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.

Comments

Post a Comment

Popular posts from this blog

Anti-Libertarian: re-post

The most pointed critique of social security and liberalism in general is the libertarian critique. The problem with libertarians, for a liberal, is that we have too much in common. We both believe in individual rights, tolerance of individual differences, and dislike government prescription of religion. The basic difference, it seems to me, is the different answers we give to Cain's (with thanks to the Captain - my original version had the corpse asking the question!) famous question: "Am I my brother's keeper?" That's not really my basic bitch against the libertarians though. My real complaint is the same as my complaint against most religion - its premise is a fraud. For those who can't stand to wait for the punchline, I believe that trying to implement libertarian principles leads to tyranny or social disintegration. Demonstrating that takes some historical (and pre-historical) context. For all but the last 15,000 or so of the 100,000 years the human spec...
Read more

Uneasy Lies The Head

Uneasy lies the head that wears a crown ........... Shakespeare Henry IV, Part II. So it is with us and our slightly distant primate cousins , so it seems. A 9-year study of wild baboons in Kenya by Princeton University and the Institute of Primate Research may turn conventional assumptions of alphas males upside down. The study found that alpha males have high testosterone levels, which allows them to dominate other baboons, get access to more food, and attract better mates. This is expected. Surprisingly, though, the alpha males also have high levels of stress hormone glucocorticoid, which scientists measured from their feces samples. In fact, the stress of alpha baboons was on par with low-ranking baboons. The convention wisdom is that access to food and females provides life security and thus less stress for dominant males. Conversely, weak males who are constantly threatened by starvation and physical violence from stronger males are thought to be more stressed. The st...
Read more

We Call it Soccer

The US played its best, and maybe only good game of World Cup, but lost thanks to brilliant goalkeeping by the Swedish keeper and the bizarre method soccer uses to settle ties when three US stars could not put the ball on frame from the 12 yard spot.  At the end it came down to a blocked shot that spun in by maybe a couple of centimeters. Well, that's football - too much like life.   Which brings me to a modest proposal.  Replace the thirty minute overtimes with as many 7-player 15 minute periods as needed to settle it.  Scoring should be much easier with fewer players.
Read more