Divine Neutrality, Blog. Science, Philosophy

The Equation

June 7th, 2009

hangrBrdJennifer says, with enthusiasm, “I love equations.”

What’s to love?

An equation is a statement that says ‘this equals that’. It’s hard to imagine, from that raw and basic idea, that something called an equation could be of any use. Whether ‘this equals that’ or not seems a matter of little consequence!

But, in fact, we know that to state what things are equal can have powerful consequences.

Newton’s law – that the net force on something causes it to accelerate – is a matter of things being equal. Force = mass multiplied by acceleration. This law of nature governs an extraordinary panoply of phenomena: the solar system, the entire NASA program of space exploration, the working of engines, the nature of energy and thus of pressure and of temperature and thus our understanding of weather. It underlies thinking in engineering, geology, chemistry, biology, and, of course, physics. All from ‘this = that’.

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What is Measurement?

January 17th, 2008

The Law of Happen

I am reading some 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 state – encounters a macroscopic measuring device. In doing so the Hilbert Spaces of the two become entangled. A pointer state of the device signals the system’s state. This is the scheme set down by von Neumann in 1932 and explained and expanded upon by Schlosshauer in a 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 free electrons moves pointers.) The reaction

(photon + bound electron) yields (free 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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on Wavelet Transforms

January 2nd, 2008

cairn

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 extent 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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