The power of nothing, it seems, is not easily defeated.
Date: Wednesday, September 28, 2005 @ 21:39:46 GMT
Topic: Science

Vacuum energy: something for nothing?

01 October 2005
From New Scientist Print Edition.
David Shiga

IT doesn't sound like the kind of thing that would affect our cosmic fate. Put two metal sheets close together - very close - in a vacuum and you'll find they attract each other with a small but measurable force.

Sounds more like a simple curiosity, doesn't it? Except physicists believe that the energy source that is pushing those plates together may also be pulling the universe apart. The traditional explanation for the "Casimir effect" (it is named after the Dutchman who predicted its existence more than half a century ago) is that empty space is in fact crackling with "zero-point energy", a phenomenon arising from quantum theory. It is this energy that pushes the metal plates together.

The same zero-point energy, backed up by evidence from the Casimir effect, is also a leading candidate to explain the mysterious dark energy that seems to be expanding the universe at an ever increasing rate. If we knew more about the nature of the zero-point energy, we would know whether the universe will keep on blowing up forever or eventually collapse into a point in a reverse big bang. So that arcane little effect really does have cosmic significance.

Or so most physicists think. In a paper in the journal Physical Review D (vol 72, p 021301), however, particle physicist Robert Jaffe at the Massachusetts Institute of Technology argues that the standard interpretation of the Casimir experiment is completely unjustified. Although the force measured in the experiments is definitely real, it doesn't prove anything about zero-point energy. "It's become an urban legend in our field that the Casimir effect somehow measures quantum zero-point energy," he says. It seems that the future of our universe just got a lot more fuzzy.

Jaffe makes his case by recalling the roots of the phenomenon. Casimir's prediction of a force between parallel metal plates came out of his study of something called the van der Waals force. This arises when the electric field of an atom distorts the shapes of other atoms nearby, and has its own shape distorted in turn. The electric fields of these distorted atoms then cause the atoms to attract each other.

In the 1940s, Casimir was trying to figure out why the van der Waals force was weaker than expected at distances larger than a few atomic diameters, something his colleague Theo Overbeek had noticed in experiments. After doing some calculations, Casimir and his colleague Dirk Polder showed that the weakening is due to the finite speed of light. A small change in the shape of one atom does not register with its neighbours until photons, which mediate the electromagnetic force, have a chance to transmit the information to them. The lag is negligible over a few atomic diameters, but as the distance increases to nanometres it weakens the force significantly. Casimir derived an elegant new formula for the long-distance van der Waals force, which was a much better match to the experiments.

The calculation that produced the formula was quite complex, so Casimir was surprised that the end result was so simple - it involved little more than the geometry of the system, the speed of light and a number from quantum theory called Planck's constant. Astonishingly, the formula didn't even depend on the electric charge of the electrons in the atoms, which are ultimately responsible for the force.

Casimir wondered if he was missing some deeper principle that could explain the formula in a simpler way. He mentioned this while on a walk with Niels Bohr, who immediately offered a characteristically confident explanation. "Must have something to do with the zero-point energy," Bohr said offhand.

Bohr was referring to a strange prediction of the quantum theory of fields, which says that there is no such thing as perfectly empty space. Instead, even supposedly empty space is endowed with "virtual" photons and other particles that constantly pop in and out of existence everywhere. And Bohr's idea seemed to work: using only these zero-point fluctuations as his guide, Casimir successfully derived his formula for the long-distance van der Waals force between atoms.

Everyone already knew that there should be a force between the atoms; Casimir had simply found a new way to explain it. But he soon realised a much more remarkable implication of zero-point energy: it creates a force between a pair of parallel, uncharged metal plates.

Each of the virtual photons spawned by zero-point fluctuations has a certain amount of energy, corresponding to a particular wavelength of light. While virtual photons of any wavelength can appear outside the plates, only certain wavelengths are allowed between the plates.

That limitation means that when the photons hurtle at the sheets from all directions and exert pressure on them, there is more pressure from outside the plates than from the space in between them. This imbalance squeezes the plates together. For two metal sheets a centimetre square and a thousandth of a millimetre apart, the Casimir force amounts to a 10-millionth of a Newton, about a hundredth of the weight of a mosquito. That's pretty small. Physicists have nevertheless managed to measure it very precisely using atomic force microscopes and other sensitive instruments.

But none of this experimental success means Casimir's explanation is the only way to see it, and over the years a handful of physicists have come up with different explanations for the effect. In 1956 Russian physicist E. M. Lifschitz showed how to obtain Casimir's formula using only the van der Waals force between the particles of the metal sheets. And in the 1970s, the late Nobel laureate Julian Schwinger of the University of California at Los Angeles became increasingly dissatisfied with the vacuum energy concept, even though he had a major hand in developing the quantum field theory that predicts it. Schwinger set himself the daunting task of reformulating quantum field theory in a way that would banish zero-point energy of the vacuum forever. He called his approach source theory and in 1978 demonstrated, along with his UCLA colleagues Lester DeRaad Jr and Kim Milton, a way to derive the Casimir effect using only fields arising from the matter making up the sheets, and not from anything in between.

Obvious explanation

Jaffe's arguments and calculations reinforce the view that one needn't invoke vacuum fluctuations to explain the Casimir force; the most obvious explanation comes from attractions between the particles making up the metal sheets.

Each method allows one to calculate the overall effect of the interaction between the electromagnetic field and the matter making up the sheets. That's true even for Casimir's vacuum energy perspective, in which the sheets affect the field by limiting the wavelengths of light allowed between them. Although the methods differ in perspective, they all give the same answer.

