region, between corresponding n-type and to p-type generation conduction rate g, and band recombination states, corresponding rate r. Also to excitationshown are rateelectrone, and transitions drift rate betweend. This diagramn-type and is usedp-type in conduction the text to illustrateband states, photovoltaic corresponding carrier to collection,excitation rate rectification e, and drift of thermal rate d. fluctuations,This diagram and is alsoused rectification in the text ofto zero-pointillustrate photovoltaic energy fluctuations carrier ascollection, proposed rectification by Valone of [9]. thermal fluctuations, and also rectification of zero-point energy fluctuations as proposed by Valone [9]. First consider the case of photovoltaic power generation. If the diode operates as a solar cell, light absorbedFirst inconsider the p-type the case region of generatesphotovoltaic electron-hole power generation. pairs, promoting If the diode electrons operates to theas a conduction solar cell, bandlight atabsorbed a rate g thatin the depends p-type upon region the lightgenerates intensity electron-hole and other factors. pairs, Thepromoting photogenerated electrons electrons to the diconductionffuse to the band junction at region,a rate whereg that the depends built-in electricupon fieldthe light causes intensity them to driftand acrossotherthe factors. junction The to thephotogenerated n-type region electrons at rate d. diffuse The recombination to the junction rate, regir, andon, thewhere excitation the built-in rate, eelectric, are also field shown. causes Because them gto>> driftr and acrossd >> thee under junction solar to illumination,the n-type region i.e.,the at rate system d. The is far recombination from equilibrium, rate, r there, and is the anet excitation flow of electronsrate, e, are to also the shown. n-type region,Because where g >> r they and ared >> collected e under tosolar provide illumination, power. i.e., the system is far from equilibrium,The diode there would is a net operate flow of in electrons much the to samethe n-type way region, for rectifying where they thermal are collected fluctuations to provide under equilibrium,power. except that now g would represent the thermal generation rate. In this case, however, the generationThe diode rate andwould drift operate rate across in themuch junction the same would wa bey muchfor rectifying smaller thanthermal under fluctuations solar illumination. under Underequilibrium, thermal except equilibrium that now and g inwould the absence represent ofa the Maxwell’s thermaldemon generati toon influence rate. In onethis of case, the processes,however, athe detailed generation balance rate is strictlyand drift observed, rate across such the that junctiong = r and wouldd = e. be The much second smaller law of than thermodynamics under solar doesillumination. not allow Under for power thermal generation. equilibrium and in the absence of a Maxwell’s demon to influence one of theValone’s processes, proposal a detailed [9] makes balance use is of strictly power observed, generation such in a that diode g from= r and ZPE d = fluctuations e. The second described law of bythermodynamics the second term does on thenotright-hand allow for power side of generation. Equation (2). Whether this is feasible becomes a question of whetherValone’s the proposal zero-point [9] energy makes in use a diode of power is in generation a state of true in a equilibrium diode from with ZPE itsfluctuations surroundings. described It has beenby the generally second term accepted on the that right-hand the “’vacuum’ side of shouldEquation be (2). considered Whether to this be ais statefeasible of thermal becomes equilibrium a question atof thewhether temperature the zero-point of T = 0” energy [12]. Recently, in a diode using is in the a state principle of true of equilibrium maximal entropy, with its Dannon surroundings. has shown It explicitlyhas been thatgenerally zero-point accepted energy that does, the in“’vacuum’ fact, represent should a statebe considered of thermodynamic to be a equilibriumstate of thermal [24]. equilibrium at the temperature of T = 0” [12]. Recently, using the principle of maximal entropy, Dannon has shown explicitly that zero-point energy does, in fact, represent a state of thermodynamic equilibrium [24]. Therefore, it is clear that the detailed balance argument presented above for the case of thermal fluctuations also applies to ambient zero-point energy fluctuations, and a diode cannot rectify these fluctuations to obtain power. Atoms 2019, 7, 51 5 of 18

Therefore, it is clear that the detailed balance argument presented above for the case of thermal fluctuations also applies to ambient zero-point energy fluctuations, and a diode cannot rectify these fluctuationsAtoms 2019, 7, xto FOR obtain PEER power.REVIEW 5 of 18

2.1.2. Harvesting of Vacuum Fluctuations Using a Down-Converter andand Antenna-CoupledAntenna-Coupled RectifierRectifier A somewhatsomewhat didifferentfferent approach approach to to the the nonlinear nonlinear processing processing of the of ZPF the forZPF extracting for extracting usable usable power wouldpower bewould to use be an to antenna, use an antenna, diode and diode battery. and The battery. radiation The isradiation received is by received the antenna, by the rectified antenna, by therectified diode, by and the the diode, resulting and the DC resulting power charges DC powe ther battery.charges Inthe the battery. microwave In the engineering microwave domain,engineering this rectifyingdomain, this antenna rectifying is known antenna as a is rectenna known as [25 a]. rectenna Because [25]. of its Becauseν3 dependence, of its ν3 dependence, shown in Equation shown (1), in theEquation ZPF power (1), the density ZPF power at microwave density at frequencies microwave is fr tooequencies low to provideis too low practical to provide power. practical Therefore, power. to obtainTherefore, practical to obtain levels practical of power, levels a rectenna of power, must a re operatectenna at must higher operate frequencies, at higher such frequencies, as those of such visible as lightthose or of even visible higher. light There or even are diodeshigher. that There operate are atdiodes petahertz that frequencies.operate at petahertz One example frequencies. is a graphene One geometricexample is diode a graphene [26] but geometric the rectification diode [26] power but ethefficiency rectification of optical power rectennas efficiency at such of optical high frequencies rectennas isat generallysuch high lowfrequencies [27]. The is first generally question low about [27]. The ZPF first rectification question isabout how ZPF it can rectification be made practical. is how it Thecan second,be made and practical. more important The second, question and more here, isimportant whether thisquestion is feasible here, from is whether fundamental this is considerations. feasible from Ifundamental address these considerations. in turn. I address these in turn. A method to extract ZPE is proposed in a 19961996 patentpatent by MeadMead andand NachamkinNachamkin [[4],4], which describes an invention to produce lower beat frequency from high-frequency ZPF to make it more practical to rectify. The invention includes resonant microscopic spheres that intercept ambient ZPF and build its intensity at their resonant frequency. The high-intensity oscillation induces interactions between two spheres of didifferentfferent size such that a lowerlower beat-frequencybeat-frequency radiation is emitted from them. This This lower beat-frequency radiation is said to be then absorbed by an antenna and rectifiedrectified to provide DC electrical power. (Note that the beat frequency is not frequency down-conversion, which requires a nonlinear mixer. The down-conversion oc occurscurs only after the signals encounter the diode, and soso thethe antennaantenna cannotcannot actually actually pick pick up up the the short-wavelength short-wavelength ZPF, ZPF, and and the the diode diode cannot cannot rectify rectify the high-frequencythe high-frequency ZPF.) ZPF.) The The invention invention is depicted is depicted in Figure in Figure3. 3.

