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DARPA Is Researching Quantized Inertia, a Theory Many Think Is Pseudoscience

DARPA gave researchers $1.3 million to build a prototype engine that is fueled by light.
Image: Shutterstock

The Defense Advanced Research Projects Agency (DARPA) recently awarded a $1.3 million contract to an international team of researchers to study quantized inertia, a controversial theory that some physicists dismiss as pseudoscience.

Quantized inertia (QI) is an alternative theory of inertia, a property of matter that describes an object’s resistance to acceleration. QI was first proposed by University of Plymouth physicist Mike McCulloch in 2007, but it is still considered a fringe theory by many, if not most, physicists today. McCulloch has used the theory to explain galactic rotation speeds without the need for dark matter, but he believes it may one day provide the foundation for launching space vehicles without fuel.


The DARPA grant will allow McCulloch and a team of collaborators from Germany and Spain to undertake a series of experiments that will apply QI in a laboratory setting for the first time. This will involve creating experimental QI engines and using incredibly sensitive detectors to see if they can produce thrust—which would open the door for interstellar travel, satellites that never decay in orbit, and other “impossible” applications.

McCulloch told me that QI is “certainly” controversial, but also added that “DARPA is famous for taking chances on things that aren’t widely accepted if there is the potential for a huge payoff.”

The experiments are, in a way, a middle finger to the physicists who have spent the last decade dismissing QI as pseudoscientific or, as one physicist I spoke to on background described it to me, “a concatenation of buzz words and bullshit”.

Who Needs Dark Matter?

Mass is a fundamental property of all matter, but there are different ways to define it. One way is to refer to the object’s inertial mass, which describes the object’s resistance to acceleration. An intuitive way to think about this is to imagine punching a glass of water versus punching a car. Assuming that the force (the punch) applied to both objects is the same, the less massive object (the glass of water) will experience much more acceleration than the more massive object. Another way to define mass is by the object’s ability to attract other objects—this is known as an object’s gravitational mass.

In the history of physics, every experiment has shown that an object’s inertial mass is equal to its gravitational mass. This relationship was codified by Albert Einstein in the early 20th century as the “equivalence principle,” which basically states that an observer will be unable to tell the difference between the effects of a constant gravitational field and a constant acceleration.


Consider the case of someone standing in a windowless elevator. If the elevator is placed on Earth’s surface, the person will experience a constant gravitational force equal to 9.8 meters per second squared. Yet if someone were to attach rocket boosters to the elevator and accelerate it to 9.8 meters per second squared, the person inside the elevator wouldn’t be able to tell if they were rocketing through space or planted firmly on Earth’s surface.

The equivalence principle was the starting point for Einstein’s theory of general relativity and is a bedrock of classical Newtonian physics. Yet in the 20th century it became increasingly difficult to reconcile this principle with cosmological observations.

On the left is the expected motion of stars if they were only affected by visible matter—notice how their rotation is slower on the outskirts of the galaxy. On the right is the actual observed motion of stars in a galaxy—the rotational speeds are effectively the same, regardless of the distance from the galactic center. Image: University of Arizona

In particular, thousands of observations of galactic rotation show that there isn’t enough visible matter in these galaxies to account for their movement. According to classic Newtonian physics, the rotational speed of stars should decrease in proportion to their distance from the center of their host galaxy because the influence of gravity is also decreasing. Yet as Vera Rubin’s galactic observations demonstrated in the 1970s, the rotational velocities of stars didn’t decrease—it stayed the same.


This curious observation created a deep rift among cosmological physicists. Most physicists adopted Rubin’s explanation, which attributed the galactic rotation to the presence of a type of theoretical particle called dark matter.

Dark matter is invisible to the naked eye and only weakly interacts with normal matter. Yet its sheer abundance—physicists estimate dark matter accounts for 85 percent of matter in the universe—meant it could induce notable gravitational effects on large objects. Dark matter is believed to be mostly concentrated in a halo around a galaxy, and the gravitational influence of the dark matter halo is used to explain why the rotational velocity of stars doesn’t decrease on the edge of galaxies compared to their center.

Read More: The New Hunt for Dark Matter Is Taking Place Under a Mountain in Italy

In the past 50 years, some of the most sensitive and sophisticated scientific instruments ever built have been dedicated to detecting dark matter. Most of these devices are located in deep underground laboratories to shield them from cosmic radiation, but so far none of the hypothesized dark matter particles have been detected. As a result, dark matter is a theory that keeps the equivalence principle intact, but requires a particle that no one has ever detected.

Some physicists believe this is because they’ve been looking for the wrong type of particle, while others suggest we need better detectors. A more controversial opinion, however, is that the reason we haven’t detected dark matter is because it doesn’t exist.


What is Quantized Inertia?

This is the premise of modified Newtonian dynamics (MOND), a theory first proposed in the early 1980s that suggests that below a certain acceleration the relationship between gravity and distance becomes linear. Below this point, the equivalence principle no longer holds.

