Physicists puzzled by strange numbers that could explain reality

Eight-dimensional octonions may hold the clues to solve fundamental mysteries.

Physicists puzzled by strange numbers that could explain reality
  • Physicists discover complex numbers called octonions that work in 8 dimensions.
  • The numbers have been found linked to fundamental forces of reality.
  • Understanding octonions can lead to a new model of physics.

Is our reality, including its forces and particles, based on the strange properties of numbers with eight dimensions called "octonions"? A physicist thinks so, having found a way to expand 40-year-old research to reach surprising new directions.

First, a brief history of numbers.

Regular numbers that we are familiar with in our everyday life can be paired up in a special way to create "complex numbers," which act like coordinates on a two-dimensional plane. This was discovered in 16h-century Italy by the mathematician Gerolamo Cardano. As explains Natalie Wolchover of Quanta Magazine, you can perform operations on complex numbers like adding, subtracting, multiplying and dividing by "translating and rotating positions around the plane."

An Irish mathematician by the name of William Rowan Hamilton discovered in 1843 that if you pair the complex numbers in a certain way, they can form 4-D "quaternions." He was apparently so excited about figuring out that formula, that he immediately carved it into the Broome Bridge in Dublin. Not to be outdone, John Graves, a friend of Hamilton's who was a lawyer and math whiz, showed that quarternions can be paired up to become "octonions" – numbers that can assume coordinates in an abstract 8-dimensional (8-D) space.

John Graves.

Each type of numbers has been utilized extensively in the development of modern physics, with complex numbers used in quantum mechanics and even the quaternions employed in Albert's Einstein's special theory of relativity.

What hasn't been completely understood and put to work – the octonions, usually represented by the capital letter O and whose multiplication rules are encoded in a triangular diagram called the Fano plane (that looks like something the Freemasons would devise).

A mnemonic for the products of the unit octonions using the Fano plane.

The mystery of these numbers has led to speculation among researchers that they have a special purpose and can eventually explain the deeper secrets of the universe. In an email interview with Quanta Magazine, the particle physicist Pierre Ramond from the University of Florida explained that "Octonions are to physics what the Sirens were to Ulysses."

In 1973, Murat Günaydin, the then-Yale-graduate student (now professor at Penn State) and his advisor Feza Gürsey, discovered that there is an unexpected link between octonions and the strong force that keeps quarks together in an atomic nucleus. Günaydin continued his research quite outside the mainstream, looking at connecting the numbers to such ideas as string theory and M-theory.

In 2014, Cohl Furey, a graduate student at the University of Waterloo, Canada, built on Günaydin's work by finding a new use for the hard-to-imagine numbers. She devised an octonionic model that includes both the strong and electromagnetic forces. Now a postdoc in UK's University of Cambridge, Furey generated a series of results that link the octonions to the Standard Model of particle physics, in work that has been praised by other scientists. She has "taken significant steps toward solving some really deep physical puzzles," said Shadi Tahvildar-Zadeh, a mathematical physicist at Rutgers University.

Others, like the noted string theorist and Imperial College London professor Michael Duff, are more reserved, excited about her work but saying it's "hard to say" yet if it will become "revolutionary."

Furey is undeterred by working in a currently obscure field, thinking of her research as a "process of collecting clues," as she explained in an interview.

She published a paper in May 2018's The European Physical Journal C, where she consolidated several of her findings, looking to complete the standard model of particle physics and find the rightful place in our understanding of the world for the octonions.

To learn more, watch Furey explain the octonions here:

For those inclined to delve deeper into the math, check out this fascinating graphic:

Lucy Reading-Ikkanda/Quanta Magazine

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The paper is published in Astrophysical Journal Letters.

The Oort cloud

Oort Cloud graphic

Image source: NASA

Scientist believe that surrounding the generally flat solar system is a spherical shell comprised of more than a trillion icy objects more than a mile wide. This is the Oort cloud, and it's likely the source of our solar system's long-term comets — objects that take 200 years or more to orbit the Sun. Inside that shell and surrounding the planets is the Kuiper Belt, a flat disk of scattered objects considered the source of shorter-term comets.

Long-term comets come at us from all directions and astronomers at first suspected their origins to be random. However, it turns out their likely trajectories lead back to a shared aphelion between 2,000 astronomical units (AU) from the Sun to about 100,000 AU, with their different points of origin revealing the shell shape of the Oort cloud along that common aphelion. (An astronomical unit is the distance from the Sun to the Earth.)

No object in the Oort cloud has been directly observed, though Voyager 1 and 2, New Horizons, and Pioneer 10 and 11 are all en route. (The cloud is so far away that all five of the craft will be dead by the time they get there.) To derive a clearer view of the Oort cloud absent actually imagery, scientists utilize computer models based on planetary orbits, solar-system formation simulations, and comet trajectories.

It's generally assumed that the Oort cloud is comprised of debris from the formation of the solar system and neighboring systems, stuff from other systems that we somehow captured. However, says paper co-author Amir Siraj of Harvard, "previous models have had difficulty producing the expected ratio between scattered disk objects and outer Oort cloud objects." As an answer to that, he says, "the binary capture model offers significant improvement and refinement, which is seemingly obvious in retrospect: most sun-like stars are born with binary companions."

"Binary systems are far more efficient at capturing objects than are single stars," co-author Ari Loeb, also of Harvard, explains. "If the Oort cloud formed as [indirectly] observed, it would imply that the sun did in fact have a companion of similar mass that was lost before the sun left its birth cluster."

Working out the source of the objects in the Oort cloud is more than just an interesting astronomical riddle, says Siraj. "Objects in the outer Oort Cloud may have played important roles in Earth's history, such as possibly delivering water to Earth and causing the extinction of the dinosaurs. Understanding their origins is important."

Planet 9

rendering of a planet in space

Image source: Caltech/R. Hurt (IPAC)/NASA

The gravitational pull resulting from a binary companion to the Sun may also help explain another intriguing phenomenon: the warping of orbital paths either by something big beyond Pluto — a Planet 9, perhaps — or smaller trans-Neptunian objects closer in, at the outer edges of the Kuiper Belt.

"The puzzle is not only regarding the Oort clouds, but also extreme trans-Neptunian objects, like the potential Planet Nine," Loeb says. "It is unclear where they came from, and our new model predicts that there should be more objects with a similar orbital orientation to [a] Planet Nine."

The authors are looking forward to the upcoming Vera C. Rubin Observatory (VRO) , a Large Synoptic Survey Telescope expected to capture its first light from the cosmos in 2021. It's expected that the VRO will definitively confirm or dismiss the existence of Planet 9. Siraj says, "If the VRO verifies the existence of Planet Nine, and a captured origin, and also finds a population of similarly captured dwarf planets, then the binary model will be favored over the lone stellar history that has been long-assumed."

Missing in action

Lord and Siraj consider it unsurprising that we see no clear sign of the Sun's former companion at this point. Says Loeb, "Passing stars in the birth cluster would have removed the companion from the sun through their gravitational influence. He adds that, "Before the loss of the binary, however, the solar system already would have captured its outer envelope of objects, namely the Oort cloud and the Planet Nine population."

So, where'd it go? Siraj answers, "The sun's long-lost companion could now be anywhere in the Milky Way."

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