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and mathematical foundations of what was then a most unconventional theory'.2 As the audience drifted away after the lecture, Einstein invited Heisenberg back to his apartment. During the half-hour stroll to Haberlandstrasse, Einstein asked Heisenberg about his family, education and early research. It was only when they were comfortably seated in his apartment that the real conversation began, recalled Heisenberg, as Einstein probed 'the philosophical background of my recent work'.3 'You assume the existence of electrons inside the atom, and you are probably right to do so', said Einstein. 'But you refuse to consider their orbits, even though we can observe electron tracks in a cloud chamber. I should very much like to hear more about your reasons for making such strange assumptions.'4 This was just what he had hoped for, a chance to win over the 47-year-old quantum master.

'We cannot observe electron orbits inside the atom,' replied Heisenberg, 'but the radiation which an atom emits during discharges enables us to deduce the frequencies and corresponding amplitudes of its electrons.'5 Warming to his theme, he explained that 'since a good theory must be based on directly observable magnitudes, I thought it more fitting to restrict myself to these, treating them, as it were, as representatives of the electron orbits'.6 'But you don't seriously believe,' Einstein protested, 'that none but observable magnitudes must go into a physical theory?'7 It was a question that struck at the very foundations on which Heisenberg had constructed his new mechanics. 'Isn't that precisely what you have done with relativity?' he countered.

A 'good trick should not be tried twice', smiled Einstein.8 'Possibly I did use this kind of reasoning,' he conceded, 'but it is nonsense all the same.' Although it might be heuristically useful to bear in mind what one has actually observed, in principle, he argued, 'it is quite wrong to try founding a theory on observable magnitudes alone'. 'In reality the very opposite happens. It is the theory which decides what we can observe.'9 What did Einstein mean?

Almost a century before, in 1830, the French philosopher Auguste Comte had argued that, while every theory has to be based on observation, the mind also needs a theory in order to make observations. Einstein tried to explain that observation was a complex process, involving assumptions about phenomena that are used in theories. 'The phenomenon under observation produces certain events in our measuring apparatus', said Einstein.10 'As a result, further processes take place in the apparatus, which eventually and by complicated paths produce sense impressions and help fix the effects in our consciousness.' These effects, Einstein maintained, depend on our theories. 'And in your theory,' he told Heisenberg, 'you quite obviously assume that the whole mechanism of light transmission from the vibrating atom to the spectroscope or to the eye works just as one has always supposed it does, that is, essentially according to Maxwell's law. If that were no longer the case, you could not possibly observe any of the magnitudes you call observable.'11 Einstein continued to press: 'Your claim that you are introducing none but observable magnitudes is therefore an assumption about a property of the theory that you are trying to formulate.'12 'I was completely taken aback by Einstein's attitude, though I found his arguments convincing', Heisenberg later admitted.13

While Einstein was still a patent clerk he had studied the work of the Austrian physicist Ernst Mach, for whom the goal of science was not to discern the nature of reality, but to describe experimental data, the 'facts', as economically as possible. Every scientific concept was to be understood in terms of its operational definition – a specification of how it could be measured. It was while under the influence of this philosophy that Einstein had challenged the established concepts of absolute space and time. But he had long since abandoned Mach's approach because, as he told Heisenberg, it 'rather neglects