# 1927: Pilot Wave Interpretation

Today, 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 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.
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 be studying not only deBroglie’s
hypothesis and *Schrodinger 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.
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
wave mechanics. As such, deBroglie 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 expand under
the *Bohm Interpretation* discussion.