# RF resonant cavity thruster

(Redirected from EmDrive)

A radio frequency (RF) resonant cavity thruster, also known as an EmDrive, is a controversial proposed type of electromagnetic thruster with a microwave cavity, designed to produce thrust from an electromagnetic field inside the cavity. Skeptics have deemed it to be impossible.[1][2][3][4][5]

Disciplines Controversial invention Prototype resonant cavity thruster built by NASA's Eagleworks Laboratories Device produces thrust without a reaction force. 2001 Roger Shawyer No theoretical consensus over how devices could produce thrust, if at all.

Such thrusters have been hypothesized since 2001 when British engineer Roger Shawyer published details of the concept. To date, there is no theoretical consensus as to how a resonant cavity could produce such thrust.[6] As of 2017, a few tests of prototype drives have observed a small apparent thrust, while other prototypes did not show thrust, and no prototype has been successfully tested more than once.[7] Due to apparent discrepancies with the laws of physics as they are currently understood[8] and lack of reproducible evidence, many theoretical physicists and commentators have been led to label the device "impossible", explaining the observed thrust by measurement errors.[9] The arising scepticism has led many media platforms to refer to the engine as the Impossible Drive or the Impossible Space Drive.[10][11][12][13][4]

## History and contextEdit

Electromagnetic propulsion designs which operate on the principle of reaction mass have been around since the start of the 20th century. In the 1960s, extensive research was conducted on two designs which emit high velocity ionized gases in similar ways: ion thrusters that convert propellant to ions and accelerate and eject them via electric potentials, and plasma thrusters that convert propellant to plasma ions and accelerate and eject them via plasma currents. In the latter, plasma can be generated from an intense source of microwave or other radio-frequency (RF) energy, and in combination with a resonant cavity, can be tuned to resonate at a precise frequency.[14]

A low-propellant space drive has long been a goal for space exploration, since the propellant is dead weight that must be lifted and accelerated with the ship all the way from launch until the moment it is used (see Tsiolkovsky rocket equation). Gravity assists, solar sails, and beam-powered propulsion from a spacecraft-remote location such as the ground or in orbit, are useful because they allow a ship to gain speed without propellant. However, some of these methods do not work in deep space. Shining a light out of the ship provides a small force from radiation pressure, i.e., using photons as a form of propellant, but the force is far too weak (for a given amount of input power) to be useful in practice.

A true zero-propellant drive is widely believed to be impossible, but if it existed, it could potentially be used for travel in many environments including deep space. Thus, such drives are a popular concept in science fiction, and their improbability contributes to enthusiasm for exploring such designs.[6][15][16]

Conventional rocket engines expel propellant, such as when ships move masses of water, aircraft move masses of air, or rockets expel exhaust. A drive which does not expel propellant in order to produce a reaction force, providing thrust while being a closed system with no external interaction, would be a reactionless drive. Such a drive would violate the conservation of momentum and Newton's third law, leading many physicists to believe it to be impossible, labeling the idea pseudoscience.[7] On the other hand, a drive that interacts with an external field would be part of an open system, propellantless but not reactionless, like a sail catching and redirecting existing winds to move a ship.

The first proposal for an RF resonant cavity thruster came from British engineer Roger Shawyer in 2001. He invented a design with a conical cavity, calling it the EmDrive. Guido Fetta later built the Cannae Drive based on Shawyer's concept [15][16] a resonant thruster with a pillbox-shaped cavity. Since 2008, a few physicists have tested their own models, trying to confirm results claimed by Shawyer and Fetta. Juan Yang at Xi'an's Northwestern Polytechnical University (NWPU) initially reported thrust from a model they built,[17] but retracted her claims in 2016 after a measurement error was identified and an improved setup measured no significant thrust.[18][19] In 2016, Harold White's group at NASA's Eagleworks Laboratories reported a test of their own model had observed 40–100 μN of thrust from inputs of 40–80 W, in the Journal of Propulsion and Power.[20] In December 2016, Yue Chen, part of the communication satellite division of the China Academy of Space Technology (CAST), said his team had tested several prototypes using an "experimental verification platform", observed thrust, and was carrying out in-orbit verification.[21][22][23][24] In September 2017, Chen talked about this CAST project again in an interview on CCTV.[25]

## ControversyEdit

The plausibility of thrusters that emit no propellant, such as the EmDrive, is controversial, primarily because their operation would violate the conservation of momentum.[16][26]

Media coverage of experiments using these designs has been controversial and polarized. The EmDrive first drew attention, both credulous and dismissive, when New Scientist wrote about it as an "impossible" drive in 2006.[27] Media outlets were later criticised for misleading claims that a resonant cavity thruster had been "validated by NASA"[28] following White's first tentative test reports in 2014.[29] Scientists have continued to note the lack of unbiased coverage, from both polarized sides.[30]

