3.4.5.2 Pilot Wave Theory
As we mentioned in section 4.4.1, Louis de Broglie proposed in 1924 that all matter particles have the nature of waves, which was confirmed after three years with experiments on electrons diffraction. In 1927, De Broglie then proposed a new concept to explain this weird behavior, the pilot wave theory in which physical particles are associated with waves which evolve according to the Schroedinger equation. After close collaboration, Schroedinger developed his wave equation for de Broglie’s theory. Therefore, each particle follows a deterministic trajectory, which is guided by the wave-function; collectively, the density of the particles conforms to the magnitude of the wave-function. Therefore, the wave-function is not influenced by the particle, and it can exist as an empty mathematical equation.
With encouragement by Einstein, in 1952, David Bohm (1917-1992) developed this concept further and suggested a complete interpretation extended to incorporate a consistent theory of measurement, and also to address other criticisms of de Broglie’s original idea. The resulting De Broglie-Bohm interpretation is, therefore, both deterministic and realistic, since its concepts exist independently of the observer. Additionally, it is a hidden variable theory because the positions and momenta of the particle are considered to be the hidden variables. The observer doesn’t know the precise value of these variables, and also cannot know them with certainty. because any measurement must inevitably disturb the system.
Therefore, the pilot wave concept avoids many troublesome notions such as wave-particle duality, instantaneous wave-function collapse and the paradox of Schroedinger’s cat, but it introduces non-locality that is implicit in the non-relativistic formulation of Quantum Mechanics, and uses it to satisfy Bell’s theorem that introduced in 1964. However, these nonlocal effects can be shown to be compatible with the no-communication theorem, which prevents using them for superluminal communication, and so it is empirically compatible with the principles of Relativity.
More advanced Bohmian mechanics was later developed to include most of the further extensions past the spin-less version of Bohm. While de Broglie-Bohm theory has Lagrangians and Hamilton-Jacobi equations as a primary focus and backdrop, with the icon of the quantum potential, Bohmian mechanics considers the continuity equation as primary and has the guiding equation as its icon. They are mathematically equivalent in so far as the Hamilton-Jacobi formulation applies, i.e., spin-less particles. All of non-relativistic Quantum Mechanics can be fully accounted for in this theory.