Re: Neumaier's Modification of Heisenberg 4: The "Generalized HUP"
- From: "OsherD" <mdoctorow@xxxxxxxxxxx>
- Date: 22 Aug 2005 15:23:58 -0700
>>From Osher Doctorow
Wait a moment! Isn't a random variable with a finite number of values
probabilistic?
Yes, but it's like throwing away knowledge/information when you replace
Individual values with means or "expectations". If all that remains of
probability-statistics in the quantum theory is finite discrete random
variables, then in addition to the incredible loss of knowledge from
aggregating or averaging Individual values, there is an incredible loss
of knowledge from throwing away all continuous random variables.
But aren't continuous random variables outlawed by discrete energy
eigenvalues for example? Heck no!
But it gets funnier to a mathematical probability-statistics person.
Many physicists and engineers don't know that there is a considerable
parallelism between continuous and discrete probability distributions!
Surely I'm joking, Mr. Feynman or no Mr. Feynman as the saying goes?
No. Of course, it helps to take a third year college probability
course at a research university or equivalent that requires calculus.
Look at these parallels:
1) uniform distribution and equiprobable (discrete) distribution
2. exponential distribution and geometric (discrete) distribution
3. gamma distribution and Poisson (discrete) distribution except that x
goes over to parameter a + 1 or alpha + 1
This is two out of three of the maximum entropy Shannon distributions
for continuous random variables! And the normal/Gaussian approximation
holds for most known discrete distributions, the normal/Gaussian being
the third Shannon maximum entropy distribution!
What this means in simple language is that not only Neumaier but nobody
can drop continuous probability from quantum theory without dropping
the whole quantum theory.
Next question :>)
Osher Doctorow
.
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