Interpreting Bohm-like quantum potentials in "Computing quantum waves exactly from classical action"
arXiv:2605.20443 · doi:10.1098/rspa.2025.0413
Abstract
Comment on arXiv:2605.02621 [23] and arXiv:2606.05197 [24]: In contrast to his earlier comment [23] on rspa.2025.0413 [12] and answered in arXiv:2605.20443 [11], the same author of [24] does not seem to dispute any longer that the use in [12] of tools from Feynman's [5] namely - the kernel approach, which computes a wave starting at a given initial position or momentum, and is a key element in [12] to ensure that the Bohm-like quantum potential vanishes. This is directly verified in all examples of [12] as well as in the Pauli, Dirac and Maxwell derivations from classical action. This approach is very different from the standard Bohm-Madelung potential on the overall wave, as illustrated in detail in [11] for the two-slit experiment. - for the harmonic oscillator, the kernel computation directly from a Taylor series expansion, which does not involve any circularity. His second post [24] now - criticizes the use in [12], [11] of Duru and Kleinert's time-independent eigenwave equivalence of the original and the time-scaled Schrödinger equations [4], confusing this standard result with a multivariable chain rule in the time-dependent kernel computation from action in [12]. - claims that "The mathematical framework presented by the authors remains identical to the well-established semiclassical Van Vleck propagator [sic]" which requires that the "Hamiltonian is at most quadratic in position and momentum [sic]". This confuses a quadratic action in the vector case with a harmonic propagated density based on the Laplacian of the action (with harmonicity always fulfilled e.g., for holomorphic complex functions [10]. In addition, it ignores the extension of a real position to a complex or quaternion position or spin, the key result on multi-valued action branches (which enables a classical derivation of quantum randomness) and the quantization of classical action in [12].
The earlier post arXiv:2605.02621 [23], commenting on the article rspa.2025.0413 [12], was answered in arXiv:2605.20443 [11] the v3 version (May 2026) of this paper, which is kept unchanged as the second part of this update. The new post arXiv:2606.05197 [24] is answered by the first part of this post (per arXiv policy). This v5 answer on [24] is contentwise similar to the v4 answer