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Stephen Wolfram: The Path to a Fundamental Theory of Physics May Begin With a Hypergraph

Physics is the most fundamental of the sciences, dealing with matter and energy. But despite centuries of study, scientists still struggle with the basic question of how the universe works — in other words, we still lack a truly fundamental theory of physics.

And that’s something Stephen Wolfram has been thinking about for nearly 50 years. Known for his work in computer science, mathematics, and theoretical physics, Wolfram announced this week that he may have found a path that leads to a fundamental theory of physics, and that it is “beautiful.”

Stephen Wolfram

Back in the 1980s, while studying the computational universe of programs, Wolfram observed that even if a system’s rules are extremely simple, its behaviour can still be rich and complex. He later applied that discovery to his study of the non-computational, actual universe.

Wolfram says that by the end of the 1990s he had figured out some implications for space, time, gravity, etc. in physics. These would be expressed in his 2002 bestseller A New Kind of Science, which proposes that computation can inform an understanding of the physical world.

Wolfram says a fundamental theory of physics may now be within reach, and is inviting the global research community to help.

“We’ve built a paradigm and a framework,” Wolfram writes in a summary published this week on his website. “But now we need to finish the job. We need to work through a lot of complicated computation, mathematics and physics, and see if we can finally deliver the answer to how our universe fundamentally works.”

The Universe Is a Hypergraph?

Wolfram says the big answer lies in something simple and structureless: “We can think of it as a collection of abstract relations between abstract elements. Or we can think of it as a hypergraph — or, in simple cases, a graph.”

“When we draw the graph, all that matters is what’s connected to what,” he writes. “It also doesn’t matter what the elements are called — all that matters is that the elements are distinct.”

But since edges in ordinary graphs that connect pairs of nodes can hardly represent the complexity of the universe, Wolfram proposes hypergraphs, with hyperedges that can connect any number of nodes.

Examples of simple ternary hypergraph

Wolfram says hypergraphs can be produced by applying a simple rule to graphs — and doing it over and over again. When visualized, a hypergraph appears to take a definite shape which resembles the mathematical idealizations and abstractions of the universe, according to Wolfram.

“In our model, everything in the universe — space, matter, whatever — is supposed to be represented by features of our evolving hypergraph,” he writes.

Wolfram’s hypergraph illustration (6704 point section)

Wolfram sees the universe as basically a big chunk of space in which abstract points are abstractly connected to each other as a hypergraph with countless intersection points.

The Wolfram Physics Project

Wolfram says that after “zillions” of computer experiments, his team began to understand how quantum mechanics works, and identified some deep structural connections between relativity and quantum mechanics.

“Everything just started falling into place. All those things I’d known about in physics for nearly 50 years — and finally we had a way to see not just what was true, but why,” Wolfram explains in a detailed technical intro.

Wolfram has officially launched his Physics Project and will be livestreaming activities, sharing discoveries, and producing educational programs around the project. The team also plans to release more than 400 hours of videos covering previous research. Wolfram has also uploaded related working materials dating back to the 1990s as well as software tools.

“This is a project for the world. It’s going to be a great achievement when it’s done. And I’d like to see it shared as widely as possible,” he writes.

Reaction in the scientific community has varied — which is not unexpected in the face of a claim that many would regard as, well, astronomical. But history has shown that new ideas can have a tough time making a good first impression.

Sean Carroll, a California Institute of Technology physics professor and theoretical physicist specializing in quantum mechanics, gravity, and cosmology, tweeted that Wolfram’s approach is “cool and fun.” But he cautioned that science must be patient and collaborative, and that most bold ideas are wrong: “please don’t get too excited until others look it over.”

The last word goes to Wolfram, whose enthusiasm cannot be denied: “Let’s have a blast. And let’s try to make this the time in human history when we finally figure out how this universe of ours works!”

Journalist: Yuan Yuan | Editor: Michael Sarazen

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