1927: Pilot Wave Interpretation

1Today, the Copenhagen Interpretation is often described as the interpretation supported by the founders of quantum mechanics, although in reality it was primarily a limited consensus of a small group of scientists supported by the weight of authority of Niels Bohr. Therefore, this opening discussion of the various interpretations of quantum mechanics will try to provide a little more historical perspective to the sequence of events, and ideas, which to some extent came to a head in 1927. As we have already covered, in 1924, deBroglie's Phd thesis had extended the wave-particle duality debate to include matter waves, which he would describe in terms of a pilot wave that guides the particle. Subsequently, in 1926, Schrodinger presented his wave formulation of quantum mechanics, which in essence raised a question that everybody has been trying to answer ever since:

What is a quantum wave and what does the wave function represent?

Schrodinger realised that because the wave function included complex numbers, it may not be a tangible object that could be measured. However, given that the square of a complex number results in a real number, it might still be associated with some physical property that could be measured. Initially, Schrodinger had argued that the square of the wave function might correspond to the distribution of charge density at some point in spacetime. Following on from this idea, Schrodinger forwarded an initial interpretation of the wave function as a wave packet that could replace the concept of an elementary particle, e.g. electron, at the lowest level of reality. As such, Schrodinger was suggesting that all elementary particles were an illusion in as much that they only existed in the subjective reality of human perception, while in quantum reality such entities had to exist as waves. However, this interpretation was to quickly run into problems when it was argued that the component superposition waves, required to construct the wave packet, were dispersive.

Note: The issue of wave dispersion underpins a number of important assumptions within quantum mechanics, which is predicated on a relatively simple derivation linked to kinetic energy - see Wave Dispersion for original discussion. This conclusion suggests that the vacuum of space is dispersive, whereas it is generally perceived to be non-dispersive, at least, to electromagnetic waves. However, we might need to better understand the 'physical' structure of Schrodinger's wave-function in order to determine how it propagates, especially as a series of Fourier harmonics - see note after equation [19] in 'A Matter of Perspective' for more details.

Later, it was realised that Schrodinger’s waves would also have to exist in some form of abstracted multi-dimensional space, which did not align to any ‘normal’  perception of physical reality. However, over this same period, Max Born had been studying not only deBroglie’s hypothesis and Schrodinger's wave proposal, but making significant contributions to Heisenberg’s matrix formulation. As a result of this work, Born had come to reject Schrodinger’s physical interpretation of the wave function, which was already beginning to unravel, and started to forward his own alternative interpretation, which would eventually come to challenge one of the most fundamental tenets of classical physics, i.e. determinism from cause to effect. In this context, Born suggested that the square of the wave function was only representative of a probability density. As such, the time-evolution of Schrodinger’s wave equation could only help define the mathematical probability of an elementary particle occupying some point in spacetime.

So what reality, if any, would such an interpretation actually describe?

In many ways, Born’s idea would come to represent the ‘ensemble’ or ’statistical’ interpretation of quantum mechanics, which might also be described as a minimalist interpretation in that it essentially abstained from making any speculative statement concerning the nature of any physical or objective reality, although this position was considered substantial enough to help Born win the 1954 Nobel prize for Physics.

But what of deBroglie’s Pilot wave interpretation?

In the historical context of the 1927 Solvay Conference, DeBroglie tried to present his Pilot Wave  interpretation, although in many respects his idea was caught in the cross fire between Bohr’s emerging Copenhagen interpretation, which encompassed Born’s probability density, and Schrodinger's wave mechanics. As such, deBroglie's initial pilot wave interpretation never ‘took off’ as it was essentially dismissed by virtue of having no backer with the necessary ‘weight of authority’. However, we might try to summarise the salient points of this interpretation for reference:

  • It is first example of a hidden variable theory.
  • It subscribes to realism in that objects exist independently of an observer.
  • It subscribes to non-locality compatible with Bell's theorem.

It is also essentially a deterministic theory in that the position and momentum of a particle is assumed to exist, albeit as hidden variables, such that any observer cannot know the precise value of these variables, which is why uncertainty remains. Overall, an ensemble of particles have an associated matter wave, which collectively evolves as described by the Schrödinger wave equation. However, each particle will follow a deterministic trajectory, guided by the wave function, such that the density of the particles conforms to the magnitude of the wave function. While the particle is guided by the wave function, the latter is not influenced by the particle. While the Pilot Wave interpretation was not widely accepted in the pre-war years, the idea was to be later taken up, in the post-war era, by David Bohm. This aspect will be expanded under the Bohm Interpretation discussion.