[2026] The So-Called Speed of Light Is Not the Speed of Light: A No-Go on Speed-Talk for the Null Case

\PassOptionsToPackage{capitalise,nameinlink,noabbrev}{cleveref}
\documentclass[11pt]{article}

\usepackage[margin=1in]{geometry}
\usepackage{amsmath,amssymb,amsthm}
\usepackage{hyperref}
\hypersetup{colorlinks=true, linkcolor=blue, citecolor=blue, urlcolor=blue}
\usepackage{cleveref}
\usepackage{orcidlink}

\newcommand{\doi}[1]{\href{https://doi.org/#1}{#1}}
\newcommand\blfootnote[1]{%
  \begingroup
  \renewcommand\thefootnote{}\footnote{#1}%
  \addtocounter{footnote}{-1}%
  \endgroup
}
\newtheorem{proposition}{Proposition}
\newtheorem*{remark}{Remark}

\title{The So-Called Speed of Light Is Not the Speed of Light\\
\large A No-Go on Speed-Talk for the Null Case}
\author{John C. W. McKinley\,\orcidlink{0009-0005-7097-5035}}
\date{May 14, 2026}

\begin{document}
\maketitle
\blfootnote{This version published at \url{https://doi.org/10.5281/zenodo.20193205}.}

\begin{abstract}
This paper states a narrow interpretive no-go. The phrase ``speed of light''
presupposes that something is moving and that the something has a speed. In
the photon case, the literal reading fails. The photon has null proper time,
no rest frame, and no licensed intermediate spacetime history. A speed is a
rate-of-position-change assigned to a referent in a frame across time. Where
there is no licensed photon traveler, there is no persisting subject whose
motion can be tracked. Where there is no photon rest frame, there is no
photon-owned self-speed either. The constant $c$ remains in the equations
and retains its full operational role. What is denied is only the reading of
$c$ as the speed owned by a photon-object. The so-called \emph{speed of light} is therefore not the speed of light in the literal ontological sense. It is
operational shorthand for the invariant constant $c$, not a speed owned by
a photon-object. This is interpretive only.
\end{abstract}

\section{Introduction}

The phrase \emph{speed of light} is taught early and used everywhere. It
appears in introductory texts, in engineering practice, and in scientific
writing intended for general readers. As an operational shorthand it
identifies a constant that enters Maxwell's equations, the Lorentz
transformations, the relativistic metric, and the dispersion relations
of quantum field theory.

This paper does not contest the constant. It contests the phrase.

The phrase ``speed of $X$'' is a four-place structure: it requires an
$X$, a frame, a time, and a rate at which the position of $X$ changes
in that frame across that time. For ordinary objects each slot is
filled. For the photon, the relevant slots are not filled. The photon
has null proper time and no rest frame~\cite{tlmBedrock,nullProperTime,noRestFrame}.
The wavefunction's predictive success does not supply an intermediate
photon path~\cite{wavefunctionNoGo}. The companion timebound no-go
blocks the broader inference from lawful temporal governance to
traveler-bead ontology~\cite{timeboundNoGo}. The observer-side
restatement of $c$ as a registration bound, rather than a traveler-owned
speed, has been developed separately~\cite{cRegBound}.

The present paper states what follows from those results for the phrase
itself. Where no photon traveler is licensed, there is no persisting
subject whose motion can be tracked. Where no photon rest frame exists,
there is no photon-owned self-speed either. The so-called speed of light
is therefore not the speed of light when the phrase is read literally.
It survives as operational shorthand for a constant whose role in
physics is settled. What does not survive is its literal ontological
reading.

