## February 05, 2013

### No threat to quantum cryptography (at least from quirks of fluid mechanics)

A few days ago my colleague at University of Latvia,  +Andris Ambainis, has shown me a recent preprint by  +Ross Anderson and +Robert Brady. The title and the content of their paper are so provocative (e.g., "full range of quantum phenomena from completely classical motion" and "quantum cryptography is not probably secure") that it has understandably attracted some attention of the cryptography community and led to sensational news reports attributed to "Cambridge experts".

As a condensed matter physicist, I'd like to state a few things that I hope will quickly clarify this confusion.  Below are you will find a list of statements regarding  arXiv:1301.7351 by Anderson and Brady (A&B) and arXiv:1301.7540 by Brady. You don't have to trust me - run the list by any tenured physicist at your university/department.
1. There is no explicit model for entanglement (or any other kind of many-particle correlation) in Brady's "sonon" model of an electron or in the A&B preprint.
2. As a corollary, the model is irreconcilable with each of the myriad of experimental facts underlying our trust in the conventional quantum many-body theory (ie., Shcrodinger equation in Fock space). Explicitly:
1. Spectrum of any atom beyond hydrogen.
2. Superconductivity (from which Josephson-effect-based QIP is derived).
3. Anomalous value of electron's gyromagnetic ratio (which by itself long ago has fundamentally invalidated any single-particle approximation for the physical electron, including Dirac equation which Brady connects his model to).
4. Exchange interaction and ferromagnetism.
5. The Standard Model of particle physics.
3. Another corollary: in contrast to standard theory, A&B provide no alternative method to compute the outcome of any of Bell-inequality testing experiment.  (The latter belong the same myriad of experimental keyholes that quantum theory has successfully passed through).
4. Brady's use of the historical name "fine structure constant" for his estimate of the squared dimensionless Coulomb charge of the "sonon" ($\alpha < 1/49$) is misleading. There is no spin-orbit interaction in his model and hence no prediction for fine structure of atomic spectra.
One can go on and pick apart individual superficial analogies put forward by A&B that a non-specialist may mistake for valid criticism of contemporary quantum theory, but I hope that I have made it clear enough that scientific implications of the controversy stirred by A&B, if any, do not belong to the domain of physical sciences.

Cramer's transactional interpretation of quantum mechanics is consistent with experiments on Bell's inequality, as is Mead's adaptation of it. Both of these approaches are referenced in the sonon paper, together with a discussion of why the motion of sonons is consistent with them.

The underlying reason for the consistency is that Euler's equation is time reversal symmetric. Cramer's model makes use of the same time reversal symmetry. It might be thought unsatisfactory to rely on this property, which is why we suggest the alternative hypothesis, that it may be possible to interpret the sum of the advanced and retarded solutions in terms of a spacelike function. When I presented the paper to fluid dynamicists at Warwick recently, they were surprised there was any problem with there being non-local motions as a result of Euler's equation (which in turn surprised me because the equation itself is, strictly speaking, completely local). Nevertheless, this is an open suggestion regarding an interpretation. The motion itself is consistent with experiments on Bell's inequality for the reason described above.

Regarding the fine structure constant, this constant characterizes the strength of the Coulomb force, which is the definition used in the calculation.

Regarding the other matters you raise, these might be areas for further study.

Vyacheslavs Kashcheyevs said...

With all due respect, "referencing an interpretation" both in your comment and in the papers are just words with no implications to the problems stated in my post. It is a logical fallacy: Bohr's hydrogen atom model is also "consistent" with modern quantum mechanics (and any of its interpretations), but it does not imply that Bohr's quantization rules are "consistent with experiments on Bell's inequality". Same with your sonons, sorry.

No amount of interpretation or "futher study" can reconcile a fluid mechanics model of many electrons with the observed behavior of a helium atom, because there is no room for many-particle coherencies (aka entanglement, configuration interaction, Shcrodinger dynamics in Fock space, quantum correlation or any other name you assign).

Ability to reproduce non-locality of a single-particle wave and "phenomena corresponding to those of quantum mechanics, including single-slit diffraction, double-slit diffraction, quantized energy levels and tunneling through a barrier" does not bring you any closer to resolution of fundamental inconsistencies clearly stated in my post.

Joe said...

I'm also having trouble seeing how such a model can achieve bosonic and fermionic statistics.

Naveen Sharma said...
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