Physicists have confirmed the two foundational postulates of Richard Feynman's path-integral approach to quantum mechanics in a real-world experiment for the first time, nearly 80 years after Feynman first published his formulation describing how quantum systems evolve over time.
The work, led by Shi-Liang Zhu of South China Normal University in Guangzhou and detailed in Science Advances, directly measured the probability amplitudes of more than 1.4 million possible paths taken by single photons in an optical system. The results validate the first postulate with a mean absolute percentage error of 4.45% and a fidelity of 94.9%, and confirm the second postulate with 94.7% fidelity.
Feynman's 1948 formulation rests on two postulates. The first holds that a quantum particle does not travel along a single trajectory when moving from point A to point B; instead, every probable path contributes to its trajectory. The second states that all possible paths have equal probability amplitudes and differ only by a path-dependent phase factor governed by the classical action in units of the Planck constant. This differs fundamentally from classical physics, where probabilities are simply summed.
While the Schrödinger equation, the Heisenberg equation and the Feynman propagator equation are formally equivalent formulations of quantum mechanics, the first two are typically treated as fundamental postulates, whereas the Feynman propagator equation is derived from two underlying postulates. «This derivational asymmetry makes experimental tests of Feynman's postulates particularly compelling,» Zhu said.
To perform the measurement, the team divided the region between the starting point A and the end point B into a grid of points, connected adjacent points by line segments, and measured the propagator for each segment. In total, there were 17^5 possible paths. The paper's first author, Yong-Li Wen, noted that the primary challenge was achieving sufficient accuracy to reconstruct millions of path amplitudes, since even marginal errors in individual propagator measurements accumulate multiplicatively, destroying phase coherence and rendering the reconstructed path distribution nearly random.
The team overcame this through four key technical advancements: amplifying the signals; designing a customized high-precision imaging system; implementing real-time normalization via a reference beam to correct for photon fluctuation errors; and ensuring the set-up was mechanically stable on the nanoscale. These innovations improved single-photon propagator fidelity from 87.6% to 98.5%, allowing the team to resolve the global structure of path amplitudes with unprecedented precision.
The path-integral formulation has been critical for fields ranging from quantum field theory to cosmology, providing a unified framework that connects quantum mechanics with classical physics through the principle of least action. Its predictions underpin modern quantum science, from condensed matter physics to quantum statistical physics.
Zhu said the work establishes a powerful experimental framework for investigating path integrals in quantum systems. «By confirming that quantum probabilities arise from path interference and that phases are governed by classical action, we provide experimental evidence supporting the view that quantum paths reflect physical reality rather than being mere mathematical artefacts,» he said.
The high-precision propagator methodology could also be used to study quantum-to-classical transitions and decoherence mechanisms, where understanding the role of interfering paths is essential. It could be extended to probe fundamental phenomena such as entangled histories and indefinite causal order across multiple space–time points. Beyond fundamental physics, the technique may make quantum simulations of complex condensed matter and quantum field theory phenomena, including instantons and magnetic monopoles, easier.
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