1.7 Stochastic Processes
cific N-13 atom to a C-13 isotope is apparently truly random, since it seems
we fundamentally cannot determine when it will occur by calculating some
physical process underlying the disintegration. Scientistsmustuse probabil-
ity theory to describe the physical processes associated with true quantum
randomness.
Einstein found this quantum theory hard to accept. His famous remark
is that “God does not play at dice with the universe.” Nevertheless, ex-
periments have confirmed the true randomness of quantum processes. Some
results combining quantum theory and cosmology imply even more profound
and bizarre results. Again in the words of Stephen Hawking, “God not only
plays dice. He also sometimes throws the dice where they cannot be seen.”
Sources
This section is adapted from: “The Probability of Heads”, by J. B. Keller,
American Mathematical Monthly, Volume 83, Number 3, March 1986, pages
191–197, and definitions from investorwords.com. See also the article “A
Reliable Randomizer, Turned on Its Head”, David Adler, Washington Post,
August 2, 2009.
Problems to Work for Understanding
Outside Readings and Links:
- A satire on the philosophy of randomness Accessed August 29, 2009.
1.7 Stochastic Processes
Rating
Student: contains scenes of mild algebra or calculus that may require guid-
ance.
Section Starter Question
Name something that is both random and varies over time. Does the ran-
domness depend on the history of the process or only on its current state?