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Spacetime topology change and black hole information

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I’m in Erice right now, so posting may (or may not) be interrupted depending on how exciting the talks are 🙂

hep-th/0608175

Spacetime topology change and black hole information

Abstract: Topology change — the creation of a disconnected baby universe — due to black hole collapse may resolve the information loss paradox. Evolution from an early time Cauchy surface to a final surface which includes a slice of the disconnected region can be unitary and consistent with conventional quantum mechanics. We discuss the issue of cluster decomposition, showing that any violations thereof are likely to be unobservably small. Topology change is similar to the black hole remnant scenario and only requires assumptions about the behavior of quantum gravity in planckian regimes. It does not require non-locality or any modification of low-energy physics.

I don’t necessarily want to claim that topology change is plausible. But, it does suggest that we can’t make progress on the black hole information problem by low-energy means alone, since there are possible solutions that have unobservable low-energy effects and depend on how quantum gravity behaves at planck densities.

I got some email already pointing me to the following interesting papers on this issue. The first two are by Ted Jacobson and the last by Easson and Brandenberger. All discuss, in one way or another, the possibility that things which fall into black holes end up “somewhere else” and the relation to the information loss paradox.

gr-qc/0308048
gr-qc/9908031
hep-th/0103019

More. Early work by Mukhanov and Frolov on connecting deSitter space to the black hole interior (they assume strong planckian dynamics leads to a symmetrical equation of state with stress tensor proportional to g_mn, so deSitter is natural): http://prola.aps.org/abstract/PRD/v41/i2/p383_1 (too old for arXiv).

There are also apparently many loop QG papers suggesting a repulsive equation of state at planck density, which is what is needed to have expansion instead of a singularity. I haven’t tracked those papers down, but will add them here and to the revision of the paper. Also, Lee Smolin long ago proposed that black hole collapse might lead to new universe creation, although I believe that was part of a cosmological selection proposal and not to solve the information loss problem.

Interestingly, there seem to be two camps on this issue. People from a string theory background seem convinced that only the two traditional solutions are viable: locality violation and quantum xeroxing at the semiclassical horizon (possibly due to stringy effects and bh complementarity), or remnants. In the relativist community it seems people find the topology change option rather obvious and wonder why I wasn’t aware of these earlier references. I’d like to put the two sides in a seminar room somewhere to mix it up! 🙂

I came to this from the stringy side — the review articles I cite are by Strominger, Banks, Giddings and Susskind, so I thought arguing the feasibility of the topology change scenario to be an uphill fight. The very first thing I do in the paper is present the two main objections to the idea. The first objection, that pure to mixed evolution (even at an effective level) must entail energy non-conservation, seems to have been discussed before by relativists (e.g., Wald). But the second objection, regarding cluster decomposition violation (multiple baby universe creation amplitudes don’t factorize even when the black hole collapses are widely separated) does not seem to have been widely discussed.

Written by infoproc

August 29, 2006 at 3:47 am

Posted in physics

More Shiller

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Get ready for more Robert Shiller, the Yale economist who called the tech bubble, coining the Greenspan-adopted term “irrational exuberance” along the way. Shiller has been doing some nice work on historical real estate prices, finding inflation-adjusted appreciation to be quite modest over the last century. This is violently against the conventional wisdom, but then what does the madding crowd know about calculating real returns?

See this Times piece on the latest prognostication about how our housing bubble is going to end.

Earlier related posts here and here. The second link has a nice figure comparing our bubble to the Japan real estate bubble of the 80’s. You can see we could easily give back half the recent gains over, say, the next 10 years.

Written by infoproc

August 27, 2006 at 4:36 am

Posted in finance

Ouch!

with 2 comments

The graph below may soon be infamous. Thanks to a correspondent with access to expensive analyst newsletters 🙂

In case you can’t read the caption, it shows the NAHB (National Association of Home Builders) Housing Index vs. the S&P lagged by 12 months.

