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FQXI ARTICLE

October 31, 2014

Ripping Apart Einstein

Cutting the threads of the spacetime fabric and reinstating the aether could lead to a theory of quantum gravity.

March 7, 2010

PETR HOŘAVA

University of California, Berkeley

Credit: KITP, Santa Barbara

Physicists have spent decades searching for a way to reconcile the seemingly incongruous twin foundations of modern physics: quantum theory, which deals with the infinitesimally small, and Einstein’s theory of gravity, general relativity, which deals with the vast cosmos. This effort has led to a dazzling array of candidate theories—including superstring theory, loop quantum gravity, and doubly special relativity—but none have succeeded in unambiguously bridging the quantum-gravity divide. The problem: When you try to do the math to work out the strength of forces on the quantum-gravitational scale, your calculations return a maddening proliferation of infinite answers that have no physical meaning.

Now Hořava, at the University of California, Berkeley, claims to have found a solution that is both simple and—in physics terms, at least—sacrilegious. To make the two theories gel, he argues, you need to throw out Einstein’s tenet that time is always relative, never absolute.

Hořava’s controversial idea is based on the fact that the description of space and time in the quantum and relativistic worlds are in conflict. Quantum theory harks back to the Newtonian concept that time is absolute—an impassive backdrop against which events take place. In contrast, general relativity tells us that space and time are fundamentally intertwined; two events can only be marked relative to one another, and not relative to an absolute background clock. Einstein’s subjective notion of time is well accepted and is the hallmark of

"Lorentz invariance is not actually fundamental to a theory of quantum gravity," says Hořava. "But the problem so far has been that many cosmologists are wedded to the concept."

Good Gravitons

By restoring the absolute nature of time at very high energies, such as those in the early universe where quantum gravity would be important, Hořava can treat variations in space and time differently. The upshot of this is that in your calculations at very short distances you do not get such dramatic spatial variations as you do in general relativity, taming the infinities that frustrate other candidate theories of quantum gravity. This makes it possible to describe gravity on the quantum level using a well-behaved graviton—the hypothesized quantum particle thought to mediate gravity, just as the photon mediates the electromagnetic force (arxiv.org/abs/0901.3775).

The existence of an absolute

time might ensure that the

usual framework of quantum

mechanics can survive even

the most exotic regimes of

quantum gravity.

time might ensure that the

usual framework of quantum

mechanics can survive even

the most exotic regimes of

quantum gravity.

- Ted Jacobson

"The existence of an absolute time might ensure that the usual framework of quantum mechanics can survive even the most exotic regimes of quantum gravity," says physicist Ted Jacobson at the University of Maryland, College Park.

Surprisingly, Hořava’s trick is fairly commonplace in the laboratory. Condensed matter scientists looking at complex real-world systems, such as superconductors at low temperatures, have been using the idea that space and time are not on the same footing for years. Cosmologists do not usually take the lead from their condensed-matter cousins because of "sociological barriers," but the groups should look to each other for inspiration more often, says Hořava. He borrowed ideas from condensed matter models when developing his theory of quantum gravity. "In some condensed matter systems, relativistic behaviour and Lorentz invariance only emerge at lower energies," he says.

But while condensed matter physicists have shown that their models can recover relativistic behaviour as required at low energies, the big question is whether Hořava gravity can successfully morph back into the classical theory of relativity, in a way that agrees with all observations. In principle, general relativity should emerge at lower energies and larger distances. In other words: Look at a patch of the universe with infinitely powerful glasses and you would see that time and space are distinct from one another. Zoom out and the picture blurs, restoring Einstein’s more familiar spacetime fabric.

Knife-Edge

There is some support that this emergence does indeed happen from computer simulations of quantum gravity carried out by Jan Ambjørn of the Niels Bohr Institute at the University of Copenhagen and his colleagues. Ambjørn’s simulations showed that at short distances, the familiar four-dimensional spacetime of our macroscopic universe seems to shrink to just two dimensions—one space and one time. Hořava believes that his theory can explain how those spatial dimensions disappeared.

RINGING OUT EINSTEIN?

Light from a distant blue galaxy has been bent around a closer white

galaxy—as predicted over 70 years ago by general relativity—forming

an "Einstein ring." Can rivals to relativity explain such observations?

Since Hořava first proposed his theory in 2009, other researchers have used it to answer important cosmic questions about the nature of the Big Bang, dark matter and dark energy. Jacobson, however, feels there is much work still to be done before the theory can be widely accepted. "Hořava’s paper triggered a feeding frenzy, but most workers outside that frenzy remained wisely sceptical," he says.

