New Scientist: Splitting Space and Time to Unify Relativity and Quantum Theory

Rethinking Einstein: The End of Space-Time Coupling

Physicists struggling to merge gravity and quantum mechanics are cheering for a theory inspired by pencil lead, which might simply allow them to succeed.

It was a report that changed the way we think about space and time. The year was 1908, and German mathematician Hermann Minkowski was trying to understand Einstein’s fiery new idea—what we now know as special relativity, which describes how objects contract and time warps when they move very fast. “Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows,” Minkowski said, “and only a kind of union of the two will preserve an independent reality.”

Thus, space-time coupling was born—a resilient structure whose geometric form can be altered by the gravity of stars, planets, and other matter. It is a very useful concept, but if physicist Petr Hořava is right, it is merely an illusion. Working at the University of California, Berkeley, Hořava wants to split this structure in two, making space and time independent of each other. This is in order to construct a unified theory to reconcile the separate worlds of quantum mechanics and gravity—one of the most pressing tasks in modern physics.

Since Hořava published his work in January 2009, the theory has received immense attention. To date, there have been over 250 related papers. Some researchers have begun using it to explain the twin cosmological mysteries of dark matter and dark energy. Others have found that the activity of black holes might not be what we thought. If Hořava’s idea is correct, it will forever change our concepts of space and time and lead us toward a “Theory of Everything” applicable to any matter and the forces acting upon it.

For decades, physicists’ efforts to reconcile Einstein’s general relativity, used to describe gravity, and quantum mechanics, which describes particles and forces other than gravity at extremely small scales, have been hindered. The stumbling block is precisely their conflicting views on space and time. From the perspective of quantum mechanics, space and time are a static stage for particle motion. In Einstein’s theory, space and time are not only inextricably linked but their structure is also shaped by the objects within them.

One motivation for combining relativity and quantum theory to propose a theory of quantum gravity is an aesthetic desire to unify the various forces of nature. But in reality, there is more to it than that. We need a theory that can help us understand what happened in the moments after the Big Bang or near black holes—places with very strong gravitational fields.

One place where the conflict between quantum theory and relativity is highlighted is the gravitational constant G, which describes the strength of gravity. On large scales—such as the solar system or the universe itself—the value of G obtained from general relativity equations matches observations. But when you shrink down to small scales, general relativity cannot ignore the quantum fluctuations of spacetime. After considering this effect, any calculation of G yields absurd results, making precise predictions impossible.

Sudden Symmetry

Significant resources have been invested in research to resolve the differences between general relativity and quantum mechanics, and these wise investments suggest that relativity will be the loser. So Hořava began looking for ways to modify Einstein’s equations. He found inspiration in an unlikely place: condensed matter physics, including the previously mentioned material—pencil lead.

Pull apart that soft, gray graphite, and you will get a substance only one atom thick called graphene. The electrons around its surface behave like pinballs in a pinball machine. Because they are very small particles, their motion needs to be described by quantum mechanics; and because their speed is small compared to the speed of light, relativistic effects need not be considered.

However, when graphene is cooled to near absolute zero, something incredible happens: the speed of the electrons increases significantly. Now, to describe them correctly, relativity is required. It was this transition that sparked Hořava’s inspiration. One of the central ideas of relativity is that space-time possesses Lorentz symmetry: this ensures that the speed of light is constant for any observer, regardless of how fast they move, with time dilation and length contraction matching accordingly (to keep the speed of light constant).

What surprised Hořava about graphene was that the effect of Lorentz symmetry on it was not always obvious. He wondered, could it be the same for our universe? The universe we see today is a cooled universe, where the link between space and time via Lorentz symmetry is an experimental fact established with extremely high precision. But the situation in the early universe might have been very different. What if this very obvious symmetry in the current universe is not a fundamental principle of nature, but merely a phenomenon that appeared after the universe cooled from the fireball of the Big Bang, much like the phenomenon appearing in cooled graphene?

So Hořava did something incredible: he modified Einstein’s equations by removing the Lorentz symmetry condition. To his delight, doing so yielded a set of equations describing gravity consistent with other natural forces within a quantum framework: gravity as an attractive force associated with a quantum called the graviton, behaving much like electromagnetic interactions carried by photons. He also made another serious change to general relativity. Einstein’s theory does not have a specific direction of time pointing from the past to the future. But the universe seems to be evolving continuously as we observe it. So Hořava gave time a special direction (Physical Review D, Vol. 79, 084008).

With these modifications, he found that quantum field theory could describe gravitational interactions at the microscopic scale without yielding the absurd results obtained previously. “Suddenly, you have new ingredients to modify the behavior of gravity at very short distances,” Hořava said.

“Hořava gravity” is certainly not the first attempt to obtain a theory of quantum gravity. Among its many predecessors, the most famous is string theory. But Hořava gravity has a particularly attractive feature: unlike string theory, it does not have daunting mathematical requirements; instead, it can use the same mathematical tools developed for the other three natural forces. “This is a brand new attempt at a super difficult problem,” said Oriol Pujolàs, a theoretical researcher at the European Organization for Nuclear Research (CERN) near Geneva, Switzerland, “and it uses a very simple framework that is well known to us.”

