Friday, March 25, 2005

We don't need no stinkin dark energy II

David Wiltshire has opened a new front in the dark energy wars with gr-qc/0503099. He has an allegedly simple and exact model using the Kolb,
Matarrese, Notari and Riotto (KMNR) idea of super-Hubble density variations to explain apparent cosmic acceleration without dark energy.

I have been trying to understand his "spirit of Mach's principle" assumption. My current guess goes like this: At the end of inflation, the universe was nearly flat and uniform in density, so that FRW "comoving" coordinates closely approximated the actual geodesics. As the density variations amplified with time, these coordinates increasingly deviate from geodesics. Here is what I consider the money quote: " observer who would measures
no dipole anisotopy even in the observable universe, must
be referred to the time, t..." I think that means he is assuming that the observers measuring no dipole anisotropy are the ones moving along those (non-geodesic) FRW t coordinates. Meanwhile, back in the underdense bubble, our geodesics are departing from these, and are more conveniently described by a different set of FRW coordinates applying only to our bubble and which are boosted wrt the large-scale FRW coordinates. It would seem to me that this implies that observers in our local bubble who look FRW, presumeably including us, should see a dipole anisotropy. I don't know if that can be reconciled with the small dipole anisotropy we do see.

Or maybe I'm just confused. Oh wait, on that point I can give a definite yes.

I don't know if his assumption is correct, wrong, or even nonsensical, but if one of the latter, I should hope one of the smart guys could soon point out the specific error.

Friday, March 18, 2005

We don't need no stinkin dark energy

Edward Kolb and collaborators have posted a new Paper hep-th/0503117 which suggests that maybe we don't really need dark energy to explain the accelerating universe. About 10 years ago, you may recall, evidence started accumulating that the rate of expansion of the Universe was increasing.

We've known for 70 years or so that the Universe is expanding, that distant galaxies are rushing away from us, and each other, and that the more distant they are, the faster they are rushing away. As it turns out, this was predicted by Einstein's General Relativity, though the prediction was quite a nasty shock to Al when it was first noticed. This story, and everything else I will say except about the new paper, is told very well in Brian Greene's book The Fabric of the Cosmos.

In the General Relativistic picture, the long term fate of the Universe depends very critically on a parameter called Omega. If this parameter is greater than 1, the Universal expansion slows down, halts, and space becomes more and more positively curved while the Universe recollapses in a big crunch. If Omega is less than one, the U expands forever, with space becoming more negatively curved. If Omega is exactly one, though, the expansion continues but at a slower and slower pace and space remains flat. That, at least, was the picture before the acceleration of cosmic expansion was discovered. The evidence now suggests that the Universe is now expanding faster than it was a few billion years ago, but also that the Universe is flat.

Dark energy was invented to explain this apparent conflict. It is supposed to supply just enough energy to make Omega=1, thus making space flat, but also to cause space to expand due to its negative pressure (I'll let Greene explain that part). One important detail, if Omega is exactly one, it stays that way, but if it starts off just a little from from one, the deviation becomes larger and larger with time.

Cosmic inflation, the idea that the Universe underwent an enormous expansion in an extremely short time, is a sort of universal panacea for the diseases of cosmology. In particular, it tends to make space very flat and drives Omega towards one. I refer the reader (if any) to Brian Greene's book again for the details. It does have one peculiar signature: It amplifies tiny quantum fluctuations to gigantic size. Very precise measurements of the cosmic microwave background (CMB)reveal small variations with direction of the CMB with just the right spectrum to be such amplified quantum fluctuations.

The idea of Kolb and his co-authors is that some of these fluctuations could be much larger than the presently observable Universe (and we already know that some are only a little smaller). Suppose we happen to be somewhere in one of those fluctuations that happens to be slightly less than the critical density, so that Omega is slightly less than one. If I understand correctly, this means that our portion of space will expand ever more rapidly, since expansion drives down Omega, which, however, is still quite close to one due to inflation. Very far away galaxies are observed at an earlier time when Omega was closer to one, so they aren't expanding as rapidly. Nearby galaxies are observed at more recent times, so their expansion has been speeded up by the decrease in Omega. The net effect is an apparent acceleration of cosmic expansion. Kolb point out that the predictions of this idea differ slightly from those of the dark energy hypothesis, so that measurements more refined than those we have at present could distinguish the two theories.

If Kolb's idea is correct, it is a bit disappointing to those who hoped that dark energy implied some new physics.

Of course I'm not a cosmologist, so I might be misinterpreting, or oversimplifying his argument. Actually, pigs, even Capitalistimperialistpigs, aren't even very good physicists, so corrections will be welcomed if due.

Thursday, March 17, 2005

Frankly, My Dear, I don't give a damn.

Robert H. Frank, a Professor at Cornell's Johnson School of Management, has a lament for America's shamefully low savings rate in today's NYT. Unfortunately, it's not an especially honest or enlightening lament, though he does get in a few good points, like his finale.

It is clear, in any event, that the failure to save entails risks of its own to freedom. America's rapidly rising debt to foreigners now threatens the economic prosperity on which so many of our cherished liberties depend.

So what's wrong with his article?

Money invested at 7 percent interest, for example, will double every 10 years, which means that $1,000 deposited at that rate by Benjamin Franklin in the late 1700's would be worth more than $3 trillion today. The same $1,000 invested in 1945 would be worth more than $64,000.

