Lecture 1: (My unpolished notes, full of errors for lecture 1 of the LLL series)





Class 1-3 pm Monday’s

Break at 2:00


What do you expect ?


We should discuss openly the questions and strengthen our understanding through dialogue.  I will moderate. If I feel we should push on to a new topic then I will curtail discussion.


Invitation to schedule times to use the physics department resources to review material on the web or borrow text books.  There are computers, desks and parking.



There are many sites that provide introductory comments and different approaches. Here are a few that I enjoyed reading.









Our goal will be to explore, discuss, explain – The Strange World of Quant um Mechanics -. 


You might ask if it is possible to explain vision to a blind person or sound to deaf person.  The problem is the experience is hard to describe while enjoying experience itself makes things clear.   In particle physics we are confronted with a similar problem.  Our ability to perceive what is happening at the small scales is limited. How does one develop intuition or build models ?   One tried and true technique is to rely on mathematics.  The first real forays into subatomics were done by writing relationships. At the time people were trying to understand atomic spectra.










Physicist like Bohr and Schrödinger were able to produce mathematical formulas that generated the wavelengths.   Over the years a complete framework or theory of subatomic physics was developed.  Part of our intuition is based on examining the relationships and predictions. Our pictures or models however are perhaps somewhat limited because we rely on macroscopic experience to tell the story of the small scale. The first and most important point is that the theory provides a fairly complete description of subatomic phenomena.


Look at a classic problem TWO SLIT and MULTISLIT



Let us predict what will happen to light.


The picture:




So light behave like a wave.


When Maxwell finally completed the formulation of E&M. he discovered that he could write down a wave equation and that the speed dropped out as:


C=3.00 x108 m/s.


Scientists were excited. Oh BOY!  If we see a pulse traveling down a string and predict how fast the pulse should move then we can tell if the string is moving. If we see the pulse moving faster than predicted then we assume the string is moving past us in the direction of the pulse.  Slower means the opposite.


The Michelson Morely experiment and light speed for different observers is a future lecture.


QM a la Feynman/Shimony


Handout  obtained from







“Associated with every physical system is a complex linear vector space V, such that each vector of unit length represents a state of the system.


“There is a one to one correspondence between the set of eventualities (observables) concerning the system and the set of subspaces of the vector space associate with the system, such that if e is an eventuality (observable) and E Is the subspace that corresponds to it, then e is true in a state |S> if and only if any vector that represents S belong to E; and is false in the state S if and only if any vector that represents S belongs to E(orthogonal) .”   A states described by a vector that has components in both subspaces represents a state with an unspecified value for this observable e.


“If |S> is a state and e is an eventuality (observable) corresponding to the subspace E, then the probability that e will turn out to be true if the initially the system is in state |S> and an operation is performed to actualize (measure) it.

v is a unit vector representing S … and PE is the projection.”



“If 1 and 2 are two physical systems, with which the vector spacesV1 and V2 are associated, then the composite system 1 + 2 consisting of 1 and 2 is associated with the tensor product V1 x V2.”


“If a system is in a nonreactive environment between 0 -> t, then there is a linear operator U(t) such that  U(t) |v> represents the state of the system at time t if |v> represents the state of the system at time 0. Furthermore, ||U(t) v||2 = || v||2 for all v in the vector space.”