Tag: Topology

Visualizing Knots in Spacetime

In Knot Physics, elementary fermions—like electrons and quarks—are topological defects in the spacetime manifold, which we often refer to as knots.1 We can think of spacetime as a 3-dimensional manifold that changes over time; as such, the fermions of Knot Physics are topological defects in that 3-dimensional manifold.

To understand their topology, we first consider the 2-dimensional version of these topological defects and then extend the concept to 3 dimensions. We will use a process known as topological surgery, where we take familiar manifolds and then cut and glue them to create the topological defects.

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Origins

One of the most common questions that people ask about Knot Physics is why we are not affiliated with an institution. There are many advantages to working in academia, especially when it comes to communicating new ideas. The credentials that come along with an academic position are very helpful for reaching an audience. That said, there are also many constraints, including numerous demands on the time and attention of the researcher. 

When this project began, it was just an idea. Developing the idea required long periods of talking to no one and staring at walls—uninterrupted blocks of time that an academic career would not afford. As the idea progressed, it became clear that it had substance. Eventually, it was a fully formed theory that had developed as independent research.

From idea to theory

The theory began as a question: Can all of physics be described using only the spacetime manifold? General relativity succeeded in describing gravity as curvature of spacetime. Could that description be extended to particles? If spacetime can bend, perhaps it can bend so much that it forms a knot. What if those knots are the elementary particles?

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