The Woodward effect, also referred to as a Mach effect, is part of a hypothesis proposed by James F. Woodward in 1990. The hypothesis states that transient mass fluctuations arise in any object that absorbs internal energy while undergoing a proper acceleration. Harnessing this effect could generate a reactionless thrust, which Woodward and others claim to measure in various experiments. Hypothetically, the Woodward effect would allow for field propulsion spacecraft engines that would not have to expel matter. Such a proposed engine is sometimes called a Mach effect thruster (MET) or a Mach Effect Gravitational Assist (MEGA) drive. So far, experimental results have not strongly supported this hypothesis, but experimental research on this effect, and its potential applications, continues. The Space Studies Institute was selected as part of NASA's Innovative Advanced Concepts program as a Phase I proposal in April 2017 for Mach Effect research. The year after, NASA awarded a NIAC Phase II grant to the SSI to further develop these propellantless thrusters. The effect is controversial within mainstream physics because the underlying model proposed for it appears to be faulty, resulting in violations of energy conservation as well as momentum conservation. According to Woodward, at least three Mach effects are theoretically possible: vectored impulse thrust, open curvature of spacetime, and closed curvature of spacetime. The first effect, the Woodward effect, is the minimal energy effect of the hypothesis. The Woodward effect is focused primarily on proving the hypothesis and providing the basis of a Mach effect impulse thruster. In the first of three general Mach effects for propulsion or transport, the Woodward effect is an impulse effect usable for in-orbit satellite station-keeping, spacecraft reaction control systems, or at best, thrust within the solar system. The second and third effects are open and closed space-time effects. Open curved space-time effects can be applied in a field generation system to produce warp fields. Closed-curve space-time effects would be part of a field generation system to generate wormholes. The third Mach effect is a closed-curve spacetime effect or closed timelike curve called a benign wormhole. Closed-curve space is generally known as a wormhole or black hole. Prompted by Carl Sagan for the scientific basis of wormhole transport in the movie Contact, Kip Thorne developed the theory of benign wormholes. The generation, stability, and traffic control of transport through a benign wormhole is only theoretical at present. One difficulty is the requirement for energy levels approximating a 'Jupiter size mass'. Kenneth Nordtvedt showed in 1988 that gravitomagnetism, which is an effect predicted by general relativity but hadn't yet been observed at that time and was even challenged by the scientific community, is inevitably a real effect because it is a direct consequence of the gravitational vector potential. He subsequently showed that the gravitomagnetism interaction (not to be confused with the Nordtvedt effect), like inertial frame dragging and the Lense–Thirring precession, is typically a Mach effect. The Woodward effect is based on the relativistic effects theoretically derived from Mach's principle on inertia within general relativity, attributed by Albert Einstein to Ernst Mach. Mach's Principle is generally defined as 'the local inertia frame that is completely determined by the dynamic fields in the Universe.' The conjecture comes from a thought experiment: 'Ernst Mach (1838–1916) was an Austrian physicist […] contemporary of Einstein, to whom he suggested a thought experiment: What if there was only one object in the universe? Mach argued that it could not have a velocity, because according to the theory of relativity, you need at least two objects before you can measure their velocity relative to each other. Taking this thought experiment a step further, if an object was alone in the universe, and it had no velocity, it could not have a measurable mass, because mass varies with velocity. Mach concluded that inertial mass only exists because the universe contains multiple objects. When a gyroscope is spinning, it resists being pushed around because it is interacting with the Earth, the stars, and distant galaxies. If those objects didn't exist, the gyroscope would have no inertia. Einstein was intrigued by this concept, and named it "Mach's principle."' A formulation of Mach's principle was first proposed as a vector theory of gravity, modeled on Maxwell's formalism for electrodynamics, by Dennis Sciama in 1953, who then reformulated it in a tensor formalism equivalent to general relativity in 1964. In this paper, Sciama stated that instantaneous inertial forces in all accelerating objects are produced by a primordial gravity-based inertial radiative field created by distant cosmic matter and propagating both forward and backward in time at light speed: 'Inertial forces are exerted by matter, not by absolute space. In this form