\documentclass[12pt]{article}
% Encoding and fonts
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{lmodern}
\usepackage{microtype}
% Layout
\usepackage[margin=1in]{geometry}
\usepackage{setspace}
\onehalfspacing
% Math and theorem environments
\usepackage{amsmath,amssymb,amsthm}
\newtheorem{proposition}{Proposition}
% Bibliography and links
\usepackage[numbers,sort&compress]{natbib}
\PassOptionsToPackage{capitalise,nameinlink,noabbrev}{cleveref}
\usepackage[colorlinks=true,linkcolor=blue,citecolor=blue,urlcolor=blue]{hyperref}
\usepackage{orcidlink}
\usepackage{cleveref}
% Header
\usepackage{orcidlink}
\usepackage{fancyhdr}
\pagestyle{fancy}
\fancyhf{}
\lhead{Wavefunction Prediction Does Not License a Photon Path}
\rhead{John C. W. McKinley}
\cfoot{\thepage}
\setlength{\headheight}{14pt}
\title{\textbf{Wavefunction Prediction Does Not License a Photon Path}\\
\large A Short Interpretive No-Go}
\author{John C. W. McKinley
\orcidlink{0009-0005-7097-5035}}
\date{April 12, 2026}
\begin{document}
\maketitle
\begingroup
\footnotetext{\scriptsize This version published at \url{https://doi.org/10.5281/zenodo.19504772}.}
\endgroup
\begin{abstract}
This paper makes one narrow interpretive no-go claim. The mathematical success of
the wavefunction in predicting lawful absorption outcomes does not license the
conclusion that a photon follows an intermediate spacetime path between endpoints.
For the photon, relativistic null structure withholds the ordinary timelike template of
internal duration, traversed route, and intermediate history. The wavefunction assigns
amplitudes---mathematical quantities whose combination determines the probabilities of
observed outcomes---and organizes the lawful structure of absorption events without
thereby describing where the photon is in between.
\end{abstract}
\section{Introduction}
This paper is narrow by design. It does not revise quantum mechanics, alter quantum field
theory, or introduce a new dynamical law. It makes a single interpretive claim about what
may be inferred from wavefunction prediction in the photon case.
The target is not the wavefunction as mathematics. Its predictive success is not in dispute.
The target is the extra step from successful prediction of lawful absorption outcomes
to the claim that the formalism thereby tells us where the photon is in between, or what intermediate
spacetime path it follows between endpoints.
That step is not licensed. For the photon, relativistic null structure---the lightlike case
in relativity, in which no proper time elapses along the path\footnote{\scriptsize See footnote \ref{fn:lightlike}.} and no rest frame exists for
the photon---withholds the ordinary timelike template of internal duration, traversed route,
and intermediate history. Prediction of an absorption point is not identification of an
intermediate photon path.
The same point covers interference, here understood as the patterned enhancement and
suppression of detector outcomes under fixed experimental conditions. Repeated trials under
fixed experimental conditions yield stable patterns in localized detector outcomes, and
standard quantum theory accounts for those patterns through the combination of quantum
amplitudes. What does not follow is that the lawfully weighted regions in the formalism
identify where the photon is in between. Lawful outcome structure is not path ontology.
The broader null-case restriction used here has already been developed elsewhere:
null proper time withholds an internal photon duration
\cite{McKinleyNullProperTime}, the absence of a rest frame withholds the
standard persistence template \cite{McKinleyNoRestFrame}, null curves do not
supply carrier histories \cite{McKinleyNullCurves}, and the minimal structural
statement of the Timeless Light Model compresses those restrictions into the
claim that the photon is not a particle in transit \cite{McKinleyBedrock}.
\section{The No-Go}
\begin{proposition}
The mathematical success of the wavefunction in predicting lawful absorption
outcomes does not license the conclusion that a photon follows an intermediate spacetime
path between endpoints.
\end{proposition}
\begin{proof}
The wavefunction contributes to the calculation of amplitudes, probabilities, and
outcome structure. That establishes predictive success. It does not by itself establish that
the formalism describes where a photon is between emission and absorption.
In the photon case, the added path claim is further blocked by relativistic null structure.
For a photon, no proper time elapses along the
null path\footnote{\label{fn:lightlike} \scriptsize A path of this kind has zero spacetime interval, written $ds^2 = 0$, which implies that no proper time elapses along it, written $d\tau = 0$. Here $\tau$ (tau)
denotes proper time, that is, the time recorded by a clock traveling with the object,
and $d$ denotes an infinitesimal increment. In relativity, a path with this zero-interval
character is called \textit{null} or \textit{lightlike}. This is what is meant here by
\textit{relativistic null structure}. For a photon, it means there is no elapsed internal
time along the path itself. In that sense, the null case withholds the ordinary timelike
template of an internally unfolding middle.}, no rest frame is available, and thus the ordinary timelike
template of internal duration, traversed route, and intermediate history is withheld. There is
therefore no internally timed or spatially traversed middle for the wavefunction to describe.
The same point covers interference, including approaches in which all
mathematically allowed routes between endpoints enter the calculation. In such
approaches, the routes function as terms contributing to the predicted outcome,
not as trajectories assigned to a persisting physical carrier.
Hence the mathematical success of the wavefunction in predicting lawful absorption
outcomes does not license the conclusion that a photon follows an intermediate spacetime
path between endpoints.
\end{proof}
\section{Conclusion}
The result is interpretive clarity. The mathematical success of the wavefunction in
predicting lawful absorption outcomes does not by itself justify the conclusion that a
photon follows an intermediate spacetime path between endpoints, because in the photon
case relativistic null structure already withholds the ordinary timelike template of an
internally timed and spatially traversed middle.
The wavefunction may continue to govern amplitudes, interference structure, and detector
statistics without being turned into a description of where the photon is in between.
What is removed is only the unlicensed inference from predictive success to transit ontology.
\begin{thebibliography}{99}
\bibitem{McKinleyNullProperTime}
J.~C.~W.~McKinley,
\textit{Taking Null Proper Time Seriously: An Interpretive Clarification of Null Proper Time},
Zenodo (2025).
DOI: \href{https://doi.org/10.5281/zenodo.18004632}{10.5281/zenodo.18004632}.
\bibitem{McKinleyNoRestFrame}
J.~C.~W.~McKinley,
\textit{No Rest Frame, No Persistence: A Kinematic Constraint on Photon Interpretation},
Zenodo (2025).
DOI: \href{https://doi.org/10.5281/zenodo.18005884}{10.5281/zenodo.18005884}.
\bibitem{McKinleyNullCurves}
J.~C.~W.~McKinley,
\textit{Null Curves Without Carriers: Resolving an Ontological Tension in Relativistic Geometry},
Zenodo (2025).
DOI: \href{https://doi.org/10.5281/zenodo.18028886}{10.5281/zenodo.18028886}.
\bibitem{McKinleyBedrock}
J.~C.~W.~McKinley,
\textit{A Minimal Structural Statement of the Timeless Light Model},
Zenodo (2026).
DOI: \href{https://doi.org/10.5281/zenodo.19167403}{10.5281/zenodo.19167403}.
\end{thebibliography}
\end{document}