Physicists measure amplitudes of 1.4 million photon paths to test Feynman's postulates

Zhu said the Schrodinger equation, the Heisenberg equation and Feynman's propagator equation are formally equivalent formulations of quantum mechanics ^[4]. They differ in standing. "However, while the first two are typically treated as fundamental postulates, the Feynman propagator equation is derived from two underlying postulates. This derivational asymmetry makes experimental tests of Feynman's postulates particularly compelling," he said ^[5].

The first postulate says a particle moving from A to B follows no single trajectory; every possible path contributes ^[6]. The second says each path carries an amplitude of the same magnitude, with only the phase varying, and that phase is set by the classical action in units of the Planck constant ^[7]. The probability of arrival is the absolute square of the summed amplitudes. A classical calculation would add the probabilities instead ^[8]. The formulation built on these two statements has been central to quantum field theory and cosmology, and it links quantum mechanics to classical physics through the principle of least action ^[3].

The experimental design turns that sum into a measurement problem. "We did this by dividing the region between the starting point A and the end point B into a grid of points. We connected adjacent points by line segments and then measured the propagator for each segment," Zhu said ^[10]. A path is a chain of segments, so its amplitude is assembled from segment measurements ^[10][14]. From those pieces the team reconstructed amplitudes for "more than 1.4 million possible paths taken by single photons in an optical system," in Zhu's words ^[9]. The same Physics World report then quotes him as saying "In total, there are 175 possible paths" ^[11]. Read as 17 to the fifth power, that figure is 1,419,857, consistent with the 1.4 million ^[1]. A superscript lost in formatting is the likely explanation, and the paper would settle it.

Building paths from parts is also where the experiment could have failed. Yong-Li Wen, the paper's first author, said that "because there were so many possible paths that the photons could take, the primary challenge in our experiments was to achieve 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" ^[14]. The team credits four technical changes, among them signal amplification, a customized high-precision imaging system and real-time normalization against a reference beam to correct for photon fluctuations ^[15].

The paper reports that 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 with a fidelity of 94.7% ^[12][13]. That leaves a gap of about 5 percentage points from perfect agreement in each case ^[2]. The thing these figures don't tell you is how a wrong rule would have scored on the same data. The Physics World account does not report a fidelity for a classical sum of probabilities, or for paths of unequal magnitude, run through the same reconstruction.

I think the first-direct-test label holds, with its conditions stated. It covers single photons in one optical system, on a finite grid of paths ^[9][10]. Physics World reports that the 1948 postulates had never been tested directly before ^[2]. A version with massive particles, or with a finer grid where Wen's multiplying errors would have more segments to compound across, would be a separate experiment ^[14].