If you trade on this information, please send a portion of proceeds to me. Note, though, that past performance is no guarantee of future returns 🙂

Written by infoproc

August 25, 2006 at 11:55 pm

Posted in finance

Perelmania

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The New Yorker has a nice article on Perelman, his proof of the geometrization and Poincare conjectures, the politics surrounding the proof, and S.T. Yau’s antics. If the article is correct (see end of excerpts below), Yau’s maneuvering is directly related to Perelman’s declining the Fields medal. Note he has not said whether he would decline the $1 million Clay Foundation prize 😉

One of the authors is Sylvia Nasar, who wrote A Beautiful Mind. The writers actually went to St. Petersberg to track down the elusive genius, and have reconstructed the history behind his decade of work to produce the proof.

…In 1982, the year that Shing-Tung Yau won a Fields Medal, Perelman earned a perfect score and the gold medal at the International Mathematical Olympiad, in Budapest.

…In 1993, he began a two-year fellowship at Berkeley. While he was there, Hamilton gave several talks on campus, and in one he mentioned that he was working on the Poincaré. Hamilton’s Ricci-flow strategy was extremely technical and tricky to execute. After one of his talks at Berkeley, he told Perelman about his biggest obstacle. As a space is smoothed under the Ricci flow, some regions deform into what mathematicians refer to as “singularities.” Some regions, called “necks,” become attenuated areas of infinite density. More troubling to Hamilton was a kind of singularity he called the “cigar.” If cigars formed, Hamilton worried, it might be impossible to achieve uniform geometry. Perelman realized that a paper he had written on Alexandrov spaces might help Hamilton prove Thurston’s conjecture—and the Poincaré—once Hamilton solved the cigar problem. “At some point, I asked Hamilton if he knew a certain collapsing result that I had proved but not published—which turned out to be very useful,” Perelman said. “Later, I realized that he didn’t understand what I was talking about.” Dan Stroock, of M.I.T., said, “Perelman may have learned stuff from Yau and Hamilton, but, at the time, they were not learning from him.”

By the end of his first year at Berkeley, Perelman had written several strikingly original papers. He was asked to give a lecture at the 1994 I.M.U. congress, in Zurich, and invited to apply for jobs at Stanford, Princeton, the Institute for Advanced Study, and the University of Tel Aviv. Like Yau, Perelman was a formidable problem solver. Instead of spending years constructing an intricate theoretical framework, or defining new areas of research, he focussed on obtaining particular results. According to Mikhail Gromov, a renowned Russian geometer who has collaborated with Perelman, he had been trying to overcome a technical difficulty relating to Alexandrov spaces and had apparently been stumped. “He couldn’t do it,” Gromov said. “It was hopeless.”

Perelman told us that he liked to work on several problems at once. At Berkeley, however, he found himself returning again and again to Hamilton’s Ricci-flow equation and the problem that Hamilton thought he could solve with it. Some of Perelman’s friends noticed that he was becoming more and more ascetic. Visitors from St. Petersburg who stayed in his apartment were struck by how sparsely furnished it was. Others worried that he seemed to want to reduce life to a set of rigid axioms. When a member of a hiring committee at Stanford asked him for a C.V. to include with requests for letters of recommendation, Perelman balked. “If they know my work, they don’t need my C.V.,” he said. “If they need my C.V., they don’t know my work.”

…Perelman had posted a thirty-nine-page paper entitled “The Entropy Formula for the Ricci Flow and Its Geometric Applications,” on arXiv.org, a Web site used by mathematicians to post preprints—articles awaiting publication in refereed journals. He then e-mailed an abstract of his paper to a dozen mathematicians in the United States—including Hamilton, Tian, and Yau—none of whom had heard from him for years. In the abstract, he explained that he had written “a sketch of an eclectic proof” of the geometrization conjecture.

