PHYS 182 Lecture Notes - Lecture 12: Neutrino, Thermonuclear Weapon, Energy Flux
PHYS182: Our Evolving Universe
2017-10-19 LEC 12
Review
• Classic particle à wave function Ψ(x)
o Wave particle duality
• Heisenberg uncertainty relation
o ∆x∆p>h
o The more accurately you localize the position of a particle, its momentum becomes more
uncertain
Up until now: non-relativisitic quantum mechanics
• This works for chemistry, most of physics experiments, doesn’t work if you’re talking about very
high speeds and very high energies
o I.e. doesn’t work for cosmology for anything close to c
Extension to Special Relativity
• x (position) becomes position and time (x, t)
• p (momentum) becomes momentum and energy (p, E)
• If quantum mechanics should be extended to special relativity then the uncertainty in position and
momentum will have to be:
o ∆x∆p>h
o ∆t∆E<h (analogous uncertainty)
o Normally write ∆x∆p~h and ∆t∆E~h
Quantum Vacuum fluctuation
• There is no such thing as a vacuum, there are particle-antiparticle pairs
• As soon as the energy uncertainty is greater than 2mc2 then you have enough energy to create
particle-antiparticle pairs
• Applications in astronomy:
o Black holes radiate Hawking radiation
§ Near the horizon of the black hole, space is curved so much that one of the
particles in the particle-antiparticle pair can disappear into the black hole
o Cosmology: Vacuum fluctuations cause “everything we see”
Particles
• Elementary vs. composite
o Atoms were initially viewed as elementary, but now we know that they are composite
o Rutherford experimentally discovered that an atom consists of electrons orbiting a
nucleus
§ The electron is an elementary point particle with no radius
§ Nucleus is composite, made out of quarks bound by gluons which are
elementary
o Photons (particles of light) are elementary
• Bosons vs. Fermions
o Distinguished by a property called spin: internal angular momentum
o If you visualize a point particle as a ball, you can visualize the spin as rotation of the ball
o Bosons have integer spin à 0, 1, 2
§ Photons and gluons are bosons à carriers of forces
Document Summary
Review: classic particle wave function (x, wave particle duality, heisenberg uncertainty relation, x p>h, the more accurately you localize the position of a particle, its momentum becomes more uncertain. Up until now: non-relativisitic quantum mechanics: this works for chemistry, most of physics experiments, doesn"t work if you"re talking about very high speeds and very high energies. I. e. doesn"t work for cosmology for anything close to c. Extension to special relativity: x (position) becomes position and time (x, t, p (momentum) becomes momentum and energy (p, e) If quantum mechanics should be extended to special relativity then the uncertainty in position and momentum will have to be: x p>h, t e
