Can we find evidence for quantum gravity? That’s a major puzzle in Physics. This might be possible using a simple table-top experiment, according to Jacob Bekenstein, at the Hebrew University of Jerusalem. Why should we take him seriously? Bekenstein is best known for studying the thermal properties of black holes, showing that entropy is proportional to the surface area of a black hole’s event horizon, recently announced an amazing proposal to use single photons for probing what is known as “quantum foam.” The quantum foam idea was introduced in 1955 by the American physicist John Archibald Wheeler, and is believed to exist on length scales so small that quantum fluctuations affect the very structure or texture of space–time.

Bekenstein’s proposal is one of the the latest assaults in the quest to understand how quantum mechanics might be unified with Einstein’s General Theory of Relativity. Such a Unified Field Theory has escaped the grasp of physicists since they first began to understand the quantum and relativistic worlds in the early 20th century.

Why? A major challenge in coming up with a workable theory of quantum gravity is a complete lack of experimental evidence. The effects of quantum gravity are only expected to be measurable over extremely small distances. VERY VERY extremely small distances. But Bekenstein may have invented a clever loophole.

A few of the competing theories of quantum gravity suggest that experiments must probe distances smaller than the Planck length, which is 1.61 x 10^–35 meters. To Probe this scale using an accelerator would involve colliding particles at enormous energies of more than 10^16 TeV. This would be well beyond the capabilities of the Large Hadron Collider, which has a maximum collision energy of 14 TeV, or indeed of almost any conceivable future collider. Bekenstein’s

proposal could be done in a small physics lab mostly using existing equipment. He thinks.

What is a Planck length? The Planck length can be defined from three fundamental physical constants: the speed of light in a vacuum, Planck’s constant, and the gravitational constant. The physical significance of the Planck length is an argumentative topic of research. Sincethe Planck length is so many orders of magnitude smaller than any current instrument could possibly measure, there is currently no way of probing this length scale directly. Research on

the Planck length has therefore been primarily theoretical. By the generalized uncertainty principle, the Planck length is in principle, within a factor of order unity, the shortest measurable length. If so, no improvements in measurement instruments could change that.

In some formulations of quantum gravity, the Planck length is the length scale at which the structure of spacetime becomes dominated by quantum effects. Thus it would become impossible to determine the difference between two locations less than one Planck length apart. The precise effects of quantum gravity are unknown. Many physicists take Wheeler’s suggestion seriously, that spacetime might have a discrete or “foamy” structure at the Planck length scale.

If large extra dimensions exist, as was proposed by Nima Arkani-Hamed, Savas Dimopoulos, and Gia Dvali in 1998, then the measured strength of gravity may be much smaller than its true (small-scale) value. In this case the Planck length would have no fundamental physical significance, and quantum gravitational effects would appear at other scales. But the LHC experiments have given no suppport to that theory.

In string theory, the Planck length is the order of magnitude of the oscillating strings that form elementary particles, and shorter lengths do not make physical sense. But String theory is only one approach to a Unified Field Theory, and is not yet supported by experiment.

In LQG – loop quantum gravity — area is quantized, and the Planck area is, within a factor of order unity, the smallest possible area value.

In doubly special relativity, the Planck length is observer-invariant. Bottom line, the search for laws of physics valid at the Planck length has become a part of the search for TOE, the Theory Of Everything.

What’s the table top proposal? Such an experiment would fire single photons at a piece of glass or crystal, suspended by an extremely fine thread. When the photon moves from the vacuum into the material, it loses speed, because the material has a higher refractive index than that of the vacuum. Thus, a tiny amount of momentum is transferred to the material, causing it to move an extremely small distance. For a blue photon with a wavelength of 445 nanometers, Bekenstein says it would cause a 150 milligram piece of high-lead glass to deflect by about 2 x 10^–35 meters, pretty close to the Planck length. The premise is is that if a photon is detected on the other side of the material, it means that the mass was deflected by a distance greater than the Planck length. But – and here’s the kicker – if the energy of the photon is reduced (or alternatively the mass of the glass increased) until the deflection becomes equal to or smaller than the Planck length, then quantum gravity will affect how the glass responds to each photon.

Bekenstein indicates that the presence of the foam would prevent the glass from recoiling in exactly the same way when struck by a succession of identical photons. By analogy to electromagnetic fluctuations which can have measurable effects on much larger objects (for example in the Casimir force), spacetime fluctuations might also affect how an object moves extremely small distances. For Bekeinstein’s proposed experiment, photons would not be able to travel

through the glass, which would be observed as a drop in the number of photons detected on the other side. An easily measured effect!

Bekenstein admits that the experiment is “challenging”, yet claims that it “is not beyond what experimental physicists can do today.” Creating and detecting single photons is a routine part of quantum-optics experiments in labs around the world. Minimizing the effects of thermal noise will also be tricky, with Bekenstein calculating that the apparatus must be cooled to about 1 Kelvin (one degree above absolute zero) and operated in an ultrahigh vacuum of

about one ten-billionth of a Pascal. But both constraints are achievable with existing technology.

Bekenstein is not the only physicist to have proposed a table-top probe of quantum gravity. Earlier in 2012, for example, Igor Pikovski and colleagues at the University of Vienna and Imperial College London described in Nature Physics a way of making optical measurements on a mechanical oscillator with a mass close to the Planck mass. A Planck mass is the unit of mass in the system of natural units known as Planck units. It is defined to be the square root of the Planck constant times the speed of light divided by the gravitational constant. This comes to 21.7651 micrograms.

Pikovski told physicsworld.com that Bekenstein’s plan seems feasible. “A big advantage is that physicists can control single photons very well and detect them extremely efficiently,” he says. Pikovski also points out that the technique could prove very useful even if experimental issues prevent it from probing distances down to 10^–35 meters. Why? Because some theories of quantum gravity predict that quantum foam or some other effect of quantum gravity could emerge at length scales as great as 10^–25 meters.

It is not clear whether the table-top experiments proposed by Bekenstein, Pikovski or others can succeed, yet Pikovski believes that laboratory measurements will provide important information about quantum gravity within a decade or so.

Table-top experiments gave changed the world before. Remember the Millikan Oil Drop Experiment? That told us the mass of the electron, and won a Nobel Prize.

REFERENCES:

“Table-top test targets quantum foam”, 29 Nov 2012, by Hamish

Johnston, editor of physicsworld.com

http://physicsworld.com/cws/article/news/2012/nov/29/table-top-test-targets-quantum-foam

http://en.wikipedia.org/wiki/Planck_length

http://math.ucr.edu/home/baez/planck/node2.html

“Is a tabletop search for Planck scale signals feasible”, Jacob D. Bekenstein

(Submitted on 16 Nov 2012)

http://arxiv.org/abs/1211.3816

Quantum gravity theory is untested experimentally. Could it be tested with tabletop experiments? While the common feeling is pessimistic, a detailed inquiry shows it possible to sidestep the onerous requirement of localization of a probe on Planck length scale. I suggest a tabletop experiment which, given state of the art ultrahigh vacuum and cryogenic technology, could already be sensitive enough to detect Planck scale signals. The experiment combines a single photon’s degree of freedom with one of a macroscopic probe to test Wheeler’s conception of “spacetime foam”, the assertion that on length scales of the order Planck’s, spacetime is no longer a smooth manifold. The scheme makes few assumptions beyond energy and momentum conservations, and is not based on a specific quantum gravity scheme.

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