Physics:Quantum vacuum thruster

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A Venn diagram illustrating the set of Q thrusters tested at NASA, as per page 40 of Harold White's 2013 report titled "Warp Field Physics".[1] The set of Q-Thrusters has as subsets RF resonant cavity thrusters and Mach Lorentz thrusters
A diagram illustrating the theory of Q thruster operation

A quantum vacuum thruster (QVT or Q-thruster) is a theoretical system hypothesized to use the same principles and equations of motion that a conventional plasma thruster would use, namely magnetohydrodynamics (MHD), to make predictions about the behavior of the propellant. However, rather than using a conventional plasma as a propellant, a QVT would interact with quantum vacuum fluctuations of the zero-point field.[2][3]

The concept is controversial and generally not considered physically possible. However, if QVT systems were possible they could eliminate the need to carry propellant, being limited only by the availability of energy.[4]

History and controversy

The name and concept is controversial. In 2008, Yu Zhu and others at China's Northwestern Polytechnical University claimed to measure thrust from such a thruster, but called it a "microwave thruster without propellant" working on quantum principles.[5] In 2011 it was mentioned as something to be studied by Harold G. White and his team at NASA's Eagleworks Laboratories,[6] who were working with a prototype of such a thruster. Other physicists, such as Sean M. Carroll and John Baez, dismiss it because the quantum vacuum as currently understood is not a plasma and does not possess plasma-like characteristics.

Theory of operation

Prototype resonant cavity thruster built by NASA Eagleworks

A vacuum can be viewed not as empty space but as the combination of all zero-point fields. According to quantum field theory the universe is made up of matter fields whose quanta are fermions (e.g. electrons and quarks) and force fields, whose quanta are bosons (i.e. photons and gluons). All these fields have some intrinsic zero-point energy.[7] Describing the quantum vacuum, a Physics Today article cited by White's team describes this ensemble of fields as "a turbulent sea, roiling with waves associated with a panoply of force-mediating fields such as the photon and Higgs fields".[8] Given the equivalence of mass and energy expressed by Albert Einstein's E = mc2, any point in space that contains energy can be thought of as having mass to create particles. Virtual particles spontaneously flash into existence and annihilate each other at every point in space due to the energy of quantum fluctuations. Many real physical effects attributed to these vacuum fluctuations have been experimentally verified, such as spontaneous emission, Casimir force, Lamb shift, magnetic moment of the electron and Delbrück scattering;[9][10] these effects are usually called "radiative corrections".[11]

Casimir forces on parallel plates due to vacuum fluctuations

The Casimir effect is a weak force between two uncharged conductive plates caused by the zero-point energy of the vacuum. It was first observed experimentally by Lamoreaux (1997)[12][13] and results showing the force have been repeatedly replicated.[14][15][16][17] Several scientists including White have highlighted that a net thrust can indeed be induced on a spacecraft via the related "dynamical Casimir effect".[18][19] The dynamic Casimir effect was observed experimentally for the first time in 2011 by Wilson et al.[20][21] In the dynamical Casimir effect electromagnetic radiation is emitted when a mirror is accelerated at extremely high rates.[citation needed] When the speed of the mirror begins to match the speed of the photons,[dubious – discuss] some photons become separated from their virtual pair and so do not get annihilated. Virtual photons become real and the mirror begins to produce light.[dubious – discuss] This is an example of Unruh radiation.[22] A publication by Feigel (2004)[23] raised the possibility of a Casimir-like effect that transfers momentum from zero-point quantum fluctuations to matter, controlled by applied electric and magnetic fields. These results were debated in a number of follow up papers[24][25][26][27][28] in particular van Tiggelen et al. (2006) found no momentum transfer for homogeneous fields, but predict a very small transfer for a Casimir-like field geometry. This cumulated with Birkeland & Brevik (2007)[29] who showed that electromagnetic vacuum fields can cause broken symmetries (anisotropy) in the transfer of momentum or, put another way, that the extraction of momentum from electromagnetic zero-point fluctuations is possible in an analogous way that the extraction of energy is possible from the Casimir effect.[30][31][32] Birkeland & Brevik highlight that momentum asymmetries exist throughout nature and that the artificial stimulation of these by electric and magnetic fields have already been experimentally observed in complex liquids.[33][34] This relates to the Abraham–Minkowski controversy, a long theoretical and experimental debate that continues to the current time. It is widely recognized that this controversy is an argument about definition of the interaction between matter and fields.[35][36] It has been argued that momentum transfer between matter and electromagnetic fields relating to the Abraham-Minikowski issue would allow for propellant-less drives.[37]

