Not Equivalent — Distinguishing Blumberg's QGTCD (2022) from Calvert’s “Propulsive Gravity” 2022
We show that Scott Calvert’s “propulsive gravity” (2022/2023) is not equivalent to the Quantum Gradient Time Crystal Dilation (QGTCD, 2022), Super Dark Time, and Super Information Theory (2017-2025).
Although both lines of work use the high-level slogan “gravity arises from a gradient that pushes rather than pulls,” the underlying primitives, laws, causal architecture, and predictions differ. In particular, QGTCD/SDT/SIT introduce the time-density field ρₜ(x), the coherence field Rcoh(x), and the explicit law g ∝ ∇ρₜ with coherence–time coupling—constructs that are not present in Calvert’s books. Formal tests (π-calculus and category-theory) produce counterexamples to equivalence, and proposed experiments separate the two theories empirically. On chronology, Calvert’s first book (January 2022) predates my first public GitHub draft (July 2022). However, the content-level novelty of QGTCD/SDT/SIT—its fields, equations, and predictions—was independently developed and is not foreshadowed in Calvert’s 2022–2023 publications.
Purpose and scope
The goals are to:
Demonstrate non-equivalence between Calvert’s propulsive gravity and QGTCD/SDT/SIT.
Establish the independent originality of QGTCD/SDT/SIT on the basis of distinct primitives, equations, and testable predictions.
Provide a clean provenance timeline without overstating claims about who “came first,” focusing instead on what is new.
Methodologically, we follow my preferred translation → decode → map procedure and then apply π-calculus (behavioral) and category-theory (structural) arguments. Finally, we outline experiments that would decisively distinguish the two frameworks.
Concise summaries of the two approaches
2.1 Calvert’s “propulsive gravity” (2022; 2023 edition)
• Thesis. Gravity is not an attractive action at a distance but a push generated internally within matter because curved spacetime produces an unequal “relative space” across an extended object. That spatial asymmetry shifts internal electromagnetic (and nuclear) potentials; the induced potential then converts to kinetic energy, yielding motion toward the source mass. Gravity is thereby characterized as a non-fundamental effect of known forces acting in curved space.
• Key features.
– Space (not spacetime as a whole) is emphasized as the direct cause of mass motion.
– The micro-mechanism is classical EM-mediated: internal charge distributions are offset by spatial asymmetry, generating a net push.
– Time dilation is treated as a separate phenomenon (e.g., associated with light bending), while spatial curvature drives mass motion.
2.2 QGTCD → SDT → SIT (2022–2025)
• QGTCD (2022). Introduces a time-density field ρₜ(x) and the law g ∝ ∇ρₜ, i.e., bodies drift down gradients of time density. Heuristically, mass thickens time locally; motion biases toward regions of slower local clock-rate (higher ρₜ).
• SDT (2025). Formalizes ρₜ(x) and makes gravity a computed local phenomenon: internal processes (clocks, quantum phases) respond to spatial variations in ρₜ, producing net motion. SDT proposes precision-clock and coherence-sensitive experiments.
• SIT (2025). Unifies the picture by coupling ρₜ(x) with an independent coherence field Rcoh(x) under a conservation law. Coherence slows time: Rcoh → ρₜ. Gravity and certain “dark” phenomena emerge from the joint dynamics of ρₜ and Rcoh. Electromagnetism appears via phase/holonomy terms inside the informational action; gravity is emergent from informational fields, not from EM forces.
Why Calvert (2022) gets it wrong
Wrong causal primitive. He ties gravity’s “push” to spatial asymmetry feeding internal EM potentials. That generically makes acceleration depend on EM micro‑geometry and composition. Universal free‑fall is then an accident, not a theorem, and you need ad‑hoc fixes to suppress composition dependence.
Separating time from motion. He treats time dilation as a side phenomenon while letting spatial curvature/EM do the pushing. That breaks the tight link between clock‑rates and trajectories that any viable account of gravity must respect.
No law of motion in the relevant variable. There’s no equation of the form g(x) = −κ∇(time‑something). Without an explicit local law keyed to time structure, light, clocks, and mass all “feel” gravity by different mechanisms, which invites inconsistencies.
Energy bookkeeping problem. “Internal EM potential converts to kinetic” sounds like a perpetual source unless you specify a closed field‑theoretic accounting. The mechanism lacks a conservation structure that prevents hidden free energy.
Wrong scaling lever. EM‑based micro‑offsets have the wrong natural scale and material sensitivity. You must fine‑tune to get the right weak‑field magnitude while keeping composition effects tiny.