Figure 3. Mead and Nachamkin’s invention [4] [4] for produc producinging a beat frequency from zero-point fieldfield radiation, and collecting, and rectifyingrectifying it.it. The non-identicalnon-identical microscopic resonant spheres interact with ambient zero-point fieldsfields to produce radiation at a beat frequency.frequency. This radiation is absorbed in the loop antenna and rectifiedrectified inin thethe circuit.circuit. Mead and Nachamkin’s approach can be broken down into three steps: Mead and Nachamkin’s approach can be broken down into three steps: (a) Producing lower beat frequency radiation from the ambient ZPF; (a) Producing lower beat frequency radiation from the ambient ZPF; (b) Collecting the beat-frequency radiation at the diode by the antenna; (b) Collecting the beat-frequency radiation at the diode by the antenna; (c) Rectification of the concentrated radiation by the diode. Step (a) is a process akin to that performed by the diode described in the previous section, except that in the current case the ZPF produces an intermediate beat frequency whereas in the previous case the ZPF fluctuations in a diode were down-converted to DC. Therefore, this step operating with incoming radiation under equilibrium must observe a detailed balance of rates. Regarding steps (b) Atoms 2019, 7, 51 6 of 18

Step (a) is a process akin to that performed by the diode described in the previous section, except that in the current case the ZPF produces an intermediate beat frequency whereas in the previous case the ZPF fluctuations in a diode were down-converted to DC. Therefore, this step operating with incoming radiation under equilibrium must observe a detailed balance of rates. Regarding steps (b) and (c), under equilibrium a source, antenna and load are in detailed balance, such that the power received by the antenna from the source and transferred to a load is equal to the power transmitted back to the source [28]. If steps (a) and (b) could provide a greater-than-equilibrium concentration of power to the diode, then the diode in step (c) would no longer be operating under equilibrium. When driven far from equilibrium the harvesting efficiency would be limited to the Carnot efficiency in a quantum heat engine, unless the extra energy somehow created some coherence [29]. However, as argued above, the concentration of power at the diode cannot occur under equilibrium. In summary, when applied to the harvesting of vacuum fluctuations each of the three steps in the ZPF down-converter system is subject to a detailed balance of rates, and therefore, the system cannot provide power.

2.1.3. Nonlinear Processing of Background Fields in Nature If nonlinear processing of ZPFs were sufficient to extract energy, one would expect to see the consequences throughout nature. Naturally occurring nonlinear inorganic and organic materials would down-convert the ZPF, for example, to the infrared. The result would be constant warmth emanating from these nonlinear materials. Such down-conversion may exist, but through detailed balance there must be an equal flux of energy from the infrared to higher-frequency background ZPF. For ZPFs to provide usable power, an additional element must be added beyond those providing nonlinear processing of ambient fields.

2.2. Mechanical Extraction Using Casimir Cavities The attractive force between two closely spaced conducting, i.e., reﬂecting, plates of a Casimr cavity was predicted by Casimir in 1948 [11], and is given by Equation (3). This attractive force was later shown to apply also to closely spaced dielectric plates [30], and becomes repulsive under certain conditions [31]. The potential energy associated with the Casimir force is considered next as a source of extractable energy [5,6]. The simplest way to extract energy from Casimir cavities would be to release the closely spaced plates so that they could accelerate together. In this way, the potential energy of the plate separation would be converted to kinetic energy. When the plates hit each other, their kinetic energy would be turned into heat. The Casimir cavity potential would be extracted, albeit into high-entropy thermal energy. If this energy conversion could be carried out as a cyclic process, electrical power obtained from this heat would be subject to the limitations of the Carnot eﬃciency:

Th Tc ηmax = − (4) Th where Th is the temperature of hot source and Tc is the temperature of the cold sink.

2.2.1. Energy Exchange between Casimir Plates and an Electrical Power Supply In 1984, Forward described a diﬀerent concept [2] for extracting energy from the mechanical motion of Casimir plates, one that maintains the low entropy of the Casimir cavity’s potential energy through the extraction process. A coiled Casimir plate is shown in Figure4. The attractive Casimir force between spaced-apart coils of the Casimir plates is nearly balanced by the injection of electric charge from an external power supply causing the plates to repel each other. As the plates move together due to the attractive Casimir force, they do work on the repulsive charge, resulting in a charge Atoms 2019, 7, 51 7 of 18

ﬂow and transfer of energy to the power supply. In this way, the coming together of the Casimir plates provides usable energy, and maintains the low entropy of the original attractive potential energy. Atoms 2019, 7, x FOR PEER REVIEW 7 of 18 Forward made no attempt to show how this would provide continuous power, since once the plates Atomscame 2019 together, 7, x FOR all PEER the availableREVIEW potential energy would be used up. 7 of 18

Figure 4. Slinky-like coiled Casimir cavity, as conceptualized by Forward [2]. He used this device conceptFigure 4.to Slinky-likedemonstrate coiled how one Casimir might cavity, convert as the conceptualized vacuum fluctuation by Forward potential [2]. energy He used from this Casimir device Figure 4. Slinky-like coiled Casimir cavity, as conceptualized by Forward [2]. He used this device attractionconcept to to demonstrate electrical energy. how one As the might plates convert approa thech vacuum each other fluctuation the repulsion potential of positive energy fromlike-charges Casimir concept to demonstrate how one might convert the vacuum fluctuation potential energy from Casimir resultsattraction in a to current electrical that energy. charges As up the an plates external approach power eachsupply. other the repulsion of positive like-charges attractionresults in ato current electrical that energy. charges As up the an plates external approa powerch each supply. other the repulsion of positive like-charges results in a current that charges up an external power supply. 2.2.2.2.2.2. Cyclic Cyclic Power Power Extraction Extraction from from Casimir Casimir Cavity Cavity Oscillations Oscillations 2.2.2.In InCyclic Forward’s Forward’s Power concept, concept,Extraction described described from Casimir in in the the Cavityprevious previous Oscillations section, section, energy energy is is extracted extracted from from the the Casimir Casimir force until the plates have come together, but continuous power extraction would require a cyclic forceIn until Forward’s the plates concept, have comedescribed together, in the but previous continuous section, power energy extraction is extracted would from require the Casimir a cyclic process. In a series of publications, Pinto proposed an engine for the extraction of mechanical energy forceprocess. until In the a series plates of have publications, come together, Pinto proposed but continuous an engine power for the extraction extraction would of mechanical require a energycyclic from Casimir cavities [6]. His concept makes use of switchable Casimir cavity mirrors. A schematic process.from Casimir In a series cavities of publications, [6]. His concept Pinto makes proposed use of an switchable engine for Casimirthe extraction cavity of mirrors. mechanical A schematic energy depiction of the process is shown in Figure 5. In step (a) the Casimir cavity plates are allowed to move fromdepiction Casimir of the cavities process [6]. is His shown concept in Figure makes5. In use step of (a)switchable the Casimir Casimir cavity cavity plates mirrors. are allowed A schematic to move together in response to their attraction, and the reduction in potential energy is extracted (for depictiontogether in of response the process to theiris shown attraction, in Figure and 5. the In reductionstep (a) the in Casimir potential cavity energy plates is extracted are allowed (for example,to move example, by the Forward method). In step (b) one of the plates is altered to change its reflectivity. togetherby the Forward in response method). to their In step attraction, (b) one of and the platesthe reduction is altered toin changepotential its reflectivity.energy is extracted Because of (for the Because of the altered state, the attractive Casimir force is reduced or reversed and the plates can then example,altered state, by the the Forward attractive method). Casimir forceIn step is reduced(b) one of or the reversed platesand is altered the plates to change can then its be reflectivity. separated be separated using less energy than was extracted when they came together, as depicted in step (c). Becauseusing less of energythe altered than state, was the extracted attractive when Casimir they came force together,is reduced as or depicted reversed in and step the (c). plates After can they then are After they are separated, the plates are restored to their original state, and the cycle is repeated. beseparated, separated the using plates less are energy restored than to theirwas extracted original state, when and they the came cycle together, is repeated. as depicted Puthoff inanalyzed step (c). a Puthoff analyzed a system of switchable Casimir cavity mirrors and calculated the potential power Aftersystem they of switchable are separated, Casimir the cavity plates mirrors are restored and calculated to their theoriginal potential state, power and thatthe couldcycle beis repeated. produced that could be produced by Casimir plates as a function of vibration frequency and mass [32]. Puthoffby Casimir analyzed plates a as system a function of switchable of vibration Casimir frequency cavity and mirrors mass [and32]. calculated the potential power that could be produced by Casimir plates as a function of vibration frequency and mass [32].