A QVT system seeks to make use of this predicted Casimir-like momentum transfer. It is argued that when the vacuum is exposed to crossed electric and magnetic fields (i.e. E and B-fields), it will induce a drift of the entire vacuum plasma which is orthogonal to that of the applied E x B fields.[38] In a 2015 paper White highlighted that the presence of ordinary matter is predicted to cause an energy perturbation in the surrounding quantum vacuum such that the local vacuum state has a different energy density when compared with the "empty" cosmological vacuum energy state.[39] This suggests the possibility of modelling the vacuum as a dynamic entity as opposed to it being an immutable and non-degradable state. White models of the perturbed quantum vacuum around a hydrogen atom as a Dirac vacuum consisting of virtual electron-positron pairs. Given the nontrivial variability in local energy densities resulting from virtual pair production, he suggests the tools of magnetohydrodynamics (MHD) can be used to model the quasiclassical behavior of the quantum vacuum as a plasma.

White compares changes in vacuum energy density induced by matter to the hypothetical chameleon field or quintessence currently being discussed in the scientific literature.[39] It is claimed the existence of a “chameleon” field whose mass is dependent on the local matter density may be an explanation for dark energy.[40][41] A number of notable physicists, such as Sean Carroll, see the idea of a dynamical vacuum energy as the simplest and best explanation for dark energy. Evidence for quintessence would come from violations of Einstein's equivalence principle and variation of the fundamental constants[42][43] ideas which are due to be tested by the Euclid telescope which is set to launch in 2020.[44]

Systems utilizing Casimir effects have thus far been shown to only create very small forces and are generally considered one-shot devices that would require a subsequent energy to recharge them (i.e. Forward's "vacuum fluctuation battery").[45] The ability of systems to use the zero-point field continuously as a source of energy or propellant is much more contentious (though peer-reviewed models have been proposed).[46] There is debate over which formalisms of quantum mechanics apply to propulsion physics under such circumstances, the more refined Quantum Electrodynamics (QED), or the relatively undeveloped and controversial Stochastical Quantum Electrodynamics (SED).[47] SED describes electromagnetic energy at absolute zero as a stochastic, fluctuating zero-point field. In SED the motion of a particle immersed in the stochastic zero-point radiation field generally results in highly nonlinear behaviour. Quantum effects emerge as a result of permanent matter-field interactions not possible to describe in QED[48] The typical mathematical models used in classical electromagnetism, quantum electrodynamics (QED) and the standard model view electromagnetism as a U(1) gauge theory, which topologically restricts any complex nonlinear interaction. The electromagnetic vacuum in these theories is generally viewed as a linear system with no overall observable consequence.[49] For many practical calculations zero-point energy is dismissed by fiat in the mathematical model as a constant that may be canceled or as a term that has no physical effect.[50]

The 2016 paper by White highlights that stochastic electrodynamics (SED) allows for a pilot-wave interpretation of quantum mechanics. Pilot-wave interpretations of quantum mechanics are a family of deterministic nonlocal theories distinct from other more mainstream interpretations such as the Copenhagen interpretation and Everett's many-worlds interpretation. Pioneering experiments by Couder and Fort beginning in 2006[51] have shown that macroscopic classical pilot-waves can exhibit characteristics previously thought to be restricted to the quantum realm. Hydrodynamic pilot-wave analogs have been able to duplicate the double slit experiment, tunneling, quantized orbits, and numerous other quantum phenomena and as such pilot-wave theories are experiencing a resurgence in interest.[52][53][54][55] Coulder and Fort note in their 2006 paper that pilot-waves are nonlinear dissipative systems sustained by external forces. A dissipative system is characterized by the spontaneous appearance of symmetry breaking (anisotropy) and the formation of complex, sometimes chaotic or emergent, dynamics where interacting fields can exhibit long range correlations. In SED the zero point field (ZPF) plays the role of the pilot wave that guides real particles on their way. Modern approaches to SED consider wave and particle-like quantum effects as well-coordinated emergent systems that are the result of speculated sub-quantum interactions with the zero-point field[48][56][57]

