Rincewind

Swonsont, I appreciate your emphasis on the need for evidence to support any new model. While the Standard Model primarily addresses particle physics, its principles and extensions often intersect with cosmological models, particularly in explaining the conditions of the early universe and the formation of structures such as galaxies. The JWST observations challenge the timeline for early galaxy formation, suggesting that galaxies formed earlier and more rapidly than the current models predict. This discrepancy invites us to consider alternative frameworks that might better align with these observations. As Richard Feynman once said, "It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong." The FTS model offers a novel perspective by introducing a dual-time framework (Atomic Time and Ephemeris Time) and hypothesising matter shrinkage over cosmic time. This approach provides alternative explanations for cosmic expansion and the nature of dark energy, potentially addressing the observed discrepancies. While I agree that evidence is crucial, the FTS model's alignment with recent observations and its ability to offer coherent explanations for unresolved issues in standard cosmology warrant its consideration. Exploring alternative models like FTS can lead to a more comprehensive understanding of the universe, especially when existing models face significant observational challenges, challenges that were predictable with this model before the challenges were observed. Joigus, I appreciate your thoughtful critique. Let's address the points you've raised: Matter Shrinkage and Overall Acceleration: The Fractal Topology of Space-Time (FTS) model posits that matter undergoes a diminishing isomorphic transformation over cosmic time, leading to an apparent acceleration in the universe's expansion. This does not imply a trivial rescaling but rather an intrinsic transformation that aligns with the evolving cosmic background. The energy-momentum tensor in Einstein's equations would indeed be affected, but the FTS model accounts for this by considering the uniform scaling of all interactions within their local frame. Fractal Nature: The "fractal" aspect of the FTS model refers to the self-similar scaling properties observed over different cosmic epochs. This fractal scaling is evident in the way atomic forces and distances evolve relative to the cosmic background, maintaining the invariance of fundamental interactions while appearing different over time. Markus Hanke's Objection: Markus Hanke's concern about breaking physics by shrinking atoms is addressed by the FTS model's premise that all interactions scale uniformly within their local frame. Atomic forces, such as electromagnetic binding, depend on relative distances rather than absolute sizes. The perceived contraction is relative to the evolving cosmic background, not an intrinsic modification of atomic forces. This ensures that fundamental laws remain invariant within atomic scales but appear different over cosmic time due to fractal scaling in Ephemeris Time (ET). Redshift-to-Distance Observations: The scaling effects proposed by the FTS model are gradual over deep cosmic time. Observations of redshift-to-distance relationships support this gradual scaling, as space within gravity-bound systems, such as our spiral galaxy, shows no evidence of expanding space. This fits with observations of other galaxies and addresses the discrepancy in standard Friedmann-Robertson-Walker (FRW) models, which assume uniform expansion across all regions. Standard Model Discrepancies: The standard model of cosmology assumes uniform expansion, yet observations show no evidence of expansion within gravity-bound systems. The FTS model offers an alternative explanation by proposing that atomic time-based distances scale with the atoms, preserving the local frame's interactions while accounting for the observed discrepancies. In summary, the FTS model provides a coherent framework that aligns with both relativistic and cosmological observations, offering alternative explanations for unresolved issues in standard cosmology. As Richard Feynman once said, "It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong." The FTS model's alignment with recent observations warrants its consideration as a viable alternative framework.

Joigus, while I appreciate your adherence to the principles of general relativity, I believe there is a fundamental misunderstanding of the FTS model's approach. The FTS model does not rely on a fixed metric background in the traditional sense. Instead, it introduces a dual-time framework consisting of Atomic Time (AT) and Ephemeris Time (ET), which enables the reinterpretation of cosmic phenomena. Dual-Time Framework: Atomic Time (AT): Defined by atomic vibrations and essential for precise timekeeping. Ephemeris Time (ET): Historically used in astronomy, invariant to relativistic effects, providing a stable measure of time displacement. Scaling and Matter Shrinkage: The FTS model hypothesises that matter undergoes a diminishing isomorphic transformation as it travels through ET over cosmic time. This leads to an apparent acceleration in the universe's expansion, offering an alternative explanation to dark energy. Relativistic Effects and Observations: The model explains variations in the Hubble constant (H0) measurements as dependent on relativistic time dilation effects on instruments, contributing to the Hubble tension. Cyclic Universe: The FTS model extends to an infinite, positionally background-dependent universe, represented as a horn torus with infinitely many aeons of time connected by a central Big Bang. Emergent Gravity: Gravity is understood as an emergent effect dependent on the rate at which future distances diminish, with matter undergoing uniform shrinking relative to an absolute background. In essence, the FTS model respects the principles of general relativity while offering a novel perspective on cosmic phenomena. It does not discard the importance of the interval but rather reinterprets it within a dual-time framework that aligns with both relativistic and cosmological observations.

