Timeless Propagation Without FTL: Null Geodesics and Superposition in FLRW Cosmology

Timeless Propagation Without FTL: Null Geodesics and Superposition in FLRW Cosmology Author: Cameron Brogan-Higgins Abstract In this paper I argue that in an FLRW universe, massless excitations propagating along null geodesics provide a rigorous model of “timeless traversal” that avoids the pitfalls of faster-than-light (FTL) speculation. Along null worldlines, proper time vanishes: for the system itself, no time elapses between emission and detection. For comoving observers, however, propagation takes a finite coordinate time determined by the conformal-time interval ∆η = ∫(dt/a(t)). On any constant-time slice, the quantum state is spatially extended, with nonzero detection probabilities within the light cone and zero outside (microcausality). The Hubble parameter H = (da/dt)/a sets the causal scale via the comoving Hubble radius R_H = (aH)^(-1), which determines null connectivity. This framework shows that “timeless traversal” and “many places at once” can be rigorously modeled within relativity and quantum field theory, without invoking FTL matter, while aligning naturally with the thermodynamic arrow of time. Keywords: arrow of time, FLRW cosmology, null geodesics, horizon entropy, Hubble parameter, quantum superposition, timeless propagation, causal horizons, relativity, thermodynamics 1. Introduction The classical arrow of time is usually defined in thermodynamics, while the cosmological arrow is tied to expansion. In addition, quantum theory describes particles as extended in space, “many places at once.” A natural question arises: can these concepts be understood in a unified way through relativity and cosmology, without invoking FTL motion? I propose that null propagation in FLRW, combined with the causal role of the Hubble parameter, provides such a framework. 2. Claim (Physically Correct) In an FLRW universe, a massless (or ultra-relativistic) wave packet propagates from event A to event B along a null geodesic. Along its worldline the proper time satisfies dτ = 0. Thus, for the system itself, no proper time elapses between emission and detection (“timeless propagation”). For any comoving observer, the travel requires a finite coordinate time given by the conformal-time interval: ∆η = ∫ (dt / a(t)). On each constant-time slice, the quantum state is spatially extended; detection probabilities are nonzero within the light cone. 3. Cosmological Linkage The Hubble parameter H = (da/dt)/a sets the causal scale via the comoving Hubble radius R_H = (aH)^(-1). During expansion (H > 0), R_H determines which regions can exchange null signals. Apparent superluminal recession speeds v_rec = H D at large separations arise from metric expansion, not local motion. They do not allow FTL signalling and are consistent with null propagation. 4. What This Gives and Avoids - No FTL matter: massless null propagation replaces “faster-than-light” speculation. This is standard in GR and QFT, with dτ = 0 along null paths. - Apparent “many places at once”: the spatially extended wavefunction on a Cauchy slice resembles simultaneous presence, but is simply quantum superposition, not literal multi-location. - Cosmological linkage: the causal structure determined by R_H aligns with the thermodynamic arrow of time, reinforcing the equivalence between entropy increase and expansion. 5. Minimal Formalism (Teaching-Clean) - Geometry: FLRW metric, spatially flat for simplicity: ds^2 = -dt^2 + a^2(t) dx^2 = -a^2(η)(dη^2 - dx^2). - Null path: ds^2 = 0 ⇒ dη = ± d|x|. Proper time: dτ^2 = dt^2 - a^2 dx^2 = 0 ⇒ τ_B - τ_A = 0. - Travel time (comoving observer): ∆η = ∫(dt / a(t)), ∆t = ∫ a(η) dη > 0. - Causality: In QFT on curved spacetime, field commutators vanish outside the light cone (microcausality). Detection probabilities are confined to null-related regions; no spacelike influence. - Hubble scale: v_rec = H D may exceed c for large D, but this is not a particle velocity. Causal contact is governed by null geodesics and horizon scales, e.g. R_H = (aH)^(-1). 6. Corrected Statement A massless wave packet in FLRW propagates along a null path with zero proper time, while observers register finite coordinate time. Its spatially extended wavefunction reflects standard quantum superposition. The causal scales are governed by the Hubble radius, ensuring that apparent “timeless traversal” and “many places at once” are entirely consistent with relativity and quantum field theory, without invoking FTL matter. 7. Discussion This framework illustrates that the intuitive picture of instantaneous travel can be rigorously reformulated as null propagation, which is timeless in proper time but spatially extended in quantum description. The Hubble parameter provides the link between global cosmology and local propagation, ensuring consistency with the thermodynamic arrow. This does not propose new physics but clarifies the relation between relativity, cosmology, and quantum interpretation. 8. Conclusion In FLRW cosmology, null propagation and superposition combine to show how “timeless traversal” is possible without FTL motion. The Hubble parameter defines causal horizons, aligning the arrow of time with expansion. This perspective highlights a unification of cosmological expansion, relativity, and quantum interpretation within established physics.