MOND is an intriguing theory, but one of its major weaknesses is that the transition point where Newtonian dynamics breaks down has to be “tuned” to fit observational data and a satisfactory justification for this adjustment of the transition point still hasn’t been given.

In response, McCulloch proposed the quantized inertia theory, which accounts for an object’s inertial mass independent of its gravitational mass. By decoupling an object’s inertial mass and gravitational mass, McCulloch claims to be able to explain the observed galactic rotations using only their visible matter. This is done by invoking the Unruh effect, originally theorized by the physicist Bill Unruh in 1976.

An important implication of QI, and one of the main reasons it is so controversial, is that it abandons the equivalence principle. The inertial mass of an object is no longer coupled to its gravitational mass and is instead explained by the effects of Unruh radiation on the object.

The Unruh effect states that an accelerating object will perceive an increase in temperature (Unruh radiation) that would not be noticed by an object at the same location traveling at a constant speed.


In QI theory, an object accelerating to the left produces a horizon to the right. This horizon is a limit beyond which information cannot reach the object due to how fast information can travel—the speed of light. The horizon acts like a wall for the Unruh radiation insofar as it damps or suppresses this radiation on the right. The suppressing effect creates a radiation imbalance so that there is more radiation on the left (the “warm Unruh bath”) than on the right (the “cold Unruh bath”). This excess of radiation works against the initial acceleration of the object because it “bangs into” the object as it moves to the left.

A further difficulty for the theory is that physicists are divided on whether the Unruh effect has ever been observed. McCulloch is “fairly certain” that it has been seen in past experiments. He is in for a challenge, however, since the DARPA contract will require him and his colleagues to apply the Unruh effect in an experimental engine.

“QI explains inertia for the first time,” McCulloch said at a TED talk earlier this year. “In a sense it unifies physics. I’m using horizons that come from relativity, but quantum waves which come from quantum physics. Actually demonstrating this in a lab is going to be very difficult because we’re going to need very high accelerations and it’s not quite known how to damp quantum waves yet. If we do it though, we should be able to launch a capsule without fuel.”


QI, the EmDrive, and Interstellar Starships

So how can a theory meant to be an alternative to dark matter be harnessed to create a new type of propulsion system powered by electromagnetic radiation (read: light)? The fundamental idea would be to create a sort of “shield” that would dampen the Unruh radiation produced by a highly accelerated object so that it increases the object’s acceleration, rather than impedes it. Thus, a shield placed above a rocket, say, would help increase its acceleration vertically.

“I believe QI could be a real game changer for space science,” McCulloch said in a statement after receiving the DARPA contract. “I always thought it could be used to convert light into thrust, but it also suggests ways to enhance that thrust. It is hugely exciting to now have the opportunity to test it.”

If McCulloch and his team are successful, it would represent an unprecedented breakthrough in propulsion systems. It would be particularly applicable in space, where achieving the speeds necessary to reach escape velocity usually requires large amounts of chemical propellant. (The downside of this, of course, is that rockets must carry their propellant with them on their journey. If you want to lift more into space, you’re going to need more fuel, and in order to carry more fuel, you’re going to need more fuel, and so on.)

Unlike a traditional rocket engine, a QI-based thruster would simply need enough power to fuel an electric core. This core would be highly accelerated to produce the Unruh radiation that could be harnessed for propulsion using a conductive shield to dampen the Unruh waves. The exact design for a QI-based engine hasn’t been worked out yet, but that’s part of what McCulloch and his colleagues will be investigating with their DARPA contract.


The EmDrive developed by NASA researchers. Image: NASA

It’s a radical idea, but McCulloch isn’t the only physicist looking into exotic propulsion systems. Last year, it was revealed that researchers at NASA were building an EmDrive, a so-called “impossible engine” that uses high frequency radio waves to produce thrust. The NASA researchers claimed to have produced a miniscule amount of thrust with their experimental engine, but attempts to replicate their results have turned up empty-handed.

Although McCulloch sees applications of his QI theory being used to develop the EmDrive, other researchers investigating exotic propulsion aren’t buying the hype. So far, some of the most convincing work on the EmDrive has focused on mach effects, a theory of acceleration first advanced by the Call State Fullerton physicist James Woodward in the early 1990s.

According to Woodward’s theory, when an object is accelerated some of the force generated isn’t converted into kinetic energy but is stored as potential energy in the object. As the acceleration of the object changes so too does the internal energy of the object, which manifests as a change in the resting mass of that body.

Read More: The Fact and Fiction of the NASA EmDrive Leak

Woodward says inertia results through the gravitational attraction of all the objects in the universe, whose gravitational force is related to their mass. If an object’s mass changes during acceleration because some of the force is temporarily stored in object, so too does its inertia, or resistance to that acceleration. This imbalance created in the process propels the object forward without expelling matter, in theory providing the foundation for a reactionless engine.