Perelman had not mentioned the proof or shown it to anyone. “I didn’t have any friends with whom I could discuss this,” he said in St. Petersburg. “I didn’t want to discuss my work with someone I didn’t trust.” Andrew Wiles had also kept the fact that he was working on Fermat’s last theorem a secret, but he had had a colleague vet the proof before making it public. Perelman, by casually posting a proof on the Internet of one of the most famous problems in mathematics, was not just flouting academic convention but taking a considerable risk. If the proof was flawed, he would be publicly humiliated, and there would be no way to prevent another mathematician from fixing any errors and claiming victory. But Perelman said he was not particularly concerned. “My reasoning was: if I made an error and someone used my work to construct a correct proof I would be pleased,” he said. “I never set out to be the sole solver of the Poincaré.”

Gang Tian was in his office at M.I.T. when he received Perelman’s e-mail. He and Perelman had been friendly in 1992, when they were both at N.Y.U. and had attended the same weekly math seminar in Princeton. “I immediately realized its importance,” Tian said of Perelman’s paper. Tian began to read the paper and discuss it with colleagues, who were equally enthusiastic.

On November 19th, Vitali Kapovitch, a geometer, sent Perelman an e-mail:

Hi Grisha, Sorry to bother you but a lot of people are asking me about your preprint “The entropy formula for the Ricci . . .” Do I understand it correctly that while you cannot yet do all the steps in the Hamilton program you can do enough so that using some collapsing results you can prove geometrization? Vitali.

Perelman’s response, the next day, was terse: “That’s correct. Grisha.”

…Perelman repeatedly said that he had retired from the mathematics community and no longer considered himself a professional mathematician. … “It is not people who break ethical standards who are regarded as aliens,” he said. “It is people like me who are isolated.” We asked him whether he had read Cao and Zhu’s paper. “It is not clear to me what new contribution did they make,” he said. “Apparently, Zhu did not quite understand the argument and reworked it.” As for Yau, Perelman said, “I can’t say I’m outraged. Other people do worse. Of course, there are many mathematicians who are more or less honest. But almost all of them are conformists. They are more or less honest, but they tolerate those who are not honest.”

The prospect of being awarded a Fields Medal had forced him to make a complete break with his profession. “As long as I was not conspicuous, I had a choice,” Perelman explained. “Either to make some ugly thing”—a fuss about the math community’s lack of integrity—“or, if I didn’t do this kind of thing, to be treated as a pet. Now, when I become a very conspicuous person, I cannot stay a pet and say nothing. That is why I had to quit.” We asked Perelman whether, by refusing the Fields and withdrawing from his profession, he was eliminating any possibility of influencing the discipline. “I am not a politician!” he replied, angrily. Perelman would not say whether his objection to awards extended to the Clay Institute’s million-dollar prize. “I’m not going to decide whether to accept the prize until it is offered,” he said.

Mikhail Gromov, the Russian geometer, said that he understood Perelman’s logic: “To do great work, you have to have a pure mind. You can think only about the mathematics. Everything else is human weakness. Accepting prizes is showing weakness.” Others might view Perelman’s refusal to accept a Fields as arrogant, Gromov said, but his principles are admirable. “The ideal scientist does science and cares about nothing else,” he said. “He wants to live this ideal. Now, I don’t think he really lives on this ideal plane. But he wants to.”

Written by infoproc

August 23, 2006 at 9:42 pm

Posted in Uncategorized

Pop!

with 3 comments

Bubbles last longer than you expect, and deflate faster than you expect. Has the US housing bubble finally popped? Will it be a hard, soft or hard-soft landing? The Fed is clearly convinced the housing slowdown is well underway, and that it will reduce inflation and economic growth.

The WSJ reports today on some of the associated mayhem. It’s anecdotal journalism, but backed up by statistical data as well.

PIMCO’s Bill Gross has been betting on a slowdown for some time — and taking the pain while waiting. This article describes how hard trading can be, even for a superstar like Gross. Another interesting tidbit is that PIMCO actually sends out researchers posing as house buyers to test markets around the country.

Excerpts from both articles below.

