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Physics + MathPhysics & Math

Is General Relativity Too Perfect?

Physicists are looking for flaws in Einstein's 100-year-old theory of gravity.

ByPaul HalpernThe Nature of RealityThe Nature of Reality
Is General Relativity Too Perfect?

This November, Einstein’s theory of general relativity will celebrate its 100th anniversary. Despite its advanced years, Einstein’s soon-to-be centenarian theory is holding up remarkably well. That’s good news for many physicists who work in the field. But plenty of others would be happy to see it kick the bucket–or at least display some age spots, wrinkles and creaky joints. Why would anyone want Einstein’s venerable theory to show its age? Countless other hypotheses, with even grander ambitions, are waiting in the wings, hoping for a stumble.

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Even Einstein saw his own masterful theory of gravity as transitional. Shortly after he completed it in late 1915 and published it in 1916, he began to contemplate extending its scope to include the other then-known natural force, electromagnetism. Could an all-encompassing version of general relativity be developed, he wondered, that included Maxwell’s equations of electromagnetism? Only then could nature be described through a single set of equations. (We now know about the weak and strong nuclear forces, which would also need to be included in a complete unification.)

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Einstein’s imagination was stimulated when the German mathematicians Hermann Weyl and Theodor Kaluza sent him papers suggesting paths toward the unification of general relativity and electromagnetism. Weyl suggested a modification that redefined the four-dimensional equivalent of length by including an extra factor called a “gauge.” In standard general relativity, the shortest distance between two spacetime events is determined exclusively by the geometry of the region, which, in turn, is set by the distribution of mass and energy. Einstein showed that mass and energy warp spacetime and bend linear paths into curves. Weyl’s formulation added an extra “dial” representing electromagnetism that altered paths even further.

Kaluza’s proposal provided additional wiggle room in a different way: by including an otherwise undetectable fifth dimension. The extra variables that the higher dimension provided could be used to represent electromagnetic influences. Einstein found each suggestion incomplete, but intriguing, and began to work on his own unification schemes. He spent the rest of his life fruitlessly searching for a unified field theory.

Einstein and his contemporaries wanted to bring all of the natural forces—gravity, electromagnetism, strong, and weak—under one umbrella. Today’s physicists have another motivation: quantizing gravity. While the other three natural forces can be described through quantum field theories involving the interactions of exchange particles—photons, gluons, and W and Z bosons, respectively—that yield reasonable answers through a kind of probabilistic tally, attempts to do the same with gravity have failed so far. Physicists have proposed a gravitational exchange particle called the graviton but have not been able to work it into a (standard) quantum field theory that produces finite answers; the calculations simply “blow up” to infinity, like dividing by zero.

A pioneer in early efforts to quantize gravity was Einstein’s research assistant Peter Bergmann, who explored quantum gravity ideas after he became a professor at Syracuse University. As Bergmann wrote in his first research paper on the subject :

“At the present time, two great theoretical structures in physics can lay claim to containing significant parts of the ‘truth’ which to unearth must remain the principal aim of both the experimental and the theoretical physicist. One of these structures is modern quantum physics as applied to both mechanical and field theoretical problems; the other is the general theory of relativity.”

The idea behind Bergmann’s efforts, subsequent work by Bryce DeWitt and John Wheeler, and more recent ideas such as loop quantum gravity is to identify certain geometric quantities as the “canonical variables” (basic descriptions of behavior) of a quantum description of gravity, akin to how position, momentum and other parameters serve that descriptive role in ordinary quantum mechanics. Then, by replacing those variables with mathematical functions called operators one can attempt to devise equations that can be solved to yield a spectrum of quantum states.

Ultimately general relativity would be replaced with a way of representing the likelihood of every possible quantum state instead of just one, an approach physicists call “sum over histories.” It is like exchanging a single card that displays the unique history of the universe for a deck of cards comprising a medley of possibilities. The actual dynamics emerge from weighing the different possibilities—just as the outcome of a gin rummy game depends on a weighted tally of all the cards on the table.

Given his dislike for probabilistic quantum mechanics, Einstein was not altogether pleased with Bergmann’s endeavor or other attempts to quantize gravity. “You are now on your own,” he told Bergmann.

Bergmann also tried another approach, known as scalar-tensor theory, or Brans-Dicke theory (after Carl Brans and Robert Dicke, two of its developers), which involves replacing the gravitational constant with a field that can vary across space and time. The goal is to make gravity’s strength an organic component of how the matter and energy in the universe are arranged. Otherwise the gravitational constant is simply arbitrary—eternally set to a particular value.

Today, the most heavily trodden road toward unification is superstring theory (known as M-theory in its generalized form). Superstring theory proposes that energetic strands of dimensions too minuscule to observe directly oscillate in various ways, producing vibrating states that can be associated with known particle types, like quarks, electrons, and photons. Superstring theory also predicts a particle that looks like a perfect match for the graviton, the hypothetical particle that carries the force of gravity.

The catch: The unification proposed by superstring theory would be fully realized only at extraordinarily high energies—what is called the Planck scale energy of roughly two billion Joules per particle. That is quadrillions of times higher than the energies produced in our most powerful particle-smasher, the Large Hadron Collider. Not since the tiniest fraction of a second after the Big Bang has any place in the universe been that hot. Therefore testing the full version of superstring theory and its predictions for gravitation is close to impossible.

Fortunately, some versions of superstring theory (and M-theory) predict modifications to general relativity at much lower, and potentially testable, energy scales. You can think of it like heating water: Even before it hits a full boil, you start to see tiny bubbles breaking the surface. Physicists and astronomers are now beginning to look for small but measurable departures from the predictions of general relativity, the first “tiny bubbles” indicating that the theory would “boil” into something much different at far higher energies.

Physicists have been searching for flaws in general relativity for as long as the theory has existed. So far, general relativity has passed all tests with “flying colors,” as physicist Clifford Will relates . Thus if any flaws are to be found that open the door to new theories, we will need novel experiments of even higher precision. The newly-upgraded Laser Interferometer Gravitational-wave Observatory (LIGO) offers just such an opportunity. With detectors in Louisiana and Washington state, LIGO is poised to make the first direct detection of gravitational waves, ripples in spacetime predicted by Einstein and Nathan Rosen in 1937. A space-based cousin, the Laser Interferometer Space Antenna (LISA) is being planned, with a pilot mission called LISA Pathfinder due to be launched later this year. Perhaps gravitational waves, once detected, will reveal subtle deviations from conventional general relativity.

Another promising test involves a newly discovered pulsar, PSR J0337+1715 , locked in a gravitational dance with two orbiting stars. Because pulsars, the rapidly spinning, radiating remnants of collapsed massive stars, act as high-precision clocks, putting out regular bursts of radiation, this triple system could offer the most precise measure yet for general relativity’s predictions.

On the cusp of its 100th anniversary, general relativity has passed every test it’s faced. But to unite it with other forces, physicists may need to modify the masterpiece. Will general relativity show signs of frailty, or continue to be as robust as ever? To the chagrin of starry-eyed theorists, the old-timer may have life in it yet.

Go Deeper
Editor’s picks for further reading

NASA: 2015: The Centennial of General Relativity
NASA’s Physics of the Cosmos (PCOS) Program presents a list of events honoring the 100th anniversary of general relativity.

The New York Times: General Relativity’s Big Year?
In this Op-Ed essay, science writer Philip Ball celebrates the beginning of general relativity’s anniversary year with a review of past and present tests of the theory.

Princeton University Press: The Collected Papers of Albert Einstein
Choose from more than 30,000 documents in this open-access archive of Einstein’s writings.