This is one of the reasons why many physicists have eagerly begun studying Hořava’s theory. Other theories of quantum gravity, including string theory and loop quantum gravity, are more difficult for newcomers to enter.

Beautiful mathematics is all well and good; the true test of a theory, however, is how well it works in the real world. So how is it performing? Some clues suggesting Hořava might be right come from a theory called Causal Dynamical Triangulations, another exploration of quantum gravity that stitches together small segments of space and time. This method was pioneered by Jan Ambjørn and his colleagues at the Niels Bohr Institute in Copenhagen, Denmark. They used computer simulations to analyze the behavior of space-time but were puzzled by the results of their model: when they zoomed in or out (on the length of each segment of space or time), they found that the weights of three-dimensional space and one-dimensional time changed in a way they could not understand. When zoomed out, space and time were on equal footing, consistent with Lorentz symmetry. But when zoomed in, time played a much larger role than space.

Beyond Einstein

Ambjørn believes this means that the contraction of space and time is not consistent—just as you would expect in Hořava’s quantum gravity theory if Lorentz symmetry were broken (see arxiv.org/abs/1002.3298). “So, if you perform these computer simulation experiments,” Ambjørn said, “then to some extent Hořava’s theory will be consistent with the experiments.”

But Hořava’s work has not been without its challenges. The recent unprecedented attention has revealed some flaws, which is not unexpected. The first appeared in June 2009, only five months after Hořava published his paper. If his theory is correct, it should look like general relativity at low energies. However, Pujolàs, Diego Blas, and Sergey Sibiryakov at EPFL in Lausanne pointed out that this was not the case for the systems they analyzed, meaning Hořava’s theory would always conflict with experimental observations (see arxiv.org/abs/0906.3046). Initially, the theory seemed doomed. Subsequently, in the months following their initial paper, Pujolàs and his colleagues realized that this inconsistency only appeared in special cases and that the theory would eventually lead to general relativity at low energies (see arxiv.org/abs/0909.3525).

This is good news for those who have already used Hořava’s gravity theory to study astronomical and cosmological mysteries such as black holes, dark matter, and dark energy. Take black holes as an example. In general relativity, a black hole is the result of space and time being different parts of the same structure. A black hole warps spacetime so much that it can suck in anything around it. Nothing can escape a black hole’s gravity because nothing can exceed the speed of light.

By breaking the symmetry of space and time, Hořava’s theory changes the physical properties of black holes—especially microscopic black holes that might be produced at high energies. What this means for the formation of these black holes, and whether they look like those described in general relativity “is a big question,” Pujolàs says, and it is one of the topics researchers are discussing in their correspondence.

Hořava gravity might also help in understanding the long-puzzling dark matter. The motion of stars and galaxies observed by astronomers seems to require more matter in the universe than is observed; without it, galaxies and galaxy clusters would fly apart. But this conclusion comes from the equations of motion derived from general relativity. What if these equations deviate slightly? Could this explain the observed speeds of stars and galaxies without resorting to the effects of dark matter?

Shinji Mukohyama decided to find out. When he derived the equations of motion from Hořava’s theory, he found they contained an extra term not present in the equations derived from general relativity—and the effect of this extra term is very similar to dark matter. Depending on its value, you might not need some or even most of the dark matter (see arxiv.org/abs/0905.3563). “Part of the universe’s dark matter distribution might be obtained through modified Einstein equations,” Hořava said.

Dark energy remains an even more daunting problem. To explain the accelerated expansion of the universe over the past few billion years, physicists expect the vacuum of space-time to contain inherent energy, leading to the concept of dark energy. But there is a major problem. Particle physics theory predicts the strength of dark energy to be about 120 orders of magnitude larger than observed, and general relativity cannot explain this massive discrepancy. Here, Hořava’s theory might also come to the rescue. It contains a parameter that can be fine-tuned so that the vacuum energy predicted by particle physics is reduced to a small positive amount, consistent with the observed motion of stars and galaxies (see arxiv.org/abs/0907.3121).

However, whether this conception is correct is difficult to reveal—as Roberto Casadio of the University of Bologna and his colleagues admitted after performing this calculation. This is because, with the parameters in Hořava’s formula set to meet the necessary values, their predictions would only deviate from the results of Einstein’s relativity at energies much, much higher than those currently obtainable in laboratories.

Of course, the universe has the final say. Improved observations of supermassive black holes containing strong gravitational fields will show whether general relativity requires necessary corrections. This will pave the way to quantum gravity, as Hořava has done, much like how the measurement of Mercury’s orbital anomaly revealed the incompleteness of Newton’s laws and opened the door for Einstein.

Despite being at the center of the discussion, Hořava remains calm. Hanging in his Berkeley office is a 17th-century Dutch map showing California as an island detached from the West Coast of the United States. He keeps its reminder in mind: “We have found some exciting new continents. But we are still far from correctly obtaining all the information.”

Original English Text: Rethinking Einstein: The end of space-time.txt