Controversy and criticism

Some notable physicists have found the Q-thruster concept to be implausible. For example, mathematical physicist John Baez has criticized the reference to "quantum vacuum virtual plasma" noting that: "There's no such thing as 'virtual plasma' ".[58] Noted Caltech theoretical physicist Sean M. Carroll has also affirmed this statement, writing "[t]here is no such thing as a ‘quantum vacuum virtual plasma,’...".[59] In addition, Lafleur found that quantum field theory predicts no net force, implying that the measured thrusts are unlikely to be due to quantum effects. However, Lafleur noted that this conclusion was based on the assumption that the electric and magnetic fields were homogeneous, whereas certain theories posit a small net force in inhomogeneous vacuums.[60]

Notably, the violation of energy and momentum conservation laws have been heavily criticized. In a presentation at NASA's Ames Research Center in November 2014, White addressed the issue of conservation of momentum by stating that the Q-thruster conserves momentum by creating a wake or anisotropic state in the quantum vacuum. White indicated that once false positives were ruled out, Eagleworks would explore the momentum distribution and divergence angle of the quantum vacuum wake using a second Q-thruster to measure the quantum vacuum wake.[61] In a paper published in January 2014, White proposed to address the conservation of momentum issue by stating that the Q-thruster pushes quantum particles (electrons/positrons) in one direction, whereas the Q-thruster recoils to conserve momentum in the other direction. White stated that this principle was similar to how a submarine uses its propeller to push water in one direction, while the submarine recoils to conserve momentum.[62] Hence, the violations of fundamental laws of physics can be avoided.

Other hypothesized quantum vacuum thrusters

A number of physicists have suggested that a spacecraft or object may generate thrust through its interaction with the quantum vacuum. For example, Fabrizio Pinto in a 2006 paper published in the Journal of the British Interplanetary Society noted it may be possible to bring a cluster of polarisable vacuum particles to a hover in the laboratory and then to transfer thrust to a macroscopic accelerating vehicle.[63] Similarly, Jordan Maclay in a 2004 paper titled "A Gedanken Spacecraft that Operates Using the Quantum Vacuum (Dynamic Casimir Effect)" published in the scientific journal Foundations of Physics noted that it is possible to accelerate a spacecraft based on the dynamic Casimir effect, in which electromagnetic radiation is emitted when an uncharged mirror is properly accelerated in vacuum.[64] Similarly, Puthoff noted in a 2010 paper titled "Engineering the Zero-Point Field and Polarizable Vacuum For Interstellar Flight" published in the Journal of the British Interplanetary Society noted that it may be possible that the quantum vacuum might be manipulated so as to provide energy/thrust for future space vehicles.[65] Likewise, researcher Yoshinari Minami in a 2008 paper titled "Preliminary Theoretical Considerations for Getting Thrust via Squeezed Vacuum" published in the Journal of the British Interplanetary Society noted the theoretical possibility of extracting thrust from the excited vacuum induced by controlling squeezed light.[66] In addition, Alexander Feigel in a 2009 paper noted that propulsion in quantum vacuum may be achieved by rotating or aggregating magneto-electric nano-particles in strong perpendicular electrical and magnetic fields.[67]

However, according to Puthoff,[65] although this method can produce angular momentum causing a static disk (known as a Feynman disk) to begin to rotate,[68] it cannot induce linear momentum due to a phenomenon known as "hidden momentum" that cancels the ability of the proposed E×B propulsion method to generate linear momentum.[69] However, some recent experimental and theoretical work by van Tiggelen and colleagues suggests that linear momentum may be transferred from the quantum vacuum in the presence of an external magnetic field.[70]