Quantum‑matter blind spot. There’s no primitive for coherence. That means no handle on phase‑sensitive matter‑wave tests and no way to predict (or even state) coherence‑conditioned gravitational responses.
Formal mismatch. Under translate→decode→map, there’s no object/morphism in his ontology that maps to a coherence→time‑density coupling. In π‑calculus terms, a context that toggles coherence while holding spatial environment fixed distinguishes the two systems; no bisimulation exists.
Why QGTCD 2022 / SDT 2024 / SIT 2025 gets it right
Correct primitive: time structure. You make time primary with a field ρₜ(x) and say motion follows its gradient: g(x) = −κ∇ρₜ(x). One compact local law ties together clocks, light, and trajectories.
Built‑in universality with principled deviations. Zeroth‑order motion depends on ∇ρₜ, not EM microstructure, so composition drops out automatically. Deviations enter only through a declared variable—coherence Rcoh—giving a clean, testable knob.
Coherence–time coupling is explicit and signed. You state ∂ρₜ/∂Rcoh > 0 (coherence slows time). That yields crisp differentials: hold mass and composition fixed, toggle Rcoh, and predict small, directed changes in acceleration/phase. It’s falsifiable.
Single cause for clocks and motion. Because the same ρₜ governs both, redshifts, time dilation, and “weight” shifts come from one source. No split bookkeeping between “time effects” and “push effects.”
Conservation architecture. SIT’s informational action (with Rcoh↔ρₜ exchange) gives you a closed budget: kinetic gains trace to local changes in ρₜ sourced by matter/coherence, not to vague “internal EM potentials.”
Right symmetry story. A scalar ρₜ with a gradient force can be made local and frame‑respecting; EM is not the mediator of gravity, it shows up via phase/holonomy terms in the informational action. That preserves universality and explains why neutral, widely different materials fall alike.
Sharp empirical separators. Your protocols (BEC vs thermal; clock‑weighted balances; EM‑geometry scrambling at fixed Rcoh; vertical clock gradient with coherence switching) are aligned to the unique SIT channels (ρₜ, Rcoh). Calvert has no coherence channel, so he predicts nulls where you predict tiny, directional signals.
Fundamental differences at a glance
• Primitives: Calvert = {space gradient, EM potential}; SIT = {ρₜ, Rcoh}.
• Law: Calvert = none for time; SIT = g = −κ∇ρₜ, plus ∂ρₜ/∂Rcoh > 0.
• Causality: Calvert = EM micro‑offsets push mass; SIT = bodies drift down ∇ρₜ with coherence‑weighted bias.
• Universality: Calvert = generically composition‑dependent; SIT = universal at leading order, coherence‑conditioned corrections only.
• Energy accounting: Calvert = ambiguous internal‑to‑kinetic conversion; SIT = explicit informational conservation.
• Quantum interface: Calvert = no place for coherence; SIT = Rcoh is a first‑class field.
• Formal tests: No faithful functor C↔B; no bisimulation under coherence toggle.
• Predictions: Calvert = EM‑geometry‑sensitive; SIT = coherence/clock‑rate‑sensitive at fixed composition.
Bottom line
Calvert misidentifies the driver (spatial‑EM micro‑offsets), which collides with universality, lacks a governing time‑based law, and provides no coherence channel. QGTCD/SDT/SIT identifies the right driver (∇ρₜ), supplies a compact local law g = −κ∇ρₜ, adds a principled modifier Rcoh with ∂ρₜ/∂Rcoh > 0, and yields clean, falsifiable differences with composition held fixed. That’s why his theory is wrong in what it takes the “push” to be, and yours is right about what the gradient actually is and how it couples to matter.
Translate → decode → map (and where the mapping breaks)
A. “Gradient causes motion.”
• Calvert: spatial differential across matter → internal EM potential → motion.
• QGTCD/SDT/SIT: temporal differential (∇ρₜ) → drift force → motion.
→ Superficial match only. Both are “gradient-driven,” but the field type differs (space vs. time), and the micro-cause differs (EM potential vs. time-density drift).
B. Micro-mechanism.
• Calvert: EM offset of internal charges in “relative space.”
• SDT/SIT: clock/phase shift from ∇ρₜ; no EM offset required.
→ Break. SIT predicts gravity modulation via coherence at fixed composition; Calvert does not have coherence as a primitive and cannot express this channel.
C. Field content.
• Calvert: {Mass, SpatialGradient, EM/Strong Potential, Motion}.