In 2006, responding to the New Scientist piece, mathematical physicist John C. Baez at the University of California, Riverside, and Australian science-fiction writer Greg Egan, said the positive results reported by Shawyer were likely misinterpretations of experimental errors.[31]

In 2014, Harold White's conference paper suggested that resonant cavity thrusters could work by transferring momentum to the "quantum vacuum virtual plasma."[32] Baez and Carroll criticized this explanation, because in the standard description of vacuum fluctuations, virtual particles do not behave as a plasma; Carroll also noted that the quantum vacuum has no "rest frame", providing nothing to push against, so it can't be used for propulsion.[9][33] In the same way, physicists James F. Woodward and Heidi Fearn published two papers showing that the amount of electron-positron virtual pairs of the quantum vacuum, used by White as a virtual plasma propellant, cannot account for thrusts in any isolated, closed electromagnetic system such as a quantum vacuum thruster.[34][35]

Physicists Eric W. Davis at the Institute for Advanced Studies in Austin, and Sean M. Carroll at the California Institute of Technology,[36] said in 2015 that the thrust reported in papers by both Tajmar and White were indicative of thermal effect errors.

## Designs and prototypesEdit

Simplified schematic drawing of an EmDrive prototype by Tajmar and Fiedler, according to Shawyer's model

### EmDriveEdit

In 2001, Shawyer founded Satellite Propulsion Research Ltd, in order to work on the EmDrive, a drive that he said used a resonant cavity to produce thrust without propellant. The company was backed by a "Smart Award" grant from the UK Department of Trade and Industry.[16] In December 2002, he described a working prototype with a total thrust of about 0.02 newtons powered by an 850 W cavity magnetron. The device could operate for only a few dozen seconds before the magnetron failed, due to overheating.[37]

#### Second device and New Scientist articleEdit

In October 2006, Shawyer conducted tests on a new water-cooled prototype and said that it had increased thrust.[38] He planned to have the device ready to use in space by May 2009 and was considering making the resonant cavity a superconductor.[38]

New Scientist magazine[39] featured the EmDrive on the cover of 8 September 2006 issue. The article portrayed the device as plausible and emphasized the arguments of those who held that point of view. Science fiction author Greg Egan distributed a public letter stating that "a sensationalist bent and a lack of basic knowledge by its writers" made the magazine's coverage unreliable, sufficient "to constitute a real threat to the public understanding of science". Especially, Egan said he was "gobsmacked by the level of scientific illiteracy" in the magazine's coverage, alleging that it used "meaningless double-talk" to obfuscate the problem of conservation of momentum. The letter was endorsed by mathematical physicist John C. Baez and posted on his blog.[31][9] New Scientist editor Jeremy Webb responded to critics, stating:

It is a fair criticism that New Scientist did not make clear enough how controversial Roger Shawyer’s engine is. We should have made more explicit where it apparently contravenes the laws of nature and reported that several physicists declined to comment on the device because they thought it too contentious ... The great thing is that Shawyer's ideas are testable. If he succeeds in getting his machine flown in space, we will know soon enough if it is ground-breaking device or a mere flight of fancy.[27]

New Scientist also published a letter from the former technical director of EADS Astrium, who stated: "I reviewed Roger’s work and concluded that both theory and experiment were fatally flawed. Roger was advised that the company had no interest in the device, did not wish to seek patent coverage and in fact did not wish to be associated with it in any way",[40] and a letter from physicist Paul Friedlander, who stated

As I read it, I, like the thousands of other physicists who will have read it, immediately realised that this was impossible as described. Physicists are trained to use certain fundamental principles to analyse a problem and this claim clearly flouted one of them ... The Shawyer drive is as impossible as perpetual motion. Relativistic conservation of momentum has been understood for a century and dictates that if nothing emerges from Shawyer’s device then its centre of mass will not accelerate. It is likely that Shawyer has used an approximation somewhere in his calculations that would have been reasonable if he hadn’t then multiplied the result by 50,000. The reason physicists value principles such as conservation of momentum is that they act as a reality check against errors of this kind.[41]

#### Later workEdit

In 2007, the UK Department of Trade and Industry granted SPR an export licence to Boeing in the US.[42] In December 2008, Shawyer was invited to The Pentagon to present on the EmDrive, and in 2009 Boeing confirmed they wanted to license the technology.[43] The UK Ministry of Defence agreed to a technology transfer, and SPR designed, built and tested a thruster for use on a test satellite. According to Shawyer, the 10-month contract was completed by July 2010 and the thruster, giving 18 grams of thrust, was transferred to Boeing. Boeing did not however license the technology and communication stopped.[44] Questioned on the matter in 2012, a Boeing representative confirmed that Boeing Phantom Works used to explore exotic forms of space propulsion, including Shawyer's drive, but such work has since ceased. They confirmed that "Phantom Works is not working with Mr. Shawyer,” adding that the company is no longer pursuing those explorations.[15]

In 2013 and 2014, Shawyer presented ideas for 'second-generation' EmDrive designs and applications, at the annual International Astronautical Congress. A paper based on his 2014 presentation was published in Acta Astronautica in 2015.[45] It describes a model for a superconducting resonant cavity and three models for thrusters with multiple cavities, with hypothetical applications for launching space probes.