Given that JWST observations challenge SM’s timeline for early galaxy formation, it seems timely to explore whether alternative models, like FTS, could offer insights that standard cosmology struggles to reconcile. Would you argue that unanticipated observational discrepancies should prompt re-evaluation of existing models, or do you believe they should simply lead to modifications within the current framework? Your request for a framing is valid, but it presupposes that scaling must occur relative to a fixed metric background, a perspective deeply embedded in standard cosmology. FTS challenges this assumption by proposing that scale itself evolves over Ephemeris Time (ET), rather than space expanding relative to an underlying metric. This means that conventional definitions of 'size' and 'motion' must be reconsidered, not within the confines of an expanding metric, but as intrinsic transformations within matter itself. Are you open to exploring how such a shift might resolve discrepancies that currently require dark matter? Markus, you raise an important point regarding the energy-momentum tensor and its connection to the Riemann tensor. While GR describes gravitational interactions through curvature, the Riemann tensor is fundamentally a local descriptor; it captures how matter moves along geodesics within curved spacetime. However, this does not necessarily mean it dictates how scale itself evolves over cosmological time. FTS does not require a vanishing Riemann tensor because it does not treat gravitational effects as irrelevant; it acknowledges that locally, GR’s dynamic paths accurately describe motion. The distinction is that over large-scale cosmic evolution, scaling transformations become the dominant factor rather than curvature-dependent mechanisms. In FTS, time symmetry is preserved via ET ∝ AT, meaning energy remains conserved without relying on hidden mass corrections like dark matter. Instead of adjusting curvature tensors to explain observed discrepancies, FTS modifies the underlying assumptions about cosmic scaling, removing the need for an expanding metric. Would you agree that local curvature descriptions (Riemann tensor) do not necessarily dictate how global cosmic evolution must behave, or do you argue that metric expansion is the only viable framework for large-scale structure formation?

Joigus, your framing assumes that scaling must occur relative to a fixed cosmic background, but this is precisely where FTS diverges from standard cosmology. Standard cosmology implicitly treats space as expanding against a metric framework, which functions as an underlying reference. While this avoids an explicit ether concept, it still relies on an assumed backdrop against which cosmic expansion is measured. FTS, on the other hand, eliminates the need for this metric-dependent expansion by proposing that scale itself evolves over Ephemeris Time (ET), meaning size, distance, and velocity transform dynamically rather than referencing an underlying spatial grid. Rather than introducing an ether-like medium, FTS removes the dependence on an absolute metric altogether, allowing cosmic evolution to be governed by intrinsic scaling rather than extrinsic spatial expansion. It’s not about being ‘right’, it’s about ensuring that we thoroughly explore the implications of different models. If Standard Cosmology has unresolved discrepancies, such as its reliance on dark matter, then considering an alternative framework like FTS isn’t about proving one person correct; it’s about refining our understanding of cosmic mechanics. Are you interested in discussing whether FTS offers a viable alternative, or is the focus now shifting away from the physics itself?

While some hypothesised entities, like neutrinos or Pluto, were later confirmed through direct detection, others, such as the planet Vulcan, were ultimately disproven when deeper physical theories (GR) explained the discrepancies. Dark matter has remained undetected despite decades of focused searches, which raises the possibility that it, too, is an incorrect hypothesis masking a deeper issue in cosmology. Rather than assuming unseen mass must exist, alternative frameworks, such as FTS, suggest that the apparent anomalies may instead stem from how we interpret time scaling and energy conservation rather than requiring invisible matter. Given historical precedent, is it not reasonable to question whether dark matter is the next 'Vulcan', rather than a confirmed entity awaiting discovery?

You argue that rescaling atoms does not work, but this assumes that atomic structures are shrinking relative to a fixed cosmic background. FTS does not propose absolute contraction, it fundamentally reinterprets scale evolution in relation to Ephemeris Time (ET). One critical distinction between FTS and standard cosmology comes from Noether’s theorem: In General Relativity (GR), time symmetry is not globally preserved, meaning energy conservation is not strictly upheld over cosmic time scales. This is why energy loss in cosmic redshift is often treated as a natural consequence of expansion. In contrast, FTS maintains time symmetry, as ET scales proportionally to AT (ET ∝ AT). This means that energy is conserved across all scales, rather than appearing to dissipate over time. If atomic structures were truly 'shrinking' in an absolute sense, energy inconsistencies would arise. However, because time symmetry is restored in FTS, energy preservation remains intact, eliminating the need for dark matter or external corrective mechanisms. Would you argue that GR’s lack of strict energy conservation is a preferable framework, or do you acknowledge that a model maintaining time symmetry and energy conservation could provide a more fundamental solution?

