A Classical Quantum Conundrum – When To Be or Not To Be… a Wave?

An animation showing the formation of the typical wave-particle duality interference pattern.Wav-icles?

Ever since French physicist Louis de Broglie first described the wave-particle duality in 1926, scientists have struggled to come to terms with this strange particularity of our natural World when observed at the quantum level.  Waves can be particles, and particles can be waves.  But are entities waves AND particles all at the same time?

For almost a century now, “reality” has been a rather esoteric concept.  Because the laws of Quantum Physics seem to suggest that particles spend much of their time in a ghostly state, lacking in even the most basic properties, such as a definite location, and instead existing everywhere and nowhere at once.  Quite frankly, this idea would make anyone scratch their head!  But there’s even more to it because you see…  Only when a particle is measured does it suddenly materialise, appearing to pick its position as if by a roll of the dice!

This idea that Nature is inherently probabilistic, that particles have in fact no hard properties, merely “likelihoods”, until they are actually observed or measured, is directly implied by the standard equations of quantum mechanics.  However, a set of surprising experiments involving fluid mechanics has revived the old skepticism about that particular worldview.

And the bizarre results have been fuelling interest in an almost forgotten version of Quantum Mechanics, one that never gave up the idea of a single, concrete reality.

The nature of wave-particle duality seems decidedly impossible to understand, precisely because…  Wait for it!  Someone has yet to observe “something” being both a particle and a wave in the Physical World!  At least, that is what physicists used to think…


The “Copenhagen Interpretation”

A diagram explaining the formation of a double-slit interference pattern.
When light illuminates a pair of slits in a screen (left), the two overlapping wavefronts cooperate in some places and cancel out in between, producing the well-known pattern. This interference pattern appears even when particles are shot toward the screen one by one, as if each particle passes through both slits at once, like a wave.

The received interpretation of Quantum Mechanics holds that particles play out all possible realities simultaneously.  Thus, each particle is represented by a “probability wave” displaying these possibilities.  The wave collapses to a definite state only when the particle is observed (or measured).

However, the equations of Quantum Mechanics do not explain how a particle’s properties become tangible at the moment of measurement, nor do they explain how reality picks which form to take at such times.

Yet the calculations work.

A classic experiment in Quantum Mechanics that demonstrates the probabilistic nature of reality involves firing a particle beam (electrons) towards a pair of slits in a screen.  So far, so simple.  When no one keeps track of each electron’s trajectory, the electron beam seems to pass through both slits simultaneously, and over time it creates a wavelike interference pattern of bright and dark stripes on the other side of the barrier.

Now, here is the odd thing about matter.  When a detector is placed in front of one of the slits, its measurement causes the particles to lose their wavelike omnipresence, collapse into definite states, and travel through either one slit or the other.  At this point, the interference pattern vanishes!

The double-slit experiment is at the crux of Quantum Mechanics, and it is impossible to explain in any classical way.

The probabilistic version of the theory, championed by Danish physicist Niels Bohr (1885-1962), involves a single equation that represents likely and unlikely locations of particles as the peaks and troughs of a wave.  Bohr interpreted this probability-wave equation as a complete definition of the particle.  But French physicist Louis de Broglie (1892-1987) urged his colleagues to use two equations: one equation to describe a real, physical wave; another equation to link the trajectory of an actual, concrete particle to the variables in that wave equation, as if the particle interacts with, and is propelled by the wave rather than being defined by it.

As de Broglie explained to the illustrious physicists present at the 1929 Solvay Conference, his “pilot-wave” theory of Quantum Mechanics made the same predictions as Bohr’s probabilistic formulation, but without the ghostliness or mysterious collapse.


De Broglie’s Quantum Dynamics

In Louis de Broglie’s pilot-wave scenario, each electron passes through just one of the two slits, but it is influenced by a pilot wave that splits and travels through both slits.  Like flotsam in a current, the particle is drawn to the places where the two wavefronts cooperate, and does not go where they cancel out.

De Broglie explained this beautifully in his seminal Nobel Lecture of 12th December 1929:


The Wave Nature of the Electron

A black and white photograph of Louis de Broglie.
Aged just 37, Prince Louis de Broglie became the 1929 Nobel Prize for Physics Laureate “for his discovery of the wave nature of electrons”.  Just the start of a long series of distinguished awards that followed…

[…] I was attracted to theoretical physics by the mystery enshrouding the structure of matter and the structure of radiations, a mystery which deepened as the strange quantum concept introduced by Planck in 1900 in his research on black-body radiation continued to encroach on the whole domain of physics.

