Eric Weinstein proposes a Geometric Unity theory. It is presented to argue that the seemingly baroque features of the standard model of particle physics are in fact inexorable and geometrically natural when generalizations of the Yang-Mills and Dirac theories are unified with one of general relativity.
Attempting to reconcile Einstein’s Field Equations with the Yang-Mills equations and the Dirac equation was Eric Weinstein’s goal. The Field Equations control the curvature of space-time and represent our theory of gravity, whereas the Yang-Mills and Dirac equations represent our theory of particle interactions on a quantum level.
The particles described by the Standard Model – the stuff of nature that is revealed in accelerators such as the Large Hadron Collider – fall into three “generations”. In the first generation we see the electron, the electron neutrino, six quarks and their anti-particles, making 16 in total. But then rather bizarrely in the second generation we have another version of these particles which look exactly the same but are heavier than the first generation.
The heavier version of the electron is called the muon. The physicist Isadore Rabi famously quipped on hearing about the muon: “who ordered that?” It didn’t seem to make sense that you should have a heavier version of all the particles in the first generation. What was the logic in that? To compound things, there is a third generation heavier again than the second whose electron partner is called the tau particle.
One of the challenges facing fundamental physics has been to provide a natural explanation for these three generations. Weinstein’s theory does this by revealing the presence of a new geometric structure involving a much larger symmetry at work, inside which the symmetry of the Standard Model sits. What is so compelling about the geometry involving this larger symmetry group is that it explains why you get two copies of something with 16 particles but also that the third generation is something of an imposter. At high energies it will actually behave differently to the other two.
Not only that, it also predicts a slew of new particles that we can start looking for in our colliders. The particles in the Standard Model have a property called spin. The particles we see in the three generations we’ve seen to date all have spin 1/2. But Weinstein’s symmetry is predicting that we will see new particles with spin 3/2 exhibiting familiar responses to the nongravitational forces together with a slew of new exotic particles with familiar spin but unfamiliar responses to the forces of the standard model.
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