Quantum mechanics, a field which scientists believe explains all natural phenomena, was considered by Nobel Laureate Richard Feynman to be impossible to understand in its entirety. University of Toronto physicists Aephraim Steinberg and Jeff Lundeen have made new developments in the field by resolving a paradox of quantum mechanics. The physicists used a principle called “weak measurement” to prove Hardy’s paradox, which refers to the ability of something to be in two different states at the same time. Schrödinger’s cat is a common example: if a cat is underneath a box, to an onlooker the cat is both alive and dead until the box is opened and someone looks inside.
Hardy’s paradox is based on an experiment in which an electron and a positron (the antiparticle of an electron) are sent along intersecting paths. Although the particles are supposed to annihilate each other when they meet, they don’t. Both particles simultaneously hit their respective sensors when they reach the end of their paths.
After two years of research, Steinberg and Lundeen have proven Hardy’s paradox. Using weak measurement, along with several theoretical tools they developed, they demonstrated that the positron and electron were, in fact, in the annihilation region at the same time. “We realized that a two-photon ‘switch’ we had developed for applications in quantum computing would be precisely the key needed to perform Hardy’s paradox, which had been a seemingly impossible proposal for over ten years,” writes Steinberg.
Quantum particles have a tendency to behave in strange ways. For example, an electron can spin in two directions, or be in two different places at the same time. The particles in the experiment were able to disturb each other without obliteration because they can simultaneously exist in two locations. It was unclear as to how this could occur, as particle detectors were unable to measure the particles’ paths: once in place, the detectors would disturb the particles, leading to inaccurate results. Hardy’s paradox becomes obsolete once measurements are used in the experiment, so it seemed that determining the exact locations of the particles in the overlapping region was impossible.
This is where the concept of “weak measurement” comes into play. The detector used in weak measurement has a pointer that, upon taking a measurement, moves less than the level of uncertainty, leaving the experiment undisturbed. As different physical states of the particles—known as superpositions—are left unobstructed, it is possible to make measurements without interfering with the final results. However, the readings are very inaccurate, so it is necessary to repeat them a number of times, then calculate the average to get a more precise value.
Prior to Steinberg and Lundeen’s discovery, physicists had tried using weak measurement to solve Hardy’s Paradox, but received unusual results. During a number of trials, the electron detector recorded that an average of one electron passed through the annihilation region during a given period of time. The positron detector gave the same result, meaning annihilation should have occurred, as both particles were, at some point, in the same region. Yet measurements taken by an electron-positron pair detector observed zero pairs in the annihilation region. It was known that the pair was in the annihilation region at some point, as both the electron and positron reached their final destinations. However, the detector was unable to identify that a pair had passed through the region. Therefore, the paradox remained intact: the particles arrived at their final destination but were undetectable when they disturbed each other in the annihilation region.