(a) (b ) (c)

Figure 5. Casimir cavity engine for the cyclic extraction of vacuum energy, similar to system proposed Figure 5. Casimir cavity engine for the cyclic extraction of vacuum energy, similar to system proposed by Pinto [6]. In step (a) the Casimir plates move together in response to Casimir attraction, producing by Pinto [6]. In step (a) the Casimir plates move together in response to Casimir attraction, producing Figureenergy 5. that Casimir is extracted; cavity engine In step for (b) the the cyclic lower extraction plate is altered of vacuum to reduce energy, its reﬂectivity similar to system and hence proposed reduce energy that is extracted; In step (b) the lower plate is altered to reduce its reflectivity and hence reduce bythe Pinto Casimir [6]. In attraction; step (a) the In stepCasimir (c) the plates plates move are together pulled apart, in response using lessto Casimir energy attraction, than that whichproducing was the Casimir attraction; In step (c) the plates are pulled apart, using less energy than that which was energyobtained that in is step extracted; (a), and In then step the (b) cycle the lower is repeated. plate is altered to reduce its reflectivity and hence reduce obtained in step (a), and then the cycle is repeated. the Casimir attraction; In step (c) the plates are pulled apart, using less energy than that which was obtainedPinto’s approach in step (a), cannot and then work the cycleif the is Casimir repeated. force is conservative. If so, no matter what process were to be used in separating the plates, it would require at least as much energy as had been Pinto’s approach cannot work if the Casimir force is conservative. If so, no matter what process extracted by their coming together. For example, in step (b) shown in Figure 5, electrical charge might were to be used in separating the plates, it would require at least as much energy as had been be drained from at least one of the plates to modify its reflective property. This would reduce the extracted by their coming together. For example, in step (b) shown in Figure 5, electrical charge might be drained from at least one of the plates to modify its reflective property. This would reduce the Atoms 2019, 7, 51 8 of 18

Pinto’s approach cannot work if the Casimir force is conservative. If so, no matter what process were to be used in separating the plates, it would require at least as much energy as had been extracted by their coming together. For example, in step (b) shown in Figure5, electrical charge might be drained from at least one of the plates to modify its reﬂective property. This would reduce the Casimir attraction and allow the plates to be pulled apart with minimal force, after which charge would be injected back into the plates to reestablish the Casimir attraction. For a conservative force, the minimum energy required for this draining and injecting back of the electrical charge is the energy that could be obtained from the attractive force of the plates moving together. Alternatively, exposing a plate to hydrogen may be used to change its reﬂectivity [33] and hence the attraction between plates. If the force is conservative then the hydrogenation/de-hydrogenation cycle would require at least as much energy as could be extracted from the Casimir-plate attraction, and the system cycle could not produce power. A similar situation to that of the Casimir force exists with standard electric forces, which clearly are conservative. The electric attraction induced by opposite charge on two capacitor plates cannot produce cyclic power. In one analysis, a Carnot-like cycle was used to show that the Casimir force did not appear to be conservative [6], so that it would be possible to extract cyclic power. However, from an analysis of each of the steps in the cycle, Scandurra found that the Casimir force is conservative after all, consistent with the general consensus, and that the method cannot produce power in a continuous cycle [34]. In a recent publication, Pinto has supported this conclusion and its implications [35]. Generalizing from the conservative nature of the Casimir force, it appears that any attempt to obtain net power in a cyclic fashion from changing the spacing of Casimir cavity plates cannot work. In a different sort of mechanical extraction, it may be possible to use vacuum fluctuations as nanoscale hammers to heat surfaces [36], or even to account for the expansion of the Universe via parametric resonance [37].

