In Chapter 3 of "QED:
The Strange Theory of Light and Matter", Electrons and their Interactions ",
Richard Feynman justifies some of the simplifications he made in the first two
chapters of the book. He, for example, explains why we get the correct
answer for the probability of partial reflection of photons from glass by
imagining that all the reflection takes place at the surfaces of glass.
Then he gives an outline of the theory of Quantum Electrodynamics (QED), for
which he, Julian Schwinger, and Sin-Itiro Tomonaga jointly received the Nobel
Prize in 1965.
QED must be a relativistic theory for two reasons.
(1) A major player is the photon, which moves with the speed of light.
(2) Particles are created and annihilated during the processes described by this
theory.
Feynman introduces the great simplifying tool called the Feynman diagram. Using Feynman diagrams as a graphical computational aid, one can keep track of all the possible ways that a system of particles can develop from a given initial state to a different final state.
For this extra credit assignment read Chapter 3 of "QED:
The Strange Theory of Light and Matter " by
Richard P. Feynman (Princeton University Press, 1985). You can listen to
Richard Feynman delivering the actual lectures at
http://www.vega.org.uk/video/subseries/8.
You will find a link to chapter 3 under course materials on Blackboard.
As you read, answer the following questions.
What are the three basic interactions to produce all of the phenomena associated with light and electrons?
Refer to figure 59 on page 93. Assume each of two
excited atoms, located at space-time points 1 and 2 respectively, is
stimulated by a disturbance to emit an electron. The electrons are
indistinguishable. Given this emission, write down a formula for the
probability that one of them arrives at a detector located at space-time
point 3 and the other at a detector located at space-time point 4.
NOTE: In analyzing the left-hand figure, we multiply the amplitudes for the
concomitant events E(1 to 4)*E(2 to 3). This multiplication was originally
explained on QED page 72. In quantum mechanics we multiply the
amplitudes. By contrast, in classical physics we multiply
probabilities. Suppose Alice flips a coin in the physics building and
Bob flips a coin in the chemistry building. These flips are
independent or concomitant. The probability that Alice's coin will
come up heads is 1/2 and the probability that Bob's coin will come up heads
is 1/2. The probability that BOTH coins will come up heads is
(1/2)*(1/2) = 1/4, i.e. a multiplication.
In quantum mechanics, however, we multiply not the probabilities but the
amplitudes for the concomitant events. To obtain the probability we take the
square of the magnitude of the final amplitude. Arrows can cancel,
probabilities cannot. This is the great difference between classical
physics and quantum physics.
Refers to Figure 60, page 94. Look at the left-hand diagram in that figure and at the expression for the corresponding amplitude given near the bottom of page 94. Write down the corresponding expression for the amplitude for the right-hand diagram in Figure 60.
Refer to Figure 68, page 104:
For glass, the six small arrows shown in the figure, when added, approximately make up 1/4 of the circumference of a circle of radius 0.2. (There is an angle of 90^{o} between the two radius vectors that are drawn.) What is the length of the resulting arrow?
What is the probability of detection for this thickness of glass? (Refer to page 25.)
How many more arrows would one have to add, or how much thicker would the glass have to be, to get a total amplitude of zero?
In general, does the length of the resultant arrow for reflection depend on the thickness of the glass?
Refer Figure 71, page 111. A photon is emitted at space-time point 1 and another photon is emitted at space-time point 2. Write down the resultant amplitude for both photons to reach space-time point 3. Express this resultant amplitude in terms of the amplitudes P(1 to 3) and P(2 to 3). Write down the expression for the probability that the two photons will arrive at space-time point 3 using this amplitude.
Use Microsoft Word to prepare a report that contains your answers to these questions.
For extra credit (up to 5 points) hand in or email your report before the extra credit 3 due date.