Gustavo Niz at the University of Nottingham, UK, notes that physicists have found that in its original form, Hořava theory has plenty of "pathologies" and does not recover general relativity. "However, the idea behind the model is encouraging and scientists have ideas on how to cure all these secondary problems," he says.

Among those attempting to fix the original model are Diego Blas and Sergei Sibiryakov at the Swiss Federal Institute of Technology (EPFL) in Lausanne, and Oriol Pujolas at CERN near Geneva. Their work has revealed a flaw in the model: Minor variations in the initial conditions used in calculations in Hořava gravity can give dramatically different results (arxiv.org/abs/0909.3525). The culprit is a unique and unstable "breathing mode" in which space can locally expand or contract, wreaking havoc with your answers. To address this problem, they’ve modified Hořava’s initial proposal, making it harder for this breathing mode to develop. They have dubbed their formulation "extended Hořava gravity."

“In my view, the extended version of Hořava gravity is the only currently viable approach and needs to be extensively analysed,” says Jacobson.

Einstein’s Aether?

Jacobson’s own current research, funded by FQXi, examines the short distance structure of space and the quantum vacuum as space expands. He is also now looking at connections between Hořava gravity and an earlier modification of relativity, dubbed "Einstein-aether theory" that he had proposed a decade back.

Nineteenth-century physicists believed light waves must move through an "aether"—a medium that permeates all of space, allowing light to propagate just as sound waves move through air. However, a series experiments by Michelson and Morley failed to find any evidence that Earth moves through an aether. Einstein’s theory of relativity was the final nail in the aether’s coffin, because it explained that light moves through a vacuum.

Jacobson does not believe that the nineteenth-century aether exists. However, within Einstein-aether theory—in contrast to general relativity—there is a preferred time that can be used as an absolute reference to mark events against. It is as if spacetime were filled with a fluid—an aether—which defines a "rest frame" at each event.

The list of potential experimental

signatures includes modified orbits,

gravitational radiation, the structure of

neutron stars and black holes.

signatures includes modified orbits,

gravitational radiation, the structure of

neutron stars and black holes.

- Ted Jacobson

Jacobson has shown that some of the tests proposed to confirm or rule out Einstein-aether theory over the years could also falsify Hořava gravity (http://arxiv.org/abs/1001.4823). "The list of potential experimental signatures includes everything gravitational: from modified

For now though, Hořava remains modest, and is glad that others are examining his work. "My papers present the basic idea but don’t present a full theory yet," he says. "It is still unclear which of the possible different trajectories is best."

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STEVE AGNEW wrote on October 28, 2014

Actually, you have good resilience. It is important to stick to your principles as long as you possibly can...maybe even until the end...

The universe is all about prediction. The better we predict action, the better we survive and thrive. No model will ever be perfect. Perfection is the enemy of the good.

All we look for are better predictions of action, not perfection of some high-minded ideal. Anyway, that is what I look for.

I liked your questions about permanent magnets...

Actually, you have good resilience. It is important to stick to your principles as long as you possibly can...maybe even until the end...

The universe is all about prediction. The better we predict action, the better we survive and thrive. No model will ever be perfect. Perfection is the enemy of the good.

All we look for are better predictions of action, not perfection of some high-minded ideal. Anyway, that is what I look for.

I liked your questions about permanent magnets...

AKINBO OJO wrote on October 27, 2014

Steve, I believe Einstein and Minkowski know more about Lorentz invariance than those of us blogging here. Let me shake your faith in it a little although you may be unshakeable. Starting with two rephrased quotes from the master himself, with amendments meant for clarification. You can view the original...

"… according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special...

Steve, I believe Einstein and Minkowski know more about Lorentz invariance than those of us blogging here. Let me shake your faith in it a little although you may be unshakeable. Starting with two rephrased quotes from the master himself, with amendments meant for clarification. You can view the original...

"… according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special...

PENTCHO VALEV wrote on October 24, 2014

Fatal Acceleration in Einstein's Special Relativity

ON THE ELECTRODYNAMICS OF MOVING BODIES, by A. Einstein, June 30, 1905: "From this there ensues the following peculiar consequence. If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other...

Fatal Acceleration in Einstein's Special Relativity

ON THE ELECTRODYNAMICS OF MOVING BODIES, by A. Einstein, June 30, 1905: "From this there ensues the following peculiar consequence. If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other...

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