Concerning the constancy of the speed of light, we indicate that Feynman's sum-over-paths theory of quantum mechanics implicitly relates also to velocities of a photon from C to infinity through the paths, and not only to paths alone taken by the photon. We suggest a modification of Feynman's approach according to which every single photon not only travels from source to destination in all possible paths, but also in all the velocities from zero to infinity, through each of the paths. Matter, however (as already suggested by Israel Shapira several years ago), is tuned to interact with photons only at the special relative velocity C. It follows that the behavior of light as stated by the second postulate of special relativity can result from this suggested physics. We propose experimental setups that challenge special relativity in this regard.
Concerning the constancy of the speed of light, we indicate that Feynman's sum-over-paths theory of quantum mechanics implicitly relates also to velocities of a photon from C to infinity through the paths, and not only to paths alone taken by the photon. We suggest a modification of Feynman's approach according to which every single photon not only travels from source to destination in all possible paths, but also in all the velocities from zero to infinity, through each of the paths. Matter, however (as already suggested by Israel Shapira several years ago), is tuned to interact with photons only at the special relative velocity C. It follows that the behavior of light as stated by the second postulate of special relativity can result from this suggested physics. We propose experimental setups that challenge special relativity in this regard.
Special Relativity (SR) is the cornerstone for modern physics and variety of applications. SR is based on two postulates, the principle of relativity (the first postulate) and the principle of constancy of speed of light (the second postulate). Recently we have (1) shown that the light propagate as particles/photons in the "pure" wave experiments, such as in double slit and grating experiments; (2) proposed experiments to measure the speed of the photons by an observer moving relative to the source and thus, to test the second postulate for photons. In this article we propose a classroom experiment to test the second postulate. If the experiments show the existence of interference pattern (the negative result), the constancy of the speed of the photons holds, namely the second postulate of SR is experimentally confirmed. If the experiments show no interference pattern (positive result), then the propagation speed of photons is not constant, namely, the second postulate of SR is disproved. Either negative result or positive results would be profoundly significant.
The technical problem in Feynman’s proposal to formulate quantum mechanics in terms of a sum over histories of a particle is that this sum over histories must be performed in imaginary time rather than in the real time that everyone experiences [1]. In this paper, for the derivation of Lorentz transformation from the postulates of Special theory of Relativity, the concept of De Broglie quantum waves is introduced which leads to the conclusions that the derivation of Lorentz transformation does not need the postulate of constancy of light speed in free space in case the postulate of phase coincidence of De Broglie quantum waves is introduced. Consequently, a new proposal is formulated that combines Quantum mechanics and the special theory of relativity and overcomes the technical problem in Feynman’s proposal.
The experimental validation of fundamental thought experiments in quantum mechanics has profoundly advanced quantum science and technology while deepening our understanding of quantum mechanics. However, experimental studies of the path integral formulation, a cornerstone of quantum physics, remain scarce, especially regarding the two fundamental postulates proposed by Feynman in 1948, neither of which has been directly tested. Here, we present a theoretical proposal for the direct experimental test of Feynman’s postulates, achieved through the development of a rigorous propagator-based approach. Furthermore, we perform comprehensive measurements of single photon’s probability amplitudes for more than 1.4 million (17 5 ) paths, achieving high fidelity in propagator measurements and enabling complete reconstruction of the path probability amplitudes. The results confirm both postulates: (i) that quantum probabilities emerge from the coherent superposition of all possible paths and (ii) that all possible paths have equal-magnitude amplitudes, whereas each path’s phase is determined by the classical action (in units of ħ ). This work not only resolves a longstanding foundational gap but also establishes a general experimental framework for investigating path integrals in contemporary quantum systems.
When a single photon passes through a slit, the principles of quantum mechanics regarding the boundary conditions of the wave function hide a specific condition: within the wave packet of the photon, the speed of information transmission perpendicular to the direction of photon propagation is infinite. This does not violate Relativity, as it does not conflict with the Principle of Constancy of Light Velocity. In the direction parallel to the propagation of the photons, the speed of information transmission matches c. However, in other directions, the speed of information transmission can exceed c. Causality is not an immutable law of nature, it is not easily overturned at the macro level, while it is not so at the quantum level. Cause and result are mutually causal in different reference frames. Assuming that the angle between the direction of information transmission inside the wave packet and the direction of photon propagation is θ, quantum mechanics utilizes the special case of θ=π/2 to handle wave functions, while the establishment of Relativity is based on the special case of θ=0. Relativity and quantum mechanics can be viewed as two specific instances of a unified theory.
