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# Quantum computers have failed. So now for the science

## Bouncing oil droplets reveal slippery truth behind the magical promises

### Universal possibilities

Speculative theories started to flourish. Are we living in just one of zillions of parallel universes, with new ones being spawned all the time and every possible future being fact somewhere? Might the quantum magic enable processes that work faster than light or even reach backwards in time? Could we use entangled photons to do not just provably secure cryptography, but even teleportation?

Such exciting ideas have attracted many serious researchers as well as science fiction writers, and fired optimism that a quantum computer might be more powerful than a classical one. There have also been many variants on Freedman and Clauser's experiment. But as for using any of them to do real work, no-one's even got to first base. Why might this be?

During the summer of 2013, the physicist Robert Brady and I figured out how the bouncing droplets work. It turns out that you can indeed get quantum phenomena from a classical mechanism, but only when there's a long-range order. In the droplet case, the necessary order comes from the driving oscillation, which means that the wave fields created by droplets bouncing on the same tray are coherent, no matter where on the tray they are. This lets the droplets interact with each other.

For example, there's an inverse-square force of attraction between two droplets bouncing in phase on the same surface; this plays the same role in droplet systems that the electrostatic force plays in quantum electrodynamics. There is also an analogue of the Lorentz contraction, in that the wave field of a moving droplet is foreshortened. Putting the two together, we get an analogue of the magnetic force. We thus have an analogue of Maxwell's equations. Finally, Schrödinger's equation emerges as the modulation of the droplet wave field. So we found an elegant mathematical explanation for a remarkable and beautiful lab experiment that had puzzled the physics community for almost a decade.

People remained sceptical, with many prominent physicists still saying that fluid models were unlikely to solve the quantum mystery (for example, in the *Wired* piece). The quantum-computing people continued to be scornful; we got a bit of abuse from them (with one even suggesting helpfully that professors who utter opinions outside their main field of research should be euthanised).

So could we extend the model from two dimensions to three? Over the Christmas break we found the answer. The key was realising that James Clerk Maxwell had already done most of the work in 1861, in his famous paper *On physical lines of force* which unveiled Maxwell's equations to the world. This was a key catalyst for the second industrial revolution that brought us electric power, radio and much else.

In this paper, Maxwell modelled magnetic lines of force as vortices in a fluid-like medium. The electric field is then the mean force density, while the magnetic vector potential is the mean momentum density. This was inspired in part by Faraday's model, in which light waves propagated along magnetic lines of force. We realised that if we modelled Maxwell's magnetic line of force as what experts in fluid dynamics call a phase vortex, then perturbations propagating along it act just like photons.

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