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Robert Brady - Home

[current research topic]

I am an industrial research fellow at the Computer Laboratory.


Emergent quantum mechanics It has become popular for undergraduates to reproduce these simple experiments showing quantum-like diffraction, tunnelling and energy levels in a classical fluid. These experiments seem to fly in the face of conventional quantum theory. Ross Anderson and I reconcile these experiments with the theory. See this introductory presentation for undergraduates.

In particular we show that classical fluid mechanical systems violate Einstein's separability principle and consequently they violate Bell's inequality presentation paper more.


My PhD [contents 1 2 3 figs 4 ] was in theoretical and experimental superconductivity at the Cavendish Laboratory in Cambridge. I did a postdoc at the National Bureau of Standards in Boulder, Colorado and became a fellow of Trinity College, Cambridge.

By calculating how the phase of the superconducting order parameter [defined in Brian Josephson's thesis] transforms as the superconductor accelerates and rotates, I established a quantitative relationship with the electromagnetic field [pdf] and a correction to the London moment of a rotating superconductor [pdf], which was a candidate at the time for measuring the ratio of charge to mass of the electron. I predicted a new effect which could be used to make a superconducting gyroscope with no moving parts, published here. Subsequently Jim Zimmerman and I measured it experimentally [pdf and figures]. In principle the effect could be used to measure gravitational fields and waves [pdf] but the sources of noise are likely to make the apparatus impracticable.


Working with Robin Ball, I electrolysed copper sulfate solution and measured the current as a function of time. The results were published in Nature. As copper deposits on the cathode, any protrusions grow faster, resulting in a chaotic instability. This is why the copper electrodeposit is black -- something I remembered from school.

It turns out that the mass of copper within radius r of a point cathode is proportional to rD. We could measure D because the mass of copper is proportional to the total charge transferred, and the radius is proportional to the current. The experimental result was D = 2.43 ± 0.03, in agreement with previous simulation work.

Subsequently I wrote a computer progaram to model this behaviour. This briefly held the record for the largest simulations (we were using a timeshare on an IBM and our competitors were using a supercomputer -- we lost this crown when my algorithm was adopted on these computers). The program was used in papers together with Robin Ball, Giuseppe Rossi and Bernard Thompson [1 2 3 4].

Computer science

Computer optimisation algorithms often reach an impasse. A typical example is the travelling salesman problem, where the computer is asked to find the shortest route through, say, 100 cities. You start with a route (any route), and successively see if a small random change reduces the length -- if it does, you adopt it, otherwise you reject it.

Such algorithms do not perform very well. For example, if the computer has found a good route round England but a poor route around Scotland, it must temporarily make the English route longer in order to improve the Scottish route - a problem which it is computationally expensive to overcome.

Biological evolution encounters the same problem. But if you can out-evolve your competitors, you will win in the long run. There have been billions of years to solve this problem - and the answer is sex. Learning from this, I created multiple solutions to the travelling salesman problem, and performing a 'cross-over'. In the above example, a solutions with a good route round England would be crossed with others, some of which would have a good route round Scotland. I beat the then-fastest algorithms for the travelling salesman problem. The paper was published in Nature.

Together with Ross Anderson and Robin Ball, I demonstrated that computer programmers face the worst of all possible worlds when it comes to bugs: Murphy's law, the fitness of evolving species, and the limits of software reliability.

The irrotational motion of a compressible inviscid fluid

My current research topic combines my experience in quantum effects and in computing. See this paper. The consequences for quantum computing are set out in a paper with Ross Anderson here.

There is a separate page on this topic with links to animations and presentations.

Industrial computing

I founded Brady plc, which employs 250 people and is listed on the London stock exchange. We supply software covering the supply chain and financing of commodity extraction, processing and recycling. Contact the company directly if you would like to know about our graduate internship and recruitment programme.

Other activities

I help teach the lab's second-year software engineering course and the Judge Business School's entrepreneurship course.

I mentor technology startups and am the treasurer of the Cambridge Angels. I am a director of Cambridge Intellectual Property Ltd, which analyses patents, and I am chairman of Undo Software Ltd, which supplies reverse debugging tools that allow you to execute a program backwards until you reach a breakpoint.

I play the game of real tennis (which is the game they played before they invented lawn tennis) with a handicap of 63.

By default, when I post a paper here I license it under the relevant Creative Commons license, so you may redistribute it with attribution but not modify it. I may subsequently assign the residual copyright to an academic publisher.

Contact details

University of Cambridge Computer Laboratory
JJ Thomson Avenue
Cambridge CB3 0FD, England

Tel: +44 7770 75 66 35