Using conservation of momentum to detect the Planck scale quantum foam

Arxiv – Is a tabletop search for Planck scale signals feasible? (8 pages)

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 speci c quantum gravity scheme

A particle accelerator would require 10**19 GeV to detect the Planck scale.

We propose the idea for a table-top experiment which, depending on the outcome, may confi rm the radical texture of sub-Planckian spacetime, and decide whether the Planck scale is very small or merely microscopic. The idea, in brief, is to use a single optical photon which traverses a dielectric block to engender a translation of the block which can be arranged to be of order the Planck scale. The translation does not hinge on giving a permanent impulse to the block. Certifi cation that the tiny translation actually occurred is to be had from detecting the photon after transit through the block and relying on momentum conservation. But, as discussed below, translation by a distance of order `P is expected to be disfavored. Thus if in a series of like experimental runs the frequency with which the photon is found to get through the block falls short of expectations (from the block’s classical transmission coeffi cient), this may signal that spacetime is rough” at the relevant scale. The scale at which spacetime ceases to be smooth could thus be experimentally determined.

Set up of suspended blocks showing (dotted) the alternative paths for the photon. E is the single-photon emitter, D and D’ are the single-photon detectors. BS denotes the beamsplitter and M the mirror. DL is the fiber optics delay line, and EB are the electronics that trigger D and D’ through cable C. The optical elements to widen the beam before and focus it after each block are left out for clarity. In the real experiment the blocks would hang side by side.

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This experiment requires no device more exotic than a laser and a fridge (the block has to be cooled to close to zero to minimise thermal perturbations). Nothing about it is beyond the state of the art. Indeed, the test could be performed today on a tabletop in a well-equipped lab.

That’s not to say it will be easy. Bekenstein is a big cheese in the world of theoretical physics but colleagues will want to be sure that his argument is water tight before embarking on such an experiment.

If it is, then Bekenstein’s table top experiment could be up and running in the very near future offering the first potential glimpse of quantum foam.

Of course, the failure to find quantum foam would also be interesting. The latest thinking is that gravity is an emergent phenomenon through a kind of thermodynamic process. This does not require quantum foam.

So the failure to detect quantum foam, although not a proof of the emergent gravity theories, would certainly be a hugely interesting discovery too.

The feasibility of translating the c.m. of a macroscopic block of dielectric by a distance of order Planck’s length without first localizing it has been demonstrated. This translation is not measured but inferred by momentum conservation involving a single optical photon which crosses the block. It is argued that such translation may occasionally be at odds with the non-smooth texture of spacetime on Planck scale. Contradiction is then avoided if the photon is reflected by the block more often than predicted by classical electrodynamics. An experimental set up is proposed to detect this transmission anomaly, even if tiny; it compares the eff ect of the same photon on the above mentioned block and on a similar block which gets translated a distance much larger than Planck’s. It is shown that the thermal noise that might compromise the experiment is su fficiently suppressed by operating the blocks in an ultrahigh vacuum at temperature below 0.5 degrees Kelvin.

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