By studying how photons travel through a double slit, physicists in Canada have now shown that some photons follow “surreal trajectories” that appear to defy the laws of physics. Upon closer inspection, however, the experiment reveals that the behaviour of these rogue photons can be explained using the principle of quantum entanglement. The work has resolved a 25-year-old debate based on an alternative interpretation of quantum mechanics.

In the conventional interpretation of quantum mechanics, the motion of a particle is defined by a wave function that gives the probability of the particle being at a certain place at a certain time. The uncertainty principle means that a precise measurement of the particle’s position at a specific time will result in a large uncertainty in what its momentum is at that time – and vice versa. As a result, the concept of a trajectory in the sense of a unique path followed by an object does not exist in quantum mechanics.

In 1952 David Bohm came up with an alternative interpretation of quantum mechanics in which a particle follows a trajectory that is guided by a “pilot” wave function. The probabilistic nature of quantum mechanics would arise from the fact that the initial conditions of the particle are unknown – this is built into the pilot wave function. A precise measurement of the position of a Bohmian particle, for example, would alter the wave function such that a simultaneous measurement of the particle’s momentum must lie within the bounds of the uncertainly principle.

Surreal paths

In 1992 Berthold-Georg Englert and colleagues argued that under certain circumstances – such as when a particle passes through a double slit – some Bohmian trajectories defied explanation. Dubbed “surreal trajectories”, their assertion sparked a debate in the quantum-physics community as to the validity of Bohm’s approach to quantum mechanics. Now, Aephraim Steinberg and colleagues at the University of Toronto have measured surreal trajectories and showed that they are consistent with quantum theory.

The team used a technique called “weak measurement” to trace out the set of trajectories taken by photons through a double slit. This technique involved a gentle probing of the direction of motion of the photons to build up an understanding of the possible routes taken by photons through the apparatus. Crucially, each measurement is so gentle that it does not have a significant effect on the pilot wave function. (See “In praise of weakness“).

Their “double-slit” experiment begins with the production of a pair of photons that are entangled in terms of their polarization. Photon-1 is then sent into a polarizing beam splitter, which produces two parallel beams – one with horizontal polarization and the other with vertical polarization.

Tiny shift

The researchers also perform a weak measurement on the transverse velocity of photon-1 after it emerges from the slits. This is done by passing the photon through a calcite crystal, which causes a tiny shift in its polarization, which is proportional to its transverse velocity. Using focusable optics, the team was able to measure the transverse velocity at different locations, as the photons travel over a distance of about 5 m. Using this information, Steinberg and colleagues were able to build up a set of trajectories taken by the photons.

Because photon-1 and photon-2 are entangled, a measurement of the polarization of photon-2 will reveal which slit photon-1 passed through. However, when Steinberg and colleagues looked at the set of photon-1 trajectories that should have passed through the lower slit (according to photon-2’s polarization), they found that some of the trajectories appeared to have taken photon-1 through the upper slit – and vice versa. These are the surreal trajectories predicted by Englert and colleagues.

However, closer examination of the data revealed that this apparent surrealism depended upon where along the trajectory the measurements were made. Indeed, Steinberg and colleagues identified cases in which photon-1 begins on a trajectory from the lower slit, but then swerves upward into a trajectory that appears to be from the upper slit. Using a technique called quantum-state tomography, they were able to monitor the polarization of photon-2 during this swerve, and saw its value rotate from horizontal (indicating the lower slit) to vertical (indicating the upper slit). As a result, a measurement on photon-2 at the end of the trajectory gives the “wrong” slit.

Vivid illustration

Steinberg and colleagues believe that the photon’s swerve is thanks to quantum interference that occurs when they emerge from the slits. As well as resolving the surreal-trajectory problem, the experiment also provides a vivid illustration of how a property of one entangled particle – the polarization of photon-2 – can be affected by the trajectory of its distant partner.

Rainer Kaltenbaek of the University of Vienna describes the work as “a beautiful experiment that challenges our everyday thinking”. He adds that it “illustrates one of the central issues that quantum entanglement poses for Bohmians”.

The experiment is described in Science Advances.