Internal Dynamics Decoupled from Center-of-Mass Motion: Clarifying the Conceptual Roots of the Century-Long Debate on Relativistic Temperature Transformation

The century-long debate on the relativistic transformation of temperature—with threemutually exclusive formulas T′ = T/γ (Planck-Einstein), T′ = Tγ (Ott-Arzel`ıes), andT′ = T (Landsberg)—has persisted since 1907. We argue that this controversy stems froma fundamental category confusion: conflating quantities describing the intrinsic state of asystem with those describing its global kinematic appearance. We propose the internalmotion decoupling hypothesis: the intrinsic temperature of a thermodynamic system isuniquely determined by the microstate distribution in its center-of-mass (Butler-Møller)frame and is orthogonally independent of the system’s bulk uniform motion. Based onthe Liouville theorem and detailed balance conditions in covariant statistical mechanics,we demonstrate the self-consistency of this hypothesis: a Lorentz transformation of thesystem’s bulk motion does not alter the microscopic collision dynamics by which internalthermal equilibrium is established; hence the scalar temperature marking that equilibriummust be a Lorentz invariant, yielding T′ = T. We further provide a step-by-step analysis ofthe Planck and Ott derivation chains, showing that their derivations are mathematicallyself-consistent but rest on different presuppositions about the boundary conditions ofa thermodynamic system. The controversy is thus identified as a definitional disputerather than a mathematical inconsistency. We propose a decisive experimental test using1collinear laser spectroscopy on cooled heavy-ion beams in a storage ring, with conservativesystematic error estimation, capable of distinguishing the three theories at the 10−4 level.While the conceptual roots of the debate are clarified here, the empirical resolution awaitsexperimental implementation.