Physicists at South China Normal University in Guangzhou reported in Science Advances on August 26, 2026, that they had tested the two postulates behind Richard Feynman’s path-integral formulation of quantum mechanics with single photons. The authors described them as “the two fundamental postulates proposed by Feynman in 1948, neither of which has been directly tested.” Feynman set them out in a paper in Reviews of Modern Physics.
Under the first, as the team tested it, the probability that a particle reaches a point is the squared magnitude of a sum of complex numbers called amplitudes, one for each path the particle could take. Under the second, every path’s amplitude has the same magnitude and a phase equal to the path’s classical action divided by the reduced Planck constant. The action is a standard quantity in classical mechanics, calculated from a particle’s kinetic and potential energy along a path.
The authors wrote that their results confirm both postulates but that “more refined methodologies are required” to settle whether all the paths are physically real.
Yong-Li Wen and Li-Man Tian contributed equally to the paper. Its corresponding authors are Enke Wang, Hui Yan, and Shi-Liang Zhu, the last two also affiliated with Hefei National Laboratory.
How the team measured the paths
The team treated the sideways spread of 795-nanometer photons in free space as the motion of a quantum particle in one dimension. It divided a strip about 97 micrometers wide into 17 positions and the propagation into five steps of 15 millimeters each. The team used a slit 15 micrometers wide to set each photon’s starting position.
For each step, the team measured the propagator, the complex amplitude for a photon to move from one position to another. Inside a stabilized interferometer, an instrument that splits light and recombines it, the team used the photons’ polarization as a measurement pointer, a property that carries the measurement result. It recorded single photons with an intensified camera.
The team then computed each path’s amplitude by multiplying the five single-step propagators along it. With the starting position fixed, the grid contains 17 to the fifth power, or 1,419,857, paths.
Results for the two postulates
For the first postulate, the authors reported excellent agreement between the photon distribution the camera recorded and the distribution predicted by squaring the sum of the measured path amplitudes. That predicted distribution differed from the theoretical one by a mean absolute percentage error of 4.45%, a measure of the average gap between two sets of values.
Interference is the adding and canceling of amplitudes from different paths. Without interference, the result would be the classical sum of the separate paths’ probabilities. The authors reported significant deviation between that classical sum and the measured distribution.
For the second postulate, the team found that the reconstructed amplitudes had equal magnitudes and that their phases followed the classical action, with a fidelity of 94.7%. Fidelity is a measure of overlap between the measured and theoretical results, where 100% means a perfect match.
The squared amplitudes of individual paths scattered with a mean absolute percentage error of 17.4%. When the authors ran a simulation based on their measured propagator errors, they obtained 18.0%.
Earlier work and next steps
The group built on its 2023 Nature Photonics paper, in which it measured single-photon propagators to demonstrate the quantum principle of least action. The authors wrote that by changing the setup, they raised the fidelity of their propagator measurements from 87.6% to 98.5%.
In their discussion, the authors wrote that each photon’s behavior was consistent with a superposition, or combination, of all the paths, “supporting the view that the paths are more than mere mathematical artifacts.”
The authors proposed applying the method to tests of entangled histories and indefinite causal order, two lines of research in which sequences of events, or their order, can themselves be in superposition. They also proposed extending it to systems with interactions or in curved spacetime.
The authors wrote that researchers could use the approach to develop “previously unexplored quantum simulation techniques that use path integrals” for studying condensed matter systems, such as solids and liquids. The team posted its data on Dryad, an open data repository.
Update, November 12, 2026: In a September 25 Physics World article, corresponding author Shi-Liang Zhu was quoted as saying that “quantum paths reflect physical reality rather than being mere mathematical artefacts.” The experiment tested predictions of the path-integral calculation, and the statement about physical reality is Zhu’s interpretation.