2.3. Pumping Atoms through Casimir Cavities

2.3.1. Zero-Point Energy Ground State and Casimir Cavities There is a fundamental difference between the equilibrium state for heat and for ZPE. It is well understood that one cannot make use of thermal fluctuations under equilibrium conditions. To use the heat, there must be a temperature difference to promote a heat flow to obtain work, as reflected in the Carnot efficiency of Equation (4). We cannot maintain a permanent temperature difference between a hot source and a cold sink in thermal contact with each other, without expending energy, of course. Similarly, without differences in some characteristic of ZPE in one region as compared to another, it is difficult to understand what could drive a flow of ZPE to allow its extraction. If the ZPE represented the universal ground state, we could not make use of ZPE differences to do work. But the entropy and energy of ZPE are geometry dependent [38], and are a function of the boundary conditions [39]. In this way ZPE fluctuations differ fundamentally from thermal fluctuations. Inside a Casimir cavity the ZPF density is different than outside, a difference that is established as a result of the different boundary conditions inside and out. A particular state of thermal or chemical equilibrium can be characterized by a temperature or chemical potential, respectively. For an ideal Casimir cavity having perfectly reflecting surfaces it is possible to define a characteristic temperature that describes the state of equilibrium for zero-point energy and which depends only on cavity spacing [33]. In a real system, however, no such parameter exists because the state is determined by boundary conditions in addition to cavity spacing [40], such as the cavity reflectivity as a function of wavelength, spacing uniformity, and general shape. The next approach to extracting power from vacuum fluctuations makes use of the step in the ZPE ground state at the entrance to Casimir cavities. According to stochastic electrodynamics (SED), the energy of classical electron orbits in atoms is determined by a balance of emission and absorption of vacuum energy [41,42]. By this view of the atom, electrons emit a continuous stream of Larmor radiation as a result of the acceleration they experience in their orbits. As the electrons release energy their orbits would spin down were it not for absorption of vacuum energy from the ZPF. This Atoms 2019, 7, 51 9 of 18 balancing of emission and absorption has been modeled and shown to yield the correct Bohr radius in hydrogen [43–45]. Accordingly, based on unpublished suggestions by B. Haisch and H.E. Puthoff, the orbital energies of atoms inside Casimir cavities should be shifted if the cavity spacing blocks the ZPF required to support a particular atomic orbital. However, under particular simplifying assumptions this shift is not predicted [46]. This reduction of orbital energy inside Casimir cavities is not associated withAtoms a reduced 2019, 7, x FOR temperature, PEER REVIEW as the entire system is in thermal equilibrium. Unlike with the Lamb9 of shift,18 the orbital energy is not just modified by the ZPF but is directly supported by it, and so the reduction ZPF required to support a particular atomic orbital. However, under particular simplifying in energyassumptions inside this a Casimir shift is not cavity predicted is expected [46]. This to bereduction much larger of orbital than energy the change inside inCasimir the Lamb cavities shift is as predictednot associated by cavity with quantum a reduced electrodynamics temperature, as [47 the]. entire system is in thermal equilibrium. Unlike withWe the do Lamb not attemptshift, the toorbital assess energy whether is not SEDjust mo isdified valid, by which the ZPF is wellbut is beyonddirectly supported the scope by of it, this investigation,and so the reduction but rather in simplyenergy makeinside usea Casimir of the cavity implications is expected of SED to be theory much to larger develop than of the process change for potentialin the Lamb ZPE harvesting.shift as predicted Currently, by cavity only quantum a semi-classical electrodynamics analysisusing [47]. SED has been used to predict this shiftWe of do ground not attempt state orbital to assess energies. whether Although SED is much valid, of which SED theory is well has beyond been appliedthe scope successfully of this in producinginvestigation, results but rather that are simply consistent make withuse of standard the implications quantum of mechanics SED theory [40 to, 42develop,44], particularly of process for with thepotential inclusion ZPE of harvesting. spin in the Currently, SED analysis only [a48 semi-classical], there have analysis not been using any SED reports has been to date used in to which predict this orbitalthis shift energy of ground shift has state been orbital replicated energies. using Although quantum much electrodynamics. of SED theory has An been exploratory applied successfully experiment to testin for producing a shift in results the molecular that are consistent ground state with of st Handard2 gas flowingquantum through mechanics a 1 [40,42,44],µm Casimir particularly cavity was carriedwith out,the inclusion but without of spin a definitive in the SED result analysis [49]. [48], there have not been any reports to date in which this orbital energy shift has been replicated using quantum electrodynamics. An exploratory 2.3.2.experiment The Extraction to test for Process a shift in the molecular ground state of H2 gas flowing through a 1 µm Casimir cavity was carried out, but without a definitive result [49]. In a 2008 patent [8], Haisch and Moddel describe a method to extract power from vacuum fluctuations2.3.2. The thatExtraction makes Process use of this ground state reduction inside Casimir cavities. The process of atoms flowing into and out from Casimir cavities is depicted in Figure6. In the upper part of the loop, gas is pumpedIn first a 2008 through patent a region[8], Haisch surrounded and Moddel by aradiation describe absorber,a method andto extract then through power afrom Casimir vacuum cavity. fluctuations that makes use of this ground state reduction inside Casimir cavities. The process of As the atoms enter the Casimir cavity, their orbitals spin down and release electromagnetic radiation, atoms flowing into and out from Casimir cavities is depicted in Figure 6. In the upper part of the depicted by the outward pointing arrows, that is extracted by the absorber. On exiting the cavity at loop, gas is pumped first through a region surrounded by a radiation absorber, and then through a the top left, the ambient ZPF re-energizes the orbitals, depicted by the small inward pointing arrows. Casimir cavity. As the atoms enter the Casimir cavity, their orbitals spin down and release The gas then flows through a pump and is re-circulated through the system. The system functions electromagnetic radiation, depicted by the outward pointing arrows, that is extracted by the absorber. likeOn a heatexiting pump, the cavity pumping at the energy top left, from the ambient an external ZPF source re-energizes to a local the absorber.orbitals, depicted The amount by the of small power 22 producedinward inpointing a small arrows. toaster-sized The gas system then flows producing through roughly a pump 10 andtransitions is re-circulated into through and out the from system. Casimir cavitiesThe system per second functions was like estimated a heat pump, to be pumping approximately energy 1from kW. an The external power source required to a tolocal pump absorber. the gas throughThe amount the cavities of power was produced estimated in to a be small well toaster-sized below 1 W [system8]. producing roughly 1022 transitions intoInitial and out studies from on Casimir energy caviti emissiones per from second this was system estimated have to been be approximately carried out [50 1]. kW. We firstThe power examine therequired results andto pump then the discuss gas through the thermodynamics the cavities was issues estimated that are to be related well below to the 1 process. W [8].

FigureFigure 6. System6. System to to pump pump energy energy continuously continuously from from the the vacuum, vacuum, as as proposed proposed by by Haisch Haisch and and Moddel Moddel [ 8]. As[8]. gas As enters gas theenters Casimir the Casimir cavity thecavity electron the electron orbitals orbitals of the gasof the atoms gas spinatoms down spin indown energy, in energy, emitting Larmouremitting radiation, Larmour shownradiation, as small shown arrows as small pointing arrows outwards. pointing Theoutwards. radiant The energy radiant is absorbed energy andis extracted.absorbed When and extracted. the atoms When exit the the Casimir atoms exit cavity, the theCasimir atomic cavity, orbitals the atomic are recharged orbitals toare their recharged initial levelto bytheir the ambient initial level zero-point by the ambient ﬁeld, shown zero-point by the field, inward shown pointing by thesmall inward arrows. pointing The small ﬁgure arrows. is reprinted The fromfigure Ref. is [ 49reprinted]. from Ref. [49].

Initial studies on energy emission from this system have been carried out [50]. We first examine the results and then discuss the thermodynamics issues that are related to the process.

