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Quantum Mechanics Meets Einstein: Horava 2010-08-11

Posted by clype in Articles of Interest, Discovery, Science.
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It was a speech that changed the way we think of space and time.

The year was 1908, and the German mathematician, Mr.Hermann Minkowski, had been trying to make sense of Mr.Albert Einstein’s hot new idea — what we now know as special relativity — describing how things shrink as they move faster and time becomes distorted.

‘Henceforth space by itself and time by itself are doomed to fade into the mere shadows,’ Mr.Minkowski proclaimed,
‘And only a union of the two will preserve an independent reality.’

And so space-time — the malleable fabric whose geometry can be changed by the gravity of stars, planets and matter — was born.

It is a concept that has served us well, but if Czech physicist Mr.Petr Horava is right, it may be no more than a mirage.

Mr.Horava, who is at ‘The University of California, Berkeley‘, wants to rip this fabric apart and set time and space free from one another in order to come up with a unified theory that reconciles the disparate worlds of quantum mechanics and gravity — one the most pressing challenges to modern physics.

Since Mr.Hořava published his work in 2009-01, it has received an astonishing amount of attention.

Already, more than 250 papers have been written about it. Some researchers have started using it to explain away the twin cosmological mysteries of dark matter and dark energy. Others are finding that black holes might not behave as we thought.

  • If Mr.Horava’s idea is right, it could forever change our conception of space and time and lead us to a ‘theory of everything’, applicable to all matter and the forces that act on it.

For decades now, physicists have been stymied in their efforts to reconcile Einstein’s General Theory of Relativity, which describes gravity, and Quantum Mechanics, which describes particles and forces (except gravity) on the smallest scales.

The stumbling block lies with their conflicting views of space and time. As seen by Quantum Theory, space and time are a static backdrop against which particles move. In Einstein’s theories, by contrast, not only are space and time inextricably linked, but the resulting space-time is moulded by the bodies within it.

Part of the motivation behind the quest to marry relativity and quantum theoryto produce a theory of quantum gravity — is an aesthetic desire to unite all the forces of nature, but there is much more to it than that; we also need such a theory to understand what happened immediately after The Big Bang or what’s going on near black holes, where the gravitational fields are immense.

One area where the conflict between quantum theory and relativity comes to the fore is in the gravitational constant, G, the quantity that describes the strength of gravity. On large scales — at the scale of the solar system or of the universe itself — the equations of general relativity yield a value of G that tallies with observed behaviour. But when you zoom in to very small distances, general relativity cannot ignore quantum fluctuations of space-time. Take them into account and any calculation of G gives ridiculous answers, making predictions impossible.

Something has to give in this tussle between general relativity and quantum mechanics, and the smart money says that it’s relativity that will be the loser. So Mr.Horava began looking for ways to tweak Mr.Einstein’s equations. He found inspiration in an unlikely place: the physics of condensed matter, including the material of the moment — pencil lead.

Pull apart the soft, grey graphite and you have a flimsy sheet of carbon atoms just one atom thick, called graphene, whose electrons ping around the surface like balls in a pinball machine. Because they are very small particles, their motion can be described using quantum mechanics; and because they are moving at only a small fraction of the speed of light there is no need to take relativistic effects into account.

But cool this graphene down to near absolute zero and something extraordinary happens: the electrons speed up dramatically.

Now relativistic theories are needed to describe them correctly.

It was this change that sparked Mr.Horava’s imagination; one of the central ideas of relativity is that space-time must have a property called Lorentz symmetry: to keep the speed of light constant for all observers, no matter how fast they move, time slows and distances contract to exactly the same degree.

What struck Mr.Horava about graphene is that Lorentz symmetry isn’t always apparent in it. Could the same thing be true of our universe? He wondered. What we see around us today is a cool cosmos, where space and time appear linked by Lorentz symmetry — a fact that experiments have established to astounding precision. But things were very different in the earliest moments. What if the symmetry that is apparent today is not fundamental to nature, but something that emerged as the universe cooled from The Big Bang fireball, just as it emerges in graphene when it is cooled?

So Mr.Horava did the unthinkable and amended Mr.Einstein’s equations in a way that removed Lorentz symmetry. To his delight, this led to a set of equations that describe gravity in the same quantum framework as the other fundamental forces of nature: gravity emerges as the attractive force due to quantum particles called gravitons, in much the same way that the electromagnetic force is carried by photons. He also made another serious change to general relativity. Mr.Einstein’s theory does not have a preferred direction for time, from the past to the future, but the universe as we observe it seems to evolve that way. So Mr.Horava gave time a preferred direction (Physical Review D, vol 79, p 084008).

With these modifications in place, he found that quantum field theories could now describe gravity at microscopic scales without producing the nonsensical results that plagued earlier attempts.

‘All of a sudden, you have new ingredients for modifying the behaviour of gravity at very short distances’ Mr.Horava says.

‘Horava gravity’ is, of course, not the first attempt to devise a theory of quantum gravity. Of its many predecessors, the most popular is string theory.

But ‘Horava gravity’ has one particularly appealing feature: unlike string theory, which requires mastery of daunting mathematics, it can be studied using the same mathematical tools that have been developed for the three other fundamental forces of nature.

‘It is a completely new approach to a very difficult problem,’ says Mr.Oriol Pujolas, a theoretician at the CERN laboratory, near Geneva, Switzerland.
‘Yet it’s a very simple framework we know very well.’