Experiments

In 2013, the Eagleworks team tested a device called the Serrano Field Effect Thruster, built by Gravitec Inc. at the request of Boeing and DARPA. The Eagleworks team has theorized that this device is a Q-thruster.[1] The thruster consists of a set of circular dielectrics sandwiched between electrodes; its inventor describes it device as producing thrust through a preselected shaping of an electric field.[71] Gravitec Inc. alleges that in 2011 they tested the "asymmetrical capacitor" device in a high vacuum several times and have ruled out ion wind or electrostatic forces as an explanation for the thrust produced.[72] In February through June 2013, the Eagleworks team evaluated the SFE test article in and out of a Faraday Shield and at various vacuum conditions.[1] Thrust was observed in the ~1–20 N/kW range. The magnitude of the thrust scaled approximately with the cube of the input voltage (20–110 μN).[73] As of 2015, the researchers have not published a peer-reviewed paper detailing the results of this experiment.

Using a torsion pendulum, White's team claimed to have measured 30–50 μN of thrust from a microwave cavity resonator designed by Guido Fetta in an attempt at propellant-less propulsion. Using the same measurement equipment, a non-zero force was also measured on a "null" resonator that was not designed to experience any such force, which they suggest hints at "interaction with the quantum vacuum virtual plasma".[74] All measurements were performed at atmospheric pressure, presumably in contact with air, and with no analysis of systematic errors, except for the use of an RF load without the resonant cavity interior as a control device.[75] In early 2015, Paul March from that team made new results public, claiming positive experimental force measurements with a torsional pendulum in a hard vacuum: about 50 µN with 50 W of input power at 5.0×10−6 torr, and new null-thrust tests.[76] The claims of the team have not yet been published in a peer-reviewed journal, only as a conference paper in 2013.[77]

Yu Zhu and Juan Yang previously claimed to have measured anomalous thrust arising from a similar device, using power levels roughly 100 times greater, and measuring thrust roughly 1000 times greater.[5] A followup paper later identified the source of that anomalous thrust as experimental error.[78]

Current experiments

The 2006 Woodward effect test article
Plot diagram of the 2006 Woodward effect test results

In 2015, Eagleworks attempted to gather performance data to support the development of a Q-thruster engineering prototype for reaction-control-system applications in the force range of 0.1–1 N with a corresponding input electrical power range of 0.3–3 kW. The group planned to begin by testing a refurbished test article to improve the historical performance of a 2006 experiment that attempted to demonstrate the Woodward effect. The photograph shows the test article and the plot diagram shows the thrust trace from a 500g load cell in experiments performed in 2006.[79]

The group hoped that testing the device on a high-fidelity torsion pendulum (1–4 μN at 10–40 W) will unambiguously demonstrate the feasibility of this concept, perhaps via an on-orbit detailed test objective (DTO) to test operation in outer space.[6]

