Tuesday March 25, 2008 7:00 am Lethbridge, Alberta

This page last updated on: Sunday, April 20, 2008 9:17 AM

It is -10 C with a high forecast of +6 C. Sunrise 7:23 Sunset 19:51 Hours of daylight: 12:28

A. Morning Musings

Home. Now to get my head around what needs to be done. The coffee is ready. That may help.

I have added the images to the March 23 page that shows our walk in the North Saskatchewan river valley in Edmonton.

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

7:30 am

Quantum: A Guide for the Perplexed (2003)

Jim Al-Khalili

Chapter 4 Spooky Connections

This is a modification of yesterday's notes, adding an image and improving on some of the notes.

"In this chapter we investigate a few more of the strange concepts forced upon us by quantum mechanics. At the root of them all is the wavefunction. ... Just because we have mathematical formulae that allow us to calculate and predict properties of an atom does not mean that the wavefunction is a mathematical description of the atom itself or worse still that the wavefunction is the atom." [p. 80]

Superposition. The idea of superposition is not unique to quantum mechanics but is a general property of all waves. It is simply the process of adding different waves together. The result is called an interference pattern. The conceptual problem arises when one looks at the result of adding two such waves. This may mean that the resulting wavefunction describes a body that is in two different places at the same time, or of a body that has different velocities at different times. "... a quantum particle can be in a combination of two or more states at the same time." [p. 94]

As I see it the problem arises because when we consider a body (e.g. an electron) as a particle we can describe both its position and its velocity. However when we look at the wavefunction, or the wave emanating out from a position, we then have a consequence that occupies all of the space that the wave might have travelled in the time since the body was first observed. The two descriptions are not equivalent. One describes the motion at a single coordinate, the other describes the motion from an infinity of possible perspectives.

There is an excellent diagram on page 84 that illustrates the idea of superposition in terms of probability distributions.

p84

Particle Interferometers. "Interferometers are devices that highlight the way a single particle can travel along two paths at once ..." [p. 88]

I follow his description, but feel that I have been misled by his words. If I am using the wavefunction description then I have no difficulty seeing that various parts of the wave are in different locations at the same time. In fact, at any instant of time, there are an infinity of possible locations (e.g. anywhere on the circumference of a circle corresponding the wave at that instant) that describe where the "particle" is.

The particle may be a photon, an electron, a neutron or even an atom or a molecule. This makes sense to me as it is a consequence of de Broglie's idea that there can be both energy waves and matter waves. The problems of interpretation arise when we try to think about both possibilities at the same time.

Nonlocality. "... two quantum particles (or two separate parts of the spread-out wavefunction of the same particle) can somehow remain in touch with each other however far apart they are." [p. 94]
Entanglement. The idea is that two particles can "become correlated in the sense that their fates will be intertwined for ever, however far apart they get - until, that is, one of them interacts with a measuring device." [p. 94]
EPR Experiment. Einstein, Podolsky & Rosen (in 1935) came up with a thought experiment that highlights the idea that we cannot consider a particle to have a well-defined position unless we look at it.

I am not totally sure that I understand the nuances of this chapter, but it seems to me that there are no paradoxes - that it is a matter of mixing two different ways of viewing - one that emphasizes the particle nature and one that utilizes the wavefunction. But the fact that this is considered a serious debate for almost a century suggests that I may be missing something.

I think my best strategy for the moment is to continue reading the next chapter.

Tags: physics, science, quantum

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Tuesday March 25, 2008 7:00 am Lethbridge, Alberta

A. Morning Musings

B. Actual Learning Activities

7:30 am

Chapter 4 Spooky Connections