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Before getting to gravity, recall that forces are transmitted by a 'mediator' which are always bosons EM: the photon, strong force: gluon, weak force: W± & Z. When the symmetry corresponding to the force carrier is unbroken the force carriers are massless (m=0). (2/n)pic.twitter.com/7Y38aPPQOa
What about Gravity? The symmetry corresponding to gravity is the most respected symmetry in all physics & goes by many names It's the one underlying Einstein's General Theory of Relativity: General Covariance/Gauge-Lorentz Symmetry/ Diffeomorphism Invariance (3/n)pic.twitter.com/Y5DyRN2qMg
Because this symmetry (General Covariance) has never been observed to be violated, physicists were convinced that the gauge field corresponding to gravity corresponded to an exact, unbroken symmetry I would then immediately follow, then, that the graviton is massless
But wait!, says de Rahm.. Perhaps Lorentz symmetry could just be an *approximate* symmetry of nature This would happen if the graviton (hμν) has a mass--mass terms for gauge fields always break gauge invariance But!.. look at the first tweet.. (5/n)pic.twitter.com/cgEyMtE73l
Boom! We see that the graviton (metric; hμν) contains the exponential potential we expected! TL;DR: If the graviton has a mass~hubble rate (H), then large scale gravity can act repulsive and reproduce the Dark Energy observations, with no Dark Energy at all! (n/n)pic.twitter.com/bN8NKU4jAp
I’m actually rather proud of this mini explanation of gauge gravity
Mathematicians would say that general covariance aka diffeomorphism invariance is simply the nonexistence of a preferred coordinate system i.e. GR is formulated on a manifold. GR _additionally_ assumes the .existence of a Lorentzian metric, subject to the Einstein equations.
This is very helpful thank you!
Idk I respect some other symmetries more
The standard model has 2 kinds of symmetries (gauge and global) and some papers are predicting that the global ones must only be approximate. Their basic tools are quantum error correction, the AdS/CFT correspondence, and quantum field theory.
Did you know the work of Harlow / Ooguri? Check this out https://arxiv.org/abs/1810.05338
Are all Invariant functions Isomorphisms?
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