Their mathematical models may offer a new perspective on fundamental aspects of reality — including why our universe is expanding the way it does, and how this has to do with the tiniest lengths allowed in quantum mechanics. These topics are central to understanding our universe and part of one of the great mysteries of modern physics.
The two scientists stumbled upon this new idea while working on something completely different: the study of graphene sheets. They realized that experiments on the electrical properties of stacked graphene sheets yielded results similar to small universes, and that this fundamental phenomenon could generalize to other areas of physics. In stacked graphene, new electrical behavior arises from interactions between individual sheets, so perhaps unique physics can emerge from interacting layers elsewhere as well – perhaps in the universe about the entire universe in theory.
“We think this is an exciting and ambitious idea,” said Galitski, who is also the Chesapeake Chair Professor of Theoretical Physics in the Department of Physics. “In a sense, it works so well by naturally ‘predicting’ fundamental features of our universe, like inflation and the Higgs particle that we describe in a follow-up preprint, that it almost makes Doubtful.”
The special electrical properties of laminated graphene and its possible connection to our reality as a “twin” come from the special physics created by the patterns known as moiré. A moiré pattern forms when two repeating patterns — from hexagonal atoms in a graphene sheet to a grid of window screens — overlap and one of the layers is twisted, offset or stretched.
The pattern that emerges can be repeated over enormous lengths compared to the underlying pattern. In the graphene stack, the new pattern changes the physical properties of the flakes, especially the behavior of electrons. In a special case known as “magic angle graphene,” the moiré pattern repeats about 52 times the length of a single flake pattern, while the energy levels that govern electron behavior drop dramatically, allowing for new behaviors, including superconductivity .
Galitski and Parhizkar realized that the physics in two sheets of graphene could be reinterpreted as the physics of two two-dimensional universes, in which electrons occasionally hop between universes. This inspired the two researchers to generalize mathematics to universes composed of any number of dimensions, including our own four-dimensional universe, and to explore whether similar phenomena produced by moiré could arise in other areas of physics. This opened a path of discovery that confronted them with a major problem in cosmology.
“We discussed whether we could observe moiré physics when two real universes coalesce into one,” Parhizkar said. “When you ask this question, what are you looking for? First, you have to know the length scale of each universe.”
Length scales — or scales of physical values in general — describe the level of accuracy associated with anything you look at. Ten billionths of a meter is important if you’re measuring the size of an atom approximately, but that scale is useless if you’re measuring a football field because it’s on another scale. Theories of physics place fundamental constraints on some of the smallest and largest scales that make sense in our equations.
The cosmic scale that Galitski and Parhizkar focused on is known as the Planck length, which defines the smallest length consistent with quantum physics. The Planck length is directly related to a constant in Einstein’s field equations of general relativity — the cosmological constant. In the equation, this constant affects whether the universe — outside the influence of gravity — tends to expand or contract.
This constant is fundamental to our universe. So, to determine its value, scientists theoretically just need to look at the universe, measure some details like how fast galaxies are moving against each other, plug everything into the equation and work out what the constant must be.
This straightforward plan ran into a problem because our universe contains both relativistic and quantum effects. Even on cosmological scales, quantum wave effects across the vast vacuum of space should influence behavior. But when scientists tried to combine the relativistic understanding of the universe that Einstein gave us with a theory about the quantum vacuum, they ran into problems.
One of the problems is that whenever researchers try to use observational data to get close to the cosmological constant, they calculate a value that is much smaller than they would expect based on other parts of the theory. What’s more, depending on how much detail they include in the approximation, the value jumps sharply, rather than centered on a consistent value. This lingering challenge is known as the cosmological constant problem, or sometimes called the “vacuum catastrophe.”
“This is the largest — by far the largest — discordance between the measurements and what we can predict from theory,” Parhizkar said. “It means something is wrong.”
Since moiré patterns can create huge scale differences, the moiré effect seems like a natural lens to look at. Galitski and Parhizkar created a mathematical model (which they called moiré gravity) that split Einstein’s theory of how the universe changed over time in two, and introduced additional terms into the mathematics that allowed the two theories to interact. Instead of looking at the energy and length scales of graphene, they were looking at the cosmological constant and length of the universe.
Galitski said the idea arose spontaneously while they were working on a seemingly unrelated project funded by the John Templeton Foundation to study hydrodynamic flow in graphene and other materials to simulate astrophysical phenomena .
By analyzing their model, they showed that two interacting worlds with a large cosmological constant can overturn the expected behavior from a single cosmological constant. The behavior resulting from the interaction is governed by a shared effective cosmological constant, which is much smaller than a single constant. The calculation of the effective cosmological constant circumvents the researchers’ problem of bouncing around its approximation, as the effects of the two universes in the model cancel each other out over time.
“We’re not claiming — ever — that this solves the cosmological constant problem,” Parhizkar said. “To be honest, that’s a very arrogant claim. It’s just a good insight that if you have two universes with huge cosmological constants, say 120 orders of magnitude larger than what we observe, if you combine them, There is still a chance of getting a very small effective cosmological constant from them.”
In preliminary follow-up work, Galitski and Parhizkar have begun to build on this new argument by delving into a more detailed model of two interacting worlds — which they call “two worlds.” By our normal standards, each of these worlds is a separate complete world, and each is filled with a matching set of all matter and fields. As mathematics allows, they also include fields that live in two worlds at the same time, which they call “amphibious fields”.
The new model yielded additional results that the researchers found intriguing. When they put the math together, they found that parts of the model looked like important fields in reality. More detailed models still suggest that two worlds can explain a small cosmological constant, and provide details on how such a “two world” imprints a distinct signature on the cosmic background radiation — from the earliest days of the universe light that has always existed.
In real-world measurements, this characteristic may be seen — or certainly not. Therefore, future experiments could determine whether this unique perspective inspired by graphene deserves more attention, or is simply an interesting new addition to a physicist’s toy box.
“We haven’t explored all the effects — that’s a hard thing to do, but it’s a good thing that the theory is experimentally falsifiable,” Parhizkar said. “If it’s not falsified, then it’s very interesting because it solves the cosmological constant problem while describing many other important parts of physics. I personally don’t hold out for that – I think it’s actually quite big Not real.”