2.3.3. Experimental Test of Radiant Emission Due to Gas Flow Atoms 2019, 7, 51 10 of 18

Atoms 2019, 7, x FOR PEER REVIEW 10 of 18

2.3.3.Atoms ExperimentalFor 2019 a, 7 working, x FOR PEER Test gas REVIEW ofof Radiant xenon, a Emission Casimir Duecavity to spacing Gas Flow of approximately 0.1 µm is required10 of to18 suppressFor a workingthe frequency gasof for xenon, the outer a Casimir orbital [8]. cavity In an spacing initial set of of approximately experiments cavities 0.1 µm were is required formed to For a working gas of xenon, a Casimir cavity spacing of approximately 0.1 µm is required to suppressusing spaced-apart the frequency optical for the flats, outer but orbitalbecause [ 8of]. the In an narrow initial spacing set of experiments required, even cavities the thick were optical formed suppress the frequency for the outer orbital [8]. In an initial set of experiments cavities were formed usingflats spaced-apart bowed too much optical to flats,provide but sufficiently because of theuniform narrow spacing. spacing More required, reliable even cavities the thick were optical formed flats fromusing Whatman spaced-apart polycarbonate optical flats, Nuclepore but because flexible of the membranes narrow spacing with pore required, sizes of even 0.1, the0.2, thickand 0.4 optical µm. bowed too much to provide sufficiently uniform spacing. More reliable cavities were formed from Toflats form bowed metallic too muchCasimir to cavitiesprovide goldsufficiently was thermall uniformy evaporated spacing. More at two reliable angles cavities onto the were pore formed walls. Whatman polycarbonate Nuclepore flexible membranes with pore sizes of 0.1, 0.2, and 0.4 µm. To Thefrom coverage Whatman was polycarbonate confirmed by Nuclepore scanning electronflexible membranes microscope with(SEM) pore inspection, sizes of 0.1,as shown 0.2, and in 0.4 Figure µm. form metallic Casimir cavities gold was thermally evaporated at two angles onto the pore walls. The 7.To form metallic Casimir cavities gold was thermally evaporated at two angles onto the pore walls. coverageThe coverage was confirmed was confirmed by scanning by scanning electron electron microscope microscope (SEM) (SEM) inspection, inspection, as shown as shown in Figurein Figure7. 7.

(a) (b)

Figure 7. SEM images of coated(a) Nanopore polycarbonate membrane shown(b) at two magnifications. In (a) the white line corresponds to a length of 2 µm, and in (b) to 0.1 µm. The figure is reprinted from FigureRef.Figure [49]. 7. 7.SEM SEM images images of of coated coated Nanopore Nanopore polycarbonate polycarbonate membrane membrane shown shown at at two two magnifications. magnifications. InIn (a) the(a white) the white line corresponds line corresponds to a length to a length of 2 µ m,of and2 µm, in and (b) toin 0.1(b)µ tom. 0.1 The µm. figure The isfigure reprinted is reprinted from Ref. from [49 ]. CoatedRef. [49]. and uncoated membranes having a diameter of 25.4 mm were mounted into a holder andCoated placed and in an uncoated evacuated membranes stainless-steel having chamber. a diameter Gas offlowed 25.4 mminto werethe top mounted of the membrane into a holder at a and placedpressure inCoated an of evacuated 1 and to 10uncoated Torr, stainless-steel and membranes was pumped chamber. having out Gasa bediameterlow, flowed with intoof the25.4 the pumping mm top were of the modulated mounted membrane intoat at0.5 a a holder pressureHz to offacilitate 1and to 10placed Torr, lock-in in and an detection wasevacuated pumped of stainless-steel emission out below, from withchamber. the the device. pumping Gas Aboveflowed modulated theinto device the attop 0.5a ofpyroelectric Hz the to membrane facilitate detector lock-inat a detectionmeasuringpressure of of emission emission 1 to 10 fromTorr,in the theand wavelength device. was pumped Above range theout of 0.6 devicebe low,to 5 aµmwith pyroelectric was the placedpumping detector outside modulated measuring the chamber at 0.5 emission facingHz to in thethefacilitate wavelength device lock-in through range detection an of 0.6infrared-transparent of to emission 5 µm was from placed theZrSe outsidedevice. window. theAbove chamberAdditional the device facing ex perimentala pyroelectric the device details throughdetector are an infrared-transparentdescribedmeasuring in emission Ref. [49]. ZrSe in the window. wavelength Additional range of experimental 0.6 to 5 µm was details placed are describedoutside the in chamber Ref. [49 ].facing the device through an infrared-transparent ZrSe window. Additional experimental details are FourFour di differentfferent gases gases (He, (He, Ar, Ar, N N22,, andand Xe) were were used used to to test test both both coated coated and and uncoated uncoated membranes. membranes. described in Ref. [49]. EmittedEmitted radiation radiation from from filters filters with with aa 0.20.2 µµmm porepore size is shown in in Figure Figure 8.8. Four different gases (He, Ar, N2, and Xe) were used to test both coated and uncoated membranes.

Emitted radiation7 from filters with a 0.2 µm pore size is shown in Figure 8.

7 6 He

6 5 He

5 4 Ar Uncoated membrane Uncoated

4 Ar 3 membrane Uncoated N2 Xe 3 2 N2 Xe

Radiated Power (arbitrary units) (arbitrary Power Radiated 1 Radiated Power (arbitrary units) (arbitrary Power Radiated 1 membrane Gold-coated 0 0 5 10 15 20 25 30 35 Gold-coated membrane Gold-coated 0 Gas Flow Rate (sccm) 0 5 10 15 20 25 30 35 Figure 8. Measured radiation emitted using N , Ar, Xe and He gasses flowing through uncoated and Figure 8. Measured radiation emitted usingGas N2, FlowAr, Xe Rate and He (sccm) gasses flowing through uncoated and goldgold coated coated polycarbonate polycarbonate filters filters havinghaving 0.20.2 µµmm pore size [49]. [49]. Figure 8. Measured radiation emitted using N2, Ar, Xe and He gasses flowing through uncoated and gold coated polycarbonate filters having 0.2 µm pore size [49]. Atoms 20192019,, 77,, 51x FOR PEER REVIEW 1111 of of 18 Atoms 2019, 7, x FOR PEER REVIEW 11 of 18 Emission of radiation from all the membranes was clearly measured, with lower output from Emission of radiation from all the membranes was clearly measured, with lower output from the gold-coatedEmission of membranes radiation from than allfrom the the membranes uncoated waspolycarbonate. clearly measured, To assess with how lower the radiation output from was the gold-coated membranes than from the uncoated polycarbonate. To assess how the radiation was theproduced gold-coated a series membranes of tests was than carried from out. the uncoated polycarbonate. To assess how the radiation was produced a series of tests was carried out. 2.3.4. Test of Frictional Heating as a Source for the Observed Radiation 2.3.4.2.3.4. Test Test of of Frictional Frictional Heating as a Source for the Observed Radiation We compared the radiated power from the filters with different pore diameters. In Figure 9 we WeWe compared compared the the radiated radiated power power from from the the filters filters wi withth different different pore pore diameters. diameters. In Figure In Figure 9 we9 show the signal measured for helium gas flowing through 0.1, 0.2, and 0.4 µm pore diameter showwe show the thesignal signal measured measured for forhelium helium gas gas flowin flowingg through through 0.1, 0.1, 0.2, 0.2, and and 0.4 0.4 µmµm pore pore diameter membranes. The highest signal was registered from the 0.1 µm filter. One possible explanation for membranes.membranes. The highesthighest signalsignal was was registered registered from from the the 0.1 0.1µm µm filter. filter. One One possible possible explanation explanation for why for why that diameter produced the largest signal is that the smaller sizes suppress ZPFs having whythat diameterthat diameter produced produced the largest the largest signal issignal that the is smallerthat the sizes smaller suppress sizes ZPFs suppress having ZPFs frequencies having frequencies that more closely match the atomic outer orbital frequencies, and hence, give rise to frequenciesthat more closely that more match closely the atomic match outer the orbitalatomic frequencies, outer orbital and frequencies, hence, give and rise hence, to greater give radiation rise to greater radiation from the ZPE. Alternatively, the smaller diameters produce a higher pressure drop greaterfrom the radiation ZPE. Alternatively, from the ZPE. the Alternatively, smaller diameters the smaller produce diameters a higher pressure produce drop a higher and couldpressure give drop rise and could give rise to more frictional heating, as discussed below. andto more could frictional give rise heating, to more as frictional discussed heating, below. as discussed below. Radiated Power (arbitrary units) (arbitrary Power Radiated Radiated Power (arbitrary units) (arbitrary Power Radiated

