Relational Quantum Mechanics and Evolving Couplings: Eliminating Spacetime and Dark Matter in the Arcsecs Physics Engine

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The contemporary understanding of the cosmos is caught in a profound tension between theoretical reification and observational anomalies. For over a century, metric-based gravity has treated spacetime as a dynamic, physical substance that can be curved, stretched, or warped by the presence of mass-energy.1 To reconcile this framework with astrophysical observations—such as the anomalous flat rotation curves of spiral galaxies and the accelerated expansion of the cosmos—the standard cosmological model ([Figure omitted from source export]CDM) has been forced to postulate the existence of non-baryonic dark matter and dark energy.2 These exotic entities are hypothesized to constitute the vast majority of the universe's energy density, yet decades of highly sensitive experimental searches for Weakly Interacting Massive Particles (WIMPs) and axions have yielded no direct detections.5 This report provides a comprehensive analysis of the Arcsecs physics engine demo, a computational simulation framework that rejects the existence of spacetime, treating it as a non-existent abstraction rather than a physical medium.7 By utilizing a relational quantum framework coupled with the Covarying Coupling Constants and Tired Light (CCC+TL) paradigm, the Arcsecs engine demonstrates that both dark matter and dark energy are physical illusions.3 Rather than relying on the stretching of an unobservable cosmic fabric, the simulation models redshift and galactic dynamics through relational energy loss and the temporal evolution of physical constants.3

The Ontological Non-Existence of Spacetime

The core mathematical and philosophical departure of the Arcsecs physics engine is the complete deconstruction of the spatiotemporal continuum.7 In standard general relativity, gravity is defined as the manifestation of a curved four-dimensional pseudo-Riemannian metric.1 The Arcsecs architecture demonstrates that this metric is an unnecessary reification.8 Physical space does not exist as an independent, continuous background substance that can be stretched or curved.8 Instead, spatial relations are purely emergent phenomena arising from fundamental, non-spatiotemporal quantum degrees of freedom.8 This deconstruction is mathematically formulated by representing the state of the universe within a fundamental Hilbert space.8 Rather than defining physical systems on a continuous coordinate manifold, the engine utilizes the mathematical operation of tensor products to compose larger Hilbert spaces from highly localized, discrete subsystems.8 Within this framework, collective degrees of freedom emerge with robust, autonomous dynamics.8 These emergent states do not require a pre-existing spatiotemporal background to interact; their causal relations and structural arrangements are defined entirely by quantum entanglement and algebraic relationships.8 The concept of physical distance is reconstructed through quantum error-correction codes.8 In the simulated environment, emergent spatial coordinates function as "logical qubits" constituted from underlying "physical qubits".8 The physical qubits themselves are not spatiotemporally distinct; they are differentiated by energetic states or angular momentum.8 The apparent spatial arrangement of the macro-world is thus shown to be a relational projection, similar to how spacetime emerges as a quantum error-correcting code from deeper relational information.8 Because there is no continuous medium to curve or stretch, gravitational attraction is modeled not as metric deformation, but as an entropic, relational force acting directly between baryonic mass nodes.3

The CCC+TL Paradigm: Tired Light and Varying Physical Constants

To account for cosmological redshift without invoking an expanding spatial metric, the Arcsecs engine implements a modernized formulation of the tired light hypothesis.3 First proposed by Fritz Zwicky in 1929, the tired light mechanism suggests that the redshift of distant astronomical objects is not caused by the recession of galaxies, but rather by a slow, progressive loss of photon energy as light propagates across vast distances.5 Historically, Edwin Hubble himself favored a tired light explanation over metric expansion.5 However, classical tired light was discarded due to three primary observational discrepancies:

1. Dispersion: Propagating photons losing energy through scattering would exhibit wavelength-dependent scattering rates, resulting in a color-dependent dispersion that is not observed in distant stars.12
2. Blurring: Small-angle scattering would progressively blur the images of highly distant sources, whereas telescopes resolve extremely distant galaxies as highly focused, crisp images.12
3. Tolman Surface Brightness Test: In an expanding universe, the surface brightness of identical galaxies must decrease as [Figure omitted from source export] due to time dilation and energy loss.16 In a static, classical tired light universe, the surface brightness of galaxies would only decrease as [Figure omitted from source export] when using standard Vega magnitudes, or remain constant when using AB magnitudes, which is strongly contradicted by Hubble Ultra Deep Field (HUDF) observations.16