the principle contains two ideas: 1. Inertial forces have a dynamical rather than a kinematical origin, and so must be derived from a field theory [or possibly an action-at-a-distance theory in the sense of J.A. Wheeler and R.P. Feynman…] 2. The whole of the inertial field must be due to sources, so that in solving the inertial field equations the boundary conditions must be chosen appropriately.' Sciama's inertial-induction idea has been shown to be correct in Einstein's general relativity for any Friedmann–Robertson–Walker cosmology. According to Woodward, the derivation of Mach effects is relativistically invariant, so the conservation laws are satisfied, and no 'new physics' is involved besides general relativity. As previously formulated by Sciama, Woodward suggests that the Wheeler–Feynman absorber theory would be the correct way to understand the action of instantaneous inertial forces in Machian terms. 'A first image to understand would be filming a sequence where a rock is thrown in the middle of a pond, making concentric ripples on the water propagating towards the shore. Running the sequence backwards (thinking it as seeing events running backward in time) we then observe concentric waves propagating from the shore towards the center of the pond, where a rock emerges. The thing to understand is that advanced waves coming back from the future never propagate farther into the past than the rock hitting the water that initiated all of the waves.' The Wheeler-Feynman absorber theory is an interpretation of electrodynamics that starts from the idea that a solution to the electromagnetic field equations has to be symmetric with respect to time-inversion, as are the field equations themselves. Wheeler and Feynman showed that the propagating solutions to classical wave equations can either be retarded (i.e. propagate forward in time) or advanced (propagate backward in time). The absorber theory has been used to explain quantum entanglement and led to the transactional interpretation of quantum mechanics, as well as the Hoyle-Narlikar theory of gravity, a Machian version of Einstein's general relativity. Fred Hoyle and Jayant Narlikar originally developed their cosmological model as a quasi steady state model of the universe, adding a 'Creation field' generating matter out of empty space, an hypothesis contradicted by recent observations. When the C-field is not used, ignoring the parts regarding mass creation, the theory is no longer steady state and becomes a Machian extension of general relativity. This modern development is known as the Gravitational Absorber Theory. As the gravitational absorber theory reduces to general relativity in the limit of a smooth fluid model of particle distribution, both theories make the same predictions. Except in the Machian approach, a mass changing effect emerges from the general equation of motion, from which Woodward's transient mass equation can be derived. A resulting force suitable for Mach effect thrusters can then be calculated. While the Hoyle-Narlikar derivation of the Mach effect transient terms is done from a fully nonlinear, covariant formulation, it has been shown Woodward's transient mass equation can also be retrieved from linearized general relativity. Further research has shown that this term is only significant when mass-energy fluctuations are in the distant sources, many light-years away. When the mass fluctuation is generated locally, as it must be for any propulsion device since fluctuations in distant objects cannot be controlled, the effect is a high order term that is too small to be used for propulsion or be measured in a laboratory. According to Woodward, a transient mass fluctuation arises in an object when it absorbs 'internal' energy as it is accelerated. Several devices could be built to store internal energy during accelerations. A measurable effect needs to be driven at a high frequency, so macroscopic mechanical systems are out of question since the rate at which their internal energy could be modified is too limited. The only systems that could run at a high frequency are electromagnetic energy storage devices. For fast transient effects, batteries are ruled out. A magnetic energy storage device like an inductor using a high-permeability core material to transfer the magnetic energy could be specially built. But capacitors are preferable to inductors because compact devices storing energy at a very high energy density without electrical breakdown are readily available. Shielding electrical interferences are easier than shielding magnetic ones. Ferroelectric materials can be used to make high-frequency electro-mechanical actuators, and they are themselves capacitors so they can be used for both energy storage and acceleration. Finally, capacitors are cheap and available in various configurations. So Mach effect experiments have always relied on capacitors so far. When the dielectric of a capacitor is submitted to a varying electric power (charge or discharge), Woodward's hypothesis predicts a