Gas Flow Rate (sccm) Gas Flow Rate (sccm) Figure 9. Effect of diameter on radiated power, as measured for He gas flowing through uncoated FigureFigure 9. EffectEffect of of diameter diameter on on radiated radiated power, power, as as measured for He gas flowing flowing through uncoated polycarbonate filters of 0.1 (blue diamonds), 0.2 (red squares), and 0.4 µµm (greed triangles) pore polycarbonate filters filters of of 0.1 0.1 (blue diamonds), 0.2 0.2 (r (reded squares), squares), and and 0.4 0.4 µmm (greed triangles) pore pore diameter sizes. diameterdiameter sizes. sizes. To testtest forfor frictionalfrictional heating,heating, wewe examinedexamined whetherwhether the membrane might work as a passivepassive To test for frictional heating, we examined whether the membrane might work as a passive element dissipating heatheat asas a result of the pressure drop of gas flowing flowing through it. Results for different different element dissipating heat as a result of the pressure drop of gas flowing through it. Results for different gases flowingflowing through 0.20.2 µµmm uncoateduncoated membranemembrane areare shownshown inin FigureFigure 10 10.. gases flowing through 0.2 µm uncoated membrane are shown in Figure 10.

XeXe ArAr

N2 N2 Pressure Drop (Torr) Pressure Drop (Torr) HeHe

Gas Flow Rate (sccm) Gas Flow Rate (sccm) Figure 10. PressurePressure drop verses gas flow flow through 0.2 µµmm uncoated filterfilter for didifferentfferent gases.gases. Figure 10. Pressure drop verses gas flow through 0.2 µm uncoated filter for different gases. These results are in excellent agreement with the studies done by Roy and Raju on the gas flow These results are in excellent agreement with the studies done by Roy and Raju on the gas flow through microchannels [51]. The pressure drop depends linearly on gas flow and the slope is different through microchannels [51]. The pressure drop depends linearly on gas flow and the slope is different Atoms 2019, 7, 51 12 of 18

Atoms These2019, 7, resultsx FOR PEER are REVIEW in excellent agreement with the studies done by Roy and Raju on the gas12 flowof 18 through microchannels [51]. The pressure drop depends linearly on gas flow and the slope is different for different different gases with xenon being the most resistiveresistive and helium being the least. If these frictional losses are what produce heating and the the measured measured radiation, radiation, the the power power should should depend depend quadratically quadratically on the gas flow. flow. This This would would amplify amplify the the differences differences seen for for the the different different gases, with xenon xenon producing producing the largest heating and helium the smallest, as shown inin FigureFigure 1111..

sses60 model Xe 50 Ar

30 N2 20 He 10 Calculated Power (Torr x sccm) (Torr Power Calculated 0 0246810 Gas Flow Rate (sccm) Figure 11. Calculated power from frictional loss based upon pressure drop for each of the gases. Figure 11. Calculated power from frictional loss based upon pressure drop for each of the gases. This trend in radiated power is the opposite of what was observed in the data of Figure8, calling This trend in radiated power is the opposite of what was observed in the data of Figure 8, calling the frictional heating model into question. On the other hand, helium is more thermally conductive the frictional heating model into question. On the other hand, helium is more thermally conductive than xenon, and so if the signal measured in Figure8 somehow involves thermal conduction—despite than xenon, and so if the signal measured in Figure 8 somehow involves thermal conduction—despite the fact that it is radiation and not conduction that is being measured—the greater thermal conductivity the fact that it is radiation and not conduction that is being measured—the greater thermal of helium may give rise to gas trend that was observed. conductivity of helium may give rise to gas trend that was observed. Another issue with the frictional heating model is that the measured power, shown in Figure9, Another issue with the frictional heating model is that the measured power, shown in Figure 9, depends linearly rather than quadratically on the flow. This observation does not necessarily rule depends linearly rather than quadratically on the flow. This observation does not necessarily rule out out frictional losses as a source for the measured radiation. The reason is that the system has more frictional losses as a source for the measured radiation. The reason is that the system has more elements taking part in the process, with gas in the chamber transferring its energy to the walls. This elements taking part in the process, with gas in the chamber transferring its energy to the walls. This might affect the power dependence on the flow and cause it to appear linear. The frictional heating might affect the power dependence on the flow and cause it to appear linear. The frictional heating does not appear to be the source for the measured signal both because the gas order is wrong and does not appear to be the source for the measured signal both because the gas order is wrong and because the dependence on pressure is wrong. Still, it cannot be ruled out entirely. because the dependence on pressure is wrong. Still, it cannot be ruled out entirely. 2.3.5. Test of the Joule-Thomson Effect as a Source for the Observed Radiation 2.3.5. Test of the Joule-Thomson Effect as a Source for the Observed Radiation Another possible mechanism for the emission could be the Joule–Thomson effect [52]. To test for this,Another we replaced possible themechanism membrane for withthe emission a 12.5 µ mcould thick be Mylar the Joule–Thomson film having a effect single [52]. hole To 3 test mm for in this,diameter, we replaced far too large the membrane to give rise with to any a measurable12.5 µm thick ZPF Mylar effect. film The having results area single shown hole in Figure3 mm 12in. diameter, far too large to give rise to any measurable ZPF effect. The results are shown in Figure 12. The phase measured by the lock-in amplifier was 180◦ off from the phase measured in the experiment withThe phase the nanopore measured membrane, by the lock-in indicating amplifier cooling. was 180° For xenon, off from argon, the phase and nitrogen measured the in Joule–Thompson the experiment withcoeffi cientthe nanopore is expected membrane, to produce indicating cooling from coolin expansiong. For xenon, under theargon, measurement and nitrogen conditions. the Joule– We Thompsoncould clearly coefficient distinguish is theexpected heating to we produce observed cooling from flowing from theexpansion gases through under thethe Casimir measurement cavities conditions.from this measured We could Joule–Thompson clearly distinguish eff ect.the heating This rules we it observed out as a sourcefrom flowing for the the observed gases through radiation. the Casimir cavities from this measured Joule–Thompson effect. This rules it out as a source for the observed radiation. Atoms 2019, 7, 51 13 of 18 Atoms 2019, 7, x FOR PEER REVIEW 13 of 18