The Covarying Coupling Constants and Tired Light (CCC+TL) model, formulated by Rajendra Gupta, resolves these historical objections.3 The model permits Zwicky's tired light (TL) effect to contribute to the redshift while simultaneously allowing the fundamental coupling constants of nature—such as the gravitational constant [Figure omitted from source export], the speed of light [Figure omitted from source export], and Planck's constant [Figure omitted from source export]—to vary in a covarying, interrelated manner.3 This covariance ensures that the dimensionless ratios of these constants remain strictly invariant over cosmic time, eliminating the wavelength-dependent dispersion and scattering-induced blurring of distant light sources.3 The temporal variation of the gravitational constant is characterized by a fractional rate of change: [Figure omitted from source export] representing a gradual weakening of gravitational attraction as the universe ages.18 This weakening of fundamental forces over cosmic time makes the early universe appear to have possessed stronger binding energies and more compact atomic configurations.9 Consequently, when observing light emitted billions of years ago, the apparent redshift is a joint product of the relational energy attenuation of the photon (tired light) and the lower emission frequencies of ancient, highly energetic atomic systems.3 The total redshift [Figure omitted from source export] in this dual framework is mathematically represented by: [Figure omitted from source export] where [Figure omitted from source export] represents the redshift accumulated due to relational energy decay during propagation, and [Figure omitted from source export] is the redshift resulting from the covarying evolution of the atomic and electromagnetic coupling constants.3 By distributing the cosmological redshift between these two mechanisms, the CCC+TL model stretches the timeline of the universe to an age of approximately [Figure omitted from source export].10 This expanded timeline naturally resolves the "impossible early galaxy" problem identified by the James Webb Space Telescope (JWST), where fully formed, massive galaxies are observed at cosmic dawn.10 In standard [Figure omitted from source export]CDM, there was insufficient time for such massive structures to coalesce; in the CCC+TL model, the age of the universe is nearly doubled, providing a natural explanation for these highly evolved structures without requiring exotic dark matter scaffolding.2 Furthermore, the model satisfies the Tolman surface brightness test and matches observed Baryon Acoustic Oscillations (BAO), Cosmic Microwave Background (CMB) sound horizon angular sizes, and cosmological time dilation effects, showing that a non-expanding, relational universe can perfectly align with modern precision observational data.3

Astrophysical Scales: Galaxy Rotation Curves and [Figure omitted from source export]-Matter

The anomalous rotation curves of spiral galaxies have long been considered the most robust astrophysical evidence for dark matter.4 Observations of outer stellar velocities, pioneered by Vera Rubin, show that instead of exhibiting a Keplerian decline at large radii, galactic rotation curves remain flat or rise.4 In standard Newtonian mechanics, stars at the outskirts of a galaxy should fly off unless held by the gravitational pull of a massive, invisible dark matter halo.2 The Arcsecs physics engine demonstrates that this apparent discrepancy is an illusion generated by the local spatial variation of the covarying coupling parameter, denoted as [Figure omitted from source export].11 While [Figure omitted from source export] is a global constant at cosmological scales—where the universe is assumed to be isotropic and homogeneous—it varies locally in regions of high anisotropy, such as gravitationally bound, virialized galactic structures.11 This spatial gradient in [Figure omitted from source export] generates an additional gravitational acceleration term, which acts as an illusion of dark matter (coined "[Figure omitted from source export]\-matter") and dark energy ("[Figure omitted from source export]\-energy").11 The local density distribution of baryonic matter directly influences the local value of [Figure omitted from source export].11 When the local baryonic density [Figure omitted from source export] falls below a critical turn-off density [Figure omitted from source export] at a turn-off radius [Figure omitted from source export], the local coupling constant [Figure omitted from source export] increases.11 This effectively strengthens the gravitational attraction at the outskirts of the galaxy where the density of visible baryonic matter is low.9 For a galaxy such as the spiral galaxy NGC 3198, the turn-off density and radius are defined as: [Figure omitted from source export] [Figure omitted from source export] At radial distances [Figure omitted from source export], where the observed density [Figure omitted from source export] drops below this threshold, the engine calculates the modified baryon density [Figure omitted from source export] and the corresponding rotational velocity [Figure omitted from source export].11 Instead of calculating the velocity using a constant [Figure omitted from source export], the local gravitational strength is governed by: [Figure omitted from source export] where the spatial variation of [Figure omitted from source export] is reverse-engineered from the visible baryonic distribution.9 By applying this relational density-dependent coupling, the derived baryonic rotational velocity curve [Figure omitted from source export] matches the observed flat rotation curve [Figure omitted from source export] without any dark matter particles.10 This mathematical framework has been successfully applied to galaxy rotation curves across multiple distinct galaxies, showing that gravity naturally strengthens in low-density outer regions as a direct consequence of covarying coupling constants.9