transient mass fluctuation arises according to the transient mass equation (TME): δm_0 = (1 / (4πG)) * [ (1 / (ρ_0 * c^2)) * (∂P/∂t) - (1 / (ρ_0 * c^2))^2 * (P^2 / V) ] where: - m_0 is the proper mass of the dielectric, - G is the gravitational constant, - c is the speed of light in vacuum, - ρ_0 is the proper density of the dielectric, - V is the volume of the dielectric, - P is the instantaneous power delivered to the system. This equation is not the full Woodward equation as seen in the book. There is a third term, - (∂/∂t (ϕ / c^2))^2, which Woodward discounts because his gauge sets ϕ / c^2 ≈ 1; the derivatives of this quantity must therefore be negligible. The transient mass equation shows that when the dielectric material of a capacitor is cyclically charged then discharged while being accelerated, its mass density fluctuates, by around plus or minus its rest mass value. Therefore, a device can be made to oscillate either in a linear or orbital path, such that its mass density is higher while the mass is moving forward, and lower while moving backward, thus creating an acceleration of the device in the forward direction, i.e. a thrust. This effect, used repeatedly, does not expel any particle and thus would represent a type of apparent propellantless propulsion, which seems to be in contradiction with Newton's third law of motion. However, Woodward states there is no violation of momentum conservation in Mach effects: 'If we produce a fluctuating mass in an object, we can, at least in principle, use it to produce a stationary force on the object, thereby producing a propulsive force thereon without having to expel propellant from the object. We simply push on the object when it is more massive, and pull back when it is less massive. The reaction forces during the two parts of the cycle will not be the same due to the mass fluctuation, so a time-averaged net force will be produced. This may seem to be a violation of momentum conservation. But the Lorentz invariance of the theory guarantees that no conservation law is broken. Local momentum conservation is preserved by the flux of momentum in the gravity field that is chiefly exchanged with the distant matter in the universe.' Two terms are important for propulsion on the right-hand side of the previous equation: - The first, linear term (1 / (ρ_0 * c^2)) * (∂P/∂t) is called the impulse engine term because it expresses mass fluctuation depending on the derivative of the power, and scales linearly with the frequency. Past and current experiments about Mach effect thrusters are designed to demonstrate thrust and the control of one type of Mach effect. - The second, quadratic term - (1 / (ρ_0 * c^2))^2 * (P^2 / V) is what Woodward calls the wormhole term, because it is always negative. Although this term appears to be many orders of magnitude weaker than the first term, which makes it usually negligible, theoretically, the second term's effect could become huge in some circumstances. The second term is driven by the first impulse engine term; when fluctuations reach a very high amplitude and mass density is driven very close to zero, mass should achieve very large negative values very quickly, with a strong non-linear behavior. In this regard, the Woodward effect could generate exotic matter. Applications of propellantless propulsion include straight-line thrusters or impulse engines, open curved fields for starship warp drives, and closed curved fields such as traversable benign wormholes. The mass of the electron is positive according to the mass–energy equivalence E = mc^2, but this invariant mass is made from the bare mass of the electron 'clothed' by a virtual photon cloud. According to quantum field theory, as those virtual particles have an energy more than twice the bare mass of the electron, mandatory for pair production in renormalization, the nonelectromagnetic bare mass of the 'unclothed' electron has to be negative. Using the ADM formalism, Woodward proposes that the physical interpretation of the 'wormhole term' in his transient mass equation could be a way to expose the negative bare mass of the electron, in order to produce large quantities of exotic matter that could be used in a warp drive to propel a spacecraft or generate traversable wormholes. Current spacecraft achieve a change in velocity by the expulsion of propellant, the extraction of momentum from stellar radiation pressure or the stellar wind, or the utilisation of a gravity assist ('slingshot') from a planet or moon. These methods are limiting in that rocket propellants have to be accelerated as well and are eventually depleted, and the stellar wind or gravitational fields can only be utilized locally in the Solar System. In interstellar space and bereft of the above resources, different forms of propulsion are needed to propel a spacecraft, and they are referred to as advanced or exotic. Impulse engine: If the Woodward effect is confirmed and if an engine can be designed to use applied Mach effects, then a spacecraft may be possible that