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What do bar magnets, Mexican hats and the early Universe have in common? This video works through such a thought, beginning with magnetism and builds up to explaining the origins of Electroweak theory - where 2 of the 4 Fundamental Forces of Nature become one of the same.
Magnetism in materials is due to the overall Spin angular momentum of electrons within it. Above the Curie Temperature, materials are Paramagnets, showing only induced magnetism when in the magnetic field. Below this critical temperature, and the material transitions into becoming a 'permanent' ferromagnet. At the Curie Temperature, all of the randomly orientated paramagnetic spins spontaneously align in a random direction which breaks symmetry within the system.
We examine the form of the Mexican hat potential (Energy) in each case and draw conclusions onto different types of excitations which can occur throughout the material (such as Magnons/Spin Waves in magnets). Goldstone's Theorem tells us we get a massless excitation (particle) each time a symmetry is broken. This combined with gauge fields gives a way for force mediating particles (Bosons) to gain mass through the Higgs Mechanism.
Combined with ideas from the standard model of particle physics and quantum field theory (QFT), the fact that the weak nuclear force bosons can carry charge, the fundamental interaction unit of electromagnetism becomes peculiar, suggesting the two forces could have separated from a combined force due to spontaneous symmetry breaking. The temperatures needed for the unification only naturally occurred one trillionth of a second after the Big Bang in the very early Universe. This is ElectroWeak theory, and could be extended to include the Strong Nuclear Force in a Grand Unified Theory (GUT) which could lead to supersymmetry and supersymmetric particles in the early universe.
The observation of mass in fermions (normal matter) as well as discovery of the Higgs Boson in 2012 is supporting evidence of ElectroWeak. If gravity could somehow be included, this could lead to the Theory of Everything, although theories of quantum gravity are needed first. Quantum Mechanics explains the really small and Einstein's General Relativity the very large, however quantum gravity is not understood. Could String Theory or Quantum Loop gravity provide an answer? Nonetheless, the concepts discussed in this video provide insight on how humanity might someday reach there.
0:00 - Fundamentals of Paramagnetism and Ferromagnetism
1:31 - Quantum Mechanics, Spin and the Origin of Magnetism
3:13 - Energy, Order and Physical Symmetry
5:25 - Spontaneous Symmetry Breaking
7:25 - Order Parameter and the Mexican Hat Potential
8:25 - Massive and Massless Excitations/Particles (Goldstone Modes and Bosons)
10:29 - Gauge Fields and the Higgs Mechanism
12:07 - Relation to the Four Fundamental Forces of Nature, the Standard Model and Higgs Boson
14:08 - Early Universe and ElectroWeak Unification
15:00 - Grand Unified Theories, QM, GR and Quantum Gravity