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20 S C I E N T I F I C A M E R I C A N J U N E 2 0 0 6

C osmology was always going to be trouble for particle physics. Tradition-al quantum theory predicts that the

vacuum of space should bubble over with short-lived “virtual” particles, whose com-bined energy, represented by the so-called cosmological constant, would have long ago blown galaxies far and wide like grease on water at the touch of detergent. Lately, try-ing to make sense of why the cosmological constant is tiny, physicists have toyed with

a concept based on string theory. Called the landscape model, it supposes that many uni-verses with different cosmological constants are realized in a larger multiverse. Despite long-standing hopes to the contrary, land-scapers now have found that singling out a universe from this array is mathematically nigh impossible.

In 1998 astronomers discovered that the universe’s expansion is accelerating at a rate consistent with a cosmological constant

Hard LandscapeFINDING OUR UNIVERSE IN STRING THEORY APPEARS IMPOSSIBLE BY JR MINKEL

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Seeking to assess the effect of third-party prayer on patient outcomes, in-vestigators found no evidence for divine

intervention. They did, however, detect a possible proof for the pow-er of negative thinking.

The three-year Study of the Therapeutic Effects of Intercessory Prayer (STEP), published in the April 4 American Heart Journal, was the largest-ever at-tempt to apply scientific methods to measure the in-fluence of prayer on the well-being of another. It examined 1,800 patients undergoing heart-bypass surgery. On the eve of the operations, church groups began two weeks of pray-ing for one set of patients. Each recipient had a pray-ing contingent of about 70, none of whom knew the

patient personally. The study found no dif-ferences in survival or complication rates compared with those who did not receive prayers. The only statistically signifi cant

blip appeared in a subgroup of patients who were prayed for and knew it. They experi-enced a higher rate of postsurgical heart ar-rhythmias (59 versus 52 percent of unaware subjects).

The research team—a psychologist, cler-gy and doctors from six institutions, includ-ing Harvard Medical School and the Mayo Clinic—speculated that nerves might have been to blame. “We know that high levels of adrenaline from the anxiety response can make fibrillation worse,” said Charles Bethea, a physician at Integris Baptist Heart Hospital, a study site in Oklahoma City, in an April press conference. “The patient might think, ‘Am I so sick that they have to call in the prayer team?’” Dean Marek, chief chaplain at the Mayo Clinic, saw the problem as a possible fl aw in the study de-sign: “The sense of community was not there. You could call it impersonal prayer rather than intercessory prayer.”

Stopping short of suggesting that the healing power of prayers by friends and fam-ily might reside in the personal connections rather than in the prayers, the authors stated that they have no plans for a follow-up study. This one, sponsored largely by the John Templeton Foundation, cost $2.4 million.

No Prayer PrescriptionSEND GOOD VIBRATIONS, BUT KEEP IT TO YOURSELF BY CHRISTINE SOARES

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PR AYER showed no therapeutic effect in a large trial.

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10–120 times the value predicted by quantum theory. String theory, which unites gravity with quantum mechanics, offered the hope of explaining the at-tenuated cosmological constant. It re-casts particles as one-dimensional strings, or fi laments of energy, which play around in tiny tangles of extra spa-tial dimensions. The shape of the tangles infl uences the properties of strings and therefore the vacuum’s energy. But no mathematical principle forces the extra dimensions to fold in a unique way.

One approach is to assume that many universes exist and that we neces-sarily fi nd ourselves in one where the constant is hospitable to life. In 2000

Joseph Polchinski of the University of California, Santa Barbara, and Raphael Bousso, now at U.C. Berkeley, proposed that in the string picture, magnetic fi eld–like quantities called fl uxes, when coiled in various combinations inside the extra dimensions, could generate enough dif-ferent cosmological constants to include the one we observe. This set of vacuum energies (or vacua, as physicists like to refer to universes) has been dubbed the anthropic landscape of string theory.

In principle, physicists might like to examine one or a few vacua having the right cosmological constant to see if they offer testable predictions. The huge number of choices—at least 10120 vacua—seemed to demand vast compu-tational power, perhaps even a quan-tum computer.

Unfortunately, the latest analysis suggests that no advanced machine or clever programming will cut much into the search time, according to Michael R. Douglas of Rutgers University and Frederik Denef, now at Catholic Uni-versity in Louvain, Belgium. They have discovered that the task falls into a no-torious category of problems called NP-complete. An example is the “subset sum” problem, which asks, given some group of integers (1, –17, 6,435, and so on), fi nd a subset that adds up to 0. In these problems, the time needed to check the answer grows relatively slow-ly with the size of the subset, whereas the time typically needed to identify that subset grows exponentially—the twin hallmarks of NP-completeness.

Analogously, the problem in the landscape model is to add the energies of fl uxes up to the desired value for the whole vacuum, 10–120. The individual fl ux energies are represented by arrows, or vectors, all one inch in length and pointing in random directions. The game is to find a set of arrows that, when linked up end to end, leaves a gap between head and tail (the two ends) of 10–120 inch. A group of vectors very near to the desired result is enormously likely to be thrown off by the next ran-domly pointing vector. “The old ambi-tion of exactly fi nding the precise vacu-um in which we live may be intractable,” Denef sums up. “The Douglas-Denef paper is surely a problem for drawing conclusions about what the landscape predicts,” asserts Thomas Banks of U.C. Santa Cruz.

But perhaps scrutinizing all those vacua is unnecessary; Bousso notes that the vacua confi gurations may be imma-terial—like atoms in a lump of iron. “It wouldn’t really occur to you to attempt to fi gure out precisely where every atom is,” he says. In that case, statistics de-rived from many vacua, rather than trying to make predictions from a sin-gle one, might be more useful. So for landsca pers, getting around the intract-able may all depend on asking the right ques tions.

JR Minkel is a frequent contributor.

10–120

Final arrow

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L ANDSC APE MODEL ANALOGY connects up inch-long arrows to create a loop with a gap of 10–120 inch at the end. The fi nal arrow, picked at random from an infi nite collection, is unlikely to close the loop properly.

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