could maintain a steady acceleration into and through interstellar space without the need to carry along propellants. Woodward presented a paper about the concept at the NASA Breakthrough Propulsion Physics Program Workshop conference in 1997, and continued to publish on this subject thereafter. Even ignoring for the moment the impact on interstellar travel, future spacecraft driven by impulse engines based on Mach effects would represent an astounding breakthrough in terms of interplanetary spaceflight alone, enabling the rapid colonization of the entire solar system. Travel times being limited only by the specific power of the available power supplies and the acceleration human physiology can endure, they would allow crews to reach any moon or planet in our solar system in less than three weeks. For example, a typical one-way trip at an acceleration of 1 g from the Earth to the Moon would last only about 4 hours; to Mars, 2 to 5 days; to the asteroid belt, 5 to 6 days; and to Jupiter, 6 to 7 days. Warp drives and wormholes: As shown by the transient mass fluctuation equation above, exotic matter could be theoretically created. A large quantity of negative energy density would be the key element needed to create warp drives as well as traversable wormholes. As such, if proven to be scientifically valid, practically feasible and scaling as predicted by the hypothesis, the Woodward effect could not only be used for interplanetary travel, but also for apparent faster-than-light interstellar travel: - The negative mass could be used to warp spacetime around a spaceship according to an Alcubierre metric. - Enough exotic matter could also be concentrated into a point of space to create a wormhole, and prevent it from collapsing. Woodward and others state that exotic matter could defocus energy at the outer mouth of the wormhole (making it a white hole) and shape the throat of such a gravitational singularity flat enough to avoid horizon and tidal stresses, resulting in an 'absurdly benign traversable wormhole' linking two regions of distant spacetime (like stargates), usable for instant interstellar/intergalactic travel or time travel. Two patents have been issued to Woodward and associates based on how the Woodward effect might be used in practical devices for producing thrust: - In 1994, the first patent was granted, titled: 'Method for transiently altering the mass of objects to facilitate their transport or change their stationary apparent weights' (US patent 5280864). - In 2002, a second patent was granted, titled: 'Method And Apparatus For Generating Propulsive Forces Without The Ejection Of Propellant' (US patent 6347766). - In 2016, a third patent was granted and assigned to the Space Studies Institute, covering the realistic realizations of Mach effects: 'Parametric amplification and switched voltage signals for propellantless propulsion' (US patent 9287840). Woodward and his associates have claimed since the 1990s to have successfully measured forces at levels great enough for practical use and also claim to be working on the development of a practical prototype thruster. No practical working devices have yet been publicly demonstrated. The NIAC contract awarded in 2017 by NASA for the development of Mach effect thrusters is a primary three-task effort, two experimental and one analytical: 1. Improvement of the current laboratory-scale devices, in order to provide long duration thrust at levels required for practical propulsion applications. 2. Design and development of a power supply and electrical systems to provide feedback and control of the input AC voltage, and resonant frequency, that determine the efficiency of the MET. 3. Improve theoretical thrust predictions and build a reliable model of the device to assist in perfecting the design. Predict maximum thrust achievable by one device and how large an array of thrusters would be required to send a probe (size 1.5 m diameter by 3 m, total mass 1245 kg including 400 kg of payload) a distance of 8 light-years away. Mach-Lorentz Thruster (MLT): A former type of Mach effect thruster was the Mach-Lorentz thruster (MLT). It used a charging capacitor embedded in a magnetic field created by a magnetic coil. A Lorentz force appears and acts upon the ions inside the capacitor dielectric. In such electromagnetic experiments, power can be applied at frequencies of several megahertz. However, a problem with some of these devices was discovered in 2007 by physicist Nembo Buldrini, called the Bulk Acceleration Conjecture, which pointed out that the object in which the mass fluctuations occur must be undergoing bulk acceleration at the same time, rather than just internal ion acceleration. Mach Effect Thruster (MET) or MEGA drive: To address this, Woodward designed a new device using capacitors and a series of thick PZT (lead zirconate titanate) piezoelectric disks. In first tests, Woodward used a capacitor shuttled back and forth between PZT actuators, with small PZT portions acting as accelerometers ('squeezometers'). He