Simple Nature - Light and Matter

Exercise 13D: The Einstein-Podolsky-Rosen paradox

A nucleus having zero angular momentum undergoes symmetric fission into two fragments, each
with`= 1. By conservation of momentum, they fly off back to back, and by conservation of
angular momentum their angular momenta are also opposite. Let’s say that except for this
correlation, the two angular momentum vectors are randomly oriented.

1. Warm-up: Suppose Alice measures thexof particle A, and Bob measuresxof fragment B.
   Make a table of the probabilities of the outcomes.
   particle B
   x=− 1x= 0 x= 1 x=− 1
   particle A x= 0 x= 1


2. In a 1935 paper that ended up being one of the most frequently cited physics papers of all
   time, Einstein and his collaborators considered a scenario similar to the following. Suppose now
   that Alice measuresx, but Bob measuresz. It shouldn’t matter who goes first, but let’s say
   that Alice does. Using the results of exercise C, compute the probabilities in the row assigned
   to your group. Take into account the factor of 1/3, because in this table, as in the first one,
   we’re talking about the probability of a certain result for Aanda certain result for B.

Bob’s probabilities

`z=− 1 `z= 0 `z= 1

1/3 of the time, Alice gets`x=−1 =⇒

1/3 of the time, Alice gets`x= 0 =⇒

1/3 of the time, Alice gets`x= 1 =⇒

total probabilities for Bob

3. Can Alice send information to Bob by deciding whether or not to measure her particle’s`x?

Exercises 955