These are exciting days for physics, with several recent experimental observations providing important information on some of the most important mysteries of nature. The Large Hadron Collider at CERN has found the Higgs boson, the last missing particle in the Standard Model, advancing our understanding of the origin of the mass of fundamental particles. The discovery by astrophysicists that the expansion of the universe is accelerating implies that 75% of the universe is composed of "dark energy." And a recent trailer for Avengers: Age of Ultron suggests an explanation for the long-standing open question: can the Hulk lift Thor’s hammer?

The scene in question aired Oct. 28 during an episode of Marvel’s Agents of S.H.I.E.L.D. on ABC. In this clip, the Avengers are relaxing in their street clothes in Tony Stark’s penthouse apartment, and are discussing the "enchantment" on Thor’s hammer, Mjolnir, which stipulates that it can only be lifted by those "deemed worthy," and whoever does so will "possess the power of Thor." Thor places his hammer on a coffee table (actually, as shown below, it is resting partially on some books on the table), and various heroes attempt to pick up the hammer, to no avail. Thor then hefts the hammer and casually flips it into the air.

And thus one proposal for why the hammer is unliftable is put to rest. Astrophysicist and Director of the Hayden Planetarium, Dr. Neil deGrasse Tyson, has speculated that, if Mjolnir is composed of neutron star matter, the densest material in the universe outside of a black hole, then it would weigh as much as three hundred billion elephants. Water has a density of one gram per cubic centimeter, and lead has a density of eleven grams per cubic centimeter, but they pale compared to neutron star matter, which has a density of one hundred million million grams per cubic centimeter. In this case Mjolnir would weigh roughly twelve thousand trillion pounds. I know Tony Stark is rich, but even if he could buy a coffee table that could support such a weight, I can’t imagine any book, even an impenetrable physics text, that could bear up under this force. No, we must look elsewhere for an explanation as to why only Thor (and a few select others—more on this in a moment) can raise Mjolnir.

Norse mythology and Marvel Comics tell us that Mjolnir is composed of "uru metal," forged ages ago by the blacksmith Etri in the heart of a dying star. Presumably uru metal is magical in nature, and thus conveys the enchantment placed on it by Thor’s father, Odin. But in this matter we are not concerned with the fantasy of myths or comic books, but the real world of Hollywood movies.

In the 2011 film Thor, the Norse "gods" are identified as a race of alien beings, whose science is so advanced compared to twenty-first century Earth that their abilities appear not unlike magic to us (explicitly invoking Arthur C. Clarke’s third law). In this case, we can speculate as to the properties that uru metal must have in order to account for the experimental evidence in the Thor and Avengers films.

In the first Thor film, when Odin prepares to banish his wayward son to Earth, he whispers to the hammer: "whoever holds this hammer, if he be worthy, shall possess the power of Thor." In these days of interactive, voice recognition software in smartphones, such reprogramming of the hammer’s operating system through speech commands hardly counts as ‘magic.’ But how the nanotech embedded within the hammer executes Odin’s instructions does defy present-day science.

In the Avengers: Age of Ultron clip, Tony Stark speculates that there is a biosensor in the hammer’s shaft that recognizes when Thor has grasped Mjolnir. He is correct, in a sense—though it is not Thor’s fingerprints that the hammer is reading. Most likely it is taking some complex biological and psychological profile that calculates the "worthiness" of whoever is trying to lift the hammer. This is consistent with the scene in the clip where Steve Rogers (Captain America) is able to move the hammer (albeit slightly), while Tony Stark and Jim Rhodes, using thruster-assisted Iron Man and Iron Patriot gloves, are unable to budge Mjolnir at all. But if someone the hammer’s nanotechnology has determined to be "unworthy" tries to raise Mjolnir, how does it prevent itself from being moved?