later built devices made exclusively of PZT disks. Forward momentum during mass increase is transferred to a brass end cap via elastic collision, while the subsequent decrease in mass density occurs during backward movement. The stack operates in a Faraday cage on a sensitive torsion arm in a vacuum chamber. Future plans include scaling thrust using high-κ dielectric nanocomposite polymers like PMN, PMN-PT, or CCTO. Resonant cavity thruster: Another proposed propellantless thruster, a resonant cavity thruster (such as the EmDrive), has been proposed to operate via a Mach effect. Asymmetric microwave cavities with surface currents and evanescent waves were tested by Harold White's team, reporting anomalous thrust, though these findings have been challenged as potential interactions between electric cables and Earth's magnetic field. From his initial paper onward, Woodward has claimed that this effect is detectable with modern technology. Experimental history includes: - In 1990, Woodward's original paper included an experiment with results. - In 1999, Thomas L. Mahood reported thrusts ranging from 0.03 to 15 µN in a torque pendulum vacuum chamber setup. - As of 2003, Hector Brito and Sergio Elaskar (Argentina) reported thrusts of about 50 µN. - In 2004, Paul March (Lockheed Martin) presented a replication at STAIF. - In 2004, John G. Cramer and coworkers (University of Washington) conducted NASA-funded tests that yielded inconclusive results due to electrical interference. - In 2006, Paul March and Andrew Palfreyman reported results exceeding predictions by one to two orders of magnitude. - In 2006, Martin Tajmar, Nembo Buldrini, Klaus Marhold, and Bernhard Seifert (Austrian Research Centers) studied the effect using a µN thrust balance and recommended further tests. - In 2010, Ricardo Marini and Eugenio Galian (IUA, Argentina) reported negative results, attributing measured effects to spurious electromagnetic interference. - In 2011, Harold 'Sonny' White and the NASA Eagleworks team reran 2006 devices with improved force sensors. - In 2012 and 2013, Woodward and Heidi Fearn (California State University, Fullerton) conducted null tests and investigated spurious causes (thermal, electromagnetic, Dean drive). - In 2014, Nembo Buldrini at FOTEC (Austria) qualitatively confirmed the presence of the effect on a thrust balance in high vacuum while recommending more investigation. Inertial frames: Inertial frames are in constant rectilinear motion relative to one another, but the underlying mechanism causing them to exist remains an open question in physics. Marc Millis noted that propellantless propulsion research must revisit unfinished physics regarding the origin of inertial frames against which momentum conservation is referenced. Conservation of momentum: In 2001, John Whealton et al. of Oak Ridge National Laboratory challenged the mathematical foundation of Woodward's hypothesis, noting laboratory results could be explained by time-varying thermal expansion, and that the F = d(mv)/dt expansion produces a dm/dt * v term that cancels out Woodward's predicted inertial force. Woodward responded that the dm/dt * v term vanishes in the instantaneous rest frame of the device and does not represent a physical force. Woodward maintains that momentum and energy are conserved globally through field exchanges with all distant matter in the universe. A Mach effect thruster acts not as an electrical-to-kinetic energy transducer, but as a gravinertial transistor controlling the flux of the gravitational field. Magnitude of force: Under Hoyle-Narlikar scalar-tensor gravity, José Rodal showed in 2019 that forces generated by local mass-energy fluctuations are higher-order terms that are too small to produce useful propulsion or detectable laboratory forces unless situated near extremely massive objects such as neutron stars. Measured laboratory effects are thus likely attributable to error sources. In 2009, Harold 'Sonny' White proposed the Quantum Vacuum Fluctuation (QVF) conjecture, replacing Sciama's gravinertial field with the quantum electrodynamic (QED) vacuum field to create momentum fluxes. This theoretical device is called a quantum vacuum plasma thruster (QVPT) or Q-thruster. Unlike Woodward's Mach effect thruster exchanging momentum with cosmic matter, White's concept posits pushing off virtual particle-antiparticle pairs. However, Woodward and Fearn demonstrated that virtual electron-positron pairs in a quantum vacuum cannot account for thrust in isolated, closed electromagnetic systems like the QVPT or EmDrive. Woodward's claims of potential breakthrough spaceflight technology have generated coverage across popular media (CNET, Boing Boing, Scientific American, io9), university news outlets (CSUF News), and specialized space media. Woodward was also featured in an interview for the television series Ancient Aliens (Season 7, Episode 1) discussing warp drives and stargates. Despite popular interest, significant skepticism remains within the wider scientific community.