![](data:image/png;base64,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)
news & views
FLUIDS
Quantum physics dropwise
Classical wave-driven particles can mimic basic quantum properties, but how far this parallel extends is yet to be
seen. Evidence for quantum-like mirages in a system of droplets moving on a fluid surface pushes the analogy into
many-body territory.
Tomas Bohr
I
nterference and superposition of particle
motion was, until recently, believed to
be unique to quantum mechanics. These
concepts are useful for describing extended
fields — or waves — whose effects can be
overlaid at each point in space, but seem
incompatible with localized particles
following well-defined orbits. This belief
was recently shown to be wrong for a class
of wave-driven particles via experiments on
millimetric silicon droplets bouncing on a
silicon bath
1
. Now, writing in Nature Physics,
Pedro Sáenz and colleagues
2
have shown that
a particle in the same system slowly builds
up a spatial probability distribution that is
closely correlated with the average wave field
it excites.
It may seem strange that a fluid
drop can actually ‘bounce’ on a fluid
surface without being swallowed by the
surrounding fluid. But, in fact, a thin
layer of air between the drop and the fluid
persists, constantly being renewed if the
oscillations are sufficiently fast
3
. When
driven violently enough, these drops will
start ‘walking’ across the surface
1
.
Curiously, this is closely connected with
a discovery made by Michael Faraday in
1831
4
. Forcing a dish containing a thin
plane fluid layer into vertical vibrations (for
example, using a violin bow), he noticed that
sufficiently strong vibrations would cause a
pattern of standing waves, which he called
crispations, to form on the fluid surface.
In other words, a fluid layer subjected to
vertical oscillations is intrinsically unstable.
If these oscillations are strong enough, the
fluid will spontaneously generate standing
waves, and just below this threshold the
surface will be extremely sensitive. So a
bouncing drop can create, if not a big splash,
then at least large and long-lived standing
surface waves — still without merging with
the fluid.
Droplets can even be propelled along the
fluid surface by these waves
1
. It is somewhat
counterintuitive that standing waves can
create motion. It is a bit like moving on
caterpillar tracks, sequentially laying down
a new segment in order to move forward. A
drop that happens, by chance, to bounce —
almost touching the surface — at a position
slightly displaced from where it took off
(emitting its last wave), will bounce on a
slightly tilted surface. This imparts a small
horizontal momentum to the drop. The
next bounce will thus create standing waves
centred at a displaced position, and, if the
decay time of these waves is sufficiently long,
this can lead to sustained horizontal motion.
The walking drop depends on its
standing wave for its motion and the wave
exists only because of the droplet. So the
particle and the wave form an inseparable
unit akin to the quantum description of
particles — in particular, the ‘pilot waves’
introduced by de Broglie in 1924
5
just prior
to the discovery of quantum mechanics and
triggering its wave mechanical formulation.
How far can this analogy be taken?
As yet, we do not know. One of the first
striking observations with walking droplets
was spatial discretization. Placing the
vibrator and the walking drop on a rotating
table produces a system that closely
imitates a charged particle circulating
magnetic field lines
6
. Indeed, the walker’s
motion is changed from rectilinear to
circular, and, surprisingly, only certain
orbits are allowed — just like in the Bohr
model of the hydrogen atom. Replacing
Planck’s constant by the wavelength of
the Faraday standing waves multiplied
by the mass and velocity of the drop, one
gets a sequence of radii matching the
Bohr–Sommerfeld quantization rules, the
so-called old quantum theory preceding
quantum mechanics proper. The full
quantum mechanical treatment gives
quantized orbits with similar mean radius,
but the details are different, because the
eigenstates do not correspond to well-
defined orbital radii.
To get closer to the heart of quantum
mechanics and challenge the statistical
‘Copenhagen interpretation’, one can use
wave-driven particles to imitate individual
quantum processes in the hope of obtaining
the ‘realist’ model of quantum mechanics
that would have made Einstein and many
others so happy. Thus one should be able
to describe particles in a superposition of
eigenstates, like an entangled pair, or like
an electron or a photon passing through
the double-slit experiment. Indeed,
evidence for ‘quantum’ interference has
already been seen in a droplet version of
the double-slit experiment
7
, even though
one can easily observe through which slit
the droplet passes, as part of its wave field
can go though the other slit and create
interference (Fig.1). This, however, is not
correct:obviously walking droplets can be
influenced by their own wave field or that of
another droplet, but quantum interference is
something very special.
To determine the quantum probability
amplitude of going from one point of
measurement to another, all paths between
them have to be taken into account, each
contributing a probability amplitude
determined by the classical action for the
given path. In the drop experiments that is
Fig.1 | The walking droplet double-slit
experiment. The double-slit experiment became
emblematic of the interpretation of quantum
mechanics through the discussions between Bohr
and Einstein in 1927. A ‘walking droplet’ is seen on
its way across the surface of a shallow vibrating
layer of silicon oil. The triangular droplet emitter,
the barriers and the two rectangular slits can
be seen beneath the fluid surface. The walking
droplets closely resemble quantum particles
driven by a ‘pilot wave’, but how far the analogy
can be taken is presently unknown. Reproduced
from ref.
8
, APS.
NATURE PHYSICS | www.nature.com/naturephysics
© 2017 Macmillan Publishers Limited, part of Springer Nature. All rights reserved.