Sunday March 23, 2008 7:00 am Edmonton, Alberta

This page last updated on: Sunday, April 20, 2008 9:15 AM

It is -3 C with a high forecast of +2 C. Sunrise 7:28 Sunset 19:52 Hours of daylight: 12:24

A. Morning Musings

Easter. We plan to take a walk in the river valley then return for a home-cooked Easter dinner. Overall a laid-back day.

I have received an email indicating that my amazon.ca order has been shipped. The estimated day of arrival is April 1.

My Tim Hortons coffee is almost ready. It is tempting to begin reading one of the books I bought yesterday, but I will resist this and continue with what I am presently reading.

Learning Category	Planned Activities for Today	Time
Literature	Begin morning with a Rumi reading
Literature	Continue reading "The Way the Crow Flies" by Ann-Marie MacDonald	1 hr
Science	Continue reading "Quantum: A Guide for the Perplexed" by Jim Al-Khalili	1 hr

B. Actual Learning Activities

7:20 am

Quantum: A Guide for the Perplexed (2003)

Jim Al-Khalili

Chapter 3 Probability and Chance

I have read the entire chapter, enjoyed it, and I think I understood the important points. Now to make a few notes on the key points.

A Newtonian system refers to a situation where one can predict, in principle, the outcome of an event from a knowledge of the initial position and conditions of motion of the constituent elements. This is sometimes called a "clockwork" universe.
A quantum mechanical system has probabilities built into the very nature of the theory. In principle, one cannot be more precise than to state a probability of a particular outcome.
"One way out of this dilemma would simply be to say that quantum mechanics is not the whole story, and that the unpredictability of radioactive decay is indeed due to our ignorance. What we are lacking is a deeper understanding of Nature whereby we are able to predict exactly when any given nucleus might decay, just as a fuller knowledge of all the forces involved in a toss of a coin would allow us to predict its outcome. If this were true we would need to go beyond quantum mechanics to find the answer. We will see in Chapter 6 how Albert Einstein held this view." [p. 59]

I am looking forward to reading Chapter 6. I have some sympathy for this view, but I view this as a matter of the mathematical model that we have adopted to describe the phenomena. Thus the issue is one of finding (creating?) a different mathematical model that does at least as good a job of prediction as the quantum mechanics model and then provides more precise predictions for other situations.

This idea has two components. One is whether such a mathematical model exists at this point in time, and the other is whether we would recognize such a model as being relevant to the present situation of understanding the physical universe at a sub-atomic level (and at a cosmological level).

I must have another look at Roger Penrose's book, "The Road to Reality", which discusses the relationship between mathematics and physics.

"Much of the credit for the development of the theoretical understanding of quantum mechanics belongs to the Austrian physicist Erwin Shrodinger, who took the ideas of de Broglie and put them on a firm mathematical footing. It is important to note that there are several mathematical ways in which the behavior of a quantum system like an electron or an atom can be described, and Schrodinger's approach was just one of them." [p. 64]
"Solving the Schrodinger equation provides us with a mathematical quantity called the wavefunction. This is where all the probabilistic nature of quantum mechanics comes in." [p. 64]
"Most physicists believe ... that all the time we are not tracking the motion of the electron, its wavefunction is all we have at our disposal to describe it. ... As soon as we look, the wavefunction is said to 'collapse' and the electron becomes a localized particle." [p. 67]
There are two different wavefunctions for describing an electron: a position wavefunction and a momentum wavefunction. If we know one of these we can compute the other. But it turns out that the mathematics says that the more precise you have one measurement the less precise is the other measurement. This is known as the Heisenberg uncertainty principle.
The period 1925 - 1927 was important for the development of quantum mechanics. The key people were Wolfgang Pauli, Werner Heisenberg, Max Born, Paul Dirac and Erwin Schrodinger.

I am almost a third of the way through this book, and am still understanding it. The credit goes to Jim Al-Khalili. This is a great way to begin the morning. I am alert and able to handle the material without difficulty. At least so far.

Tags: physics, science, quantum

6:00 PM

A super day. A very good breakfast, a glorious walk in the river valley, a few chores around the house, and a great Easter dinner about to be served. Perfect.

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