[…] For a long time physicists had been wondering whether light was composed of small, rapidly moving corpuscles.  This idea was put forward by the philosophers of Antiquity and upheld by Newton in the 18th Century.  After Thomas Young’s discovery of interference phenomena and following the admirable work of Augustin Fresnel, the hypothesis of a granular structure of light was entirely abandoned and the wave theory unanimously adoptedThus the physicists of last century spurned absolutely the idea of an atomic structure of light.  Although rejected by optics, the atomic theories began making great headway not only in chemistry, where they provided a simple interpretation of the laws of definite proportions, but also in the physics of matter where they made possible an interpretation of a large number of properties of solids, liquids, and gases.  In particular they were instrumental in the elaboration of that admirable kinetic theory of gases which, generalised under the name of statistical mechanics, enables a clear meaning to be given to the abstract concepts of thermodynamics.

[…] Some thirty years ago, physics was hence divided into two: firstly the physics of matter based on the concept of corpuscles and atoms which were supposed to obey Newton’s classical laws of mechanics, and secondly radiation physics based on the concept of wave propagation in a hypothetical continuous medium, i.e. the light ether or electromagnetic ether.  But these two physics could not remain alien one to the other; they had to be fused together by devising a theory to explain the energy exchanges between matter and radiation – and that is where the difficulties arose.  While seeking to link these two physics together, imprecise and even inadmissible conclusions were in fact arrived at in respect of the energy equilibrium between matter and radiation in a thermally insulated medium: matter, it came to be said, must yield all its energy to the radiation and so tend of its own accord to absolute zero temperature!

A black and white photograph taken at the Solvay Conference in 1927 - The picture shows a number of physics giants, including De Broglie and Einstein.
Louis-Victor de Broglie (centre) attending the 5th Solvay Conference in 1927, with only a handful of the Physics legends who were present on that day: E. Schrödinger, E. Verschaffelt, W. Pauli, W. Heisenberg, A. H. Compton, M. Born, Ch.-E. Guye, P. Langevin and of course, Albert Einstein.

[…] “A wave must be associated with each corpuscle and only the study of the wave’s propagation will yield information to us on the successive positions of the corpuscle in space”.  In conventional large-scale mechanical phenomena, the anticipated positions lie along a curve which is the trajectory in the conventional meaning of the word.  But what happens if the wave does not propagate according to the laws of optical geometry, if, say, there are interferences and diffraction?  Then it is no longer possible to assign to the corpuscle a motion complying with classical dynamics, that much is certain.  Is it even still possible to assume that at each moment the corpuscle occupies a well-defined position in the wave and that the wave in its propagation carries the corpuscle along in the same way as a wave would carry along a cork?

[…] Thus to describe the properties of matter as well as those of light, waves and corpuscles have to be referred to at one and the same time.  The electron can no longer be conceived as a single, small granule of electricity; it must be associated with a wave and this wave is no myth; its wavelength can be measured and its interferences predicted.  It has thus been possible to predict a whole group of phenomena without their actually having been discovered.  And it is on this concept of the duality of waves and corpuscles in Nature, expressed in a more or less abstract form, that the whole recent development of theoretical physics has been founded and that all future development of this science will apparently have to be founded.


A photograp showing a "walker" observed in the Couder-Fort experiment of 2006.
A photograph of the Couder-Fort experiment lit with diffuse light showing the wave pattern as the walker crosses the aperture. The droplet is seen bouncing through one slit, while its trajectory is deflected by the interference of the reflected waves from two slits. The picture was taken at a time when the trajectory, initially perpendicular to the aperture, was deflected by the interference with reflected waves.  Source: Couder-Fort, 2006

De Broglie could not predict the exact place where an individual particle would end up, since pilot-wave theory predicts only the statistical distribution of outcomes (bright and dark stripes), but neither could Bohr’s version of events.

Bohr claimed that particles do not have definite trajectories, while de Broglie argued that they do, but that we cannot measure each particle’s initial position well enough to deduce its exact path.  In principle, the pilot-wave theory is deterministic.  The future evolves dynamically from the past, so that, if the exact state of all particles in the Universe were known at any given instant, their states at all future times could theoretically be calculated.

From this point on, that much was clear…  Erm!