See also

References

  1. ↑ 1.0 1.1 1.2 White, Harold (2013). "Eagleworks Laboratories: Warp Field Physics". NASA Technical Reports Server (NTRS) 20140000851. https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20140000851.pdf. 
  2. ↑ White, Harold; March, Paul; Lawrence, James; Vera, Jerry; Sylvester, Andre; Brady, David; Bailey, Paul (2016). "Measurement of Impulsive Thrust from a Closed Radio-Frequency Cavity in Vacuum". Journal of Propulsion and Power 33 (4): 830–841. doi:10.2514/1.B36120. 
  3. ↑ Joosten, B. Kent; White, Harold G. (2015). "Human outer solar system exploration via Q-Thruster technology". 2015 IEEE Aerospace Conference. pp. 1–14. doi:10.1109/AERO.2015.7118893. ISBN 978-1-4799-5379-0. https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20140013174.pdf. 
  4. ↑ White, H.; March, P. (2012). "Advanced Propulsion Physics: Harnessing the Quantum Vacuum". Nuclear and Emerging Technologies for Space. http://www.lpi.usra.edu/meetings/nets2012/pdf/3082.pdf. 
  5. ↑ 5.0 5.1 "The Performance Analysis of Microwave Thrust without Propellant Based on the Quantum Theory". http://en.cnki.com.cn/Article_en/CJFDTOTAL-YHXB200805027.htm. 
  6. ↑ 6.0 6.1 "Eagleworks Laboratories: Advanced Propulsion Physics Research". NASA. 2 December 2011. https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20110023492_2011024705.pdf. Retrieved 10 January 2013. 
  7. ↑ Milonni, Peter W. (1994). The Quantum Vacuum: An Introduction to Quantum Electrodynamics. London: Academic Press. p. 35. ISBN 9780124980808. https://books.google.com/?id=uPHJCgAAQBAJ&lpg=PP1. 
  8. ↑ Bush, John W. M. (2015). "The new wave of pilot-wave theory". Physics Today 68 (8): 47–53. doi:10.1063/PT.3.2882. Bibcode: 2015PhT....68h..47B. http://newfos.arizona.edu/sites/default/files/uploads/documents/Pilot_Waves_Phys_Today_Aug_2015.pdf. Retrieved 30 November 2016. 
  9. ↑ Milonni, Peter W. (1994). The Quantum Vacuum: An Introduction to Quantum Electrodynamics. London: Academic Press. p. 111. ISBN 9780124980808. https://archive.org/details/quantumvacuumint00milo. 
  10. ↑ Greiner, Walter; Müller, B.; Rafelski, J. (2012). Quantum Electrodynamics of Strong Fields: With an Introduction into Modern Relativistic Quantum Mechanics. Springer. pp. 16. doi:10.1007/978-3-642-82272-8. ISBN 978-3-642-82274-2. https://books.google.co.uk/books?id=Wh3-CAAAQBAJ. 
  11. ↑ Bordag, Michael; Klimchitskaya, Galina Leonidovna; Mohideen, Umar; Mostepanenko, Vladimir Mikhaylovich (2009). Advances in the Casimir Effect. Oxford: `Oxford University Press. p. 4. ISBN 978-0-19-923874-3. https://books.google.com/?id=CqE1f_s5PgYC. 
  12. ↑ Lamoreaux, S. K. (1997). "Demonstration of the Casimir Force in the 0.6 to 6μm Range". Phys. Rev. Lett. 78 (1): 5–8. doi:10.1103/PhysRevLett.78.5. Bibcode: 1997PhRvL..78....5L. http://web.mit.edu/~kardar/www/research/seminars/Casimir/PRL-Lamoreaux.pdf. 
  13. ↑ Yam, Philip (1997). "Exploiting Zero-Point Energy". Scientific American 277 (6): 82–85. doi:10.1038/scientificamerican1297-82. Bibcode: 1997SciAm.277f..82Y. http://www.toriah.org/articles/yam-1997.pdf. Retrieved 18 December 2016. 
  14. ↑ Mohideen, Umar; Roy, Anushree (1998). "Precision Measurement of the Casimir Force from 0.1 to 0.9μm". Phys. Rev. Lett. 81 (21): 4549–4552. doi:10.1103/PhysRevLett.81.4549. Bibcode: 1998PhRvL..81.4549M. 
  15. ↑ Chan, H. B.; Aksyuk, V. A.; Kleiman, R. N.; Bishop, D. J.; Capasso, Federico (2001). "Quantum Mechanical Actuation of Microelectromechanical Systems by the Casimir Force". Science 291 (5510): 1941–1944. doi:10.1126/science.1057984. PMID 11239149. Bibcode: 2001Sci...291.1941C. https://www.mit.edu/~kardar/research/seminars/Casimir/Science-Capasso.pdf. 
