Every path counts - Feynman's postulate leaves the blackboard
For 78 years the sum over histories was a calculation we trusted but never watched. A single-photon experiment has now measured the paths themselves, and the idea sits underneath more of today's technology than most engineers realise.
In 1948 Richard Feynman published a strange instruction for predicting where a quantum particle ends up. Do not ask which route it took. Assume it took all of them. Give every route an arrow of the same length, turn each arrow by an angle set by that route's classical action, add the arrows head to tail, and square the length of the result. That number is the probability.
Physicists have used this recipe ever since. It built quantum electrodynamics, it runs through the Standard Model and cosmology, and it gives the cleanest explanation of why the everyday world looks classical. What nobody had done was check its two founding assumptions directly, in a laboratory, rather than through their downstream predictions. That changed this week.
What was actually measured
A team led by Shi-Liang Zhu at South China Normal University, with Yong-Li Wen as first author, sent single photons through an optical system and divided the space between a start point A and an end point B into a grid. They measured the propagator, the quantum amplitude for hopping from one grid point to its neighbour, for every short segment. Because amplitudes along a route multiply, those segment measurements let them reconstruct the amplitude of every complete route stitched from them, more than 1.4 million paths in all. The work appears in Science Advances.
Both postulates survived with fidelities close to 95 per cent. The first, that every possible path contributes, matched with a mean absolute percentage error of about 4.5 per cent. The second, that every path contributes with equal magnitude and differs only in phase, held with comparable fidelity.
The hard part was precision. When you multiply segment amplitudes together, small errors compound, and the phase coherence that the whole theory depends on dissolves into noise. The group raised the fidelity of each single-photon propagator measurement from 87.6 to 98.5 per cent by amplifying signals, building a custom imaging system, normalising against a reference beam in real time, and holding the apparatus stable at the nanometre scale. Keep that compounding problem in mind. It will come back when we talk about quantum computers.
The postulate, stated plainly
Feynman's claim has two parts. First, a particle travelling from A to B does not follow one trajectory; every conceivable path contributes. Second, and more radical, all of those paths contribute equally in size. Nature does not prefer the straight line. Each path differs only in its phase, and that phase is the classical action along the path divided by Planck's constant.
This is not how probabilities normally combine. Classically you add the probabilities of alternatives. Feynman adds amplitudes, complex numbers with direction, and only then squares. Arrows pointing the same way reinforce; arrows pointing opposite ways cancel. The animation above shows it happening. Each path is coloured by its phase on a colour wheel , and the right-hand panel lays the arrows end to end.
Here is the beautiful consequence. For paths far from the classical one, a tiny change of route changes the action a lot, so neighbouring arrows point in wildly different directions and cancel. Near the classical path the action is stationary, neighbouring arrows agree, and they add up. The arrows trace a Cornu spiral whose two coiled ends contribute almost nothing; the straight stretch in the middle does the work. Drag the ħ slider down and watch the band of cooperating paths shrink toward the straight line. That is the principle of least action emerging from pure interference. Newton's trajectory is not a law the particle obeys. It is a consensus that the paths reach.
Zhu makes a point about why testing this matters. The Schrödinger equation, the Heisenberg equation and Feynman's propagator are mathematically equivalent, but the first two are usually taken as starting axioms while Feynman's is derived from these two deeper postulates. That asymmetry makes a direct test of the postulates more than a formality. It checks the foundation, not a consequence.
Why this matters for technology you use
It is tempting to file this under philosophy of physics. That would be a mistake, because the sum over paths is already a working tool in several industries. The experiment confirms the physical footing for machinery engineers are running today.