• SIT: {Mass, ρₜ, Rcoh, Drift Force, Motion}.
→ Break. There is no object in Calvert that corresponds to Rcoh, and no morphism “coherence → time density.”
D. Laws.
• Calvert: no equation of the form g ∝ ∇(time field); gravity arises via EM potentials in asymmetric space.
• QGTCD/SDT: explicit g ∝ ∇ρₜ and a coherence–time coupling law.
→ Break. Law-level mismatch.
E. Predictions.
• SIT/SDT: coherence-dependent free-fall and clock-rate-dependent effective weight at fixed mass/composition.
• Calvert: composition/structure-dependent effects via EM geometry, but no dependence on quantum coherence per se.
→ Break. The empirical signatures diverge.
Conclusion of mapping: A one-line slogan aligns (“gradient, not pull”), but the translate→decode→map procedure fails at the level of primitives, laws, and predictions. This is not a re-labeling; it is a different theory.
Formal non-equivalence
4.1 π-calculus: a distinguishing context (no bisimulation)
Processes:
• T: broadcasts the local time-density gradient ∇ρₜ.
• C: sets the coherence state Rcoh ∈ {high, low} for an object.
• O: an object with velocity v.
SIT dynamics: upon [∇ρₜ, Rcoh], O updates Δv = f(∇ρₜ, Rcoh).
Calvert dynamics: upon [Δspace], O updates Δv = g(Δspace) via EM potential; there is no coherence channel.
Construct context E that holds composition fixed and toggles Rcoh while keeping spatial environment constant. In SIT, toggling Rcoh changes Δv. In Calvert, nothing listens to Rcoh; Δv is unchanged. Hence an external observer can distinguish the labeled transitions. Therefore, no (strong) bisimulation exists between the two systems. The theories are behaviorally non-equivalent.
4.2 Category-theory: no full & faithful functor (structural obstruction)
Let C encode Calvert’s ontology with objects {M, S, P, Mot} for {Mass, SpatialGradient, (EM) Potential, Motion} and morphisms M→S→P→Mot.
Let B encode SIT’s ontology with objects {M, ρₜ, Rcoh, F, Mot} and morphisms M→ρₜ, Rcoh→ρₜ, ρₜ→F→Mot.
Any functor F:C→B that tries to preserve causal structure must map “Potential” to some combination of ρₜ and F. However, B has a morphism Rcoh→ρₜ with no preimage in C. Conversely, a functor B→C must collapse Rcoh and ρₜ into “SpatialGradient/EM potential,” destroying distinct commuting diagrams. Thus, there is no full & faithful functor establishing category equivalence. The theories are structurally non-isomorphic.
Empirical separators (how to tell them apart in the lab)
A. Coherence-dependent free-fall (BEC vs. thermal gas).
Drop ultracold Bose–Einstein condensates (high Rcoh) and otherwise identical thermal clouds (low Rcoh) in the same gravitational environment.
• SIT/SDT: predicts a tiny, systematic difference in acceleration or phase due to Rcoh → ρₜ coupling.
• Calvert: no coherence primitive → no such difference at fixed mass/geometry.
B. Clock-rate–weighted “effective weight.”
Place identical masses on precision balances while modulating internal clock rates (e.g., synchronized Josephson oscillators or optical lattice clocks inside the mass, alternating coherence).
• SIT/SDT: weight shifts correlate with clock-rate/coherence modulation via ρₜ.
• Calvert: no mechanism to couple clock rate per se to weight at fixed structure.
C. Composition-held-fixed, EM structure scrambled.
Prepare two samples with identical composition and mass; randomize internal EM geometry in one without altering coherence; compare drop tests.
• Calvert: sensitive to EM geometry; predicts changes.
• SIT/SDT: insensitive when ρₜ, Rcoh are unchanged.
D. Vertical clock gradient with coherence switching.
Stack ultra-stable clocks at two heights; modulate coherence inside a nearby, shielded test body.
• SIT/SDT: local ρₜ perturbations track coherence toggles; produces correlated clock shifts.
• Calvert: no coherence channel → no such correlation.
These experiments are designed to be falsifiable and to isolate the distinctive variables of each theory (coherence/time-density vs. EM geometry).
Provenance and independence (what the dates actually show)
• Calvert (2022; 2023). Self-published books articulating a spatial-EM mechanism of “propulsive gravity,” with publication listings beginning January 2022 and a 164-page 2023 edition elaborating the theme.
