Cosmological Redshift Without Expansion: Relational Simultaneity, Apparent Cooling, and a Static Block Description

Cosmological Redshift Without Expansion:Relational Simultaneity, Apparent Cooling, and a Static Block Description This work proposes a minimal and relational reinterpretation of cosmological redshift and the apparent thermal history of the Universe, formulated without invoking an expanding spacetime, a physical cosmic container, or an initial singularity. The central hypothesis is that only binary relations between physical systems exist. There are no more than two reference systems at a time: an observer and a source. Space and time are not fundamental entities, but emerge operationally from the geometric relation between frames. In particular, there is no globally evolving spacetime manifold and no physical “stretching” of space. Within this framework, the Universe can be described by a static block representation, understood strictly as a mathematical construct encoding relational projections between frames, not as a physically frozen or ontologically real four-dimensional container. The block serves only to organize how measurements performed by one system relate to states defined in another. Cosmological redshift is reinterpreted as a relational simultaneity shift between distant systems. Photons propagate along null trajectories in the relational structure, but the frequency measured by an observer depends on a Lorentz-like projection between the observer’s frame and the source’s frame. This projection is parametrized by a single scalar quantity, a rapidity-like parameter (\Phi_{AB}), defined purely by the relation between observer (A) and source (B). Under this relational projection: photon frequencies scale as (1+z = e^{\Phi_{AB}}), observed time intervals are dilated by the same factor, blackbody spectra remain exactly Planckian, with an apparent temperature scaling (T_{\text{obs}} = T_{\text{src}}/(1+z)). Crucially, the preservation of the Planck spectrum follows from the Lorentzian nature of the projection and does not require adiabatic expansion or photon energy loss mechanisms. The Cosmic Microwave Background is therefore interpreted not as evidence of a cooling Universe evolving from a hot origin, but as radiation observed near the relational horizon, where simultaneity with the observer is maximally degraded. In this picture, the notion of a “hot early Universe” is replaced by a geometric statement: the further a system is in relational terms, the more its states appear redshifted and temporally diluted when projected onto the observer’s frame. Apparent cosmic cooling is thus an observational effect arising from relational desynchronization, not from thermodynamic evolution of a global medium. The framework reproduces the leading kinematic cosmological relations—Hubble’s law at small separations, Tolman surface brightness scaling, time dilation of distant transients, and temperature–redshift scaling—without introducing a time-dependent scale factor, dark energy, or a Big Bang singularity. Importantly, the absence of a Big Bang here does not constitute a denial of observational data, but rather reflects that no global temporal origin is required within a purely relational ontology. The proposal is explicitly empirical and falsifiable. Observations that depend on more than redshift kinematics—such as primordial nucleosynthesis yields, detailed acoustic structure of the CMB, and lensing time-delay relations—provide clear tests capable of confirming or refuting the relational interpretation. This work is intended as a foundational and conceptual contribution: it does not claim to replace standard cosmology in its entirety, but demonstrates that many of its most striking observational signatures can emerge from relational simultaneity alone, without assuming an expanding Universe or a physically real spacetime container. This manuscript is current in Official Peer Review. Not final version.Copyright©2026 Alex De Giuseppe.All rights reserved. This work is protected by copyright. Any form of plagiarism, unauthorized reproduction, or misappropriation of ideas, mathematically results, or text without proper citation constitutes a violation of academic and intellectual property standards and common laws. No commercial use, adaptation, or derivative works are permitted without explicit written permission from the author. For correspondence, citations, collaboration inquiries, or feedback please contact:[e-mail] The hash files that determine ownership have been created.