Rethinking the Cosmos: How Discrete Space-Time Resolves the Expansion Paradox
Although Bianconi’s quantum entropy approach to solving the expansion of the universe is intriguing — particularly in how it removes the need for Einstein’s fixed universe equation and the postulation of dark matter — it faces deeper conceptual problems when examined critically. The fundamental issue lies in whether the universe is truly “expanding” as a property of space itself or whether it is simply a result of objects moving apart within a pre-existing framework. Our analysis suggests that what is commonly referred to as expansion is, in reality, movement. However, Bianconi’s model still relies on the assumption that entropy maximization occurs in a continuous space, which we argue is an unnecessary constraint.
This distinction can be observed in a sequence of thought experiments. If we begin with a familiar example — the Apollo spacecraft leaving Earth — it is clear that movement occurs due to an applied force rather than any intrinsic change in the structure of space. Extending this to a larger scale, the formation of the solar system involved the redistribution of mass and energy, but at no stage did space itself expand; instead, objects moved into new positions under gravitational interactions. When we scale this logic up to the Big Bang, the same principle holds: matter and energy, initially in a dense, high-energy state, moved outward due to physical forces rather than space itself stretching. At no point in these scenarios is there a need to assume that “new space” is being created — only that matter is redistributing within a pre-existing discrete structure.
Thought Experiment 1: Apollo’s Motion — A Test of Expansion vs. Movement
To begin our analysis of whether space expands or objects simply move, we start with the simplest real-world scenario: the Apollo spacecraft leaving Earth. If “expansion of space” were a fundamental principle of the universe, we should be able to detect its effects even at small scales. However, if Apollo’s increasing distance from Earth is purely a result of motion, then it suggests that cosmic expansion could also be reinterpreted as large-scale movement rather than the stretching of space itself.
In the Apollo mission, a spacecraft begins at rest on Earth’s surface. At launch, its engines exert a force, pushing it upward and away from the planet. The spacecraft moves through space, accelerating beyond Earth’s atmosphere, reaching orbit, and eventually traveling toward the Moon. At no point in this process does space itself expand — Apollo moves away from Earth due to applied forces, not because the fabric of space is stretching.
This is crucial because the increasing distance between Apollo and Earth looks exactly like “expansion” if one were to describe it mathematically using relative coordinates. If we were to naively apply the same logic used in cosmology, we could falsely claim that “the space between Earth and Apollo is expanding.” But this would be an unnecessary complication — the simpler and correct explanation is that Apollo is moving within a fixed spatial framework, and its growing distance from Earth is entirely due to motion.
Furthermore, the distance between Apollo and Earth is limited by the speed of the spacecraft, which depends on its fuel, mass, and thrust. There is no absolute speed limit preventing it from moving farther away at any given rate, except for the constraints imposed by its propulsion system. This differs from standard cosmology, where galaxies are said to recede at increasing speeds due to “expanding space” rather than their own movement. If Apollo were subject to the same logic as cosmic expansion, we would be forced to argue that the spacecraft is not actually “moving” but that Earth and Apollo are being carried apart by a growing spatial metric. This is clearly not the case — the spacecraft moves in a well-defined trajectory governed by Newtonian and relativistic mechanics.
Thus, the Apollo thought experiment demonstrates a fundamental principle: objects increasing their distance from one another does not require space itself to expand. If this is true for Apollo, then the same logic should hold at larger scales unless proven otherwise. By showing that “expansion” is unnecessary at small scales, we have reason to question whether it is necessary at cosmic scales. In the next thought experiment, we extend this idea to the formation of the solar system.
Thought Experiment 2: The Formation of the Solar System — Expansion vs. Movement
Now, we extend our analysis beyond a single spacecraft to a self-contained, larger system: the solar system. In this thought experiment, we assume that our observable universe is limited to the solar system alone. This allows us to examine whether the increasing distances between celestial objects during planetary formation require an expanding space or if simple movement within a pre-existing framework is sufficient.
At T₀, we begin with a primordial cloud of gas and dust — a high-energy, dense region of matter concentrated in a small area. This cloud has no defined structure yet, but the potential for gravitational collapse exists within it. There is no notion of “space expanding” at this stage — only the presence of a mass-energy distribution that is about to undergo transformation.
At T₁, an event occurs that disturbs the equilibrium of this gas cloud, possibly a nearby supernova shockwave. This triggers collapse under gravity, causing regions of the cloud to condense while angular momentum conservation forces the entire system into a rotating disk. At this point, matter is in motion — clumps of dust and gas begin migrating toward the center, forming the Sun, while smaller regions coalesce into early planetary embryos. Notably, the distances between forming planets increase as a result of motion, not any intrinsic change in space itself.
