Summary - Randomness

Quantum physics differs from classical physics in many ways, the most dramatic of which is that certain processes at the atomic level, such as radioactive decay, are random rather than deterministic. There is a method to the madness, however: quantum physics still rules out any process that violates conservation laws, and it also offers methods for calculating probabilities numerically.

In this chapter we focused on certain generic methods of working with probabilities, without concerning ourselves with any physical details. Without knowing any of the details of radioactive decay, for example, we were still able to give a fairly complete treatment of the relevant probabilities. The most important of these generic methods is the law of independent probabilities, which states that if two random events are not related in any way, then the probability that they will both occur equals the product of the two probabilities,

probability of A and B = P_AP_B [if A and B are independent] .

The most important application is to radioactive decay. The time that a radioactive atom has a 50% chance of surviving is called the half-life, t_1/2. The probability of surviving for two half-lives is (1/2)(1/2) = 1/4, and so on. In general, the probability of surviving a time t is given by

P_surv(t) = 0.5^t/t1/2 . Related quantities such as the rate of decay and probability distribution for the time of decay are given by the same type of exponential function, but multiplied by certain constant factors.