In October 2016, a UK patent application describing a new superconducting EmDrive was published,[46] followed by a first international version.[47] Shortly thereafter Shawyer unveiled the creation of Universal Propulsion Ltd., a new company aimed to develop and commercialise such thrusters, as a joint venture with Gilo Industries Group, a small UK aerospace company designing and selling paramotors and the Parajet Skycar.[44]

### Cannae and other drivesEdit

The Cannae Drive (formerly Q-drive),[48] another engine designed to generate propulsion from a resonant cavity without propellant, is another implementation of this idea. Its cavity is also asymmetric, but relatively flat rather than a truncated cone. It was designed by Fetta in 2006 and has been promoted within the US through his company, Cannae LLC, since 2011.[48][49][50][51][52] In 2016, Fetta announced plans to eventually launch a cubesat satellite containing a version of the Cannae Drive, which they would run for 6 months to observe how it functions in space.[53]

In China, researchers working under Yang at NWPU developed their own prototype resonant cavity thruster in 2008, publishing a report in their university's journal on the theory behind such devices. In 2012 they measured thrust from their prototype, however in 2014 they found this had been an experimental error. A second, improved prototype did not produce any measured thrust.[15][54][55]

At the China Academy of Space Technology, Yue Chen filed several patent applications in 2016 describing various RF resonant cavity thruster designs. These included a method for stacking several short resonant cavities to improve thrust,[56] and a design with a cavity that was a semicylinder instead of a frustum.[57] That December, Chen announced that CAST was conducting tests on a resonant cavity thruster in orbit,[58] without specifying what design was used. In an interview on CCTV in September 2017, Chen Yue showed some testing of a flat cylindrical device corresponding to the patent describing stacked short cavities with internal diaphragms.[59][56]

## Conservation of momentumEdit

The EmDrive appears to violate the conservation of momentum which states any interaction cannot have a net force; a consequence of the conservation of momentum is Newton's third law where for every action there is an equal and opposite reaction.[7] The conservation of momentum is a symmetry of nature.[60]

In instances where matter appears to violate conservation laws, the apparent non-conservation is in reality an interaction with the vacuum so that overall symmetry in the system is restored.[clarification needed][61] An often cited example of apparent nonconservation of momentum is the Casimir effect;[62] in the standard case where two parallel plates are attracted to each other. However the plates move in opposite directions, so no net momentum is extracted from the vacuum and, moreover, the energy must be put into the system to take the plates apart again.[63]

Assuming homogeneous electric and magnetic fields, it is impossible for the EmDrive, or any other device, to extract a net momentum transfer from either a classical or quantum vacuum.[63] Extraction of a net momentum "from nothing"[64][65] has been postulated in an inhomogeneous vacuum, but this remains highly controversial as it will violate Lorentz invariance.[63]

Both Harold White's[66][67][68][62] and Mike McCulloch's[69] theories of how the EmDrive could work rely on these asymmetric or dynamical Casimir effects. However, if these vacuum forces are present, they are expected to be exceptionally tiny based on our current understanding, too small to explain the level of observed thrust.[63][70][71] In the event that observed thrust is not due to experimental error, a positive result could indicate new physics.[72][73]

## HypothesesEdit

Various attempts have been made to come up with a potential mechanism for the apparent thrust. However, to date, there is no acceptance or consensus over how, if at all, these cavities produce thrust. Attempts to explain the thrust fall into three categories:[74]

• The thrust observed isn't real and is the result of measurement error. Most theoretical scientists who have looked at the EmDrive believe this to be the case.
• There is a change in the electromagnetic or vacuum field, such that the change in the momentum of the field balances the change in momentum of the thruster.
• There is an exhaust that isn't being measured.

The simplest and most likely explanation is that any thrust detected is due to experimental error or noise. While some experimental observations have led to a fundamentally new understanding of physics, such as the anomalous precession of Mercury which saw Newtonian gravity overturned by Einstein's general relativity or the Wu experiment which was the first observation of a broken symmetry, more often than not anomalous results which would fundamentally change our understanding of physics are eventually explained as sources of error present in the experimental set up. Famous examples of which include N-rays, faster-than-light neutrinos, the Pioneer anomaly and cold fusion.[70]

### Noise or experimental errorEdit

White's illustration of the superposition of displacements caused by thermal expansion, a pulse, and the cumulative effect of a pulse + thermal expansion

White's displacement test results

The simplest and most likely explanation is that any thrust detected is due to experimental error or noise.[citation needed] In all of the experiments set up, a very large amount of energy goes into generating a tiny amount of thrust. The strongest early result, from Yang's group in China, was later reported to be caused by a large experimental error.[18]

