by: James Kakalios

I was asked to give a talk last summer at Convergence, an annual science fiction/comics/science convention in the Twin Cities of Minneapolis and St. Paul. The premiere of Marvel Studios’ Avengers: Infinity War at the start of the summer suggested a title for my talk: “The Physics of the Infinity Stones.” This afforded me an opportunity to describe to a general audience one of the most profound theorems in physics, proved by one of the most remarkable minds of the 20th century.

As first described in Jim Starlin’s 1990 Marvel comic book Thanos Quest, the six Infinity Stones provide those who wield them with control over Mind, Space, Time, Power, Reality, or Soul. Any one of them alone confers indescribable power, while combined, they can make one a god. They are believed to be material manifestations of fundamental aspects of the universe and its physical properties. Superhero movie fans saw Thanos collect all six stones in Avengers: Infinity War. We know what the stones are, we know where in the Marvel Cinematic Universe they are, and we know who has them – but we don’t know the ‘why’ of the Infinity Stones. Is there any scientific reason for these stones to exist? For that question we must consult not Thanos, the Mad Titan, nor any celestial being, but rather the early 20th century mathematician Amalie Emmy Noether.

Emmy Noether was one of the most creative mathematicians of her, or any, time. In 1915 unable to resolve a potentially fatal flaw in Albert Einstein’s General Theory of Relativity, the mathematicians David Hilbert and Felix Klein asked for Noether’s help. What is now known as Noether’s Theorem, not only saved Einstein’s theory, but it provided a profound insight into the physical universe. And into the Infinity Stones as well.

Emmy Noether proved that the Conservation Laws of Physics (such as Conservation of Energy, Conservation of Momentum, Conservation of Electrical Charge) are direct consequences of symmetries of the physical equations that described the universe. That is, the fact that the equations of physics do not depend on what time one does an experiment is reflected in the Principle of Conservation of Energy, and that the equations look the same regardless of one’s location in space yields Conservation of Momentum. In the Marvel Universe, the physical manifestation of these symmetries and conservation principles are the Infinity Stones.

So, the fact that in the Marvel Universe there is a Time Stone implies Conservation of Energy, and there is indeed a corresponding Power Stone (Power being just the rate at which energy can be used). Similarly there is a Space Stone that can be used to teleport from one location to another. While there is no matching Momentum Stone, it is interesting that the Space Stone, when confined within the Tesseract, is the only Infinity Stone that has been weaponized, being employed to energize force beams by Hydra in Captain America: The First Avenger. Moreover, [spoilers for a billion dollar blockbuster that has been out for nearly a year] as soon as Thanos posesses the Space stone, Loki tries to stab him in the throat, and his upward thrust is frozen, as if all of his dagger’s momentum was removed.

What about the Mind Stone, first seen as part of Loki’s scepter in the Avengers film and used to control other’s thoughts, and now residing in the Vision’s forehead? What symmetry is associated with that? All mental processes are the result of ionic currents between neurons, and if one gained mastery over these currents, one could control any brain’s functions. The foundation of our understanding of electrical currents is the Principle of the Conservation of Electrical Charge (that the net charge can move from place to place, but can not be created or destroyed). Noether’s Theorem informs us that Conservation of Charge reflects the fact that the basic equations of electromagnetism do not change with respect to gauge transformations. That is, if one shifts the potentials in Maxwell’s Equations, the resulting electric and magnetic fields are unchanged, and this insensitivity leads to Conservation of Charge. So even the Mind Stone can be accounted for using the insights provided by Emmy Noether.

Not all symmetries and conservation principles yield a corresponding Infinity Stone (they have to eventually all fit on a single gauntlet, after all). What about the last two Infinity Stones – the Reality and Soul Stones? Here, if we are to ascribe a physics interpretation, we must leave the rigid confines of Noether’s theorem, and enter the quantum realm.

Quantum Mechanics, the field of physics that describes the properties of atoms and how they interact with light, is itself a subject of probabilities. One interpretation of these probabilities was put forward by Hugh Everett III who proposed that there are an infinite number of parallel universes and that the probability of a particular quantum event is reflected in the alternate histories and futures of these parallel universes. Many of these parallel Earths are very similar to our own (with perhaps a few notable differences) while others may vary greatly from our world. Presumably the Reality Stone enables whomever wields it to change our Earth to another in the multiverse and is thus the manifestation of the quantum nature of the physical universe.

And for the Soul Stone – well, that would be the conjugate pair to the Reality Stone. It reflects the one aspect of the universe that is not described by the laws of physics. As the physicist and author Sean Carroll has argued, knowing the laws of nature, knowing what is, does not inform us how we ought to live. One could no more look to a physics textbook for guidance of how we should treat each other, or what constitutes a life well lived, than one could consult a religious tome for insight into the laws of Thermodynamics. If the Reality Stone reflects the physics of multiple possible outcomes, the Soul Stone embodies those outcomes we each choose.

My audience at Convergence realized that I was not really explaining the physics of comic book magical McGuffins, but using the talk as an excuse to tell them about Emmy Noether. They loved hearing about Noether’s accomplishments, but groaned when they learned how long this mathematician, described by Albert Einstein as “the most significant mathematical genius thus far produced since the higher education of women began” had to work as a professor at Erlangen and Gottingen without pay due to her gender!

In Avengers: Infinity War the combined might of the Avengers, the Guardians of the Galaxy, Dr. Strange, the Black Panther and the warriors of Wakanda and others were called upon to resist Thanos as he gathered the Infinity Stones. As the remaining Avengers assemble in next summer’s Avengers: Endgame to try to undo the effects of Thanos’ “Snappening,” (will make sense if you’ve seen the movie) we can only hope that their resolve is the equal to that of Emmy Noether, who overcame a lifetime of barriers due to religion and gender prejudices, and persevered through her intelligence and will, making the world more understandable, and better.

James Kakalios is the Chair-Elect of the Forum on Outreach and Engaging the Public, and the Taylor Distinguished Professor in the School of Physics and Astronomy at the University of Minnesota. He is the author of several popular science books, including THE PHYSICS OF SUPERHEROES (Avery, 2009) and THE PHYSICS OF EVERYDAY THINGS (Crown, 2017).