Quantum_ Einstein, Bohr and the Great Debate About the Nature of Reality - Manjit Kumar [172]
Whereas the wave function in quantum mechanics is an abstract wave of probability, in the pilot wave theory it is a real, physical wave that guides particles. Just as an ocean current carries along a swimmer or a ship, the pilot wave produces a current that is responsible for the motion of a particle. The particle has a well-defined trajectory determined by the precise values of position and velocity that it possesses at any given time but which the uncertainty principle 'hides' by preventing an experimenter from measuring them.
On reading Bohm's two papers, Bell said that he 'saw the impossible done'.11 Like almost everyone else, he thought that Bohm's alternative to the Copenhagen interpretation had been ruled out as impossible. He asked why no one had told him about the pilot wave theory: 'Why is the pilot wave picture ignored in textbooks? Should it not be taught, not as the only way, but as an antidote to the prevailing complacency? To show that vagueness, subjectivity, and indeterminism, are not forced on us by experimental facts, but by deliberate theoretical choice?'12 A part of the answer was the legendary Hungarian-born mathematician John von Neumann.
The eldest of three brothers, the Jewish banker's son was a mathematical prodigy. When his first paper was published at eighteen, von Neumann was a student at Budapest University but spent most of his time in Germany at the universities of Berlin and Göttingen, returning only to take his exams. In 1923 he enrolled at the ETH in Zurich to study chemical engineering after his father insisted that he have something more practical to fall back on than mathematics. After graduating from the ETH and gaining a doctorate from Budapest in double-quick time, von Neumann became at 23 the youngest-ever privatdozent appointed by Berlin University in 1927. Three years later he began teaching at Princeton University and in 1933 joined Einstein as a professor at the Institute for Advanced Study, remaining there for the rest of his life.
A year earlier, in 1932, the then 28-year-old von Neumann wrote a book that became the quantum physicist's bible, Mathematical Foundations of Quantum Mechanics.13 In it he asked whether quantum mechanics could be reformulated as a deterministic theory by the introduction of hidden variables, which, unlike ordinary variables, are inaccessible to measurement and therefore not subject to the restrictions imposed by the uncertainty principle. Von Neumann argued that 'the present system of quantum mechanics would have to be objectively false in order that another description of the elementary processes than the statistical one may be possible'.14 In other words, the answer was 'No', and he offered a mathematical proof that outlawed the 'hidden variables' approach that Bohm would adopt twenty years later.
It was an approach with a history. Ever since the seventeenth century, men like Robert Boyle had studied the various properties of gases as their pressure, volume and temperature were varied, and had discovered the gas laws. Boyle found the law describing the relationship between the volume of a gas and its pressure. He established that if a certain quantity of a gas was kept at a fixed temperature and its pressure was doubled, its volume was halved. If the pressure was increased threefold, then its volume was reduced to a third. At constant temperature, the volume of a gas is inversely proportional to the pressure.
The correct physical explanation of the gas laws had to wait until Ludwig Boltzmann and James Clerk Maxwell developed the kinetic theory of gases in the nineteenth century. 'So many of the properties of matter, especially when in gaseous form, can be deduced from the hypothesis that their minute parts are in rapid motion, the velocity increasing