John Carlos Baez4d ago

The Higgs boson gives elementary particles their mass, but 98% of the visible mass in the Universe (not dark matter) comes from a less famous mechanism: chiral symmetry breaking. This is why protons and neutrons are so much heavier than their quarks!

Briefly, protons and neutrons act like bags full of a soup of virtual quark-antiquark pairs, which give them most of their mass. This soup, called a 'quark condensate', breaks a certain symmetry that exists outside the bag: 'chiral symmetry', where you change the phase of the clockwise and counterclockwise rotating quarks separately. In the quark condensate, the clockwise spinning virtual quarks are entangled with counterclockwise spinning virtual antiquarks.

https://en.wikipedia.org/wiki/Chiral_symmetry_breaking

Chiral symmetry breaking - Wikipedia

Show threadAndrej Bauer4d ago

@johncarlosbaez As a mathematician I have always imagined that I would understand the universe if someone described the Standard Model as a really fancy mathematical something-or-other, without saying things like "a neutron is a soup of quarks and anti-quarks" – these just distract from the math.

I only got a snippet of such a story from a physicist once, and I loved it. I asked what a particle really was, mathematically, and he said something like "eigenvector of a linear approximation to some-field-thing". I may be misremembering the "approximation part", but the important thing was that it was a straight mathematical answer. I felt comforted.

Where could I find out more of this? Is the Standard Model a huge vector field on a vector space, or on a manifold with Riemann metric? Can someone write down the type of the Standard Model in in type theory?

Show threadJohannes Hostert3d ago
@andrejbauer @johncarlosbaez Perhaps we should start with something simpler. What is the type-theoretical type of Newtonain mechanics? What does that question even mean?
Show threadJohn Carlos Baez3d ago
@jhostert @andrejbauer - that's too hard but we can at least give answers - many answers! - to the question "what is the type of a classical mechanical system?", with one answer being "a symplectic manifold with a smooth real-valued function on it". There is no one accepted answer.
Show threadJohannes Hostert
@johncarlosbaez @andrejbauer And the real-valued function is some sort of potential field / Hamiltonian / Lagrangian? (Admittedly, the few physics lectures I once took were years ago)
Mar 25 at 11:50pmWeb
Show threadJohn Carlos Baez3d ago

@jhostert @andrejbauer - It's called the Hamiltonian.

When you use a Lagangian, the setup is different: that's a function on a tangent bundle. And when you use a potential, the setup is different again: that's a function on a Riemannian manifold.

There are theorems relating these different formalizations of classical mechanics.