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David Bohm (1917-1992) was a very brilliant physicist and that's why people went along with him when he came up with an elegant but more complicated theory to explain the same set of phenomena (normally, more complicated theories are disqualified by the principle known as Ockham's Razor).
Bohm's theory on pilot waves follows on from some original insights by Prince Louis de Broglie (1892-1987), who first studied the wave-like properties of the behaviour of particles in 1924. De Broglie suggested that, in addition to the normal wavefunction of the Copenhagen Interpretation, there is a second wave that determines a precise position for the particle at any particular time. In this theory, there is some 'hidden variable' that determines the precise position of the photon.
Sadly, John von Neumann (1903-1957) wrote a paper in 1932 proving that this theory was impossible. Von Neumann was such a great mathematician that nobody bothered to check his maths until 1966, when John Bell (1928-1990) proved he'd bodged it and there could be hidden variables after all -- but only if particles could communicate faster than light (this is called 'nonlocality'). In 1982 Alain Aspect demonstrated that this superluminal signalling did appear to exist, although David Mermin then showed that you could not actually signal anything. There is still some argument about whether this means very much.
Bohm's theory on pilot waves, was that the second wave was indeed faster than light, and moreover it did not get weaker with distance but instantly permeated the entire universe, acting as a guide for the movement of the photon. This is why it is called a 'pilot wave'. This theory explains the paradoxes of quantum physics perfectly. But it introduces a new faster-than-light wave and some hidden mechanism for deciding where it goes -- to create an 'implicate order'.
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