- Quantum computing
- A quantum circuit is a path integral in disguise. The amplitude of any output bitstring is a sum over every sequence of intermediate basis states the register could pass through, and computation succeeds by arranging for wrong answers to cancel and right answers to reinforce. Classical simulators exploit this directly: Feynman-style path-sum simulators, and the hybrid Schrödinger–Feynman algorithm Google used to cross-check its 2019 quantum-supremacy circuits, trade memory for time by summing paths instead of storing the full state. The experiment's compounding-error problem is the same one every quantum hardware team fights. At 98.5 per cent per step, forty steps leave you near 55 per cent. Coherence is a budget, and each segment spends some of it.
- GPU supercomputing and materials design
- Rotate time into the imaginary direction and the oscillating phases become real weights, e−S/ħ. The path integral turns into something you can sample with Monte Carlo, and that is how lattice QCD computes the proton's mass and the hadronic contributions to the muon's magnetic moment on the largest GPU machines in the world. The same trick, path-integral molecular dynamics, treats light nuclei as ring polymers of beads to capture zero-point motion and tunnelling of hydrogen in water, batteries, catalysts and drug binding. Much of the accelerated computing we build infrastructure for is, at bottom, sampling Feynman's histories.
- Semiconductors
- Tunnelling through a barrier is dominated by instanton paths in imaginary time. That physics sets gate leakage in nanometre transistors and the write mechanism in flash memory. The authors also suggest their precise propagator method could make quantum simulations of instantons and magnetic monopoles easier.
- Optics and photonics
- Fermat's principle of least time is the stationary-phase limit of the photon path integral. A lens works because all paths through it to the focus are made to arrive in phase. Metalenses and metasurfaces make that design philosophy explicit, painting a phase profile onto a flat chip so that chosen paths reinforce. Computational lithography for chipmaking solves the same interference problem in reverse.
- Quantum sensing and navigation
- In an atom interferometer the measured phase is the difference in classical action between the two arms divided by ħ. That is Feynman's rule applied literally, and it is how atom gravimeters, gyroscopes and tests of the equivalence principle are calculated. As these devices move toward GPS-free navigation, the path phase becomes a position fix.
- AI agents and control
- The Feynman–Kac formula connects partial differential equations to averages over random paths, and it sits beneath diffusion models, option pricing and path-integral control. Model Predictive Path Integral control, used in robotics and autonomous driving, samples thousands of candidate trajectories and weights each by the exponential of its negative cost, a Euclidean path integral in all but name. Anyone building agents that plan by rolling out and weighting futures is using Feynman's arithmetic, minus the phases.
What the experiment does and does not settle
The authors read their result as evidence that quantum paths reflect physical reality rather than being mathematical artefacts. I would put it more carefully. As a QBist, I read the sum over histories as a consistency rule an agent uses to set expectations about a detector click, not a census of things the photon did. The experiment confirms that the rule is exactly right, to impressive precision, in the regime where you can resolve individual path amplitudes. It does not force a choice between a world of real paths and a calculus for rational belief. That question remains interpretive, and I think it is healthier to say so than to let a beautiful measurement do metaphysical work it was not designed for.
What it does settle is the engineering point. The two postulates are no longer merely inferred from their consequences; they have been measured at the level of individual amplitudes. The team now wants to use the method to study decoherence and the quantum-to-classical transition, entangled histories, indefinite causal order, and eventually interacting systems and analogue curved space-times. Each of those is a place where knowing which paths interfere, and how coherently, is the whole game.
Feynman liked to say he could not explain why nature adds arrows. He could only tell you that it does, and how to do the sum. Seventy-eight years later, someone has finally watched the arrows add.
Sources: Isabelle Dumé, "Single-photon measurements confirm Richard Feynman's vision of quantum mechanics", Physics World, 25 September 2026.
Y.-L. Wen, S.-L. Zhu et al., Science Advances, doi:10.1126/sciadv.aeh1011.
R. P. Feynman, "Space-time approach to non-relativistic quantum mechanics", Rev. Mod. Phys. 20, 367 (1948).
The animation is a schematic model: a free particle with parabolic trial paths for the first view, and a scalar two-slit sum for the second. Units are arbitrary.
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