While it’s common to speak of an 'expansion velocity' exceeding the speed of light, I stand by the idea that if a quantity can surpass c in this context, then it isn’t a velocity in the traditional, local, inertial-frame sense. In the Standard Model, galaxies beyond the Hubble Sphere appear to recede faster than light, but this is not a proper velocity measured locally. Instead, it's a coordinate effect resulting from the stretching of space as described by the metric. Locally, every comoving observer measures nearby objects with velocities well within the bounds of special relativity. In other words, if we require that real velocities—those measured in an observer's inertial frame—must always be less than c, then an 'expansion velocity' that exceeds c isn’t a physical velocity at all; it’s simply a manifestation of how we’ve chosen to codify the expansion through the Friedmann–Lemaître–Robertson–Walker metric. So when I say, 'While expansion velocity can exceed the speed of light, then it’s not a velocity,' I mean precisely that: it reflects a scaling effect of the universe’s geometry rather than a physical speed comparable to, say, a galaxy's peculiar motion within its local gravitational pocket. This is analogous to the SM’s treatment of galaxies beyond the Hubble Sphere, they’re not 'moving' through space at superluminal speeds in their local frames; rather, the metric itself is causing the separation between us and those galaxies to increase at a rate that can exceed light speed when expressed in these coordinates

Evidence Against SM’s Complete Success: The fact that standard cosmology must introduce a hypothetical form of matter—"now hypothesised as dark matter", to reconcile theory with observations is itself evidence that there’s something amiss. For example: Zwicky’s Early Work on the Coma Galaxy Cluster: Zwicky observed that the galaxies in the Coma Cluster were moving so fast that, based solely on the luminous (baryonic) mass, they should be flying apart. This led him to propose the existence of missing mass. Rubin’s Rotation Curve Discrepancies: Observations of flat galactic rotation curves, where stars in the outer parts of galaxies orbit at nearly the same speed as those closer to the centre, indicate far more mass than what is visibly present. These discrepancies force the SM to compensate with dark matter, which remains undetected directly, to explain both the binding of galaxy clusters and the anomalous galactic rotation curves. FTS’s Alternative Account: In contrast, the FTS model explains these phenomena by proposing that matter itself scales over Ephemeris Time (ET) rather than space expanding in an absolute sense. For instance, as you noted: In low baryon-dense regions (further from galactic centres), atomic time ticks faster. This means that when viewed from a region with slower AT (like near the galactic core or on Earth), objects in the outskirts seem to complete their orbits “too quickly”, naturally explaining the observed rotation curves without needing dark matter. Thus, FTS reinterprets the binding and dynamics of galaxies as a consequence of a scaling transformation over time, a mechanism that eliminates the need for a dark matter patch. So, rather than seeing these observations as problems requiring extra mass, FTS suggests they are indications that our understanding of cosmic time and scaling needs revision. This reinterpretation serves as the evidence: SM’s dependence on dark matter (an unconfirmed entity) to account for known discrepancies is a sign that an alternative explanation, like that proposed by FTS, might be more fundamental.

Expansion velocity describes how space itself expands over time, affecting the separation of distant galaxies. Escape velocity, on the other hand, is a local gravitational condition that determines whether an object remains bound to a specific mass distribution. While expansion velocity can exceed the speed of light due to metric expansion, escape velocity is always calculated relative to a gravitational potential and is not linked to cosmic-scale expansion. Observations show that galaxy clusters remain gravitationally bound despite expansion effects, implying that the mechanism governing large-scale stability involves more than just a simple velocity comparison. Would you argue that expansion should affect local gravitational escape conditions, or do you recognise the difference between metric-driven expansion and local orbital mechanics?

In FTS, the scaling function applies to matter itself, meaning that atomic structures, planetary bodies, and even galaxies scale relative to Ephemeris Time (ET). Unlike standard cosmology, which assumes spatial expansion while keeping fundamental units fixed, FTS treats cosmic evolution as a process where the physical scale itself changes over time rather than space expanding. This means that the length of a physical ruler, the frequency of emitted radiation, and the separation distances between gravitationally bound systems all shift uniformly according to the scaling function, ensuring that locally bound objects remain internally consistent while the overall cosmic structure follows a different scaling trajectory. Thus, instead of stretching space while keeping matter constant, FTS applies a scaling transformation to matter relative to its cosmic evolution in Ephemeris Time, preserving observational consistency while reinterpreting the mechanism responsible for cosmic expansion.

