Divine Neutrality

I am reading some wonderful papers on the Measurement Problem.

What strikes me is how measurement is visualized. It is visualized as taking place in a laboratory. The system - an isolated entangled state - encounters a macroscopic measuring device. In doing so the Hilbert Spaces of the two become entangled. Somehow a pointer state of the device must result. This is the scheme set down by von Neumann in 1932 and lucidly explained and expanded upon by Schlosshauer in a well written review article. Another gripping article is by Geoffrey Sewell, who says, effectively, that there is no measurement problem.

But is measurement about laboratories?

In the laboratory a photodetector signals the arrival of each photon and a counter accumulates the counts. It works because the photon is absorbed, ejecting an electron. (A current of electrons moves pointers.) The reaction

(photon + electron) yields (electron*)

is what marks the measurement.

But is not any green leaf a photodector? The photon gets absorbed via photosynthesis. The leaf’s vitality is a photon count accumulator. The reaction

(photon + water + carbon dioxide) yields (sugar + oxygen)

marks the ‘measurement’.

Surely every chemical reaction that goes to completion is a measurement event; the reactants disappear and the products appear. Isn’t every inelastic scattering a measurement event? In every such event the original quantum system is destroyed and something new emerges. It is just the property of any chemical reaction.

What, then, constitutes a measurement?

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In the October 2007 issue of Physics Today beginning on page 78 there is an article on Wavelets by Ivan Selesnick, son of my friend Stephen Selesnick. He must be a very proud father.

I read the article. I wish I understood what I read. What does sparse mean?

Here is my picture of the story: A fourier transform tells us to what extant the signal is periodic; it displays the frequencies embedded in the signal. Signal polution ‘has no frequency’ - white noise - yielding small amplitude at all frequencies. Thus it can, in the transform, be distinguished from what we are looking for - periodicity. A spectrum shows us what frequencies are present.

But signals may have distinguishing features other than frequency for which we want to search. The idea is to create a transform to display the distinguishing feature we wish to favor and to blunt what we wish to devalue. Wavelets are the transforms that do this: enhance what we favor, blunt what we devalue.

Is this a valid overview? Have I got it right?

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