Class 7

Notes index

Class 5

Origin of the Universe - Class 6

Boldface links give quick local access. Other links lead to distant Web sites (and may be slow).

Biography of James Chadwick and Pierre and Marie Curie

Biographical and other information at the Nobel prize web site:

Ernest Rutherford  -   Joseph Thomson   -   James Chadwick   -   Wolfgang Pauli
Glashow, Weinberg, and Salam

Review by Gretta Thorn.

Questions from homework:
- Interference of waves and the colors of soap bubbles. See the file soap.txt

- In Feynman's sum over paths, the phase factor associated with each path is given by the action on that path. Precisely, the phase advances by 360° (or 2p radians) when the action increases by h, where h = 6.626×10^-34 joule·sec is Planck's constant. Often instead of h one uses , which is equal to h divided by 2p

The relativistic action for a particle that moves on a path in space-time is proportional to the "proper time" measured by a clock that moves with the particle. Precisely, for a particle of mass m moving with (variable) speed v, the relativistic action is

The classical path in space-time corresponds to the "least action" and to the longest "proper time".

From the point of view of Minkowski space-time geometry, the square of the "proper time", multiplied by c², is also the negative of the square of the space-time "length" of the path. This "squared length" is measured according to dl² - (c dt)², where dl is the distance traveled during time dt (hence dl = vdt). "Least action" and "longest proper time" correspond to the most negative value of the "squared length".
In ordinary geometry the shortest path between two given points is called a geodesic. We can then say that the classical path is a geodesic in space-time, provided that we understand "shortest path" to mean the path with the smallest (i.e. most negative) "squared length".

What is quantized and when? In periodic motion, action is quantized in units of h; as a consequence, other quantities are quantized too, but not so simply.
What is action? It is a quantity with dimensions ML²T^-1; it can be energy × time, or momentum × length. Angular momentum has the same dimensions as action and is simply quantized in units of .
What is spin? It is something like the internal angular momentum of an elementary particle. However, electrons (and quarks) have spin /2, while orbital angular momentum must be an integer multiple of . Photons have spin . One often says that electrons have spin 1/2 and photons have spin 1.
What is the Pauli exclusion principle? As originally stated, it says two electrons cannot be in the same quantum state. Actually, it applies to all elementary particles with spin 1/2 (called fermions) and is mysteriously related to their unusual spin. It also applies to composite particles with half-integer spin (1/2, 3/2, etc.). Read more about it in Pauli' s Nobel Prize award speech and his biography.