Re: Download a new book on quantum mechanics and relativity.

From: Bilge (dubious_at_radioactivex.lebesque-al.net)
Date: 09/23/04 

Date: Thu, 23 Sep 2004 20:46:39 -0000

 Eugene Stefanovich:
>
>
>Bilge wrote:
>> Eugene Stefanovich:
>>
>> > I think you should read again about the difference between measurement
>> >(single act of observation, see subsection 3.2.1) and experiment
>>
>> I have thought about it. Your idea of observables and quantum mechanics
>> as a theory about ensembles is just plain wrong and contradicts every
>> quantum text I've ever seen. You don't connect theory to experiment
>> very well at all.
>
>Wave function is probability amplitude, right?

   Right.
 
>How do you think the probability is measured if not in ensemble?

  One doesn't measure a probability. One measures the outcome of a lot of
trials, obtains a statistical result and then _infers_ a probability for
that result in each _trial_. Finally one compares that inferred result to
the probability obtained from a _calculation_ to see if the two agree. If
they don't one doesn't adjust the wavefunction to match it. One declares
the theory bad.

>By definition, the probability is the ratio of the number of
>desirable outcomes of measurements to the total number of
>measurements.

  OK, then let me apply that to a test of quantum mechanics.
I prepare electrons with their spins along the x-direction.
I measure the z projection. Using your notion of quantum
mechanics, I can't know ahead of time what the probability
of finding the spin along +/-z, so I say that the probability
of +z is P_up and -z is P_down. I now count 25 particles with
+z and 75 paricles with -z. According to you, I've just
measured the wavefunction, so the wavefunction must be:

  |x> = 0.5 |+z> +/- 0.866 |-z>

  Therefore quantum mechanics tells me the right answer. Always. Does
that sound very reasonable to you? I hope not.

  Do you think perhaps that quantum mechanics might tell you the
probability amplitude for the wavefunctions _before_ the experiment, so
that you are comparing the probability given by quantum mechanics to the
_statistics_ of an experiment?

 Do you know the difference in a _probalistic_ theory and how it
relates to a _statistical_ experiment?

>So, in order to
>have probability you need to have many (preferably infinite number
>of) measurements performed on identically prepared systems. You need
>to have an ensemble.

  Oh gee. You've just pointed out some real problems here. According to you,
knowing the probability amplitude requires me to measure the probability
amplitude. Does that mean the probability for the first particle to be
in a given state depends upon the wavefunctions of each of the particles
that come after it?

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