Week 4 - Character of Physical Law
Symmetry in Physical Law
Candidate Higgs decays into 4 electrons Is any momentum missing?
The Character of Physical Law John Anderson – Week 4 The Academy of Lifelong Learning
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Symmetries Rule Nature
Old School1882 -1935 New Breed What key bit of knowledge would you save? • The world is made of atoms. - Richard Feynman • The laws of physics are based on symmetries. - Brian Greene Emmy Noether showed every invariance corresponds to a conservation law. (Energy, momentum, angular momentum.)
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Symmetry Violated - Parity
Chen-Ning Franklin T.D. Lee Chien-Shiung Wu Yang The Weak Nuclear Force Violates Parity • Yang and Lee scour literature. Strong force and E&M are good. • Wu crash projects measurement with supercooled Cobalt 60. Nobel Prize 1957 for Yang and Lee, but Wu gets no cigar.
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Parity - “Mirror Symmetry”
Equal numbers of electrons should be emitted parallel and antiparallel to the magnetic field if parity is conserved, but they found that more electrons were emitted in the direction opposite to the magnetic field and therefore opposite to the nuclear spin.
Chien-Shiung Wu 1912-1997
Hyperphysics Georgia State Univ.
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Parity Change - Right to Left Handed
x z P y Parity Operator y
x z
Right-handed Coordinates Left-handed Coordinates Parity operator: (x,y,z) to (-x,-y,-z)
Changes Right-hand system to Left-hand system
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Symmetry in the Particle Zoo
How to bring order out of chaos? Quarks. Pattern recognition. More latter.
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The Standard Model - Pithy
"Matter particles (quarks and leptons) interact with one another by various forces, each of which is mediated by the exchange of force particles (photons, gravitons(?), gluons, W's, and Z's) in accordance with various conservation laws." - Sheldon Glashow Nobel Prize 1979
Note: Need to add the Higgs Field/Particle to this description.
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Forces: A New View
Law of Nature: The Energy (Kinetic Energy + Potential Energy) of the world must be invariant under local gauge transformations. (New jargon.)
The term gauge implies measuring on some scale.
A “popular” book for us. Please read it and then Marius Sophus Lie explain it to me. Thanks. 1842 -1899
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Use Symmetries to Build Theory
The theory possesses Some theory some symmetry. Some Symmetry (e.g. Electro- [e.g. U(1) Lie magnetism) Theory can be built Group] from symmetry.
We already understand electrodynamics: not helpful.
But, let’s derive new theories for the 1) - weak and 2) - strong force from their symmetries.
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Gauge Invariance => Phase
1924 matter particles are wave-like.
Analogy: if you’re at sea, you care about
. Wavelength (momentum - p=h/λ)
. Wave height (amplitude - A) but the phase (exact time . Wave frequency (energy - E=hν) you find yourself on top of a crest) is immaterial. Fundamental symmetry of quantum mechanics: the over-all phase of the wavefunction is immaterial. Or, exchanging two electrons with different phases won’t change the Hamiltonian (energy).
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Local vs. Global Phase Change Local vs. Global Phase Change
Top of Top of Top of Top of wave wave wave wave Bottom Bottom Bottom Bottom of wave of wave of wave of wave “Global” phase change
“Local” phase change
Global phase change: Same wavelength. Adding a constant. Local phase change: Different wavelength – different physics!
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Gauge Invariance - classical to Q.M.
Classical Charge Conservation was a gauge symmetry. • Weyl (1929) gauge invariance charge conservation. • E&M theory derivable from this basic symmetry
Gauge invariance purely mathematical, not geometry.
1929: Pauli and Heisenberg introduce gauge invariance and run into problems.
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Two Parts to Local Gauge Symmetry
Local Phase Transformation changes momentum and energy. ( x)
phase e
Must add a Field and a Gauge Transformation chosen to keep system No invariant good 1 OK A A x x e • Electron and gauge field are blended together. • Key Symmetry: An electron is equivalent to another electron with a different wavelength through gauge symmetry. E, p are conserved.
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Gauge Symmetry: Real Physics
• Kick an electron and out pops a real photon - real radio waves e.g
• Gauge invariance requires
Aμ(x) to correspond to massless, spin-1 particles (known as photons)
• Maxwell’s laws fall out too.
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Symmetry-Force Connection
Force 1 - Symmetry 2 - Group to 3 - Introduce 4 -Turn on Principle Gauge Gauge Field interaction Electromag. Symmetry - U(1). A Electrons with ig 1 generator, Single 4- vector D A different phases electric charge Photon(0 mass) c
Nuclear Local symmetry SU(2) A a ig Interaction, between neutrons 3 generators 4 vector with 3 D L A st a a 1 try test and protons. Not “Isospin” not internal c case only a real symmetry. conserved. components, a 13 1,2,3 Strong Local color SU(3) G i tbGb Nuclear symmetry applied 8 generators Gluons(0 mass) b18 Interaction to quarks and Color charge gluons.
The interaction term is a fudge factor that restores the Lagrangian. That keeps the physics the same.
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Regarding Forces, We Conclude:
“It was in the twentieth century, with the development of quantum mechanics and the effort to include both the electron and the electromagnetism in one completely consistent theory, that the symmetry of gauge invariance emerged as the overarching theme. In fact, this has been the dominant theme in all twentieth-century physics - all forces are now know to be governed by gauge symmetries, descriptions of which are called gauge theories.”
Leon Lederman (Nobel Prize 1988) and Chris Hill in “Symmetry”
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