Of course you can't get anything like that interest rate unless you are a mafia loan shark or a credit card company (my apologies for the redundancy). My savings account at my friendly neighborhood Wells Fargo seems to be well south of 1% these days. The kind of interest working class Americans can get is pretty much negative when you take into account inflation.

Equally seriously, he fails to mention the key role of the Federal Government=Republican Party in the dis-savings disaster. Aside from all the direct borrowing by the government, the threat of inflation down the road is a powerful savings disincentive.

So what can the government do? End the huge deficits, for a start. Rein in the credit card companies and punish them for making bad loans. And an add on (not carve out) Social Security investment account.

Wednesday, March 16, 2005

The Persecution and Execution of Larry Summers as Performed by the Inmates of Harvard

The Faculty of Arts and Sciences at Harvard have today voted a motion of no confidence in President Lawrence Summers. His crime: speaking an unpopular truth by suggesting that science should be preferred to PC dogma. I think this will be a permanent black mark on Harvard's reputation. It does seem a shame that the reputations of its many brilliant thinkers and scholars will be tarnished by the actions of a willful majority.

This should serves as an object lesson to, say, Caltech and MIT, on the hazards of loading up your faculty with practitioners of fashionable psuedo-scholarship. It's alread too late for the Ivies.

Saturday, March 12, 2005

Abortion: Is Compromise Possible?

Every survey appears to show that about one third of Americans believe that abortion should always be legal, one third that it should never be legal, and one third that it should sometimes be legal. Most of Europe and the rest of western civilization has adopted some version of the compromise position, with abortion legal but restricted.

The de facto situation in the US is that abortion is always legal. This is a bit strange because the Supreme Court's Roe vs. Wade clearly opened the door to some regulation of abortion, but the courts have consistently thrown out laws criminalizing any abortions.

Naturally enough, abortion rights supporters want to maintain this situation, while abortion foes want to overthrow it. The survey statistics mentioned above give each some aid and comfort, since abortions rights people can claim that a large majority supports legal abortions and abortion opponents can claim that a large majority favor some prohibition of abortion. The natural way of resolving such disputes in a democracy is through legislation and compromise, but that way was cutoff by the Supremes.

The current situation is unstable, and, while I rarely agree with conservatives, I think they have a point here in saying that Roe vs. Wade was a judicial overreach. This is a situation very different from the segregation and civil rights cases, since the constitution specifically speaks to these questions in the amendments. It seems likely that President Bush will have an opportunity to appoint a justice who will overturn Roe vs. Wade, and that will probably be better for liberalism in the long run even if it makes abortion somewhat less available.

Saturday, March 05, 2005

Mozart was a Space Alien!

There are a few humans whose accomplishments seem so many standard deviations from the rest of us that it seems like they can hardly have been made of the same stuff. Archimedes, Leonardo, Newton, Shakespeare, and Mozart must have been made of some special metal, or so it would seem. I greatly admire the music of Haydn, Beethoven, and Wagner, but somehow Mozart is at another level. Similarly for the others on my list.

Evidently there is something in human nature that makes us pick out special heroes and promote them beyond ordinary mortality. The ancients promoted dead heroes and live emperors to demi-god status. You don't really need to be an all-time genius to get demi-god points, though. Michael Jordan and Tiger Woods made it too.

My own guess is that there is some evolutionary hardware installed in humans that makes us tend to exaggerate the virtues of our heroes. On a few occasions I have found myself in the capacity of leader in a potentially perilous situation. Never have I felt more confident. On other occasions I've been the follower while someone else led, and my reaction was very different. I felt timid, fearful, and dependent on the leader's judgement.

All of which is preamble to my distress at the American people's willingness to keep following a leader who values seem out of step with most Americans, who makes blunder after blunder, and seems bent on leading the nation to economic catastrophe in his zeal to destroy Social Security. On the other hand, maybe Mozart really was a Martian.

Wednesday, March 02, 2005

The Blue Academy

This obscure editorial found that the ratio of Democrats to Republicans at Stanford and Berkeley was almost ten to one. Apparently other studies have found similar ratios at other top schools. I sort of suspect that Bob Jones U and some similar institutions were not included in any of the surveys, but what should we make of this? Shocking evidence of discrimination or something less sinister? I don't know the answer, and in fact have never attended either of the institutions mentioned (though I've bought books at their bookstores and a sweatshirt at Stanford).

I can imagine some fairly overt discrimination, especially in the humanities and social sciences where ideology is tightly bound up with scholarly approach and worldview, but I think there are some other things in operation too. The cornerstones of the Republican party's program, at least in the last election, were Christianity, opposition to abortion, opposition to homosexual rights and especially homosexual marriage, gun rights, and support for the war in Iraq. Stem cell research, big government, protecting the environment, and evolution by natural selection were also Republican bugaboos. It seems pretty easy to see why a lot of science types would find the last four objectionable.

The most typical Republican voter in the last election was white, rural, a strongly religious Christian, and less educated. Most of these are under-represented in academia. Typical Democratic voters were urban, more educated, less religious or not Christian, more likely to be black or Hispanic, and less likely to be a gun owner.

None of these effects seems dramatic enough to explain the 10 to 1 ratios (or slightly less in the larger study) found. That would seem to leave discrimination or my own favorite theory: Most people smart enough to become faculty at top Universities are too smart to be Republicans.