2.5

2 Xe

1.5 Ar 1

N2 0.5 Radiated Power (arbitrary units) (arbitrary Power Radiated negligible 0 He 0 5 10 15 Gas Flow Rate (sccm)

Figure 12. Test of Joule–Thomson effect. Emitted radiation was measured for N2, Ar, Xe and He gasses Figure 12. Test of Joule–Thomson effect. Emitted radiation was measured for N2, Ar, Xe and He gasses flowing through a Mylar film having a 3 mm diameter hole. The phase of the lock-in signal indicated a coolingflowing ethroughffect. a Mylar film having a 3 mm diameter hole. The phase of the lock-in signal indicated a cooling effect. 2.3.6. Turbulence as a Potential Source for the Observed Radiation 2.3.6. Turbulence as a Potential Source for the Observed Radiation Turbulence is another possible heat source if the Reynolds number is sufficiently high, which wouldTurbulence indicate that is another the flow possible is not dominated heat source by viscosity if the Reynolds [53]. In ournumber experiment is sufficiently the rate high, at which which the gaswould flowed indicate through that thethe nanoporeflow is not cavities dominated was below by viscosity 2 cm/s, [53]. which In resultsour experiment in a Reynolds the rate number at which that isthe far gas below flowed what through would the be requirednanopore to cavities cause turbulence was below at 2 thecm/s, exit. which Furthermore, results in thea Reynolds viscosities number of the gasesthat is usedfar below in the what experiment would be have required values to that cause are turbulence very close toat eachthe exit. other Furthermore, (Xe: 0.021 cP, the Ar: viscosities 0.021 cP, Nof2 the: 0.0166 gases cP, used He: in 0.0186 the experiment cP). Even if turbulencehave values somehow that are very did produce close to radiationeach other from (Xe: the 0.021 membrane cP, Ar: it0.021 could cP, not N2: explain 0.0166 thecP, He: differences 0.0186 cP). in signal Even levelsif turbulence for thedi somehowfferent gases. did produce radiation from the membrane it could not explain the differences in signal levels for the different gases. 2.3.7. Absorption/Adsorption as a Potential Source for the Observed Radiation 2.3.7.When Absorption/Adsorption a gas is brought into as contacta Potential with Source a solid for surface the Observed its molecules Radiation are either absorbed into the solidWhen or adsorbed a gas is onbrought the surface, into contact both processes with a solid being surface exothermic. its molecules We tested are either whether absorbed this could into the be asolid source or adsorbed for the observed on the surface, radiation. both Adsorption processes being is proportional exothermic. to We the tested surface whether area. We this used could three be dia sourcefferent porefor the size observed membranes, radiation. 0.1 µm, Adsorption 0.2 µm and is 0.4 proportionalµm, having surfaceto the surface areas of area. 9.4 cm We2, 18used cm 2threeand 12.6different cm2, pore respectively. size membranes, Signal from 0.1 theseµm, 0.2 di ffµmerent and filters 0.4 µm, measured having forsurface a pressure areas of 9.4 ~5 torrcm2, did18 cm not2 varyand 12.6 with cm surface2, respectively. area. Therefore, Signal from the absorption these different/adsorption filters measured model may for be a ruledpressure out of as ~5 a possibletorr did explanationnot vary with for surface the observed area. Theref radiation.ore, the absorption/adsorption model may be ruled out as a possible explanation for the observed radiation. 2.3.8. Expected Radiation Power 2.3.8.We Expected can calculate Radiation the expectedPower radiated power assuming that each atom releases 10% of its ground stateWe orbital can energycalculate each the time expected it enters radiated a Casimir power cavity, assuming which that would each result atom in releases roughly 10% 1 eV of perits transitionground state [8]. orbital For the energy flows each we used time that it enters would a resultCasimir in cavity, the production which would of milliwatts result in of roughly power. 1 The eV measuredper transition power [8]. wasFor the below flows 1 µ weW forused all that the gaseswould and result samples. in the production Assuming thatof milliwatts roughly 20% of power. of the emittedThe measured power power was received was below by the 1 detectorµW for all facing the gases the membrane, and samples. the measuredAssuming power that roughly is three 20% orders of ofthe magnitude emitted power smaller was than received expected. by the There detector could befacing multiple the membrane, reasons for the this me discrepancy.asured power An obviousis three oneorders has of to magnitude do with the smaller pore than shape, expected. shown inThere Figure could7. Itbe is multiple far from reasons uniform, for sothis that discrepancy. only a small An fractionobvious ofone the has gas to atoms do with or moleculesthe pore shape, encountered shown Casimirin Figure cavities 7. It is far of thefrom required uniform, dimensions. so that only It isa dismallfficult fraction to assess of the how gas much atoms of or a powermolecules deficit encountered can be attributed Casimir to cavities this, but of it the is clearlyrequired large. dimensions. Another unknownIt is difficult has to to assess do with how the much direction of a ofpower the radiation. deficit can If therebe attributed is radiation to this, from but the it gas is transitions,clearly large. it mayAnother be directed unknown to thehas walls to do of with the Casimirthe direction cavity, of causing the radiation. them to If heat there up. is In radiation that case from the radiation the gas transitions, it may be directed to the walls of the Casimir cavity, causing them to heat up. In that case the radiation may be a secondary effect, with much of the power being lost to the environment by convection and conduction, and some radiation being outside the wavelength range of our detector. Atoms 2019, 7, 51 14 of 18 may be a secondary effect, with much of the power being lost to the environment by convection and conduction, and some radiation being outside the wavelength range of our detector. If the power that was radiated does not come from ZPE, then it must come from the power supplied by pumping the gas through the cavities. Based on theory and experiments of gases flowing through nanopores [50] and consistent with the data and calculations of Figures 10 and 11, the power required to pump gas through the Casimir cavities is more than three orders of magnitude lower than the expected power that could be harvested [8]. Therefore, from a simple gas flow perspective the harvested power does not come from the gas pump. The SED model adds an additional factor. One might argue that because the ground state energy of the gas atoms in the Casimir cavity is lower than that outside, they would have to surmount a potential hill to exit the cavity. The power to do that would have to come from the pumping. By that argument the power emitted when the gas entered the cavity would all be supplied by the pump, and no ZPE would be harvested. There is a flaw in that argument, however. The power would not have to be supplied by the pump because it is supplied by the ambient ZPF that the atoms encounter when they exit the cavity—that is the whole point of the system. Furthermore, we do not know of a mechanism that could translate the spherically symmetric energy radiation from the molecules into a back-pressure. Still, we cannot totally rule out this potential hill argument. In addition to these possible loss mechanisms, there are other unknowns because there are not yet a precise theory and simulations that would enable us to predict what the desired dimensions should be. Given the ambiguities it is not yet possible to know whether the measured power is consistent with ZPE being the source.