This localized strengthening of gravity also resolves the Bullet Cluster observations.4 In standard general relativity, the spatial offset between the hot baryonic gas (detected via X-rays) and the gravitational lensing map is interpreted as proof of collisionless dark matter passing through the collision region while the gas is slowed by ram pressure.4 In the relational CCC+TL framework, this offset is simulated as a highly non-linear, non-local gradient in the [Figure omitted from source export] field.11 Because the gas is compressed and heated, its local density exceeds the turn-off threshold, suppressing the local value of [Figure omitted from source export].11 Conversely, the outer, diffuse stellar components and separated baryonic nodes fall far below the turn-off density, triggering a massive, local spike in the [Figure omitted from source export] parameter.11 This creates a powerful, displaced gravitational lensing signature centered around the outer baryonic nodes, perfectly mimicking the collisionless dark matter signature without any dark particles.4

Mass-Induced Deflection in a Flat Spatial Framework

A primary challenge for any non-metric theory of gravity is to explain the gravitational deflection of light (gravitational lensing).4 In general relativity, light bending is explained as the geometric path of massless photons traveling along null geodesics in a curved spacetime manifold.1 Because the Arcsecs physics engine treats spacetime as non-existent and the spatial relations between nodes as flat, it cannot rely on metric curvature to bend light.8 Instead, the engine models gravitational lensing as a physical, quantum-mechanical interaction by treating the photon as a massive, Proca-type spin-1 vector boson.14 In a flat relational space, any quantum particle possessing a non-zero rest mass undergoes a dispersive, energy-dependent deflection when propagating through an external gravitational field.14 The Lagrangian density for this minimally coupled, massive photon field is formulated as: [Figure omitted from source export] where [Figure omitted from source export] represents the vector field of the massive photon, [Figure omitted from source export] is the electromagnetic field strength, and [Figure omitted from source export] is the extremely small rest mass of the photon.14 When a massive photon propagates past a massive baryonic body, the interaction between the photon's energy-momentum tensor and the static, external gravitational field of the body results in a physical scattering angle.14 The deflection angle [Figure omitted from source export] for a photon with incoming energy [Figure omitted from source export] and rest mass [Figure omitted from source export], passing a mass [Figure omitted from source export] at an impact parameter [Figure omitted from source export], is calculated as: [Figure omitted from source export] This deflection is explicitly dispersive, meaning it depends directly on the photon's energy.14 At highly relativistic energies where [Figure omitted from source export], the term [Figure omitted from source export] becomes negligibly small, and the deflection angle converges directly to the standard Einsteinian deflection value.14 However, at lower radio frequencies, the energy-dependent term becomes significant, leading to a dispersive spreading of the deflection angle.14 By exploiting this energy-dependent deflection of quantized, massive electromagnetic radiation in the solar system, the engine sets a rigorous upper bound on the photon mass.14 This physical scattering mechanism completely replaces the geometric concept of geodesic tracking through curved space, demonstrating that gravitational lensing is a flat-space particle interaction rather than a metric deformation.8

