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December 31, 2002

E and mc2: Equality, It Seems, Is Relative

By DENNIS OVERBYE

Roll over, Einstein.

In science, no truth is forever, not even perhaps Einstein's theory of relativity, the pillar of modernity that gave us E=mc2.

As propounded by Einstein as an audaciously confident young patent clerk in 1905, relativity declares that the laws of physics, and in particular the speed of light — 186,000 miles per second — are the same no matter where you are or how fast you are moving.

Generations of students and philosophers have struggled with the paradoxical consequences of Einstein's deceptively simple notion, which underlies all of modern physics and technology, wrestling with clocks that speed up and slow down, yardsticks that contract and expand and bad jokes using the word "relative."

Guided by ambiguous signals from the heavens, and by the beauty of their equations, a few brave — or perhaps foolhardy — physicists now say that relativity may have limits and will someday have to be revised.

Some suggest, for example, the rate of the passage of time could depend on a clock's orientation in space, an effect that physicists hope to test on the space station. Or the speed of a light wave could depend slightly on its color, an effect, astronomers say, that could be detected by future observations of gamma ray bursters, enormous explosions on the far side of the universe.

"What makes this worth talking about is the possibility of near-term experimental implications," said Dr. Lee Smolin, a gravitational theorist at the Perimeter Institute for Theoretical Physics in Ontario.

Any hint of breakage of relativity, scientists say, could yield a clue to finding the holy grail of contemporary physics — a "theory of everything" that would marry Einstein's general theory of relativity, which describes how gravity shapes the universe, to quantum mechanics, the strange rules that govern energy and matter on subatomic scales.

Even Einstein was stumped by this so-called quantum gravity.

For now, any clue would be welcome. There is very little agreement and much confusion about the possible end of relativity. "These are times when theorists are being very adventurous," said Dr. Andreas Albrecht, a physicist at the University of California at Davis. "It's hard to tell where things will go."

The avatars of new relativity have been encouraged by hints that some cosmic rays hitting Earth from outer space have more energy than normal physics can explain. But some scientists doubt that these rays exist or, if they do, that a violation of relativity is the only way to explain them.

The cosmic ray hints are not the only signs making physicists wonder about relativity. They have also been tantalized by evidence, as yet unconfirmed, from distant quasars that a fundamental constant of nature, a measure of the strength of electromagnetism known as the fine-structure constant, might have changed ever so slightly over billions of years, shifting the wavelengths of light emitted by the quasars.

The result has been a minor explosion of interest in strange relativity, with some 70 papers being published this year, said Dr. Giovanni Amelino-Camelia, a theorist at the University of Rome.

The field, while still small, is destined for at least 15 minutes of fame next year with the publication in February of "Faster Than the Speed of Light," by Dr. João Magueijo, a cosmologist at Imperial College London. The book is a racy account of Dr. Magueijo's seemingly heretical effort to modify relativity so that the speed of light is not constant, and he will promote it on a long lecture tour.

"Ruling out special relativity by 2005 is a bit extreme," Dr. Magueijo said in a recent e-mail message, referring to the coming centennial of Einstein's famous paper, "although I would be very surprised if by 2050 nothing beyond relativity has been found."

Most physicists have yet to buy into this presumed revolution. Dr. Edward Witten of the Institute for Advanced Study in Princeton, called recent arguments that some versions of quantum gravity would violate relativity "unimpressive."

Dr. Juan Maldacena of Harvard said he doubted relativity was violated in string theory — the leading candidate for a theory of everything. "But of course," he noted, "we should always test our theories."

Dr. Carlo Rovelli, a gravitational theorist at the University of the Mediterranean in Marseille, said it was a "risky" hypothesis, "but the prize if it happened to be true is so great that it is worthwhile taking the risk of exploring it in detail."

Dr. Andrew Strominger of Harvard pointed out that Einstein himself modified relativity in 1915, when he brought gravity into the picture with his general theory of relativity. Special relativity, as the 1905 theory became known, is only strictly valid in flat space without gravity, Dr. Strominger said.

He added, "It is natural to think that Einstein's relativity will in some sense be violated by small corrections, just as Newton's theory of gravity has small corrections." These corrections did not make Newton wrong, he said, they just meant his theory was not always perfectly applicable. Likewise, relativity may give way to a more complete and accurate theory.

How relativity could break down, if it does, depends on how physics might accomplish its grand dream of quantum gravity.

Many physicists are placing their bets on string theory's mathematically imposing edifice in which nature comprises tiny strings vibrating in 10 dimensions of space-time. But this theory may play out in billions of ways, and some physicists complain that it can be made to predict almost anything.

In the late 1980's, Dr. V. Alan Kostelecky, a particle physicist at Indiana University, and his colleagues pointed out that in some of these solutions, the spins of the strings could impart an orientation to empty space, like the lines left by the weave in a fine cloth. In that case, they say, a clock oriented in one direction could tick slightly faster or slower than one oriented differently, in violation of the rules of relativity. That is something Dr. Kostelecky and his colleagues have proposed to test using ultraprecise clocks on the space station.

