Einstein’s equations (Gμν=8πG/c⁴Tμν) assume spacetime is infinitely divisible. The Dean Paradox shows finite motion (1m in 1s) breaks this, making EFE a predictive tool, not reality-spacetime a "painted veil"
• Dean’s paradox highlights a core discrepancy between logical reasoning and lived reality. Logic insists that between two points lies an infinite set of divisions, making it "impossible" to traverse from start to end. Yet, in practice, the finger does move from the beginning to the end in finite time. This contradiction exposes a gap between the abstract constructs of logic and the observable truths of reality
GR’s Mathematical Framework:GR models gravity as curvature of a continuous,infinitely divisible 4D spacetime manifold, using field equations
Gμν=8πG/c4*Tμν,}, relying on differential geometry and smooth metrics
dean Paradox proves infinite divisibility false (motion crosses infinite points in finite time), falsifying continuous spacetime. Logic is a “painted veil.”
GR’s equations are a “useful fiction”; smooth manifolds (e.g., Schwarzschild solution) are logically untenable, as derivatives assume false continuity.
GR’s spacetime is ontologically false; it’s a mental myth, not empirical truth, collapsing its claim to describe reality.
Ontological Collapse of Spacetime in General Relativity: Dean Paradox Commentary
General Relativity’s Ontology:
General relativity (GR) posits that spacetime is a real, continuous entity, modeled mathematically as a smooth, infinitely divisible four-dimensional manifold. This framework allows for events to be localized with arbitrary precision and for gravity to manifest as spacetime curvature. The ontology of GR is thus inseparable from the assumption of a continuous spacetime substrate.
Dean Paradox’s Impact:
The Dean paradox exposes a fundamental contradiction: logic and mathematics require infinite divisibility between any two points, yet physical reality demonstrates that finite motion occurs in finite time. This contradiction undermines the notion that spacetime’s continuity is an empirical truth; instead, it reveals the continuum as a logical construct-a conceptual “veil” rather than an ontological reality
. The paradox’s critique extends even to discrete models (such as loop quantum gravity), since logical infinities persist between quanta, leaving the core contradiction unresolved.
“Dean's paradox highlights a core discrepancy between logical reasoning and lived reality. Logic insists that between two points lies an infinite number of divisions, but physical experience shows that objects can traverse a finite distance in finite time.”
Consequences:
· Collapse of GR’sOntology:
If spacetime’s infinite divisibility is false, then the continuous manifold central to GR is not a feature of reality but a mental construct. The empirical fact of motion falsifies both continuous and discrete models of spacetime, as both rely on logical frameworks that cannot account for finite motion without contradiction· . This leads to an ontological collapse: GR’s spacetime is no longer a description of what is, but a mathematical fiction.
· Universal Underminingof Physics’ Foundations:
The paradox’s challenge is universal. If logicand mathematics cannot capture the nature of motion and spacetime, then anyphysical theory-regardless of whether it is continuous or quantized-rests onunstable ground. Attempts to resolve the paradox with calculus or byintroducing discrete spacetime are seen as ad hoc and do not address theunderlying logical gap· Philosophical Crisis:
The Dean paradox forces a radical skepticism about the ability of any logical or mathematical system to describe reality. This aligns with the critique that “physics’ reality is untrue,” and the assertion that science, as a rational system, is undermined at its foundation
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