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Re: simulation +- hands-on experiments

People!

As I posted earlier, this experiment was necessary to assist in the verification of various theories about decay, i.e. they all assume randomicity. Fitting to a Poisson process is essential. I quote
Evans: ..... This is one of the EXPERIMENTAL (my emphasis) justifications of which many nuclear considerations rest" He then gives data from Curtiss's alpha-ray data and compares its distribution
(frequency) with the poisson "prediction." using the chi-square test. (L. F. Curtiss: J. Research Nat. Bur. Standards, 4: 595 (1930))

A BTW: I wrote earlier that the asymmetry of the poisson distrib. leads to an "error" if the detector (person counting autos, in addition to G-M counter, etc.) has non zero resolution. Evans gives
the approximate corrections for the first two moments: eq. 1.19 & 1.20:

nT ~= NT / (1 + Nt) + (N^2) (t^2) / ((1+ Nt)^2)2) (mean; N is "true" rate n is measured, t is dead time)

and: Sigma^2 (var.) ~= NT / (1 + Nt)^3

both from W. Feller: "Studies and Essays", Interscience Pubs., Inc., N.Y. (1948) [ Ch. 5, Sec. 1]

Finally, the Utah math dept. site stat./poisson pages uses the regenerative property to derive the Poisson Process -- "... the behavior of the process after an arrival [shall] be independent of the
behavior before the arrival and [be] probabilistically like the original process (regeneration)."

i.e. X 1 = T 1, X k = T k - T k-1 for k = 2, 3, .... etc. from this they derive the poisson density, etc. (I think.)

bc

Ludwik Kowalski wrote:

John Denker wrote:.

The questions that were being asked (arrival times and various
cumulative and marginal distributions) are purely mathematical
questions. They contain no physics whatsoever, and there's
no point in pretending otherwise.

An experiment with a Geiger counter, or with a different counter
of nuclear transformations, is a way to demonstrate that such
transformations are "IID events (Independent and Identically
Distributed over time)", as you referred to them yesterday.
Is this physics? How else can this fact about the nature of
radioactivity can be demonstrated?
Ludwik Kowalski


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