Modern fundamental physics rests on two great pillars: General relativity, which describes gravity, and the Standard Model of particle physics, which accounts for the other three known ‘forces’ of nature—electromagnetism, the weak nuclear force, and the strong nuclear force. These are, as far as we currently know, all that exists.
In this post, I’m going to give a brief critical overview of loop quantum gravity, the field that I worked in during my time in physics. A fairly strong understanding of physics is assumed.
Loop quantum gravity is an attempt at canonical quantisation of Einstein’s general relativity. Thus the starting point is constructing a Hamiltonian. In a flat spacetime that’s easy, but on a general spacetime manifold it’s not so easy because it requires one to define a time coordinate. The ADM formalism addresses this by assuming that spacetime is foliated. Roughly this means that our spacetime manifold \( M \) is decomposed into a family of spacelike hypersurfaces \( \Sigma_t \) labelled by a timelike coordinate \( t\). Spacelike means that any pair of points on \( \Sigma_t \) are spacelike separated - their spatial and temporal separation is such that light could not travel between them. There are in general many possible foliations of \( M \) that should all be ‘equally as good’ as each other.
Eric is a podcaster who has most notably made appearances on the Joe Rogan experience (JRE). He received a PhD in mathematical physics from Harvard in 1992, and between 2013 and 2022 he was a managing director of Thiel Capital - Peter Thiel’s investment firm.
What if I told you there was a well-known, 100-year old theory of gravity that reproduces all empirical successes of Einstein’s general relativity, and may solve a who’s who of major oustanding problems in theoretical physics?
Its called Einstein-Cartan theory, or sometimes Einstein-Cartan-Sciama-Kibble (ECSK) theory. By the way, the eponymous Kibble is my “physics grandfather” - my PhD supervisor’s PhD supervisor.
Ever since Newton/Leibniz invented the infinitesimal calculus in the latter half of the 1600s, it seems like the world has been enthralled by beauty and possibility of the continuum. This event marked the beginning of modern physics and mathematics, and there is virtually no topic in either of these fields that is not deeply interwoven with calculus.
Sometimes, though, I think they may have been a little too successful.
For many decades now, physicists have been trying to ‘unify’ quantum mechanics and Einstein’s general relativity into a quantum theory of gravity. This has proven to be very difficult, and achieving such a unification is one of the major outstanding problems in theoretical physics. To understand why, let me first give you a whistlestop tour of some topics in physics.