Saturday, July 09, 2005

Freedom

Gauge freedom to be specific. Charles H. Lineweaver and Tamara M. Davis wrote a nice article in the March Scientific American on Misconceptions about the Big Bang. One of their unifying themes was the idea that expansion of the Universe should be seen as "expansion of space" rather than "expansion through space." This is also a theme for Brian Greene in his excellent popular book The Fabric of the Cosmos as well as for blogger and cosmologist Sean Carroll in his textbook Spacetime and Geometry: An Introduction to General Relativity (also excellent). Nonetheless, it bothered me, and I even got into a debate on the subject on Lubos Motl's blog.

Thus I was gratified when this month's Scientific American included a letter from James Bjorken (yes, that James Bjorken) stating

...the concept of expansion of space as opposed to expansion through space is a "gauge choice" - it depends on the coordinates chosen.
One of the cardinal principles of Einstein's GR is "general covariance" - the theory is independent of the choice of coordinates. Lineweaver and Davis concede Bjorken's point but then compound their error by saying:
We could use systems [of coordinates] that abandon expanding space in favor of expansion through space, but they also abandon well-established principles, such as the homogeneity of the universe and Hubble's law.
No and No. It's true that homogeneity and Hubble's law are more conveniently described in Friedman Robertson Walker [expansion of space] coordinates, but GR is quite clear that choosing different coordinates doesn't change the physics - we really are free to choose the gauge. On the positive side, they did provide another inadvertant example of their thesis that even Astronomers (and Cosmologists) can be confused about the Big Bang.