A Low Energy Test of Quantum Gravity

Many (probably most) theoretical physicists suspect that the correct theory unifying quantum field theory and general relativity is some theory involving a quantum description of the gravitational field. However, we have no compelling experimental evidence for this, and it remains logically possible that gravity and quantum theory are unified some other way. (How? There are some speculative ideas, but I think it's fair to say we have no detailed theoretical proposals that look very compelling. For example, some physicists have suggested that a classical theory of the metric might be coupled to quantum matter, presumably by some sort of stochastic evolution law. However, no mathematically well-defined theory along these lines, consistent with experiment and with Lorentz invariance, has yet been produced.) If standard ideas about quantum gravity are right, one would expect the gravitational field to display the same sort of non-local correlations that quantum matter does. Bell experiments have tested and (modulo one or two loopholes -- see for example below) confirmed that quantum nonlocality of matter is indeed observed in Nature. Though it might seem obvious to conclude that the gravitational field must also display nonlocality, this does not in fact logically follow. No Bell experiment (nor any other experiment) to date has shown it to be the case. However, it can be tested by a relatively simple experiment. The experiment should either provide the first significant evidence for quantum gravity, or else (if standard intuitions are somehow wrong) establish a definite limitation on the domain of validity of quantum theory.

"Post-Quantum" Cryptography

In quantum key distribution schemes, Alice and Bob exchange quantum and classical information in order to generate a shared secret key. There are several well-known schemes, which are provably secure against eavesdropping, so long as quantum theory is correct. But what if quantum theory isn't correct? This might seem a rather academic question, since quantum theory has been confirmed in an impressive range of experiments since 1926. But cryptologists are supposed to examine their assumptions carefully. Physical theories have been superseded in the past, and there's no strong reason to think it won't happen again. (And in fact, although it's a minority view, there is a very respectable case for believing that the lingering conceptual problems in interpreting quantum theory point to some subtle defect in the theory itself.) You can't prove anything secure without making some assumptions, and in particular you can't prove any physics-based cryptography scheme secure without making some assumptions about physics. But Jonathan Barrett, Lucien Hardy and I were recently able to show that a quantum key distribution scheme can be proved secure even if quantum theory is incorrect, so long as we assume that (as special relativity suggests) it is impossible to send signals faster than light. The scheme is, admittedly, very inefficient, but it's at least a proof of principle that security guarantees can be based on either of two independent theories (quantum mechanics and special relativity), rather than on one alone. It would be very interesting to know if significantly more efficient schemes exist, or indeed if the security of standard quantum key distribution schemes can also be based on relativity. There's a popular account of this work in Physical Review Focus, linked here.

Bit Commitment and Cryptography Based on Relativity

Bit commitment is one of the main primitives of mistrustful cryptography, the branch of cryptography dealing with parties who need to exchange or process information but cannot rely on each other's honesty. In a bit commitment, Alice and Bob exchange data in a way that leaves Bob with an encrypted bit, chosen by Alice. She can later decrypt for him, if (and when) she chooses. It is quite easy to find bit commitment protocols that are secure against Alice (in the sense that she has no chance of lying to Bob when she decrypts the bit) or against Bob (in the sense that he has no chance of reading the bit unless Alice chooses to decrypt it). Finding a protocol that is secure against both parties, however, is much harder: indeed it was long believed impossible. It turns out, though, that secure (and practically feasible) bit commitment protocols can be implemented if Alice and Bob use separated sites and take account of the impossibility of signalling faster than light. (Caveat: the protocols have been proven secure against all classical attacks -- the first known protocols with this property -- and against the type of quantum attack to which non-relativistic protocols are vulnerable. Their security against general quantum attacks is conjectured but not, so far, proved.)

What's an Acceptable Risk for Destroying the Earth?

From time to time, people have raised the worry that a particular physics experiment just might destroy the Earth. The first time this was seriously considered seems to have been before the first A-bomb and H-bomb tests. More recently, the possibility was raised that, if unknown physics included some particularly unfortunate features, the RHIC experiments at Brookhaven, or the forthcoming ALICE collider experiments at CERN, could have disastrous consequences. When physicists address these worries at all, they've tended to argue that (a) something would have to be very wrong with our understanding of physics for the risk to be present at all, (b) even if it is, we can show on empirical grounds that any risk must be so small that the possibility just isn't worth worrying about. Which rather begs the question, of course: how small *is* an acceptable risk? On this point, the various analyses seem to have been extraordinarily cavalier. At various times physicists have argued for going ahead with experiments without further ado on the basis of risk bounds ranging from 1 in 5000 (!) (the first Brookhaven analysis of the RHIC experiments) through 1 in 300,000 (Compton's estimate of the probability of igniting the Earth's atmosphere in the first A-bomb test) to 1 in 50,000,000 (the CERN analysis of the RHIC experiments). It seems to me that a little thought suggests all these risk bounds are far, far too large for comfort.

New Loopholes in Bell Experiments

Bell's theorem tells us that quantum theory disagrees with the predictions of local hidden variable theories. Since the 1970s, a long sequence of experiments have produced results supporting the predictions of quantum theory and refuting those of local hidden variables. Very probably, this is because local hidden variable theories are simply wrong and quantum theory is right (at least in its predictions concerning measurements on entangled states). Still, it's a crucial enough point that one wants to eliminate every possible scintilla of doubt. Two possible loopholes in the interpretation of Bell experiments, the detector efficiency loophole and the locality loophole, have long been known: several groups are attempting to design experiments that can simultaneously close both. Another interesting loophole, the memory loophole, was recently identified, but shown to be relatively innocuous, in the sense that even models exploiting the memory loophole can be refuted by existing experimental data. But there is yet another loophole, the collapse locality loophole, which moreover is associated with a relatively natural class of alternatives to quantum theory. (Relatively natural in the sense that the alternatives are defined by some independently motivated assumptions, not contrived especially for the purpose of exploiting logically exploitable but physically implausible flaws in Bell experiments.) This loophole has yet to be closed, and may not be in the near future. To close it completely would require carrying out a Bell experiment with the two wings separated by at least 0.1 light seconds (30,000 km) or so --- this would probably require a space-based experiment. It's perhaps the last hope for diehard sceptics about quantum non-locality. (I'm not one --- my guess is that standard quantum theory will turn out to be right on this point --- but of course it would be good to resolve the question definitively by experiment.)