  16. ↑ Bressi, G.; Carugno, G.; Onofrio, R.; Ruoso, G. (2002). "Measurement of the Casimir Force between Parallel Metallic Surfaces". Phys. Rev. Lett. 88 (4): 041804. doi:10.1103/PhysRevLett.88.041804. PMID 11801108. Bibcode: 2002PhRvL..88d1804B. 
  17. ↑ Decca, R. S.; López, D.; Fischbach, E.; Krause, D. E. (2003). "Measurement of the Casimir Force between Dissimilar Metals". Phys. Rev. Lett. 91 (5): 050402. doi:10.1103/PhysRevLett.91.050402. PMID 12906584. Bibcode: 2003PhRvL..91e0402D. 
  18. ↑ White, H.; March, P. (2012). "Advanced Propulsion Physics: Harnessing the Quantum Vacuum". Nuclear and Emerging Technologies for Space. http://www.lpi.usra.edu/meetings/nets2012/pdf/3082.pdf. 
  19. ↑ MacLay, G. Jordan; Forward, Robert L. (2004-03-01). "A Gedanken Spacecraft that Operates Using the Quantum Vacuum (Dynamic Casimir Effect)". Foundations of Physics 34 (3): 477–500. doi:10.1023/B:FOOP.0000019624.51662.50. Bibcode: 2004FoPh...34..477M. 
  20. ↑ Wilson, C. M.; Johansson, G.; Pourkabirian, A.; Johansson, J. R.; Duty, T.; Nori, F.; Delsing, P. (2011). "Observation of the dynamical Casimir effect in a superconducting circuit". Nature 479 (7373): 376–379. doi:10.1038/nature10561. PMID 22094697. Bibcode: 2011Natur.479..376W. 
  21. ↑ "First Observation of the Dynamical Casimir Effect". Emerging Technology from the arXiv. 2011. https://www.technologyreview.com/s/424111/first-observation-of-the-dynamical-casimir-effect/. Retrieved 25 November 2016. 
  22. ↑ White, H.; March, P. (2012). "Advanced Propulsion Physics: Harnessing the Quantum Vacuum". Nuclear and Emerging Technologies for Space. http://www.lpi.usra.edu/meetings/nets2012/pdf/3082.pdf. 
  23. ↑ Feigel, A. (2004). "Quantum Vacuum Contribution to the Momentum of Dielectric Media". Phys. Rev. Lett. 92 (2): 020404. doi:10.1103/PhysRevLett.92.020404. PMID 14753923. Bibcode: 2004PhRvL..92b0404F. 
  24. ↑ Schützhold, Ralf; Plunien, Günter (2004). "Comment on "Quantum Vacuum Contribution to the Momentum of Dielectric Media"". Phys. Rev. Lett. 93 (26): 268901. doi:10.1103/PhysRevLett.93.268901. PMID 15698036. Bibcode: 2004PhRvL..93z8901S. 
  25. ↑ Feigel, A. (2004). "Feigel Replies". Phys. Rev. Lett. 93 (26): 268902. doi:10.1103/PhysRevLett.93.268902. Bibcode: 2004PhRvL..93z8902F. 
  26. ↑ van Tiggelen, B. A.; Rikken, G. L. J. A. (2004). "Comment on "Quantum Vacuum Contribution to the Momentum of Dielectric Media"". Phys. Rev. Lett. 93 (26): 268901. doi:10.1103/PhysRevLett.93.268901. PMID 15698036. Bibcode: 2004PhRvL..93z8901S. 
  27. ↑ Feigel, A. (2004). "Feigel Replies". Phys. Rev. Lett. 93 (26): 268904. doi:10.1103/PhysRevLett.93.268904. Bibcode: 2004PhRvL..93z8904F. 
  28. ↑ van Tiggelen, B. A.; Rikken, G. L. J. A.; Krstić, V. (2006). "Momentum Transfer from Quantum Vacuum to Magnetoelectric Matter". Phys. Rev. Lett. 96 (13): 130402. doi:10.1103/PhysRevLett.96.130402. PMID 16711970. Bibcode: 2006PhRvL..96m0402V. http://www.tara.tcd.ie/bitstream/handle/2262/38886/Momentum.pdf?sequence=1&isAllowed=y. 
  29. ↑ Birkeland, Ole Jakob; Brevik, Iver (2007). "On the Feigel Effect: Extraction of Momentum from Vacuum?". Phys. Rev. E 76 (6): 066605. doi:10.1103/PhysRevE.76.066605. PMID 18233935. Bibcode: 2007PhRvE..76f6605B. 
  30. ↑ Obukhova, Yuri N.; Hehla, Friedrich W. (2008). "Forces and momenta caused by electromagnetic waves in magnetoelectric media". Physics Letters A 372 (22): 3946–3952. doi:10.1016/j.physleta.2008.03.021. Bibcode: 2008PhLA..372.3946O. 
