PhysicsLogic / Minkowski 1908

Light Cones, Time Orientation, and Signals

Geometry constrains a signal only when the physical signal relation obeys the cone.

Definitions and assumptions

Scope and physical limitations

The independent 1+1 dimensional diagnostic uses coordinates (ct, x), in common length units. Future reach is |delta x| <= delta(ct), not merely a nonnegative squared interval. The library excludes spacelike signals under that explicit propagation bound. The paper route now requires a global chart with time and three Euclidean spatial coordinates, calibrated to its own first-frame coordinate values. Strict timelike interiors and null light-signal endpoints are distinct. Every selected direct-light signal has positive elapsed time and distance/time equal to the positive light speed. The selected boost readout separately requires an admissible subluminal boost of the same timelike event. These checks do not construct signalling devices, establish Bell factorization, or solve curved-spacetime global causality.

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Examples and distinctions

Constructed examples of this model; each answer includes the Lean statement.

Exact root statement

∀ (signals : Event → Event → Prop),
  (∀ (source target : Event), signals source target → |target.2 - source.2| ≤ target.1 - source.1) →
    ∀ (source target : Event), |target.1 - source.1| < |target.2 - source.2| → ¬signals source target
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Notes and questions

Note for

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Definitions, structures, and assumptions

Structures, classes, and inductive alternatives

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Definitions and domain choices

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Checked statements: parameters, hypotheses, and interpretation

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Constructors, projections, and other meaning dependencies

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External mathematical declarations

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