Here the answer lies with Newton’s First Law of Motion, which states that an object at rest will remain at rest, if no net force acts upon it. The key word in the last sentence is "net." When the hammer rests on the coffee table, there is a downward force on it from the gravitational attraction between the mass of the hammer and the mass of the Earth (which we refer to as its "gravitational weight") and a counter-force from the book and tabletop pushing up on the hammer. This counter-force, referred to in physics as a Normal force (as it acts perpendicular or normal to any surface) is fundamentally electrostatic in nature, and is easy to take for granted except when it fails (as when one puts a thousand ton object on a table that can only provide a counter force of several hundred pounds).

When Tony Stark tries to lift Mjolnir using his Iron Man glove, he exerts a large upward force, greater than its weight, and yet the hammer remains at rest. So where does the additional downward force come from? One can only conclude that a unique property of uru metal is that, under the proper stimulus, it can emit large quantities of gravitons. On Earth, these fundamental particles have not been experimentally confirmed to exist, but as stipulated, the Asgardians are ahead of us scientifically. Gravitons are conjectured to transmit the gravitational force, and if an object emits additional gravitons, it is equivalent to increasing its mass. Thus, when an "unworthy" person applies an upward force, the uru metal increases the hammer’s weight to exactly cancel this lift, and the hammer remains unmoved. When Tony and Rhodey simultaneously exert a larger upward force, the emission rate of gravitons increases, to again neutralize their efforts. The greater weight will not damage the tabletop, as only enough gravitons are emitted to balance out all upward forces, to keep the hammer stationary. Once the lifting force is stopped, the excess graviton emission also ceases.

The ability of uru metal to alter its interaction with gravitational fields may also account for another astounding property of Mjolnir—that when thrown, it can alter its trajectory and move, seemingly of its own volition, returning to Thor’s hand. In physics, the only valid answer to the question: How fast are you moving? is: Who’s asking? Right now if you are reading this sitting on a bench at a train station, you are at rest, while another reader on a train speeding by you is moving east at, say, 40 miles per hour. Of course, from the point of view of the reader on the train, she is the one who is stationary, and it is the bench warmer who is moving west at 40 miles per hour. And both readers are in fact racing at a dizzying speed of 67,000 miles per hour as the Earth orbits the sun, which in turn is in motion about the center of the Milky Way galaxy. All motion is relative, and the amazing properties of uru metal, which scientists are just beginning to explore (or would be, if it actually existed) must include the ability to alter its rest frame in mid-flight, so that its motion, when viewed from the perspective of a stationary observer, will be such that it returns to Thor’s hand.

An important check on any scientific result is the review and vetting by other scientists. The above arguments were described in an article I wrote on "The Materials Science of the Avengers" for Hollywood Chemistry, a collection of essays published in 2014 by the American Chemical Society (who says this isn’t the Marvel Age of shameless plugs?). I shared this information with Mark Waid, the writer at the time of Marvel Comics' The Indestructible Hulk, at the start of a storyline where the Hulk would have an adventure with Thor. In The Indestructible Hulk #8, the question of whether or not the Hulk could lift Mjolnir arose, and no less a scientific authority than physicist Bruce Banner (the Hulk’s alter ego) provides peer-review and approval of my "graviton emission proposal," as shown here:

Marvel Comics

These panels also provide experimental evidence for another speculative scientific theory. As this scene from The Indestructible Hulk #8 indicates, there are two physicists named Jim Kakalios: one a professor at the University of Minnesota who studies amorphous/nanocrystalline composite semiconductors (and writes popular science books and articles about the physics of superheroes), and another who lives in the Marvel Earth-616 universe, whose theories on uru metal are known to Bruce Banner. This provides confirmation of the Many Worlds Interpretation of Quantum Mechanics, indicating the existence of at least two parallel Earths. Whether or not there are more such worlds, with additional Jim Kakalios’s residing in the multiverse remains to be determined, but future studies of both Thor’s hammer and parallel universes now have a firm experimental foundation. After all, they couldn’t put it in a comic book or Hollywood movie if it weren’t true!

Jim Kakalios is the Taylor Distinguished Professor in the School of Physics and Astronomy at the University of Minnesota and the author of The Physics of Superheroes and The Amazing Story of Quantum Mechanics, both by Gotham Books.