  31. ↑ van Tiggelen, B.A. (2008). "Zero-point momentum in complex media". The European Physical Journal D 47 (2): 261–269. doi:10.1140/epjd/e2008-00027-1. Bibcode: 2008EPJD...47..261V. 
  32. ↑ Cho, Adrian (2004). "Focus: Momentum From Nothing". Phys. Rev. Focus 13: 3. doi:10.1103/physrevfocus.13.3. 
  33. ↑ T., Roth; G. L. J. A., Rikken (2002). "Observation of Magnetoelectric Linear Birefringence". Phys. Rev. Lett. 88 (6): 063001. doi:10.1103/PhysRevLett.88.063001. PMID 11863802. Bibcode: 2002PhRvL..88f3001R. 
  34. ↑ Croze, Ottavio A. (2012). "Alternative derivation of the Feigel effect and call for its experimental verification". Proceedings of the Royal Society A 468 (2138): 429–447. doi:10.1098/rspa.2011.0481. Bibcode: 2012RSPSA.468..429C. 
  35. ↑ Dereli, T.; Gratus, J.; Tucker, R. W. (2007). "The Covariant Description of Electromagnetically Polarizable Media". Physics Letters A 361 (3): 190–193. doi:10.1016/j.physleta.2006.10.060. Bibcode: 2007PhLA..361..190D. "Early suggestions by Minkowski and Abraham for the structure of its electromagnetic component in simple media initiated a long debate involving both theoretical and experimental contributions that continues to the current time (see e.g. ...[Feigel (2004)]...)... Although it is widely recognised that this controversy is an argument about definitions [Mikura (1976)]". 
  36. ↑ Mikura, Ziro (1976). "Variational formulation of the electrodynamics of fluids and its application to the radiation pressure problem". Phys. Rev. A 13 (6): 2265–2275. doi:10.1103/PhysRevA.13.2265. Bibcode: 1976PhRvA..13.2265M. "The energy-momentum conservation law can be derived separately for the material and the field subsystems. The energy-momentum tensor of the total system cannot be split in a unique way into the material and the field parts.". 
  37. ↑ Brito, Hector Hugo (1999). "Propellantless propulsion by electromagnetic inertia manipulation: Theory and experiment". AIP Conf. Proc. 458: 994. doi:10.1063/1.57710. Bibcode: 1999AIPC..458..994B. http://www.intalek.com/Index/Projects/Research/0994.pdf. ""However, as mentioned previously, the whole system Energy-Momentum tensor is unsymmetrical; this is a rather uncomfortable property for a system assumed to be a closed one...As a conjecture, if ZPF (Zero Point Field) were a physical reality for describing inertia (Haisch, 1994), that “excess” EM momentum could be explained as a form of “directed”, anisotropic vacuum fluctuations of EM energy. The sought extended system would then happen to be space-time itself... The issue is, as shown, highly relevant to “propellantless” propulsion and experiments to definitely settle the question were still missing besides some partialized attempts (James 1968, Walker 1975, Waker 1977, Lahoz 1979), whose results were not conclusive enough. A positive answer for the Minkowski's EM tensor would allow to obtain “jet-less” propulsive effects by EM fields manipulation, on one hand; on the other hand, it could also represents an indirect demonstration of the physical reality of ZPF, as a possible explanation for unsymmetrical energy-momentum tensors of closed systems."". 
  38. ↑ White, H.; March, P. (2012). "Advanced Propulsion Physics: Harnessing the Quantum Vacuum". Nuclear and Emerging Technologies for Space. http://www.lpi.usra.edu/meetings/nets2012/pdf/3082.pdf. 
  39. ↑ 39.0 39.1 White, Harold G. (2015). "A discussion on characteristics of the quantum vacuum". Physics Essays 28 (7): 496–502. doi:10.4006/0836-1398-28.4.496. Bibcode: 2015PhyEs..28..496W. 