“It would be difficult to characterize the position of home builders as other than in a hard landing,” says Robert Toll, chief executive of luxury home builder Toll Brothers Inc., which reported yesterday that net income fell 19% in the third quarter ended July 31. (See related article.)

In his 40 years as a home builder, Mr. Toll says, he has never seen a slump unfold like the current one. “I’ve never seen a downturn in housing without a downturn in employment or… some macroeconomic nasty condition that took housing down along with other elements of the economy,” he says. “This time, you’ve got low unemployment, you’ve got job creation, you’ve got a stable stock market and relatively low interest rates.”

Joan Guth is one homeowner who was taken by surprise. Last September, she put her stately five-bedroom home in Herndon, Va., on the market for about $1.1 million. She was confident she would get something near that price, and planned to use the proceeds to buy a retirement home in Florida. But her home in the Washington suburbs attracted few serious lookers, and in March, she cut her asking price to $899,900. Still there were no takers. Finally, on the advice of her broker, she called in an auction firm, beginning a process that would eventually reveal to her just how weak the Northern Virginia market had become. [Eventually, she gets only $500k!]

…In a speech yesterday, Michael Moskow, president of the Federal Reserve Bank of Chicago, noted: “While we factor a housing slowdown into our outlook, there is some evidence — such as higher rates of cancellation in home-building contracts — that the slowdown could be more extensive.”

With fewer consumers applying for home loans, some big mortgage lenders are already retrenching. Countrywide Financial Corp. last month announced plans to reduce costs by $500 million. Earlier this year, Washington Mutual Inc. eliminated 2,500 jobs at loan-processing centers.

Builders, who were optimistic about prospects until a few months ago, are cutting back too. KB Home, a big home builder based in Los Angeles, has eliminated 7% of its work force, or 440 jobs. In July, U.S. home builders started construction at an annual rate of 1.45 million single-family homes, down 20% from the January peak.

Last August, when Horsham, Pa.-based Toll Brothers reported that its quarterly profit had doubled, Mr. Toll boasted: “We’ve got the supply, and the market has got the demand. So it’s a match made in heaven.” Since then, Toll has cuts its guidance four times on the number of homes it expects to close on, and its share price has fallen by more than 45%. Yesterday, the company said orders for new homes in the third quarter were down 48% from a year earlier.

…At D.R. Horton Inc., the nation’s largest home builder by units built per year, executives said late last year they were confident that quarterly earnings would continue to increase even during a housing-market slump. In July, Horton reported a 21% decline in net income for the third quarter ended June 30, the first quarter in 28 years in which it didn’t report year-over-year profit growth. Horton’s chief executive, Donald Tomnitz, said the surge in home prices had priced many people out of the market.

“Every time we’ve gone into a downturn in the home-building industry, they’ve always been longer and deeper than we’ve all imagined,” Mr. Tomnitz told analysts in a July 20 conference call. “So we’re preparing for the worst, and we think this one will be longer and deeper than just the last six months.”

Bill Gross is Wall Street’s long-reigning bond king, but he is struggling to adapt to a new world.

For more than three decades, Mr. Gross, the 62-year-old chief investment officer at Pacific Investment Management Co., which has $617 billion in assets, has run the world’s largest bond mutual fund. In that time, the $95 billion Pimco Total Return Fund has handily outpaced both the bond market and almost all of its competitors. In 2000, when Germany’s Allianz AG bought Pimco, based in Newport Beach, Calif., it was so eager to keep Mr. Gross at the helm that it agreed to a pay package valued at about $200 million to keep him around through next year.

As hedge funds and other investors have been scooping up riskier bonds with the highest yields, however, it has been harder for Mr. Gross to beat the market by buying this kind of debt.

…At the same time, Mr. Gross has taken a contrarian view for many months, predicting a slowdown for the economy and an end to the Federal Reserve’s campaign to raise interest rates. For much of the year that stance didn’t work. The losses, and the added volatility, took a toll on Mr. Gross, a soft-spoken manager who usually keeps an even keel by practicing yoga.