The electron charge e is absent from Casimir's formula because he made simplifying assumptions, such as perfect electrical conductance in the plates. Those assumptions worked (in terms of matching theory to experiment) when considering good conductors such as copper or gold, which were used in the experiments that confirmed the prediction. But they also created a problem: people forgot he had made them.

The first really accurate measures of the Casimir effect were made by Steve Lamoreaux at the University of Washington in Seattle in 1997. Lamoreaux's results were a close fit with the predictions of the theory based on zero-point energy in the vacuum. As a result, physicists began to think that, because there was no reference to metallic properties in the vacuum energy formula, the Casimir effect must come out of the vacuum.

Jaffe is keen to point out that his work doesn't get rid of zero-point fluctuations altogether, and neither does it say they contain no energy. That's just as well, as physicists assume that vibrating molecules contain zero-point energy in order to correctly predict the wavelengths of light they absorb and emit. This has been well established, for example, by measuring how vacuum fluctuations alter the frequencies of light that hydrogen atoms absorb and emit, a phenomenon known as the Lamb shift. Since this same basic theory that works for molecules says that the vacuum contains zero-point energy too, there is no reason to believe otherwise. But we can't rely on the Casimir effect to give us a measure of that energy. "We have no way of measuring the energy in the vacuum, nor any properties of the vacuum in the context of our laboratory experiments," Jaffe says.

Jaffe says he finds it "disturbing" that our best theory of forces and fields predicts - even relies upon - something that is not currently measurable. But this could be an opportunity: it might help solve what has been called the most embarrassing problem in physics.

We don't know what most of the universe is made of. About 70 per cent of the content in the universe seems to be in a form that is entirely unfamiliar to us. This energy, which appears to be causing space to expand, is widely referred to as "dark energy". Our best guess at where dark energy comes from is the zero-point fluctuations in the vacuum - a guess that has traditionally been shored up by reference to the Casimir effect. Steven Weinberg of the University of Texas at Austin, for example, has written about "the demonstration in the Casimir effect of the reality of zero-point fluctuations" when discussing the runaway expansion of the universe. Another cosmologist, Sean Carroll of the University of Chicago, has argued that "the vacuum fluctuations themselves are very real, as evidenced by the Casimir effect".

However, these two researchers would be the first to admit that there is a problem with this approach. Physicists' best stab at a theory for how much energy the vacuum should contain gives an amount that is around 120 orders of magnitude bigger than the value calculated from astronomical observations (New Scientist, 5 April 2003, p 30). The force that zero-point energy creates can be both repulsive and attractive; either way, at the predicted magnitude we shouldn't even be here. "If you just take quantum field theory naively," Jaffe says, "the vacuum field energy is so large that the universe would have blown apart or squeezed back to a point long before we would ever know about it."

So maybe it's time we admitted the vacuum energy isn't quite what we had assumed. Carroll says he no longer cites the Casimir effect as evidence of vacuum energy; he now cites the Lamb shift instead. Carroll thinks there are actually two issues with physicists' interpretation of the vacuum field energy. The fluctuations exist; of that he is sure. But, he admits, the jury is still out on how much energy they might impart to the vacuum. Tests of the Casimir effect probe changes in vacuum energy for different configurations of the sheets, but not the total energy present in the vacuum. "With vacuum fluctuations, we have to distinguish between evidence for the existence of the fluctuations, and for their energy," Carroll says.

How do we do that? With difficulty. Zero-point fluctuations are described by quantum mechanics, but to understand what effects their energy might have on the universe, physicists have to turn to Einstein's theory of general relativity. Unfortunately, no one knows how to mesh general relativity with quantum mechanics to produce a coherent view of the universe - and a harmonious understanding of both the zero-point fluctuations and the accelerating expansion of the universe.

However, theories that attempt to provide a unified picture, such as string theory and supergravity, predict the existence of unknown short-range forces, and these forces might show up as anomalies in Casimir experiments if we can make sufficiently sensitive measurements (New Scientist, 19 February, p 55). Of course, if physicists succeed in creating a satisfactory theory of quantum gravity, it may also shed further light on the meaning of the Casimir effect itself.

Will the vacuum energy interpretation survive in this new perspective? No one can say for sure, but history is in its favour. Milton, who helped Schwinger formulate his source theory, thinks Schwinger's hope of eliminating vacuum energy was unfounded. Even source theory itself can be reinterpreted in terms of vacuum fluctuations. "You think you get rid of them but then they creep in the back door," he says. The power of nothing, it seems, is not easily defeated.

David Shiga is a freelance writer based in Canada

From issue 2519 of New Scientist magazine, 01 October 2005, page 34


Really real?

Though the work of Robert Jaffe at MIT might be pivotal to understanding our universe's fate, and to decisions over whether we should be chasing wisps of dark energy through the cosmos, it might also provoke a more down-to-earth course of action.

String theorist Leonard Susskind is impressed with Jaffe's clarification of the source of the Casimir effect, but suggests the whole debate over the reality of zero-point fluctuations is a tempest in a teapot. "To me, the reality of zero-point fluctuations in the Casimir case means neither more nor less than the existence of a force between conductors," he says. "We all agree that such a force does exist."

The trouble is, he suggests, physicists can't agree on what it means for something to be real - and Susskind has a radical solution in mind. "I would ban the word real from the physicist's vocabulary," he says.


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