By T₁₀, planetary formation is well underway. The inner planets — Mercury, Venus, Earth, and Mars — are taking shape through collisions and accretion, while larger gas giants — Jupiter and Saturn — are forming in the outer region. Crucially, the solar system now exhibits clear separation between inner and outer planets, but this is entirely due to gravitational interactions and conservation laws, not due to any stretching of space itself. The distance between planets is increasing, but only because their positions are evolving within a pre-existing spatial structure.
At T₂₀, the largest planets — Jupiter and Saturn — dominate the gravitational dynamics of the system. Their immense mass causes them to scatter and reposition smaller planetary bodies, further defining the structure of the solar system. The asteroid belt stabilizes between Mars and Jupiter, acting as a natural boundary between the inner and outer regions. Again, this reconfiguration of planetary positions is a result of movement governed by physical forces, not any fundamental change in the nature of space itself.
By T₃₀, the solar system has reached its present-day configuration. Planets orbit the Sun in well-defined paths, and the system exhibits a stable structure. The final planetary positions and orbital separations were determined by gravitational interactions and conservation of energy and momentum — not by the expansion of space. If we were to use the logic of modern cosmology, one could mistakenly argue that “the space between planets expanded” during this process. However, we know this is incorrect — planets simply moved into new positions dictated by natural laws.
This thought experiment reinforces a crucial insight: The increasing distances between celestial objects can be explained entirely by movement, without requiring space itself to expand. The formation of the solar system mirrors the larger structure of the universe, suggesting that cosmic-scale separation of galaxies may also be a result of motion rather than metric expansion. If “space expansion” was not needed to explain the solar system, why should it be necessary at the universal scale?
Thought Experiment 3: The Big Bang — Expansion vs. Movement
Having established that increasing separation between objects can be entirely explained through motion rather than metric expansion in both the Apollo spacecraft and the formation of the solar system, we now extend our thought experiment to the largest scale: the Big Bang and the evolution of the universe itself. If the same principles hold, then the argument for “expanding space” becomes unnecessary and redundant.
At the initial state of the universe — analogous to T₀ in our solar system model — the cosmos existed in a highly dense, high-energy state. All known matter and radiation were concentrated in a region of extreme temperature and pressure, but there was no fundamental requirement that “space itself” was small or needed to expand. The standard model of cosmology assumes that the Big Bang was the origin of space and time, but in the Metron-Chronon framework (read further essay here,) it is instead a redistribution of pre-existing energy within a structured, discrete lattice.
As the Big Bang unfolds — our equivalent T₁ phase — matter and energy begin moving outward due to physical interactions, cooling and condensing into the first elementary particles. This mirrors the collapse and redistribution of mass in the early solar system. By the time we reach T₁₀, atomic nuclei have formed, setting the stage for later structure formation. Just as in the planetary accretion phase of the solar system, the key process here is movement within a fixed spatial framework, not the creation of new space.
At T₂₀, matter begins forming large-scale structures such as galaxies, clusters, and voids. In traditional cosmology, this is where metric expansion is invoked to explain why galaxies recede from one another. However, we must now ask: if the logic of movement applied in every case up to this point, why should a new, separate mechanism be introduced at cosmic scales? If planets and galaxies formed and moved apart due to physical forces, why must we assume that their increasing separation is due to an expanding spatial metric rather than a continuation of movement dynamics?
At T₃₀, we reach the present-day universe, where galaxies continue to separate over time. The distances between them are increasing, but as we have seen, this does not require space itself to expand — only that objects are in motion due to initial energy distributions. The same principles that governed Apollo’s journey and the formation of planetary orbits should still apply here. If mainstream physics insists that space expands at the universal scale, then we must ask: what criteria are being used to determine when to invoke expansion and when to invoke movement?
This brings us to a fundamental problem with Bianconi’s model and the mainstream cosmological interpretation. If metric expansion is truly distinct from movement, then there must be a clear rule that distinguishes between the two. However, no such universally accepted criteria exist. Instead, physicists selectively categorize different cases as “movement” or “expansion” based on constraints imposed by their own theoretical models — primarily the speed of light limitation in relativity and the assumption of a continuum spacetime structure.
The hesitation to abandon metric expansion is largely driven by the reluctance to cross the speed of light barrier. In standard cosmology, distant galaxies are observed to redshift in a way that suggests recession speeds exceeding the speed of light. Since relativity forbids objects from moving faster than light within spacetime, physicists introduced metric expansion as a workaround: galaxies are not truly “moving” faster than light, they claim, but rather space itself is stretching, carrying them apart. This avoids violating relativity but creates an entirely separate paradox — why does space “expand” at large scales but not at small ones?
The Metron-Chronon framework eliminates this contradiction by rejecting the assumption that the speed of light is a universal constant across all scales. Instead, light speed is an emergent property of the local metron-chronon lattice rather than an immutable limit imposed by a continuum spacetime. Galaxies move within a discrete framework, and their separation is governed by the properties of that structure, rather than an imposed metric expansion. The mainstream hesitation to move beyond light-speed constraints and continuum models has led to an unnecessary confusion between “expansion” and “movement,” forcing a model that is mathematically convenient but physically unfounded.