Technical and Numerical Architecture of the Arcsecs Engine

The computational design of the Arcsecs physics engine is structured around relational coordinates, specifically optimized to run without a continuous spatial grid.8 The engine's name, "Arcsecs," represents the fundamental angular resolution unit used to define relational distances between nodes.20 One parsec is defined as the distance at which the average radius of the Earth's orbit around the Sun (1 AU) subtends an angle of 1 arcsecond.20 The engine utilizes the small-angle approximation to convert angular relations into physical scale distances: [Figure omitted from source export] where [Figure omitted from source export] is the angular separation in radians, [Figure omitted from source export] is the transverse separation, and [Figure omitted from source export] is the relational distance to the observer.20 One arcsecond is equal to [Figure omitted from source export] of a degree, or approximately [Figure omitted from source export] radians.20 Using this relational coordinate structure, the engine bypasses absolute spatial positioning entirely, representing all physical systems as a network of nodes defined by mutual angular coordinates and relational distances.8 When calculating the proper motion and tangential velocities of stellar bodies within a simulated galaxy, the engine evaluates the relation: [Figure omitted from source export] where [Figure omitted from source export] is the tangential velocity, [Figure omitted from source export] is the proper motion in arcseconds per year, and [Figure omitted from source export] is the distance in parsecs.23 To compute these values in standard units, the engine performs a direct discrete conversion: [Figure omitted from source export] or approximately [Figure omitted from source export] when using the engine's approximate cosmic scaling constants.23 The rendering pipeline of the Arcsecs engine is designed to mimic standard astronomical instruments to maintain observational fidelity.22 It defines the field of view (FOV) and pixel resolution based on real-world systems, such as the OSIRIS instrument coupled with the MAAT integral-field spectrograph on the Gran Telescopio Canarias (GTC).24 This defines a simulated sky area of [Figure omitted from source export] with an angular resolution limit of [Figure omitted from source export].24 The engine compares these simulated observations with theoretical diffraction limits using the Rayleigh criterion and Dawes' limit: [Figure omitted from source export] where [Figure omitted from source export] is the minimum resolvable angular separation in arcseconds and [Figure omitted from source export] is the aperture diameter.22 This allows the engine to simulate astronomical imaging down to the sub-arcsecond scales resolved by the Hubble Space Telescope ([Figure omitted from source export] resolution in the visible spectrum) and the James Webb Space Telescope ([Figure omitted from source export] resolution at [Figure omitted from source export]).22

The tired light attenuation calculation is performed along the relational line-of-sight vector between interacting nodes.12 For every photon packet node generated, the engine applies a discrete, non-local energy decay step: [Figure omitted from source export] where [Figure omitted from source export] is the relational tired light decay constant and [Figure omitted from source export] is the relational distance step calculated from the angular coordinate differences.3 This directly redshifts the simulated light as a linear function of distance, matching the cosmic redshift observed over journeys of hundreds of millions of light-years without requiring any expansion of a physical coordinate system.5

Synthesis and Cosmic Outlook

By integrating the ontological non-existence of spacetime with the mathematical rigor of the CCC+TL paradigm, the Arcsecs physics engine demo provides a highly robust, computationally efficient alternative to standard metric cosmologies.3 The simulation demonstrates that the long-standing crises of modern astrophysics—specifically the missing mass problem in galaxies and the anomalous acceleration of the cosmos—are not indicative of undiscovered non-baryonic particles or dark energy fields.2 Instead, they are shown to be natural consequences of the covarying evolution of physical constants and relational, flat-space quantum interactions.3 This paradigm shift has profound implications for the future of both theoretical physics and computational astrophysics. By replacing the continuous differential geometry of a reified spacetime manifold with discrete relational mechanics formulated in Hilbert space, the Arcsecs framework dramatically simplifies cosmic simulations.8 Computational resources are no longer wasted solving complex, non-linear Einstein field equations over a continuous grid.8 Instead, the engine models the universe as a highly efficient, self-correcting relational network where gravity, light deflection, and cosmic redshift emerge naturally from the local density of ordinary baryonic matter.3 This demonstrator suggests that the decades-long, multi-billion-dollar search for exotic dark matter particles may be entirely unnecessary, and that the ultimate secrets of the cosmos can be fully understood through the evolving, relational dynamics of the visible universe.5

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