White's 2016 paper went through about a year of peer review involving five referees, instead of a more typical two referees.[75][7] Peer review does not mean the results or observations are true, only that the referees looked at the experiment, results and interpretation and found it to be sound and sensible.[7] Brice Cassenti, a professor at the University of Connecticut and expert in advanced propulsion, spoke to one of the referees, and reported the referee did not believe the results point to any new physics, but that the results were puzzling enough to publish.[73] Cassenti believes there is a mundane explanation for the results, but the probability of the results being valid is slim but not zero.[73]

White's paper was published in the Journal of Propulsion and Power. Marc Millis and Eric Davies who ran NASA's previous advanced propulsion project, the Breakthrough Propulsion Physics Program have commented that while White used techniques that would be acceptable for checking the electric propulsion of Hall thrusters, the tests were not sufficient to demonstrate that any new physics effect exists.[72]

White discusses nine possible sources of experimental error,[7][76] arguing that most of those error sources were eliminated "fairly definitively" but that further work was needed to address possible thermal effects. He later said, "We’re still potentially even in the mode of definitively eliminat[ing] all false positives.”[75]

#### Shift in center of gravity due to thermal effectsEdit

Infrared imagery showing heating of the RF amplifier and heat sink

The largest error source is believed to come from the thermal expansion of the thruster's heat sink; as it expands this would lead to a change in the centre of gravity causing the resonant cavity to move. White's team attempted to model the thermal effect on the overall displacement by using a superposition of the displacements caused by "thermal effects" and “impulsive thrust” with White saying "That was the thing we worked the hardest to understand and put in a box". Despite these efforts, White's team were unable to fully account for the thermal expansion. In an interview with Aerospace America, White comments that "although maybe we put a little bit of a pencil mark through [thermal errors]... they are certainly not black-Sharpie-crossed-out.”[75]

Their method of accounting for thermal effects has been criticized by Millis and Davies, who highlight that there is a lack of both mathematical and empirical detail to justify the assumptions made about those effects. For example, they do not provide data on temperature measurement over time compared to device displacement. The paper includes a graphical chart, but it is based on a priori assumptions about what the shapes of the “impulsive thrust” and "thermal effects" should be, and how those signals will superimpose. The model further assumes all noise to be thermal, and does not include of other effects such as interaction with the chamber wall, power lead forces, and tilting. Because the Eagleworks paper has no explicit model for thrust to compare with the observations, it is ultimately subjective, and its data can be interpreted in more than one way. The Eagleworks test therefore does not conclusively show a thrust effect, but cannot rule it out either.[72]

White suggested future experiments could run on a Cavendish balance. In such a setup, the thruster could rotate out to much larger angular displacements, letting a thrust (if present) dominate any possible thermal effects. Testing a device in space would also eliminate the center-of-gravity issue. [75]

#### Interaction with the vacuum chamber’s wallEdit

Another source of error arises from electromagnetic interaction with the walls of the vacuum chamber.[75] White argued that any wall interaction could only be the result of a well-formed resonance coupling between the device and wall, and that the high frequency used imply the chances of this would be highly dependent on the device's geometry. As components get warmer due to thermal expansion, the device's geometry changes, shifting the resonance of the cavity. In order to counter this effect and keep the system in optimal resonance conditions, White used a phase-locked loop system (PLL). Their analysis assumed that using a PLL ruled out significant electromagnetic interaction with the wall.[20]

#### Power cablingEdit

Another source of error was a Lorentz force arising from power leads. In order to eliminate interference from cable forces, many tests have made use of Galinstan liquid metal screws to minimize such forces. However error sources can still arise from magnetic damping. Martin Tajmar in his experiment at Dresden University of Technology ran dummy tests on their experimental setup, and found magnetic interaction with power cables to be the most significant source of noise. When he replaced the galinstan liquid metal damping with oil fluid damping, and ran the experiment again, the only thrust they observed was well within the range of experimental error.[77] White's power setup may have been different; but their paper does not state if the connections are all coaxially aligned with the stand’s rotation axis, which would be required to minimize errors from Lorentz forces, and it gives no data from equivalent tests with power into a dummy load so these influences can be compared with those seen in the test run.[72]

#### Other error sourcesEdit

Other possible sources of error include air currents, tilting of the thrust stand, vibration, electrostatic interaction, outgassing and a photon rocket force. (These are unlikely to have contributed significantly to White's observations.)