A month ago, with Pimco’s bets misfiring, Mr. Gross was so stressed that he left the office, taking an unplanned vacation, sitting at his home with his wife, he says.

“I just had to leave for nine days, I couldn’t turn on business television, I couldn’t pick up the paper, it was just devastating,” Mr. Gross says in an interview at Pimco’s headquarters, near the Pacific Ocean. “We’ve increased the volatility [of the portfolio] but I’m not enjoying it. You can’t sleep at night.”

…Now, his predictions that the housing market would slump and the economy would suffer are starting to show signs of materializing, sending the bond market on an impressive rally that has sent the benchmark 10-year yield — which moves in the opposite direction of its price — down to 4.817% yesterday from 5.25%, since June 28.

…Mr. Gross remains bullish on bonds, which tend to do well in a slowing economy, in part because weakness in the housing market will discourage the Fed from raising short-term interest rates — and could even get them to cut rates in the year ahead, he says. Mr. Gross collects reams of data on the housing market and reads it at home on the weekends, and Pimco even sends “shoppers” to key markets across the country to pose as home buyers and pick up intelligence on where housing is going.

Part of his concern stems from the aggressive adjustable-rate mortgages he has seen many consumers — including two of his children — take on. He isn’t sure they will be able to handle the monthly payments when the interest rates on these mortgages adjust higher.

“We could really see a drop in home prices that hurts the economy,” he says.

Written by infoproc

August 23, 2006 at 3:06 pm

Posted in finance

On the volatility of volatility

with 2 comments

More than you might want to know about volatility of the S&P500 index in this research article I’ve written with my PhD student Brian Murray. Brian has completed his dissertation work here (four research articles on dark energy, instabilities, black holes, etc.) and has decided he wants to pursue a career as a quant. Anyone interested in hiring a sharp young problem solver, please let me know. Previous posts on volatility.

My favorite footnote from the article:
“Implied volatility which is systematically larger than realized volatility would seem to provide a risk-free arbitrage, since it means all options contracts are overpriced. In an idealized world of log-normal price fluctuations, a trader could sell options contracts and hedge away the risk by holding cash and the underlying. However, in the real world, where volatility is itself volatile, there is no foolproof way to completely hedge away the risk of selling an option. An option seller is paid a premium to bear this risk, namely the systematic difference between implied and realized volatilities.”

Title: On the volatility of volatility

Abstract: The Chicago Board Options Exchange (CBOE) Volatility Index, VIX, is calculated based on prices of out-of-the-money put and call options on the S&P 500 index (SPX). Sometimes called the “investor fear gauge,” the VIX is a measure of the implied volatility of the SPX, and is observed to be correlated with the 30-day realized volatility of the SPX. Changes in the VIX are observed to be negatively correlated with changes in the SPX. However, no significant correlation between changes in the VIX and changes in the 30-day realized volatility of the SPX are observed. We investigate whether this indicates a mispricing of options following large VIX moves, and examine the relation to excess returns from variance swaps.

Written by infoproc

August 22, 2006 at 12:30 am

Posted in finance

Invisible Asians

with 6 comments

Asian-Americans are invisible. We’re not a minority group. At least not to the politically correct intellectual contortionists at the NYTimes. Insidious racism, rather than meritocratic testing, must be responsible for the alarming decline in the representation of (certain) ethnic groups in NYC’s top high schools.

See earlier posts on how affirmative action hurts Asian-Americans (Asians have to score 50 points higher, on average, on the SAT than whites to gain admission to the same elite universities), and how the silicon valley counterpart to this NYC magnet school story is told in a less politically correct way by the WSJ.

Via GNXP:

The New York Times headline is: Minority Students Decline in Top New York Schools. The graphic? Here:

Is something off with this graphic in relation to the headline, or what? Ah, click the link in the story, and you see this:

Written by infoproc

August 20, 2006 at 3:10 pm

Posted in Uncategorized