\section{The Structure of Speed-Talk}

\begin{proposition}[Speed has a subject]
\label{prop:subject}
A speed in physics is a property assigned to a thing. The locution
``speed of $X$'' requires an $X$ whose position changes in some frame
across some time.
\end{proposition}

\begin{proof}
The kinematic notion of speed is defined as the magnitude of the rate
of change of position with respect to time, $|d\vec{x}/dt|$, where
$\vec{x}$ is the position assigned to a referent in a frame and $t$ is
a time parameter in that frame. The ratio itself belongs to the frame
description. It does not, by itself, establish the ontology of the
referent being described. To treat the ratio as the speed \emph{of}
$X$ is to treat $X$ as the subject of the assigned position-change.
Without a referent whose position is defined in a frame, the derivative
has no subject as an object-owned property. Therefore speed-talk
requires a subject.
\end{proof}

\begin{proposition}[Speed requires a frame in which the referent has a position]
\label{prop:frame}
A speed assigned to a referent presupposes a frame in which that
referent has a defined position.
\end{proposition}

\begin{proof}
The quantity $|d\vec{x}/dt|$ is frame-relative. Different frames
assign different values. For the quantity to be defined at all as the
speed \emph{of} a referent, the referent must possess a position in
the relevant frame. Where no such position is defined, no speed is
defined as an object-owned property of that referent.
\end{proof}

\begin{remark}
\Cref{prop:subject,prop:frame} are uncontroversial in ordinary
mechanics. They are stated explicitly here because they make the
photon case's failure visible without further argument.
\end{remark}

\begin{remark}
This paper does not deny that a lightlike relation, wave-packet model,
field excitation, null geodesic, or detector-to-detector correlation
can be assigned the invariant value $c$ in an inertial-frame
description. The point is narrower. A successful frame-assigned
description does not by itself license a photon-object that owns that
value as its traveler speed. The ratio may be operationally valid
without becoming the property of a persisting thing in transit.
\end{remark}

\section{The Photon Case}

\begin{proposition}[No subject]
\label{prop:nosubject}
The photon is not licensed by standard physics as a persisting object
in transit between emission and absorption.
\end{proposition}

\begin{proof}
The photon has null proper time and no rest frame. On the Timeless
Light Model reading, those constraints withhold the ordinary timelike
template of internal duration, traversed route, and intermediate
history~\cite{tlmBedrock,nullProperTime,noRestFrame,nullCurves}.
The wavefunction's predictive success does not supply an intermediate
photon path~\cite{wavefunctionNoGo}. The broader timebound no-go
blocks the inference from lawful temporal governance to traveler-bead
ontology~\cite{timeboundNoGo}. Therefore the photon is not licensed
as a persisting object in transit.
\end{proof}

\begin{proposition}[No rest frame]
\label{prop:noselfframe}
The photon has no rest frame.
\end{proposition}

\begin{proof}
Standard relativity withholds a rest frame from any null relation.
A rest frame requires a timelike worldline along which proper time
elapses. The photon's null structure provides no such worldline.
Therefore the photon has no rest frame.
\end{proof}

\begin{proposition}[No photon-owned speed]
\label{prop:nospeed}
The photon has no speed in the literal kinematic sense required by
the phrase \emph{speed of light}.
\end{proposition}

\begin{proof}
There are two possible literal readings of the phrase. First, it may
mean that a photon-object has a speed in its own frame. That reading
is blocked by \Cref{prop:noselfframe}: the photon has no rest frame,
and therefore no own-frame in which a photon-owned self-speed could
be defined.

Second, it may mean that a photon-object has a speed assigned from
another observer's frame. That reading is blocked by
\Cref{prop:subject,prop:frame,prop:nosubject}. Speed requires a
referent whose position changes in a frame across time. The photon is
not licensed as a persisting referent in transit between emission and
absorption. Therefore the frame-assigned value $c$ remains a value
assigned within the observer's description; it does not become a
kinematic property owned by a photon-object.