Shawyer has suggested that thrust from a frustum cavity is caused by a radiation pressure imbalance between the two faces of the cavity.[54] He gave a presentation on this at the International Astronautical Congress 2014, later publishing it in the peer-reviewed Acta Astronautica.[45] In it he wrote, In an EmDrive engine, microwave energy is converted to mechanical force according to the thrust equation, derived from the basic radiation pressure equation: F= 2 P0 / c. Shawyer's thrust equation, derived from Allen Cullen's equations,[78] is given by:

${\displaystyle F={\frac {2P_{0}}{c}}\ Q_{u}\left({\frac {\lambda _{0}}{\lambda _{g1}}}-{\frac {\lambda _{0}}{\lambda _{g2}}}\right)\left(1-{\frac {\lambda _{0}^{2}}{\lambda _{g1}\lambda _{g2}}}\right)^{-1}}$

where ${\displaystyle F}$  is the force, ${\displaystyle P_{0}}$  is the incident power, ${\displaystyle c}$  is the speed of light, ${\displaystyle Q_{u}}$  is the unloaded Q factor of the cavity, ${\displaystyle \lambda _{0}}$  is the wavelength of the microwaves in free space, and ${\displaystyle \lambda _{g1}}$  and ${\displaystyle \lambda _{g2}}$  are the wavelengths at the end of the largest and smallest cross-section, respectively.

Shawyer insists the EmDrive is an open system. However, physicists point out that relying only on special relativity, without emitting anything and with no interaction with an outside field or matter, makes his drive a closed system. Since the two end plates are part of the thruster and the microwaves are trapped inside the cavity, standard Einstein–Maxwell equations and the conservation of momentum show no effective thrust can occur due to any force on the cavity caused by internal electromagnetic energy.[a][79]

### Vacuum energyEdit

Harold White, the lead scientist in the NASA investigations, suggested in 2014 that their model could be an example of a quantum vacuum thruster (QVT). This is a theoretical system that would use magnetohydrodynamics to generate thrust, similar to conventional plasma thrusters, only using the fleeting vacuum quantum fluctuations of the zero-point field as an extremely low-density plasma.[20][80][81]

White's 2016 paper states that pilot-wave theories, non-mainstream interpretations of quantum mechanics based on the de Broglie–Bohm theory, may help explain how QVTs could "push off of the quantum vacuum and preserve the laws of conservation of energy and conservation of momentum.".

In 2017, a Portuguese team published a paper proposing pilot-wave theory as a possible explanation to the EmDrive thrust, that would not break conservation laws. The principle is that a sufficiently strong asymmetrical electromagnetic field could act as a pilot wave. The cavity would then be attracted toward regions of higher electromagnetic intensity. The researchers propose to increase thrust by shaping the cavity with an exponential form like that of a trumpet bell instead of a frustum.[82][83]

### Quantized inertiaEdit

A 2017 paper in EPL by Mike McCulloch[84] a lecturer in geomatics at Plymouth University, describes a method by which thrust from resonant cavities could be predicted using his own controversial approach of quantization of inertia, the "Modified Inertia Hubble-scale Casimir effect" (MiHsC).[85][86][87][88][89][90]

While this model allows the device to create thrust without breaking Newton's third law, it assumes that Unruh radiation is real.[84] The mechanism involves more Unruh radiation fitting the wide end of the cavity than its narrow end, continuously shifting the center of inertial mass of the microwaves towards the wide end: the cavity then has to move towards the small end, for momentum to be conserved.[91]

This hypothesis is testable, and McCulloch has suggested building a cavity where the length of the cavity is the same as the diameter of the small end, causing Unruh radiation to fit better in the small end, resulting in a reversal of thrust.[88]

### Photon leakageEdit

Scientists in Finland have proposed a possible explanation of this phenomenon involving the propagation of microwave photons leaking from the closed metal cavity and thereby producing an exhaust momentum, satisfying the classical action-reaction principle.[92] This explanation relies on the wave-particle duality of electromagnetic radiation, postulating that the stochastic phases of the microwaves will (with some probability) result in destructive interference between microwaves which cancels their electromagnetic fields but allows continued propagation of the microwave photon pairs, generating net thrust consistent with the impulse-momentum theorem depending on the asymmetric shape of the cavity.[92][93][94][95]

The observed thrust of experimental results has been argued to exceed the maximum efficiency of a perfectly collimated photon rocket, comprised between 3.33 and 6.67 µN/kW.[96] However, the paper follows on White's idea of a degradable quantum vacuum for effective pair production,[citation needed] and Lewis's original concept of the photon which would be the conserved entity of nature, not its carried energy:[97] The authors argue that the environment modifies photon energy and that pairing of photons within the electromagnetic energy density gradient of a resonant cavity would cause a shift down in energy, and the loss of electromagnetic potential becomes available for thrust, so according to the authors the level of energy of the paired photon when it escapes the cavity and the associated thrust efficiency remain an open question. The authors also argue that the cavity walls become transparent for the photon pair when it forms; as it has no associated electromagnetic field, it escapes the cavity to sparser surroundings.[92]