Conclusion: The Metron-Chronon Model as the Resolution to Physics Paradoxes
Through our thought experiments — progressing from the Apollo spacecraft to the formation of the solar system and ultimately to the Big Bang — we have demonstrated a consistent physical principle: objects separate due to movement, not due to an expansion of space. The prevailing assumption in modern physics that the universe expands as a stretching of the spatial metric is not a necessary physical truth but a conceptual artifact arising from the constraints of relativity and continuum-based thinking. The Metron-Chronon framework eliminates these contradictions and resolves all fundamental paradoxes in modern physics by adhering strictly to three foundational principles:
First, falsifiability — a scientific theory must be testable and, if incorrect, refutable through empirical evidence. Standard cosmology, relying on metric expansion, describes a process that cannot be directly observed; we cannot measure “space itself expanding,” only the redshift of distant galaxies, which can equally be explained by movement within a structured lattice. Similarly, the Many-Worlds Interpretation (MWI) of quantum mechanics posits an infinite branching of realities with no empirical mechanism for detecting them, making it an unscientific model. In contrast, the Metron-Chronon framework remains falsifiable: if motion alone cannot account for cosmic redshifts, or if a discrete space-time structure is contradicted by experimental data, the model can be revised or discarded.
Second, Occam’s Razor — the principle that among competing theories, the one with the fewest assumptions should be preferred. Standard physics postulates that at small scales, objects move due to forces, while at cosmic scales, space itself expands due to a separate mechanism. This artificial distinction requires additional assumptions about metric expansion, dark energy, and the fundamental nature of space-time. The Metron-Chronon model eliminates these redundancies by proposing a single, consistent rule: objects move apart at all scales due to their initial conditions and interactions, within a discrete framework where the speed of light is an emergent property rather than a universal constraint. By reducing expansion to movement, we unify small-scale and large-scale physics under the same fundamental principle.
Third, recognition of bounded observational scales — physics must acknowledge that all measurements are limited by the structure of reality itself. Our bounded observable universe spans from the smallest measurable scale, the quark, to the largest, the observable universe itself. This limitation is not due to cognitive constraints or lack of imagination but is dictated by the fundamental limits of instrumentation and measurement based on known physical laws. No existing or theoretically feasible measurement tool can probe beyond the quark scale on the microcosmic end, nor can we observe beyond the cosmic horizon at the macrocosmic extreme. These limits define what we call the observable universe, which is not necessarily the entirety of existence but rather the maximum extent to which we can empirically test reality.
The quantum logic clock stands not just as a triumph of precision but as a barrier we cannot breach. It marks the furthest point our instruments allow us to measure time meaningfully, beyond which observation collapses into uncertainty. This clock, based on laser-cooled trapped ions, achieves unparalleled precision by leveraging quantum superposition and entanglement, minimizing errors beyond what classical atomic clocks can achieve. Yet, despite its refinement, it also exposes the hard limits of measurement. As we approach the Planck time (~5.39 × 10^44 seconds), quantum fluctuations and gravitational effects become inseparable, dissolving any meaningful concept of a continuous time flow. No tool exists to measure further — not due to intellectual limitation, but because the very act of measurement ceases to be well-defined. Without a reliable instrument beyond this limit, physics is left to speculation, unable to confirm or falsify ideas that extend past the empirical.
This forces us to accept a fundamental truth: we cannot know with certainty what lies beyond these observational boundaries. There may be finer structures beneath quarks or an even greater cosmic framework beyond our universe, but within the constraints of known physics, these remain unknowable. Crucially, this does not imply that a boundary exists in any absolute sense — only that we lack the means to investigate beyond it. The same way we cannot measure below the quark scale, we cannot definitively claim that space-time extends infinitely beyond our observational reach. The Metron-Chronon framework fully embraces this reality, ensuring that all theories remain grounded in what can be tested and measured, rather than speculative assumptions about the unobservable.
By adhering to these three principles — falsifiability, Occam’s Razor, and bounded observability — the Metron-Chronon framework offers a logically consistent, testable, and fundamentally discrete model of reality. It rejects both standard physics, which remains constrained by outdated continuum assumptions and artificial mathematical constructs, and MWI, which fails to meet basic scientific criteria of testability and logical economy. Through this approach, we resolve all major paradoxes in modern physics — quantum gravity, cosmic expansion, singularities, and the nature of space-time — while maintaining a fully scientific and empirical foundation.
The fundamental conclusion is clear: space does not expand — objects move. By shifting from a metric-based interpretation of cosmic evolution to a movement-based framework within a discrete structure, we unveil a new foundation for physics — one that is free from paradoxes, firmly rooted in reality, and capable of advancing our deepest understanding of the universe.