The notion that the transition occurs where expansion velocity equals escape velocity assumes a sharp boundary, yet observations show galaxy clusters remain gravitationally bound, despite their escape velocities often being below theoretical expansion velocities, suggesting a deeper mechanism beyond a simple velocity comparison. Regarding the terminology, the interpretation of cosmic expansion has evolved significantly since Hubble first observed redshift correlations. Early models likened it to an explosion-driven dispersion, but that notion quickly became untenable; an expanding metric was necessary to explain large-scale structure formation. The Hubble Sphere (HS), as an observational boundary, would have been impossible under an explosion model, since such a scenario would imply a central point of expansion, contradicting the homogeneity and isotropy required by modern cosmology. Instead, the shift in perspective toward metric expansion allowed the HS to be framed as the transition between luminal and superluminal recessional velocities. FTS builds on this evolution by redefining cosmic expansion in terms of intrinsic scaling, not as space stretching but as matter evolving over Ephemeris Time (ET). This eliminates the need for a separate expanding metric while still aligning with the observational boundary concept that both SM and FTS recognise for HS. Renaming HS adds unnecessary complication for those aiming to engage constructively in the underlying physics rather than mere terminology debates.

The mainstream definition of the Hubble Sphere (HS) is tied to comoving distances under standard metric expansion. However, FTS doesn’t discard the concept, it reinterprets HS as a positional reference relative to scaling effects rather than as a strict comoving boundary. Both SM and FTS regard the HS as the region where objects have a recessional velocity equal to the speed of light. The difference is that FTS treats this as an apparent recessional velocity, relative to the background, no positional change is actually taking place. Standard cosmology assumes that the expansion of space itself causes objects to move apart with increasing velocity at greater distances. FTS, by contrast, proposes that what we interpret as motion is instead the result of scale-dependent transformations over Ephemeris Time (ET), meaning the change is in measured properties rather than actual spatial separation. Thus, while maintaining the concept of HS as an observational boundary, FTS avoids the need for comoving distance corrections, instead treating cosmic evolution as a scaling effect rather than an expanding metric. Whether the term ‘Hubble Sphere’ is retained or modified depends on whether mainstream assumptions should continue shaping definitions, or if FTS warrants an independent terminology for its framework. Your explanation assumes that gravitational binding overrides metric expansion locally, but standard cosmology lacks a precise mechanism for defining at what scale this transition occurs. If metric expansion were truly homogeneous, we’d expect even loosely bound systems, such as galaxy clusters, to experience some measurable expansion. Yet observations show that galaxy clusters remain stable without internal expansion, suggesting a missing factor in how expansion interacts with gravity. Do you propose a formal transition scale where gravity overrides metric expansion completely, or does the standard model leave this undefined? FTS doesn’t describe matter ‘physically shrinking’ in an absolute sense; it redefines scale evolution relative to Ephemeris Time (ET). Standard cosmology assumes space expands while objects retain constant size, but FTS replaces metric expansion with a scaling function, where matter adjusts relative to cosmic evolution. The distinction is critical: in FTS, scaling affects both measurement reference and observational interpretations, meaning there is no fixed cosmic background against which shrinking occurs. Instead, time and scale co-evolve, making perceived size a function of ET rather than a static metric.

I think you might be right, because I wrote it :)

While metric expansion describes space itself stretching between objects, FTS treats scaling as a function of matter evolving relative to cosmic time rather than an inherent change in spatial separation. The distinction is important: standard cosmology assumes space expands while objects retain constant size, whereas in FTS, matter itself scales over Ephemeris Time (ET) while spatial positioning is preserved. Thus, while both frameworks address cosmological evolution, FTS does not equate directly to metric expansion; it offers an alternative interpretation where the scaling of matter itself drives observational effects, not the stretching of space. Additionally, the FTS model requires no insertion of extra energy in the form of an arbitrary parameter, unlike certain standard models that rely on unexplained forces such as dark energy. Instead, FTS operates through inherent scaling effects, maintaining consistency without requiring an external energy source whose causal mechanism remains unknown.

The radius of the Hubble sphere (HS) depends on which model is applied, SM or FTS. Standard cosmology (SM) accounts for comoving distances due to metric expansion. FTS, however, uses D ≈ (z × c) / H₀, where distance is determined by scaling effects relative to Ephemeris Time (ET) rather than space expanding. This means that in FTS, HS is not a static comoving boundary but a positional reference that evolves based on the rate of cosmic scaling. The observer moves through ET in the frame of the measuring instrument, marking the HS as the horizon of future causality, a point where, in the past, light-speed rulers were twice as long relative to the background. It is the horizon of future causality, and a place where, in the past, light speed rulers were twice as long relative to the background. So, while the Milky Way's diameter is indeed a fraction of the Hubble sphere, significance isn’t just about scale, it’s about gravitational influence and cosmic structure. Large-scale formations like galaxy clusters, filaments, and voids shape cosmic evolution across hundreds of millions of light-years. If metric expansion were truly homogeneous, why don’t galaxies expand internally? Standard cosmology acknowledges that gravitational binding overrides expansion within certain regions, yet lacks a clear mechanism explaining exactly how this transition occurs. Regarding math, cosmology relies on both quantitative and conceptual reasoning, and the issue here is not just numbers, but the physical implications of large-scale structure in cosmic models.