How wide is a proof?
I listened to a talk this afternoon, with the title “Short theorems with long proofs”, given by Professor Colva Roney-Dougal. It has long been known in mathematics that there are short concise...
View ArticleSymmetry-breaking of the weak interaction
There are two very different aspects of the symmetry-breaking of the weak nuclear force (the force responsible for radioactive decay). One is the breaking of charge symmetry, the other is the breaking...
View ArticleBroken symmetries are parameters
The big question about the Standard Model of Particle Physics is, where do the unexplained parameters come from? The parameters are of two basic types – masses (positive real numbers) and mixing...
View ArticleAs small as possible, but no smaller
In recent posts I have argued that, since the Standard Model has around 16 to 24 parameters, and 18 symmetries, the total number of degrees of freedom is between 34 and 42, so if they are described by...
View ArticlePati-Salam revisited
The Pati-Salam model is one of the first Grand Unified Theories (GUTs) to be built, following the establishment of the Standard Model in the early 1970s. The basic idea was to extend the strong gauge...
View ArticleThe character table of the Monster
The Monster is a “simple” group with a total of 808017424794512875886459904961710757005754368000000000 elements. Its smallest real representation is as 196883 x 196883 matrices. The fact that the...
View ArticleEmergence of gravity
I promised to tell you about gravity, from the point of view of the group Sp(1) x Sp(3,1). The first point to make is that we need to factorise Sp(3,1) as SO(3,1) x Sp(1). That is, we separate out the...
View ArticleThree is the magic number
Over the course of the past year or so I seem to have converged on the idea that the fundamental algebra that is required for a theory of “everything” is the tensor product of three copies of the...
View ArticleQuest for the Holy Grail
Around New Year 2015 I found my first clue to the link between gravity and particle physics. I had come to the conclusion that this link must manifest itself in some coincidence of dimensionless...
View ArticleAre gluons particles?
There is a curious fact about the Standard Model gauge group U(1) x SU(2) x SU(3), that the unitary representation and the adjoint representation both have 12 dimensions. The unitary representation...
View ArticleThe landscape of unified theories
For over 50 years, since the establishment of the Standard Model of Particle Physics as the accepted description of the quantum forces of electromagnetism and the nuclear forces, physicists have been...
View ArticleThe proof of the math is in the physics
There is an old saying that “the proof of the pudding is in the eating”. Nowadays you never hear this said properly, because people say “the proof is in the pudding” without understanding that this is...
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