Light is never observed in transit. We see it only at the moment it is emitted and at the moment it is absorbed, with no evidence of anything occurring in between. This simple fact, combined with the constancy of the speed of light, implies that a photon experiences zero proper time between emission and detection. Once this is taken seriously, the classical picture of a photon occupying intermediate positions or following definite paths becomes unnecessary. This paper presents a clear and accessible account of the double‑slit experiment based on this geometric insight. The interference pattern is not produced by a photon “exploring” multiple routes, but by the structure of the experimental setup itself. Each detection event is one sample drawn from a distribution fixed by the context—just as a single arrow on a target reflects, but does not define, the underlying distribution of possible hits. Using Feynman’s amplitude rules and a relational interpretation developed in earlier work, we show how the observed pattern arises without invoking motion through space or physical waves passing through both slits. The result is a simple, coherent picture that remains faithful to both relativity and quantum mechanics while being understandable to motivated high‑school students. Version 1.2 (October 2026). Corrects the Lorentz-transformation derivation in Appendix A. A sign error in the left-moving light-pulse condition (Eq. 8) had produced a degenerate transformation. The corrected equations give t′ = αt + βx and x′ = c²βt + αx; reciprocity and spatial isotropy fix α² − c²β² = 1, establishing the invariance of c²dt² − dx². The standard proper-time formula and double-slit amplitude calculations are unchanged. A new note to the reader clarifies that zero proper time motivates, but does not derive, the relational interpretation: photons have no rest frame, and massive particles such as electrons also exhibit interference.
Within the framework of the ‘Pairwise Interference Model’ of light–matter interaction, it is postulated that light particles follow definite trajectories, and thus, for example, in the double-slit experiment, a particle can pass through only one of the two slits. On this premise, the interference of two photons is examined in greater detail. It is hypothesized that the interference of a photon pair requires the involvement of matter and, initially, that both molecular excitations and photons oscillate at the same frequency and that the continuity of the oscillation is not disrupted by absorption and emission. The molecular excitations in the light source are supposed to oscillate synchronously. Both photons arrive at the same point on the detector but may travel along different paths and therefore arrive at different times. Under these conditions, their phase difference, φ(2) – φ(1), is always zero. Consequently, no interference pattern can form on the detector screen and therefore the assumptions made are incorrect. Alternatively, one may assume that only the photon oscillates, whereas the excitation stores the phase, φ, possessed by the photon at the instant of absorption. In this case, φ(2) – φ(1) corresponds to the difference in travel times modulo the oscillation period, and an interference pattern can form. However, this assumption is problematic for some reasons: the nature of the matter-based memory remains unclear; according to the special theory of relativity, no time elapses for a particle travelling at the speed of light, meaning that it cannot oscillate; and the assumption contradicts Bohr’s correspondence principle. In a classical wave, the phase information propagates away from the source at the wave velocity without changing. This leads to the alternative possibility that the excitations oscillate, whereas the photons do not. Instead, the photons transport information about the phase of the excitation at the instant of emission. As can be shown, in this case, φ(2) – φ(1) likewise corresponds to the difference in travel times modulo the oscillation period. However, this hypothesis contradicts the de Broglie postulate, according to which all particles exhibit wave properties, and the relation ε = hν must therefore be interpreted differently. It also raises the question of how the dimensions of a laser, specifically the mirror separation, can influence the wavelength of the amplified light if a photon has no wavelength. Using replicator dynamics and the ‘Pairwise Interference Model’ of light–matter interaction, a simulation demonstrates that, in a simplified laser model, assuming that photons do not oscillate whereas excitations do, self-organisation gives rise to a phase pattern in the sequence of photons within the emitted light beam that corresponds to the pattern obtained by discretising a classical wave. Thus, coherent light can exhibit wave properties even if photons themselves do not. Finally, the possibility of how incoherent light acquires wave properties is briefly discussed.