From: crb7q@kelvin.seas.Virginia.EDU (Cameron Randale Bass)
Subject: Re: GROSS MISCONCEPTIONS ABOUT PROBABILITY, DETERMINISM AND LOCALITY
Organization: University of Virginia
Date: Mon, 12 Oct 1992 17:37:06 GMT

In article <1992Oct12.133138.203071@uctvax.uct.ac.za> naturman@uctvax.uct.ac.za writes:
>From the responses to my postings on QM which I have received, it is clear to 
>me that many people are grossly ignorant of basic mathematics. Here are some 
>examples of the gross misconceptions regarding probability which I have 
>encountered:
>
>Misconception (1): "Probability is independant of knowledge." To see that this 
>is false consider the case of a man who throws a coin over a wall. For him, the
>probability that the coin landed heads up is 0.5 and the probability that it 
>landed tails up is 0.5. For a man on the other side of the wall who can see the
>coin, there are two cases: If it landed heads prob(heads) = 1 and prob(tails) 
>= 0; if it landed tails then prob(tails) = 1 and prob(heads) = 0.

     You are comparing apples and oranges.  In the first case, you are
     talking about 'bare' probabilities.  In the second you are talking
     about conditional probabilities.  The probability of the guy on the other
     side of the wall seeing heads after the first guy tosses it over
     is still 0.5.  However, the conditional probability of the coin being 
     heads-up for the second guy after he has already seen that it is heads
     is trivially 1.0.

>Misconception (2): "If the probability of something occuring is 0 then it can't
>occur, and if the probability of something occurring is 1 then it must occur."
>This nonsense is related to the belief in the Value Rule in interpretations
>of QM. The Value Rule says that "if the probabilty of an observable Q having
>value q in state Psi is zero, then Q cannot have value q in state Psi". The
>Value Rule is usually only considered in realist interpretations of QM. It can
>be reworded for non-realist interpretations as follows: "if the probability of
>measuring Q in state Psi and obtaining value q, is zero, then we can never
>obtain the value q when measuring Q in state Psi". Most people recognize that
>the Value Rule fails for observables Q whose corresponding operator Q^ has 
>an uncountable spectrum of eigenvalues. But there are some ignoramuses out 
>there that seem to think that it does hold in such a case. To see that it
>doesn't consider the 1-D case and let Q be the position of a particle along an
>axis. Let Psi, for example, be given by a Gaussian wavefunction centered at the
>origin. Then no matter what value q we consider, the probability of Q having
>value q (on measurement, if you are a non-realist) is zero. Yet when you
>measure you will still get some value, and in particular that value had
>probability zero. (Tough, if you don't like it.) To see that the Value Rule
>also fails for a countable spectrum, let Psi be as before but this time let Q

     Gee, isn't this a set of measure zero?  Show me how the particle
     position defines such a set.  Exactly *when* does the particle 
     arrive at, say, x=0.

                                  dale bass
-- 
C. R. Bass                                           crb7q@virginia.edu
Department of Mechanical and Aerospace Engineering
University of Virginia
Charlottesville, Virginia                            (804) 924-7926