10C's : C6, C7, C8
C6
Quantum mechanics and the realm of the microscopic.
[See lectures, class web pages, HWs & solutions, and the
beginning part of S4 of TB1; and see also Chapter 4 of TB2.]
* Wave/particle behavior of photons: pioneered by Planck (E =
h x frequency, 1900) and Einstein (photo-electric effect, 1905).
* Wave/particle behavior of massive particles, pioneered by de
Broglie (wavelength = h/p) and Schroedinger (quantum physics wave equations,
see sample solutions shown in Fig. S4.6 of TB1.).
* Uncertainty principle, by Heisenberg, 1925.
* Exclusion principle, by Pauli, 1920's; which leads to degeneracy
pressure, a pressure unrelated to temperature.
* Existence of antiparticles for all particles, predicted by Dirac,
1928.
* Planck scales in terms of G, c, and h (or h-bar)
**
Planck length, L_p = (h G c^-3)^(1/2);
**
Planck mass, M_p = (c h G^-1)^(1/2);
**
Planck time, t_p = (h G c^5)^(1/2).
Culture:
See the Nobel Prize links to the above scientists.
C7
Building blocks of the Universe: matter
particles and force particles
[See lectures, class web pages, HWs & solutions, and
S4 of TB1; also Chapter 1 of TB2.]
* Intrinsic quantities of particles: rest mass M, spin S, electric
charge Q.
* Values of spins are quantized: integer or half-integer in the unit
of h-bar.
** Fermions: particles with (half-integer)
x (h-bar) spins; electrons, neutrinos, protons and neutrons all have
spin S = (1/2) h-bar.
** Bosons (or mesons): particles with integer
x h-bar spins; all force particles are bosons (mesons).
* Fermions do not want to share an energy/spin spot --- the Pauli
exclusion principle --- degeneracy pressure (that sustains stars by
balancing the pressure from gravity, to be discussed after Quiz 3.)
* Values of charges are quantized in the unit of e. (The symbol
e is also used for the particle electron.)
** The potential energy gained by a
particle with charge e after moving up an electric potential difference
of V is 1 eV = 1.6 x 10^-19 kg m^2 s^-2.
** Charge of electron
Q_e = -1 e; Charge of neutrino Q_neu = 0; Charge of proton Q_p
= 1 e; Charge of neutron Q_n = 0.
* Ordinary matter: Electrons, electron-type neutrinos, Protons,
neutrons, atoms, molecules, etc. See the Periodic Table, App. D of TB1
or the web link in our course web (on which you can click on each element
to find more detailed info).
* More basic building blocks of matter, as currently established by
experiments
** up-quark, u: spin S_u = (1/2) h-bar; charge
Q _u = (2/3) e,
(Masses of quarks are small, however, not well determined (because
quarks do not come out of the proton as free particles).
** down-quark, d: spin S_d = (1/2) h-bar;
charge Q _d = (-1/3) e.
** A proton is made of two up-quarks
and one down-quark, denoted by uud (so the net charge and spin come
out right), plus lots strong force particles, called gluons.
[Note that charges add up like numbers, however,
spins are vectors (quantities that have a magnitude and also orientations,
for example distances and velocities in 3-space) and they add up according
to rules of vectors.]
** A neutron is made of one up-quark and
two down-quarks, denoted by udd, plus lots of gluons.
* Electrons and neutrinos do not have inner more basic structure
, as far as current experiments can see, down to about 10^-18 m.
* Force particles are all bosons (mesons): Range of force
is inversely proportional to the mass of the force particle.
** Strong force particle: gluon (denoted
by g_st),
***
Spin S_g_st = 1 h_bar; charge Q_g_st = 0; (mass M_g_st not known, like
quarks, gluons do not come out of the protons or neutrons as free particles.)
** Electromagnetic force particle:
photons (denoted by the Greek letter gamma),
***
Spin S_gamma = 1 h_bar; charge Q_gamma = 0; mass M_gamma =0.
***
Photons moves with speed of light c and the range of force is infinite.
** Weak force particle: W^+ meson,
W^- meson, and Z^0 meson (or simply by symbol only, W^+,
W^-, and Z^0);
***
Spin of weak force particles, S_Z = S_W = 1 h_bar; Charges are as denoted
by the superscripts of the particles; Their masses are about 100 proton
mass (with mass of Z^0 slightly heavier, and the masses of W^+
** Gravitational force particle: graviton
(denoted by g_Gr), yet to be observed
***
Spin of graviton, S_g_Gr = 2 h_bar; charge Q_g_Gr = 0; mass M_g_Gr =
0 (So the force range is infinite in range and moves with speed of light
c.)
* From protons and neutrons, nuclei of atoms are made. Nuclei
plus the surrounding electrons, (electrically neutral) atoms are
formed : hydrogen, helium, etc; See the Periodic Table in TB
1; and, even better, the link given in the course web, near to this
class page.
* From atoms, molecules form: e.g., water molecule (two hydrogen
and one oxygen), etc.
* In all there are three copies (families, or generations)
of quark pairs and lepton pairs:
** (up, down) quarks and (electron, electron-neutrino)
leptons;
** (charm, strange) quarks and (muon, muon-neutrino)
leptons;
** (top, bottom) quarks and (tau, tau-neutrino)
leptons.
* Ordinary matter we know about is mostly made out of protons, neutrons,
electrons, which are from the first family, and force particles.
C8
Standard model and gauge principle
[See lectures, class web pages, HWs & solutions, and Chapter
5 of TB2.]
* Standard model is a name for the combination of electroweak
theory and strong theory
** electroweak theory:
*** matter: three families
(of flavors) of leptons and three families (flavors) of quarks, as
listed in C7;
*** force particles: photons
and the three weak force particles, as listed in C7.
*** force particles mediate
forces among matter through a "family (or flavor)" charge, of which
electric charge, e, is a manifestation.
** strong theory, in short called QCD (which
stands for Quantum Chromodynamics)
*** matter: three families
of quarks (and each quark has three colors)
*** force particles:
gluons (eight "colors");
*** force particles mediate
strong force among the matter through a "color" charge.
* The guiding principle for the standard model is the gauge principle,
as cleared made use of by the work Yang and Mills in 1954