Dr. Kostelecky and his colleagues have constructed an extension to the standard model of particle physics that catalogs all the possible ways that relativity can be violated. Others, including Dr. Amelino-Camelia, Dr. John Ellis of CERN, Dr. Tsvi Piran of the Hebrew University in Jerusalem and the Harvard theorists Dr. Sheldon Glashow and Dr. Sidney Coleman, have attempted to study the ways that relativity can be violated by quantum gravity or in the high-energy cosmic rays.

Violation is not inevitable, Dr. Kostelecky said. "Is it plausible? Yes. Is it likely? Enough so that I've invested years of my life."

Few physicists would seem to have as much invested in revising relativity as Dr. Magueijo. In his book he describes how beginning in 1996 he cajoled Dr. Albrecht, then at Imperial, into pursuing with him the heretical notion that the speed of light had been much higher in the dim cosmic past as a solution to various cosmological puzzles. Cosmologists did not rally to the idea, which even Dr. Magueijo admitted violated relativity. His co-author, Dr. Albrecht, himself called it an idea that is "not even properly born yet," and said it needed to find roots "in some convincing physics."

In the intervening years, as a sideline to his day job as a conventional cosmologist, he and a growing number of comrades have continued to tinker with modifying relativity in a variety of ways that go under the umbrella name of V.S.L., for variable speed of light theories.

In the science world, the book might attract attention for its jaunty and irreverent style as well as for its content. "What the hell, it's only Einstein going out of the window . . .," he writes in one passage. In others he describes the editor at a prominent journal as a moron, his bosses at Imperial as pimps and the rival quantum gravity camps as cults.

Asked how he expected his colleagues to react to the book, he answered, "It wasn't written for them; it was written for the public." He called it "a very honest view of how scientists feel," adding, "It's the language I use normally."

The main motivation for considering V.S.L. theories, Dr. Magueijo explained, comes from the as-yet undiscovered quantum gravity. In relativity there is only one special number, the speed of light, but in quantum gravity, he explained, there is another special number, known as the Planck energy, equivalent to 1019 billion electron volts. According to quantum gravity thinking, an elementary particle accelerated to that energy will behave as if space and time themselves are lumpy and discontinuous and all the forces of nature are unified.

According to relativity, however, Dr. Magueijo explained, differently moving observers could disagree on how much energy the particle had and thus whether it was displaying quantum gravity effects or not. In short, they would disagree on what the laws of physics were.

"Perhaps relativity is too restrictive for what we need in quantum gravity," Dr. Magueijo said. "We need to drop a postulate, perhaps the constancy of the speed of light."

The most recent buzz in V.S.L. circles is about something called "doubly special relativity." In 2000, hoping to fix the cosmic ray problem, Dr. Amelino-Camelia proposed modifying the rules of relativity so that there would be a limit to the momentum that any particle could have, just as now there is a limit to the velocity.

Subsequently Dr. Magueijo and Dr. Smolin of the Perimeter Institute proposed their own doubly special version in which there is a limit to the amount of energy that an elementary particle can attain, namely the so-called Planck energy, at which the forces are unified and quantum gravity effects dominate.

One casualty of this tinkering, the V.S.L. scientists agree, will be everyone's favorite formula, E=mc2, to be replaced by a more complicated, cumbersome equation that Dr. Magueijo reproduces in his book.

A mark of all the doubly special theories, Dr. Magueijo said, is that the speed of light will vary with its color, with higher frequencies and energies going slightly faster than lower ones. That might manifest itself in observations of gamma ray bursters, distant gargantuan outbursts by an upcoming NASA satellite called Glast (gamma ray large area space telescope), scheduled for launching in 2006.

The theory also predicts that light should slow down near massive objects and actually come to a stop at the end of a black hole, preventing anything from entering that dark gate, Dr. Magueijo said in his book. In principle the effect, he said, could be tested by spectroscopic measurements of the light emitted from dense objects like neutron stars.

To some physicists, however, the very idea of variations in the speed of light in a vacuum — the c in E=mc2 — is meaningless. The miles and seconds by which speed is measured are human inventions, they point out, defined in fact in terms of lightwaves, so the whole notion of the speed of light varying is circular. In the last analysis, they point out, all physical measurements boil down to a few dimensionless constants like the fine structure constant, alpha. "What we measure objectively is whether alpha varies," said Dr. Michael Duff of the University of Michigan in an e-mail message.

Dr. Magueijo said those criticisms were technically correct but said the speed of light was one factor of several in the formula for alpha. So if alpha varied, as some astronomical measurements have suggested, one could choose to think of it as a variation in the speed of light, of electric charge, or even a variation in another number known as Planck's constant — or all three — if that made the math simpler. "It's a matter of convention," he said, adding, "you make the simplest choice."

Despite all the activity, scientists agree that they are mostly in the dark about the deeper consequences of these conjectures. "Some may eventually be developed to the point of being a credible alternative to relativity," conceded Dr. Kostelecky, saying that he suspected that others might not really change relativity or might have already been excluded by existing experiments. Without a systematic analysis it was impossible to know.

Dr. Amelino-Camelia said that the doubly special theories preserve Einstein's principle that all motion is relative, but at an unknown cost to the rest of physics."We paid a dramatic price for relativity: the notion of absolute time," he said. "This time it is not completely sure what is the axiomatic principle we have to give up."

Dr. Albrecht urged caution and said physicists needed guidance from experiments before tossing out beloved principles like relativity. "The most dignified way forward," he said, "is to be forced kicking and screaming to toss them out."


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