  40. ↑ Khoury, Justin; Weltman, Amanda (2004). "Chameleon Cosmology". Phys. Rev. D 69 (4): 044026. doi:10.1103/PhysRevD.69.044026. Bibcode: 2004PhRvD..69d4026K. 
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  42. ↑ Carroll, Sean M. (1998). "Quintessence and the Rest of the World: Suppressing Long-Range Interactions". Physical Review Letters 81 (15): 3067–3070. doi:10.1103/PhysRevLett.81.3067. ISSN 0031-9007. Bibcode: 1998PhRvL..81.3067C. 
  43. ↑ Carroll, Sean (2011). "Dark Energy FAQ". http://www.preposterousuniverse.com/blog/2011/10/04/dark-energy-faq/. Retrieved 28 November 2016. 
  44. ↑ Clark, Stuart (2016). Amita, Gilead. ed. "Our Implausible Universe". New Scientist 232 (3097): 35. https://www.newscientist.com/article/mg23230970-800-cosmic-coincidences-the-universe-is-flat-as-a-pancake/. 
  45. ↑ Forward, Robert L. (1985). "Extracting electrical energy from the vacuum by cohesion of charged foliated conductors". Phys. Rev. B 30 (4): 1700–1702. doi:10.1103/PhysRevB.30.1700. Bibcode: 1984PhRvB..30.1700F. http://www.zpower.com/wap/documents/ZPEPaper_ExtractingElectricalEnergyFromTheVacuumByCohesionOfChargedFoliatedConductors.pdf. 
  46. ↑ Pinto, F. (1999). "Engine cycle of an optically controlled vacuum energy transducer". Phys. Rev. B 60 (21): 14740–14755. doi:10.1103/PhysRevB.60.14740. Bibcode: 1999PhRvB..6014740P. 
  47. ↑ Millis, Marc G. (2011). "Progress in revolutionary propulsion physics". 61st International Astronautical Congress, Prague (International Astronautical Federation). Bibcode: 2011arXiv1101.1063M. 
  48. ↑ 48.0 48.1 Pena, Luis de la; Cetto, Ana Maria; Valdes-Hernandez, Andrea (2014). The Emerging Quantum: The Physics Behind Quantum Mechanics. p. 95. doi:10.1007/978-3-319-07893-9. ISBN 9783319078939. https://books.google.co.uk/books?id=v0MqBAAAQBAJ. 
  49. ↑ Barrett, Terence W. (2008). Topological Foundations of Electromagnetism. Singapore: World Scientific. p. 2. ISBN 9789812779977. https://books.google.com/?id=e0-QdLqT-pIC. 
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  51. ↑ Couder, Yves; Fort, Emmanuel (2006). "Single-Particle Diffraction and Interference at a Macroscopic Scale". Phys. Rev. Lett. 97 (15): 154101. doi:10.1103/PhysRevLett.97.154101. PMID 17155330. Bibcode: 2006PhRvL..97o4101C. http://users.isy.liu.se/en/jalar/kurser/QF/assignments/Couder2006.pdf. 
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  58. ↑ https://plus.google.com/117663015413546257905/posts/WfFtJ8bYVya
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  61. ↑ https://www.youtube.com/watch?v=Wokn7crjBbA
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  74. ↑ "Anomalous Thrust Production from an RF Test Device Measured on a Low-Thrust Torsion Pendulum". https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20140006052.pdf. 
  75. ↑ Brady, David; White, Harold; March, Paul; Lawrence, James; Davies, Frank (2014). "Anomalous Thrust Production from an RF Test Device Measured on a Low-Thrust Torsion Pendulum". 50th AIAA/ASME/SAE/ASEE Joint Propulsion Conference. doi:10.2514/6.2014-4029. ISBN 978-1-62410-303-2. 
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  78. ↑ Yang, J.; Liu, X.-C.; Wang, Y.-G.; Tang, M.-J.; Luo, L.-T.; Jin, Y.-Z.; Ning, Z.-X. (February 2016). "Thrust Measurement of an Independent Microwave Thruster Propulsion Device with Three-Wire Torsion Pendulum Thrust Measurement System". Journal of Propulsion Technology(in Chinese). 37 (2): 362–371.
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