This is partly why so many physicists have taken up Mr.Horava’s theory so avidly. Other theories of quantum gravity, including string theory and loop quantum gravity, are far more difficult for newcomers to embrace.

  • Pretty mathematics is all very well; the true test is how the theory works out when it is applied to the real world.

So how does it fare? Some clues that Mr.Horava might be on the right track come from another approach to quantum gravity called Causal Dynamical Triangulation, which stitches space-time together from smaller pieces. Mr.Jan Ambjørn  of ‘The Niels Bohr Institute‘ in Copenhagen, Denmark, and his colleagues, pioneered the idea.

They used computer simulations to analyse the behaviour of space-time and were puzzled by what they found in some of their models; as they zoomed in and out, they found that the contributions from the three dimensions of space and one of time varied in a way they did not fully understand. Zoom out and space and time play equal parts, in line with Lorentz symmetry — but zoom in and time plays a far greater role than space.

Mr.Ambjørn thinks this means space and time are contracting differently — as you would expect if Lorentz symmetry is broken as it is in Mr.Horava’s theory of quantum gravity (arxiv.org/abs/1002.3298).

‘So, if you call these computer simulations “experiments”,’ says Mr.Ambjørn,
‘Then Horava’s theory and experiment have met — in a way.’

But it’s not all been ‘plain sailing’ for Mr.Horava’s work; the near-unprecedented spotlight that is being focussed on it has, not surprisingly, illuminated some cracks.

The first appeared in 2009-06 — just five months after Mr.Horava published his paper. If his theory works, then at low energies it should look like general relativity. However, Mr.Pujolas, along with Mr.Diego Blas and Mr.Sergey Sibiryakov of ‘The Swiss Federal Institute of Technology‘ in Lausanne, showed that wasn’t the case in the system they analysed, meaning that Mr.Horava’s theory would always be at odds with experimental observations (arxiv.org/abs/0906.3046).

At first, the theory seemed doomed — then within months of their initial paper, Mr.Pujolas and his colleagues realised that this disparity only appears in special circumstances and that the theory could after all lead to general relativity at low energies (arxiv.org/abs/0909.3525).

That was welcome news to those who have been using ‘Horava gravity’ to study astrophysical and cosmological mysteries such as black holes, dark matter and dark energy. Take black holes; in general relativity, these are a consequence of space and time being part of the same fabric. Black holes warp space-time so much that they suck in everything around them. Nothing can escape a black hole’s gravity because nothing can travel faster than the speed of light.

By breaking the symmetry between space and time, Mr.Horava’s theory alters the physics of black holes — especially microscopic black holes, which may form at the very highest energies. What this means for the formation of these black holes, and whether they are what they seem to be in general relativity ‘is a very big question’, says Mr.Pujolas, and one that researchers are now addressing.

‘Horava gravity’ might also help with the long-standing puzzle of dark matter. The motions of stars and galaxies that astronomers have observed seem to require there to be much more matter in the universe than meets the eye; without it, galaxies and clusters of galaxies should fly apart. But this conclusion arises from equations of motion derived from general relativity. What if these equations are slightly off? Could this explain the observed speeds of the stars and galaxies without dark matter playing a role?

Mr.Shinji Mukohyama at ‘The University of Tokyo‘ in Japan decided to find out. When he extracted the equations of motion from Mr.Horava’s theory, he found that they came with an extra term that is not present in equations derived from general relativityand that this extra term mimics the effects of dark matter. Depending on its value, you can do away with some dark matter, or even most of it (arxiv.org/abs/0905.3563).

‘It is possible that some fraction of the dark matter picture of the universe could be coming from corrections to Einstein’s equations,’ Horava says.

Dark energy is a more daunting problem still. It appears that the expansion of the universe has started to speed up in the past few billion years, and to explain it physicists have invoked the inherent energy of the vacuum of space-time. This is dark energy. But there is a big problem; the theories of particle physics predict the strength of dark energy to be about 120 orders of magnitude larger than what is observed, and general relativity cannot explain this enormous discrepancy.

Here, too, Mr.Horava’s theory may 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 the small positive value that is in line with the observed motions of stars and galaxies (arxiv.org/abs/0907.3121).

It will, however, be hard to show whether or not this picture it correct — as Mr.Roberto Casadio of ‘The University of Bologna‘ in Italy and colleagues, who did these calculations, admit. That’s because, with the parameter in Mr.Horava’s equations set to the necessary value, their predictions will deviate from those of Mr.Einstein’s relativity only at energies far, far higher than can be probed in labs today.

The universe, of course, will have the final say. Improved observations of supermassive black holes, which contain regions of intense gravity, could reveal the necessary corrections to general relativity. This could pave the way for a theory of quantum gravity, such as Mr.Horava’s, in much the same way that unexplained measurements of Mercury’s orbit showed that Mr.Newton’s laws were incomplete, opening the door for Mr.Einstein.

In the midst of all the buzz, Mr.Horava is keeping his cool. Hanging in his office in Berkeley is a 17th-century Dutch map on which California appears as an island off the west coast of America. He takes its lesson to heart.

‘We have found some new land and it’s very exciting, but we are very far from getting all the details right.’


1. Ik - 2010-08-11

I can explain gravity.



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