Along came Yves Couder and Emmanuel Fort who discovered a rather odd phenomenon in 2005.  The pair from Paris Diderot University began to study what happens when you release an oil droplet onto the surface of an oil bath, placed on a vibrating surface.

In their ground-breaking experiment, the researchers used the bouncing-droplet experiment setup to demonstrate single-slit and double-slit interference.  They discovered that when a droplet bounces toward a pair of openings in a dam-like barrier, it passes through only one slit or the other, while the pilot wave passes through both.


The Pilot-Wave Dynamics of Walking Droplets

An image showing the Probability Distribution of the walker, and Faraday wave.
The probability distribution of the walker in the circular corral, which corresponds closely to the Faraday wave mode of the cavity.

A droplet bouncing on a vertically vibrated bath can become coupled to the surface wave it generates.  The droplet thus becomes a “walker” moving at constant velocity on the interface.

The droplet gently sloshes the liquid with every bounce.  At the same time, ripples from past bounces affect its course.  The droplet’s interaction with its own ripples forms what is known as a pilot wave.

This interaction causes the droplet to exhibit a behaviour that was previously thought to be peculiar to elementary particles – including the behaviours seen as evidence that these particles are spread throughout space like waves, without any specific location, until they are measured.

The motion of these walkers was investigated as they passed through one or two slits limiting the transverse extent of their wave.  In both cases, a given single walker seems randomly scattered.  However, diffraction or interference patterns are recovered in the histogram of the deviations of many successive walkers.  The similarities and differences of these results with those obtained with single particles at the quantum scale are discussed in the paper.


The Nature of Reality…

Four photographs showing "walkers" in rotation around each other. Source: CNRS
Two “walkers” in rotation. From a to c, side views of the bouncing droplets at successive instants of time. And d, top view of the system. Source: Yves Couder/CNRS

Physicists have long realised that quantum-sized particles appear to do things that macroscopic objects do not do: they can tunnel through barriers, spontaneously arise or annihilate, or occupy discrete energy levels.  When guided by pilot waves, they found that the oil droplets are displaying quantum-like features.

Repeated trials show that the overlapping wavefronts of the pilot wave steer the droplets to certain places and never to locations in between – an apparent replication of the interference pattern in the quantum double-slit experiment that Feynman described as “impossible to explain in any classical way.”

And just as measuring the trajectories of particles seems to “collapse” their simultaneous realities, disturbing the pilot wave in the bouncing-droplet experiment destroys the interference pattern.

Droplets also seem to:

  • “tunnel” through barriers,
  • orbit each other in stable “bound states”, and
  • exhibit properties analogous to quantum spin and electromagnetic attraction.


Four diagrams showing the Pilot Wave Dynamics of the "walker" in a circular corral.
The trajectory of a droplet “walking” in a circular corral, colour coded according to speed. Note the correlation between position and speed, which results in the wavelike statistics.  (Source: Math.MIT.edu)

When confined to circular areas called corrals, they form concentric rings analogous to the standing waves generated by electrons in quantum corrals.  They even annihilate with sub-surface bubbles, an effect reminiscent of the mutual destruction of matter and antimatter particles.

In this experiment, a very important feature needs to be  pointed out.  We can detect these “pilot waves” that are steering the droplets.  And this is a fundamental point here because Quantum Mechanics tells us these pilot waves have NEVER been detected.  That is a very significant difference, and the main reason why the pilot-wave model has not caught on!

If there is physical evidence for it, physicists will adapt the model.  Yet until now, there are no deviations between the predictions of the conventional Quantum Mechanics versus Pilot-Wave Dynamics.  So, how can one tell which one to accept beyond just a matter of taste and personal preferences?

At best, it is an analogous situation to the pilot-wave picture.  Not an identical situation.  The “discovery” of magnetic monopole in the spin-ice system did not turn elementary particle physics and ElectroMagnetism upside down, because while these “monopoles” have the same characteristics as the bare monopoles, they are only analogous to them.  It is not the same thing.



The idea that pilot waves may serve to explain the peculiarities of particles dates back to the early days of Quantum Mechanics.  De Broglie was there first.

Until there is direct evidence of such pilot-wave, or until there is evidence supporting the prediction of pilot-wave but not the regular, old-fashioned Quantum Mechanics theory, we have no strong evidence to support or falsify either one.  And it is irrelevant how many droplets and wave experiments one performs.

So, that’s it?

Do we just have to accept the reality of the wave-particle?

And the idea that even close up, at macroscopic or quantum level, radiation and matter are and behave as one?