Space and Time

The finite-c group, Michelson evidence, and closing expectation are independent roots. World-line kinematics depends on finite-c invariance but introduces the world postulate independently. Causal proper-time geometry depends on the kinematics. Four-dimensional mechanics and point-charge electrodynamics then branch from the causal route. Gravity is a qualified extension of electrodynamics; the closing expectation mentions the world postulate but is not a logical consequence of the world-line route. A final route assembles all eight outputs.

The finite-c setup selects two inertial frames, a transformation belonging to the relativistic group, a finite positive invariant speed identified with light, coordinates for a common worldpoint, and two representations of the same physical situation.

The conclusion includes reference-system underdetermination by phenomena, but physical equivalence is not hidden inside covariance. The countermodel covariance_alone_does_not_identify_frames_physically blocks that shortcut.

The Michelson route separately assumes a rigid-body orientation test whose preferred-direction effect would be detectable, together with the null result.

This is motivation, not deduction of the world postulate; a formal countermodel says exactly so.

The world postulate combines natural-law covariance, absence of a preferred inertial frame, a four-dimensional world independent of projection, and frame-relative space/time projections. The material setup supplies a timelike worldline, a local rest frame, a body at rest in the second frame, and its rest length.

The world-strip calculation then gives a material speed below the invariant light speed, the measured contracted length in the other frame, and reciprocal length contraction.

The setup selects past and future cones at an origin, strictly timelike points inside each cone, a point outside both cones, and timelike and spacelike vectors. Separate null endpoints supply a past light signal to the origin and a future light signal from it. The interior points cannot serve as those direct-light endpoints.

HasCausalCoordinateRealization requires a bijective chart with a real time and three Euclidean spatial coordinates. Spacelike separation means c times absolute elapsed time is less than spatial distance; future causal reach means spatial distance is at most c times elapsed time. Available direct-light propagation has positive elapsed time and equality. SourceCoordinateCalibration connects every chart value to the selected first-frame coordinates and identifies strict cone interiors by a strict inequality. The chart is unique relative to these coordinate data, not a preferred frame of nature.

The same calculation defines proper time along the worldline, four-velocity, and four-acceleration. The velocity is normalized timelike; acceleration is orthogonal to velocity in the invariant form; and its magnitude is represented by the curvature of the associated hyperbola.

Constant mechanical mass and a motive-force vector form the dynamics setup. The supplied calculation makes the motive force orthogonal to four-velocity, constructs momentum from mass and four-velocity, motion force from mass and four-acceleration, and equates motion and motive forces.

The countermodel the_world_postulate_does_not_supply_a_force_law ensures that geometry and physical frame equivalence do not silently generate this dynamical input.

Source and test charges follow timelike worldlines. The past cone of the field point intersects the source worldline uniquely at a retarded source point. The imported calculation builds a Liénard–Wiechert potential, obtains the field from it, and constructs the point-charge four-force.

A frame-relative electric/magnetic split does not remove the underlying field; the corresponding countermodel keeps that distinction explicit.

Minkowski proposes replacing the product of charges in the point-force construction by a product of masses. With a zero-acceleration source worldline, the controlled calculation finds the correction equal to unity to the declared order, recovers Kepler's laws using proper time, and matches Newtonian observations to that order.

The final route records two author expectations: the world postulate will hold without exception, and further mathematical consequences will receive experimental confirmation. It simultaneously records that universal validity was not derived.

The inertial-frame adapter selects the two distinct frames, finite-c transformation, law, situation, invariant quadratic form as light structure, and relativistic regime. Finite-c setup supplies the inhabited two-frame and finite-light setup; the calculation establishes transformation admissibility, reexpression, light-structure preservation, and law covariance; the world postulate supplies the no-preferred-frame bridge.

The source-sensitive theorem retains this original separate-print pp. 1-8 route under the typed finiteCGroupAndWorldPostulate token. It requires the finite-c setup, hyperboloid-group calculation, natural-law covariance, and world postulate, then constructs the shared explanation without treating the established common output as derivational provenance.

The established result retains the direct selected kinematic outputs rather than the derivation route, which is reconstructible from those outputs. The model can be grounded and transferred to arbitrary theory/world semantics only from the finite-c setup plus explicit theory-use, representation, and claim-transfer bridges; grounding does not assume the group calculation, covariance, world-postulate bridge, route, or established result. A second, narrower adapter projects the lecture's light-exchange relation into shared causal locality: finite light propagation plus outside-cone causal exclusion yields no spacelike signaling. It does not assert every later notion of causal influence.