Blog for May 2026

18th May 2026 - quantum reality restored

This blog is written in Cornwall, at a location where generation after generation of my family have taken their holidays; it is a place full of wonderful memories of my grandparents, my mother and father, my uncle and aunt, my cousin, my brothers and their families, and my own wonderful family. It is a place of great beauty, of crushing waves, of sandy beaches, of stunning sunsets, and the perfect place to relax and unwind reflecting upon the topic of bringing reality to quantum measurements.

So we left the previous blogs with the tricky question of whether there is a reality to a quantum particle before it is detected; the quantum measurement problem in quantum mechanics. We had a single photon or a single electron passing through a double slit experiment, and we observed an interference pattern being formed after many of these particles had passed through; they had somehow exhibited wave-like behaviour, even though they were sent through one at a time. They seemed to have passed through both slits simultaneously as a single particle?

From the previous blog, the Bell experiment had shown that quantum mechanics is incompatible with any local realistic theory. How do we find reality in this wave particle, non-local world?

A standard interpretation of quantum mechanics, the Copenhagen interpretation, says that there is no reality to a quantum particle before it is detected, and that the quantum wavefunction, ψ(x), is just a function that allows us to calculate the probabilities of measurement outcomes; these measurement probabilities are given by the Born Rule (| ψ(x) |²). Are we to give up on reality after all?

I am a realist, and I believe there is a reality to these quantum particles, so how to reconcile this apparently impossible conflict?

There are many attempts at resolving this issue: e.g. the many world interpretation, spontaneous wave function collapse theories, quantum decoherence, but they all introduce new complexities, or new parameters, unhelpful to this particular realist; it can't be that complicated can it?

Incredibly, a solution to this issue was proposed by deBroglie, during the 1920s, and independently developed by David Bohm in the 1950s: it is know as the pilot wave theory, and it solves the reality issue with no new parameters needed!

The pilot wave theory is a nonlocal hidden variable theory, and it is fully compatible with all the predictions of quantum mechanics. It was largely overlooked due to work undertaken by the great John von Neumann who had published a proof that forbid such theories; his reputation was such that the pilot wave theory, and other similar theories, were largely ignored. His proof, however, has been shown to be incorrect!

So what is this pilot wave theory?

In the pilot wave theory, the quantum particle has an actual position and moves through time guided by a pilot wave, which is based around the quantum wave function ψ(x); the wave function represents the time evolution of the quantum system, satisfies Schrodinger's equation, and contains all the information available about the system, including the particle's position and momentum, albeit the initial conditions are not precisely defined due to the uncertainty principle.

Unlike a classical field, the wavefunction ψ(x) does not represent a physical quantity at each point in space and time. Instead the quantum wavefunction is used with Born's rule (| ψ(x) |²) to calculate the probabilities of measurement outcomes at different points in space and time.

Pilot wave theory naturally describes the state of a particle going through a double slit experiment, and naturally predicts interference. The particle has a deterministic trajectory, and the probabilities given by the Born Rule arise from our ignorance of the initial conditions of the particle; this last part is very important, as no new parameters are needed to explain the apparent ad hoc assumption of the Born Rule to standard quantum mechanics.

The initial conditions of the particle are uncertain, and typically are described by the Born rule; but if different assumptions are made with respect to this uncertainty, it can be shown that the uncertainty will eventually evolve into a distribution consistent with the Born Rule, with no new parameters needed.

The pilot wave theory is non-local meaning that the pilot wave can instantaneously affect the particle due to influences at arbitrary distances; consequently pilot wave theory does not abide with local momentum and energy conservation, but this would be expected of a non-local theory. This non-locality is what allows the pilot wave theory to reproduce all the predictions of quantum mechanics, including those that violate Bell's inequality. You can chart the trajectory of a particle through pilot wave theory as it makes its way to a screen having passed through one of the two slits and an interference pattern will result after many particles have passed through this system.

In the double slit experiment, the particle passes through one slit, but the pilot wave passes through both slits and interferes with itself, guiding the particle to a location on the screen that is consistent with the interference pattern; but you can never "see" these particles before measurement, or use their location to pass information faster than the speed of light, so it is still compatible with this aspect of relativity theory.

So the measurement problem is resolved by pilot wave theory but at the expense of being non-local. If it had not been non-local, it would not have been able to reproduce the predictions of quantum mechanics!

Importantly, the non-local aspects of quantum physics can not be used to pass information faster than the speed of light, but by definition it does violate the principle of locality, which is a key principle of relativity; there should not be a preferred reference frame for the laws of physics.

So to summarise, the pilot wave theory provides a realist interpretation of quantum mechanics, is deterministic and reversible, provides an explanation of the Born rule without the need for new parameters, and is completely compatible with all the predictions of quantum mechanics; it largely resolves the measurement problem in quantum mechanics, but at the expense of being non-local; which defines a preferred frame and particle movements do not locally conserve momentum and energy (on average they do, but not locally).

So what are the remaining issues: the non-locality of pilot wave theory defines a preferred reference frame and is therefore incompatible with relativity (although, provided quantum equilibrium is maintained one cannot directly observe the non-locality, or send signals faster than light); rather like the many worlds interpretation, a large number of empty ghost branches remain following measurement.

Interestingly, Newtonian physics is also a non-local theory and like quantum physics was used to accurately calculate the dynamics of particle behaviour without resolving this non-local issue. It took Einstein to resolve this non-local issue in Newtonian physics, through his two relativistic theories. At small velocities relativity reduces to Newtonian physics.

We are still waiting to find the equivalent for quantum physics: i.e. a more fundamental theory (like relativity compared with Newtonian physics) that has no non-local behaviour (and is therefore compatible with the principle of relativity), but which reduces to the non-local theory of quantum physics at the appropriate scale.

A lesson from Relativity theory is that it would have been very difficult to come up with relativity theory by thinking in the language of Newtonian physics. Instead a higher set of principles (i.e. the laws of physics are the same in all frames of reference, and the speed of light is constant in all frames of reference, and gravitational acceleration is indistinguishable from acceleration due to other forces) was required which under the correct assumptions, reduced to Newtonian physics; this is an example of a relativistic theory that reduces to a non-relativistic theory at the relevant scale, and it is likely that a similar approach will be required to find the more fundamental theory that unites quantum physics and relativity theory.

We will likely not discover the more fundamental theory that unites quantum physics and relativity theory by thinking in the language of quantum physics. We must think of a new framework with a higher set of principles: perhaps something that starts with information as the most fundamental quantity, or something that starts with interactions as the most fundamental quantity, which can be formulated into a relativistic quantum theory, that reduces to the non-local theory of quantum mechanics at the relevant scale.

In terms of philosophy, this suggests that we need to rethink our fundamental assumptions about the nature of reality. The local reality that we perceive around us has to be a derived or emergent concept, from a more fundamental theory or framework. The reality that we perceive is not fundamental, but is a derived or emergent concept from a more fundamental theory or framework. This is a profound shift in our understanding of local reality, and it has implications for how we think about the nature of existence and our place in the universe.

All this from observing photons in a double slit experiment; and in my case, from observing the waves collapsing on the beach in Cornwall, watching the apparently stochastic collapse of sand along the water channels from the cliffs to the sea, and waiting for the signal from the sun to travel at the speed of light to warm the shore.