Thus the self-frame reading fails because there is no photon rest
frame. The other-frame traveler reading fails because there is no
licensed photon traveler. Therefore no kinematic speed is a property
of the photon.
\end{proof}

\section{The So-Called Speed of Light}

\begin{proposition}[The so-called speed of light is not the speed of light]
\label{prop:not-speed-of-light}
The so-called speed of light is not the speed of light in the literal
ontological sense.
\end{proposition}

\begin{proof}
The phrase ``speed of light'' purports, when read literally, to name a
speed belonging to light, read physically as the photon case. By
\Cref{prop:nospeed}, no kinematic speed is a property of the photon.
Therefore the so-called speed of light is not the speed of light in the
literal ontological sense. It is operational shorthand for the invariant
constant $c$.
\end{proof}

\begin{remark}
The phrase remains operationally serviceable. It identifies the
invariant constant $c$ that enters the equations of relativity,
electromagnetism, and quantum field theory. Nothing in this paper
disturbs that role. The error lies in the literal reading, not in the
operational use.
\end{remark}

\section{What $c$ Is Instead}

The companion paper on $c$ as a registration bound gives the positive
restatement~\cite{cRegBound}. The constant $c$ is not a traveler-owned
speed. It is the invariant causal bound governing lightlike relation,
null structure, and observer-side registration in spacetime description.

The present paper adds only the linguistic verdict. Once the photon
traveler is removed, the phrase \emph{speed of light} loses its literal
referent. The operational label survives because the constant survives.
The ontological reading does not.

\section{Scope}

The proposal introduces no new equations, no new observables, and no
modification to special relativity, general relativity, quantum
mechanics, or quantum field theory. The numerical value of $c$ is
unchanged. The role of $c$ in the Lorentz transformations, the metric,
and the dispersion relations is unchanged. Standard calculations using
the phrase ``speed of light'' as operational shorthand remain valid.

The claim is only that the phrase should not be read literally as naming
a speed owned by a photon-object.

\section{Conclusion}

The phrase \emph{speed of light}, read literally, predicates a speed
of a referent that is not licensed by physics as a thing with a speed.
The photon has null proper time, no rest frame, and no licensed
intermediate spacetime history.

The no-go has two sides. There is no photon-owned self-speed, because
there is no photon rest frame. There is no photon traveler-speed
assigned from another frame, because the photon is not licensed as a
persisting object in transit whose position changes across time. The phrase therefore fails as a literal statement: it appears to name a photon-owned speed, but no such photon-owned speed is licensed.

The constant $c$ remains. Its operational role is untouched. What is
removed is only the literal reading under which $c$ was treated as the
speed of a traveling photon. There is no traveler. The so-called \emph{speed of light} is not the speed of light. There is the lawful invariant $c$, and there are lawful
spacetime appearances governed by it.

\begin{thebibliography}{9}

\bibitem{tlmBedrock}
J. C. W. McKinley.
\emph{A Minimal Structural Statement of the Timeless Light Model}.
Zenodo (2026). \doi{10.5281/zenodo.19167403}.

\bibitem{nullProperTime}
J. C. W. McKinley.
\emph{Taking Null Proper Time Seriously: An Interpretive
Clarification of Null Proper Time}.
Zenodo (2025). \doi{10.5281/zenodo.18004632}.

\bibitem{noRestFrame}
J. C. W. McKinley.
\emph{No Rest Frame, No Persistence: A Kinematic Constraint on
Photon Interpretation}.
Zenodo (2025). \doi{10.5281/zenodo.18005884}.

\bibitem{nullCurves}
J. C. W. McKinley.
\emph{Null Curves Without Carriers: Resolving an Ontological
Tension in Relativistic Geometry}.
Zenodo (2025). \doi{10.5281/zenodo.18028886}.

\bibitem{wavefunctionNoGo}
J. C. W. McKinley.
\emph{Wavefunction Prediction Does Not License a Photon Path}.
Zenodo (2026). \doi{10.5281/zenodo.19504771}.

\bibitem{timeboundNoGo}
J. C. W. McKinley.
\emph{Timebound Does Not Mean Traveler: A No-Go on Deriving
Bead-Path Ontology from Quantum Admissibility}.
Zenodo (2026). \doi{10.5281/zenodo.20114078}.

\bibitem{cRegBound}
J. C. W. McKinley.
\emph{$c$ Is a Registration Bound, Not a Traveler's Speed}.
Zenodo (2026). \doi{10.5281/zenodo.20175517}.

\end{thebibliography}

\end{document}