### Mach effectEdit

A group of scientists led by James F. Woodward claim general relativity allows propellantless propulsion using a Mach effect.[98] In a fully Machian general relativity theory like the Hoyle–Narlikar theory of gravity, inertia is a physical gravitational interaction of matter with the rest of the mass-energy in the universe, through an action at a distance instantaneous radiative reaction field. In the theory, a mass changing effect suitable for propulsion emerges from the general equation of motion.[99]

The RF resonant cavity thruster would act as a capacitor where surface currents propagate inside the cavity on the conic wall, between the two end plates; electromagnetic resonant modes create electric charges on each end plate; a Mach effect is triggered by Lorentz forces from surface currents on the conic wall; and a thrust force arise in the RF cavity, due to the variation of the electromagnetic density from evanescent waves inside the skin layer. When a polymer insert is placed asymmetrically in the cavity, its dielectric properties result in greater asymmetry, while decreasing the cavity Q factor. The cavity's acceleration is a function of all the above factors, and the model can explain the acceleration of the cavity with and without a dielectric.[34][100] Like the slingshot maneuver of a spacecraft exchanging momentum with a planet, a Mach effect gravity-assist drive is an open system where momentum is conserved when accounting for gravitational interaction. The thruster, acting as an "impulse engine" would then be propellantless, but not reactionless. In more speculative developments, the second term present in Woodward's transient mass equation indicates the mass fluctuations could theoretically become largely negative, producing exotic matter suitable for an Alcubierre warp drive.

### Warp fieldEdit

2D visualisation of spacetime distortion induced by the Alcubierre metric.

It has been suggested that time-varying electromagnetic energy density could produce a local gradient in the gravitational potential (a distortion or warping of spacetime, sometimes called "warp fields"),[101] as in the theoretical Alcubierre drive or diametric drive. Warp fields have never been observed, however they could potentially be tested using interferometry.[102] White developed the White–Juday warp-field interferometer to attempt to detect such fields over short distances. His team used one to test a symmetric resonant cavity in 2013, and observed small anomalous effects.[103] However the effects have yet to be replicated on an asymmetric cavity, or in a vacuum to prevent interference from the heating of surrounding air.[104]

Physicist Fernando Minotti, building on work by Matt Visser,[b][105] estimated the forces on asymmetric electromagnetic resonant cavities using a particular scalar–tensor theory of the Brans–Dicke type, an alternate framework for describing gravity that competes with general relativity. In Minotti's model, thrust results from gravitational forces on the cavity walls, with some scalar coupling field providing an effective negative energy source. Minotti suggested that this model implies the direction of the force produced by a resonant cavity would be dependent on its resonant mode, and the thrust magnitude would increase with the thickness and mass of the cavity walls.

However, Minotti noted that the scalar–tensor theory he used is not accepted by the majority of the scientific community, and that his linear model also erroneously predicts large gravitational effects due to the Earth's magnetic field which do not exist. He hypothesized that some nonlinear version of his model might provide a framework which does not predict such unreal effects.[c][106]

After Yang retracted her previous high power results,[18] Minotti completed a revaluation of the scalar-tensor theory fixing some inconsistencies. The equations are now derived without ad hoc conditions and Maxwell's equations are obtained in the weak field approximation with no unreal prediction.[107][108]

## Tests and experimentsEdit

### Tests by the inventorsEdit

In 2004, Shawyer reported seven independent positive reviews from experts at BAE Systems, EADS Astrium, Siemens and the IEE,[109] however these were disputed. In a letter to New Scientist, the then-technical director of EADS Astrium (Shawyer's former employer) denied this, stating

"I reviewed Roger’s work and concluded that both theory and experiment were fatally flawed. Roger was advised that the company had no interest in the device, did not wish to seek patent coverage and in fact did not wish to be associated with it in any way."[40]

In 2011, Fetta tested a superconducting version of the Cannae drive. The RF resonant cavity was suspended inside a liquid helium-filled dewar. The weight of the cavity was monitored by load cells. Fetta theorized that when the device was activated and produced upward thrust, the load cells would detect the thrust as change in weight. When the drive was energized by sending 10.5 watt power pulses of RF power into the resonant cavity, there was, as predicted, a reduction in compressive force on the load cells consistent with thrust of 8–10 mN.

None of these results have been published in the scientific literature, or replicated by independent researchers. They have been posted on their inventors' websites.[110]

In 2015, Shawyer published an article in Acta Astronautica, summarising existing tests on the EmDrive. Of seven tests, four produced a measured force in the intended direction and three produced thrust in the opposite direction. Furthermore, in one test, thrust could be produced in either direction by varying the spring constants in the measuring apparatus.[111]

### Northwestern Polytechnical UniversityEdit

In 2008, a team of Chinese researchers led by Juan Yang (杨涓), professor of propulsion theory and engineering of aeronautics and astronautics at Northwestern Polytechnical University (NWPU) in Xi'an, China, said that they had developed a valid electro-magnetic theory behind a microwave resonant cavity thruster.[17][112] A demonstration version of the drive was built and tested with different cavity shapes and at higher power levels in 2010. Using an aerospace engine test stand usually used to precisely test spacecraft engines like ion drives,[16][54][55] they reported a maximum thrust of 720 mN at 2,500 W of input power.[55] Yang noted that her results were tentative, and said she "[was] not able to discuss her work until more results are published".[16] This positive result was over 100x more thrust per input power than any other experiment, and inspired other groups to try to replicate their work.

