A centuries-old fundamental law of physics called the principle of least action has been demonstrated using quantum objects for the first time.
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| Measuring quantum properties like the wave function of photons of light has allowed researchers to test the principle of least action at a quantum level Hui Yan |
“A physicist’s ultimate dream is to write the secrets of the entire universe on a small piece of paper and the principle of least action must be on the list,” says Shi-Liang Zhu at the South China Normal University. “Our ambition was to ‘see’ [the principle] in a quantum experiment.”
Zhu and his colleagues have now done so using quantum particles of light, or photons.
The principle of least action generally requires that objects behave simply and efficiently, like light travelling between two points in a piece of glass along the quickest path. According to the principle, to determine what trajectory any object will take between two points in space and time, you need to calculate a quantity called action, which is often related to energy and momentum. You then mathematically minimise it – the trajectory that has the minimal action is the one the object will end up taking.
For ordinary objects, this is easily verified because their trajectories can be unambiguously recorded, but this isn’t true in the quantum realm, says team member Hui Yan, also at the South China Normal University.
Odd properties of quantum objects, like simultaneously being particles and waves, typically make it impossible to determine their exact trajectories. This is why the quantum version of the principle of least action is formulated in terms of quantum wave functions and propagators, both abstract mathematical concepts, as proposed by Richard Feynman in the 1940s.
A photon’s wave function mathematically describes its quantum state, while a propagator predicts how a wave function changes as the photon travels from a start to an end. Both are often regarded as just being mathematical representations because they contain imaginary numbers, or roots of negative numbers, which don’t appear on measurement devices.
Despite this complexity, in 2011, Jeff Lundeen at the University of Ottawa in Canada and his collaborators demonstrated a way to measure a photon’s wave functions, translating its imaginary numbers into measurable quantities like the polarisation of light. Zhu and his colleagues have now built a similar, but more complex, experiment in which single photons moved through a maze of tiny mirrors, lenses and crystals, each of which manipulated their properties.
They constructed this maze so that, by its end, measurable properties of the photons corresponded to imaginary parts of their wave functions and propagators in addition to parts of the quantum state that can ordinarily be measured because they are real numbers. From readings of detectors and cameras in the lab, which recorded things like polarisation and position of each photon, they reconstructed their wave functions at different points in the maze and the propagators responsible for differences between those wave functions.
This meant they had all the ingredients for testing the quantum version of the principle of least action. Zhu and his colleagues did it for two situations, one was the quantum equivalent of a ball rolling on frictionless level ground and the other of a ball stuck at the bottom of a round bowl.
Quantum states and wave functions are notorious for changing when they interact with any measurement device, so the researchers had to use an innovative “weak” measurement method that doesn’t disturb the photons too much and derive equations that can connect it to the principle of least action. Across experiments, calculations of what photons should do based on the principle returned the same result as calculations of what they did do based on measured wave functions and propagators.
“Measurements in this experiment are quite incredible, and they don’t challenge our current understanding of quantum physics. It is beautiful to see this theory made real in an experiment,” says Jonathan Leach at Heriot-Watt University in the UK.
Lundeen says there may be implicit assumptions that physicists make that could be uncovered by redefining concepts like wave functions and propagators in terms of experimental procedures and not just equations. “The hope is that coming up with lab methods for how to measure these things that are very abstract will maybe give us a better insight into what they really mean,” he says.
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