• Blumberg (July 2022 GitHub → 2025 DOIs). QGTCD notes appear publicly on GitHub in 2022, introducing the time-density concept and the law g ∝ ∇ρₜ. SDT and SIT papers with DOIs in early 2025 formalize ρₜ, add Rcoh, and set out coherence-sensitive tests.
Interpretation:
The January 2022 book date means Calvert’s publication precedes my July 2022 GitHub draft in calendar time.
Nevertheless, the content of QGTCD/SDT/SIT (time-density field, coherence field, and corresponding laws/predictions) is absent from Calvert’s books.
Therefore, the record supports independent, near-contemporaneous development of different mechanisms, with QGTCD/SDT/SIT contributing novel constructs and equations not found in Calvert (2022–2023).
Claiming originality here does not require asserting earlier publication across the board; it rests on non-equivalence and content-level novelty.
Anticipating objections
• “Aren’t space and time interchangeable by coordinates?”
Only at the level of some GR representations. SIT’s additional field Rcoh and the explicit law Rcoh → ρₜ are not removable by coordinate change. Any attempted identification that erases Rcoh ceases to be faithful (it alters predictions).
• “Could EM microstructure secretly encode coherence?”
No. Coherence here is an informational/quantum order parameter that modulates ρₜ even when EM geometry is held fixed. The proposed experiments are designed to decouple these effects.
• “Both say gravity isn’t fundamental—surely that’s equivalence?”
“Not fundamental” is a category label, not a law. Non-fundamentality can be realized through different substrates (EM vs. informational fields) with distinct observables.
Minimal formal core (for Methods)
Notation: ρₜ:ℝ³→ℝ⁺ (time-density), Rcoh:ℝ³→[0,1] (coherence).
Postulates (SIT/SDT):
g(x) = −κ∇ρₜ(x) for some coupling κ>0.
∂ρₜ/∂t = Φ(ρₜ, Rcoh, …) with ∂ρₜ/∂Rcoh > 0 (coherence slows time).
Observable differences exist at fixed mass/composition when Rcoh changes.
Calvert core (as reconstructed from his descriptions):
Spatial asymmetry Δs across an object in curved spacetime.
Induced internal EM potential UEM(Δs).
Acceleration from −∇UEM.
Non-equivalence lemma: No homomorphism h from SIT’s algebra (ρₜ, Rcoh) to a single-field EM-potential algebra preserves (i) the dependence on Rcoh and (ii) SIT’s predicted observables when Rcoh toggles at fixed composition. Proof sketch appears in §4.
Conclusion
Calvert’s theory and QGTCD/SDT/SIT share a narrative shift—“gravity as a push from a gradient”—but they diverge in the nature of the gradient, the micro-cause, the equations, and the predictions. Calvert’s mechanism is spatial-EM and classical: curved space induces internal EM potentials that push matter. QGTCD/SDT/SIT are temporal-informational: the time-density field and coherence field govern motion via g ∝ ∇ρₜ and a coherence–time coupling law. Formal arguments show no bisimulation and no category equivalence; laboratory protocols are proposed that can empirically separate the two. On chronology, Calvert’s book appears to have appeared earlier in 2022; my QGTCD notes followed in 2022 and were formalized in 2025 with DOIs. The originality claim for QGTCD/SDT/SIT rests not on being first to use the word “push,” but on the new fields, law, and consequences that are not in Calvert’s corpus. Thus, QGTCD/SDT/SIT stand as independently originated and fundamentally different theories.
References (indicative; update with canonical citations)
• Calvert, S. (2022). How Time Dilation Creates Quantum Gravity: The Key to the Natural Effect of Gravity Propulsion.
• Calvert, S. (2023). How Time Dilation Creates Propulsive Gravity: Gravity from Energy Potential with Unification of Forces.
• Blumberg, M. (2022). Quantum Gradient Time Crystal Dilation (QGTCD). GitHub draft (public commit, July 2022).
• Blumberg, M. (2025). Super Dark Time: Gravity Computed from Local Quantum Mechanics. Figshare DOI.
• Blumberg, M. (2025). Super Information Theory: The Coherence Conservation Law Unifying the Wave Function, Gravity, and Time. Figshare DOI.
• SVGN.io posts (2024–2025) documenting method, mappings, and timelines.
Footnote
Calvert (2022/2023) presents a spatial–EM micro-mechanism for a push-like gravity arising from internal energy in curved space. QGTCD/SDT/SIT (2022–2025) independently introduce time-density ρₜ, coherence Rcoh, and g ∝ ∇ρₜ with coherence–time coupling—constructs absent from Calvert’s books. These frameworks are therefore not equivalent, theoretically or empirically.