In a 2014 follow-up experiment (published in 2016), Yang could not reproduce the 2010 observation and suggested it was due to experimental error.[18] In that experiment they refined their experimental setup, using a three-wire torsion pendulum to measure thrust, and tested two different power setups. In one trial, the power system was outside the cavity, and they observed a "thrust" of 8–10 mN. In a second trial, the power system was within the cavity, and they measured no such thrust. Instead they observed an insignificant thrust below their noise threshold of 3 mN, fluctuating between ±0.7 mN with a measurement uncertainty of 80%, with 230 W of input power. They concluded that they were unable to measure significant thrust; that "thrust" measured when using external power sources (as in their 2010 experiment) could be noise; and that it was important to use self-contained power systems for these experiments, and more sensitive pendulums with lower torsional stiffness.[18]

### NASA EagleworksEdit

Since 2011, White has had a team at NASA known as the Advanced Propulsion Physics Laboratory, or Eagleworks Laboratories, which is devoted to studying exotic propulsion concepts.[113] The group has investigated ideas for a wide range of untested and fringe proposals, including Alcubierre drives, drives that interact with the quantum vacuum, and RF resonant cavity thrusters.

In 2014, the group began testing resonant cavity thrusters of their own design and sharing some of their results. In November 2016, they published their first peer-reviewed paper on this work, in the Journal of Propulsion and Power.[20][114][115][116][117]

#### EmDrive and tapered cavitiesEdit

In July 2014, White reported tentative positive results for evaluating a tapered RF resonant cavity.[32] Testing was performed using a low-thrust torsion pendulum able to detect force at the micronewton level within a sealed but unevacuated vacuum chamber (the RF power amplifier used an electrolytic capacitor unable to operate in a hard vacuum).[32] The experimenters recorded directional thrust immediately upon application of power.

Their first tests of this tapered cavity were conducted at very low power (2% of Shawyer's 2002 experiment). A net mean thrust over five runs was measured at 91.2 µN at 17 W of input power.[32] The experiment was criticized for its small data set and for not having been conducted in vacuum, to eliminate thermal air currents.

The group announced a plan to upgrade their equipment to higher power levels, to use vacuum-capable RF amplifiers with power ranges of up to 125 W, and to design a new tapered cavity that could be in the 0.1 N/kW range. The test article was to be subject to independent verification and validation at Glenn Research Center, the Jet Propulsion Laboratory and the Johns Hopkins University Applied Physics Laboratory.[32][118] As of 2016, this validation has not happened.[119]

In 2015, Paul March from Eagleworks made new results public, measured with a torsional pendulum in a hard vacuum: about 50 µN with 50 W of input power at 5.0×10−6 torr.[118] The new RF power amplifiers were said to be made for hard vacuum, but failed rapidly due to internal corona discharges. Without funding to replace or upgrade them, measurements were scarce for a time.[120]

They conducted further experiments in vacuum, a set of 18 observations with 40-80W of input power. They published the results in the American Institute of Aeronautics and Astronautics's peer-reviewed Journal of Propulsion and Power, under the title "Measurement of Impulsive Thrust from a Closed Radio-Frequency Cavity in Vacuum". This was released online in November 2016, with print publication in December.[20][115][116][117] The study said that the system was "consistently performing with a thrust-to-power ratio of 1.2±0.1mN/kW", and enumerated many potential sources of error.[20]

The paper suggested that pilot-wave theory (a controversial, non-mainstream deterministic interpretation of quantum mechanics) could explain how the device produces thrust.[20][116][117] Commenters pointed out that just because a study reporting consistent thrust was published with peer-review does not necessarily mean that the drive functions as claimed.[7][115] Physicist Ethan Siegal commented on the paper, saying that the drive most likely does not violate conservation of momentum as this would "make physics fall apart" but rather that there is something else going on. He said that "Whether it’s new physics [or] the effect’s cause simply hasn’t been determined yet, more and better experiments will be the ultimate arbiter".[74] Physicist Chris Lee was very critical of the work, saying that the paper had a small data set and a number of missing details he described as 'gaping holes'.[121] Electrical Engineer George Hathaway analyzed and criticized the scientific method described in the paper.[122]

#### Cannae driveEdit

White's 2014 tests also evaluated two Cannae drive prototypes.[32] One had radial slots engraved along the bottom rim of the resonant cavity interior, as required by Fetta's hypothesis to produce thrust;[49] another "null" test article lacked those radial slots. Both drives were equipped with an internal dielectric.[32] A third test article, the experimental control, had an RF load but no resonant cavity interior. These tests took place at atmospheric pressure.