2.3.9. Deviations from Expected Results The results deviated from what was expected in several ways.

1. The measured power is much lower than predicted, as described in the previous section. Some if not all this deviation can be attributed to inconsistent sizes and shapes of the nanopores. 2. Another unexpected result is that the uncoated polycarbonate membranes produced much more radiation than the gold-coated devices. It is expected that the metal-walled Casimir cavities are more eﬀective than the dielectric-walled cavities in suppressing interior modes, although the latter does produce the Casimir eﬀect [29] that are only slightly smaller [54]. A likely reason that more radiation was observed from the polycarbonate is that the emitted power heated the cavity walls and the emissivity of the polycarbonate walls and membrane is much greater than that of the gold. 3. We expected to see the greatest emission from the xenon atoms. Their outer orbital frequency corresponds to a wavelength (0.1 µm) that is suppressed in the 0.2 µm cavities (suppressed 1 wavelength is 2 the cavity spacing). That suppressed wavelength is farthest from the wavelength corresponding to the helium orbital (0.05 µm). The opposite was observed. We do not know the reason for this, but it may have to do with more total energy being available from the helium atoms.

2.3.10. Violations of the Second Law of Thermodynamics Putting aside the fact that radiation was observed, we consider whether there are fundamental constraints on the process. The first question is whether it conflicts with the conservative nature of the Casimir force. It does not because although Casimir plates are used, they do not move as part of the process. Therefore, this process differs from the mechanical process described in Section 2.2.2, which does make use of cyclic Casimir plate motion in an attempt to extract power from Casimir attraction. Next comes the question as to whether there is a detailed balance that would render the process invalid. If the gas were stationary, then we would expect a detailed balance of radiation to exist between the atoms and their environment at the entrance and exit to the cavity. However, the gas is Atoms 2019, 7, 51 15 of 18

ﬂowing and in such a dynamic situation could circumvent the requirement for detailed balance. A key issue here are the time scales involved. If the gas enters the Casimir cavity on a time scale that is much slower than the equilibration time, then the entire process occurs in quasi-equilibrium and detailed balance applies. In such a case, there would be no excess energy to shed, e.g., to the absorber shown in Figure6, because the orbitals would remain in equilibrium with the vacuum ZPF at each instant of the process. In summary, although the process does not overtly violate the second law, it is not clear whether equilibrium considerations render it incapable of providing harvestable energy.

2.3.11. Future Work to Investigate Gas Flow through Casimir Cavities A study based on the same concept of harvesting energy from ground state reduction was carried out by Henriques [55]. To avoid the detailed balance described above and to improve the chances for observing orbital energy shifts he optically excited the atoms as they entered the Casimir cavity. He was not able to detect any emitted radiation, but the reason might have been due to poor sensitivity in the detector. Our results are tantalizing but unfortunately inconclusive. The investigation could be improved in several ways. One is to obtain nanopores having a more consistent size and shape so that they provide uniform cavities of the desired dimensions. This would allow for a better assessment of how much power can be emitted, and whether the emitted power exceeds the pumping power. Another would be to image the radiation to determine the location of its source, and to measure its spectral dependence to determine whether it is thermal and if so at what temperature.

3. Conclusions The tremendous energy density in the zero-point field (ZPF) makes it tempting to attempt tapping it for power. Furthermore, the fact that these vacuum fluctuations may be distinguished from thermal fluctuations and are not under the usual thermal equilibrium make it tempting to try to skirt second law of thermodynamics constraints. However, the ZPF is in a state of true equilibrium, and the constraints that apply to equilibrium systems apply to it. In particular, any attempt to use nonlinear processes, such as with a diode, cannot harvest energy from a system in equilibrium. Detailed balance arguments apply. The force exhibited between opposing plates of a Casimir cavity have led to attempts to make use of the potential energy to obtain power. This cannot succeed because the Casimir force is conservative. In any attempt to obtain power by cycling Casimir cavity spacing the energy gained in one part of the cycle must be paid back in another. Thermal fluctuations, usually thought of as an expression of Planck’s law, and ZPE vacuum fluctuations, usually associated with the ground state of a quantum system, are most often treated if they were separate forms of energy. However, the zero-point energy (ZPE) density given in Equation (1) may be re-expressed in the form [56]:

4πhν3 hν ρ(hν) = coth (5) c3 2kT The fact that these two seemingly separate concepts can be merged into a single formalism suggests that thermal and ZPE fluctuations are connected fundamentally. More rigorously, Planck’s law can be seen as a consequence of ZPE [57], and is “inherited” from it [58]. In more than a century of theory and experimentation we have not been able to extract usable energy from thermal fluctuations, and it might seem that we are destined to find ourselves in a similar situation with attempts to extract usable energy from ZPE. There is, however, a distinction that can be drawn between the two cases, which has to do with the nature of the ZPE equilibrium state. The equilibrium ZPE energy density is a function of the local geometry. Two thermal reservoirs at different temperatures that are in contact with each other Atoms 2019, 7, 51 16 of 18 cannot be in equilibrium; heat will flow from one to the other. Two ZPE reservoirs having different energy densities that are in contact with each other can, however, be in equilibrium. For example, a Casimir cavity can be in direct contact (open at its edges) with the free space surrounding it such that the ZPE density inside and outside the cavity are different without any net flow of energy between the two regions. Furthermore, extracting ZPE from the vacuum does not violate the second law of thermodynamics [12]. Our apparent lack of clear success in extracting energy from the vacuum thus far leads to two possible conclusions. Either fundamental constraints beyond what have been discussed here and the nature of ZPE preclude extraction, or it is feasible and we just need to find a suitable technology.

Author Contributions: G.M. developed the analysis of the various zero-point energy harvesting methods. O.D. and G.M. conceived of and designed the experiment, and O.D. carried them out. G.M. wrote the paper. Funding: This work was funded by HUB Lab, Coolescence, and DARPA under SPAWAR Grant No. N66001-06-1-2026. Acknowledgments: Many thanks to B. Haisch and M.A. Mohamed for stimulating discussions about vacuum energy, R. Cantwell and M. McConnell for help with the experiments, and to S. Grover, B. Haisch, B.L. Katzman and J. Maclay for comments on the manuscript. Conflicts of Interest: G.M. owns stock in a company founded to develop the gas-flow energy harvesting technology, Jovion Corporation, but plays no active role in the company. Besides that, the authors declare no conflict of interest. The funding sponsors had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, and in the decision to publish the results.

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