In the case of NASA’s EmDrive tests, Woodward thinks the thrust reportedly observed by the researchers may be generated by the microwave radiation applied to the inside of a test chamber as explained by his theory of Mach effects.

When I asked Woodward if he thought that QI could be an alternative explanation for the observed EmDrive thrust, he emphatically rejected the theory.

“McCulloch's speculative conjecture about the origin of inertia depends on the appearance of electromagnetic waves in accelerating reference frames, a conjecture first proposed more than 20 years ago,” Woodward told me in an email.

According to Woodward, if inertia is explained by electromagnetic waves, then the neutron should be only two thirds the mass of a proton because of the way the electromagnetic field couples with electric charges. In reality, however, neutrons are just slightly more massive than protons. Since QI also depends on a type of electromagnetic wave (Unruh radiation), Woodward argued, it is plagued by the same mathematical incongruities.

“The prospect that his scheme will lead to a breakthrough in propulsion is quite bleak,” Woodward said. “But DARPA is in the business of funding highly improbable schemes.”

Woodward is hardly alone in his skepticism about the promise of QI. In an article written for Forbes last year, Rochester Institute of Technology physicist Brian Koberlein argued QI violated the laws of physics, particularly when it was applied to the EmDrive.


“The time-varying inertia allows the EmDrive to accelerate,” Koberlein said in his appraisal of McCulloch’s paper about QI. “The idea not only violates Newton’s third law of motion, it violates special relativity, general relativity, and Noether’s theorem. Since these are each well-tested theories that form the basis of countless other theories, their violation would completely overturn all of modern physics.”

“I’ve never been able to understand the objections to QI. No one has ever shown any evidence against the theory.”

McCulloch dismissed the criticisms as misunderstandings of how QI works. As far as Woodward’s claims were concerned, McCulloch said that QI doesn’t rely just on electromagnetic fields, but particle fields as well.

“What I’m suggesting is not electromagnetic; it’s a quantum mechanical effect,” McCulloch told me. “It’s an elegant mix of quantum mechanics and relativity. It’s got nothing to do with electromagnetics.”

As for Koberlein’s critique, McCulloch referred me to a point-by-point response he wrote to the Forbes article. In his response, McCulloch notes that the article “claims that Unruh radiation is so small it is incapable of generating an inertial force, but the author has not understood my papers: I have shown quite simply that when it is made non-uniform in space by relativistic horizons, Unruh does produce the right amount of force.”

“I’ve never been able to understand the objections to QI,” McCulloch told me on the phone. “No one has ever shown any evidence against the theory.”

Against claims that he is theorizing about pseudoscience, McCulloch argues that it is the physicists invoking dark matter who “have been on the slide into pseudoscience for decades” and that “the only reason the dark matterist haven’t noticed is they are all happily going down together, so self-correction has become impossible.” He points to 17 papers in which he uses QI to make accurate predictions without the need for constant adjustment that are often found in theories of dark matter.

Some Experiments for the Haters

The physics community is deeply divided on the reality of quantized inertia, but they won’t have to wait much longer for a resolution. Over the next four years, McCulloch and his colleagues will be designing experiments that will attempt to produce QI in a lab for the first time.

For the first year and a half of the grant, McCulloch will be working on theoretical models that will inform the design of the experiments. Then teams in Germany and Spain will build systems that attempt to produce thrust using QI.

In Germany, researchers will be using an experimental setup proposed last year by the US Army Space Command physicist Travis Taylor. As McCulloch described it to me, the experiment involves “bouncing laser light between two asymmetrical mirrors.” The system will receive an input of ten watts of power and if it is successful, will produce a peak of one Newton of thrust. (To put this in perspective, a SpaceX Falcon 9 rocket produces around 7.5 million Newtons of thrust.)

In Spain, a group of researchers led by the physicist Jose Luis Perez-Diaz, who recently spent six months working with McCulloch in the UK, will attempt to replicate an EmDrive using light instead of microwaves. In this set up, a two-watt laser beam will be fed into a fiber optic loop that is mounted on a “levitating, superconducting track.” The rapidly accelerated photons in the fiber optic loop are expected to produce Unruh radiation that can be damped using a metal conductor to create thrust.

According to McCulloch’s calculations, this experiment is only likely to produce about 0.001 Newtons of thrust—a barely detectable amount of force—but McCulloch told me the superconducting rail will be capable of registering the movement of the engine if any thrust is produced.

There is a chance, of course, that McCulloch and his collaborators are chasing a fantasy and their experiments won’t produce anything. Yet McCulloch told me he feels confident in the math behind QI and that it’s just a matter of translating his theory into an experimental setting. It’s a big gamble for all the physicists involved, but if it’s successful, it would be an unprecedented breakthrough in space exploration—and that seems worth the risk.