About the same net thrust was reported for both the device with radial slots and the device without slots. Thrust was not reported for the experimental control. Some considered the positive result for the non-slotted device a possible flaw in the experiment, as the null test device had been expected to produce less or no thrust based upon Fetta's hypothesis of how thrust was produced by the device.[9][123][124] In the complete paper, however, White concluded that the test results proved that "thrust production was not dependent upon slotting".[32]

### Dresden University of TechnologyEdit

In July 2015 an aerospace research group at the Dresden University of Technology (TUD) under Martin Tajmar reported results for an evaluation of an RF resonant tapered cavity similar to the EmDrive.[77] Testing was performed first on a knife-edge beam balance able to detect force at the micronewton level, atop an antivibration granite table at ambient air pressure; then on a torsion pendulum with a force resolution of 0.1 mN, inside a vacuum chamber at ambient air pressure and in a hard vacuum at 400 µPa (4×10−6 mbar).

They used a conventional ISM band 2.45 GHz 700 W oven magnetron, and a small cavity with a low Q factor (20 in vacuum tests). They observed small positive thrusts in the positive direction and negative thrusts in the negative direction, of about 20 µN in a hard vacuum. However, when they rotated the cavity upwards as a "null" configuration, they observed an anomalous thrust of hundreds of micronewtons, significantly larger than the expected result of zero thrust. This indicated a strong source of noise which they could not identify. This led them to conclude that they could not confirm or refute claims about such a thruster. At the time they considered future experiments with better magnetic shielding, other vacuum tests and improved cavities with higher Q factors.

Eric W. Davis, a physicist at the Institute for Advanced Studies at Austin, noted "The experiment is quite detailed but no theoretical account for momentum violation is given by Tajmar, which will cause peer reviews and technical journal editors to reject his paper should it be submitted to any of the peer-review physics and aerospace journals."[36]

### Tests in spaceEdit

In August 2016, Cannae announced plans to launch its thruster on a 6U cubesat which they would run for 6 months to observe how it functions in space. Cannae has formed a company called Theseus for the venture and partnered with LAI International and SpaceQuest Ltd. to launch the satellite. No launch date has yet been announced.[53]

In November 2016 the International Business Times reported that the U.S. government was testing a version of the EmDrive on the Boeing X-37B and that the Chinese government has made plans to incorporate the EmDrive on its orbital space laboratory Tiangong-2.[125][126]

In December 2016, Yue Chen told a reporter at China's Science and Technology Daily that his team was testing an EmDrive in orbit, and that they had been funding research in the area for five years. Chen noted that their prototype's thrust was at the "micronewton to millinewton level", which would have to be scaled up to at least 100–1000 millinewtons for a chance of conclusive experimental results. Despite this, he said his goal was to complete validation of the drive, and then to make such technology available in the field of satellite engineering "as quickly as possible".[127][128][129][130][58]

## NotesEdit

1. ^ Another leading explanation is that the EmDrive’s thrust is generated by radiation pressure, a position held by its inventor Roger Shawyer. […] Yet, according to Woodward, both of these theories are unlikely to be correct for a simple reason: Physics doesn’t allow them. By way of example, Woodward likened explaining the results seen at NASA purely in terms of microwave pressure to arguing that you can accelerate a car by getting in the driver’s seat and pushing on the windshield. "Can any disposition of microwaves inside the cavity produce thrust?" said Woodward. "There's a simple answer to that question: No, it cannot. Conservation of momentum dictates that any purely electromagnetic system that is enclosed cannot produce thrust. This is for both quantum theory and classical electrodynamics. It's physically impossible."[79]
2. ^ Certain classical systems (such as non-minimally coupled scalar fields) have been found that violate the null and the weak energy conditions. […] We will take the bubble velocity to be non-relativistic, v ≪ 1. Thus we are not focussing attention on the "superluminal" aspects of the warp bubble, […] but rather on a secondary unremarked effect: The warp drive (if it can be realised in nature) appears to be an example of a "reaction-less drive" wherein the warp bubble moves by interacting with the geometry of spacetime instead of expending reaction mass.[105]
3. ^ It appears that General Relativity might allow for such kind of reactionless propulsion, as exemplified and noted for the first time [by Lobo & Visser], where the low velocity limit of some warp drive spacetimes was analyzed. As indicated there, negative energy densities are required to accomplish that and, notably, some scalar fields present this possibility. […] The lowest mode (ν = 1.05 GHz) leads to a force much larger in magnitude and of opposite direction to that of the next two modes. This and other dependencies of the predicted force, as the proportionality to the cavity wall thickness […] can be explored experimentally with relative ease to test the theory.[106]

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