A Critical Analysis of Penrose Diagrams: A Conversation with a Scholar

A Penrose diagram is often presented as a global representation of spacetime, yet its construction removes the very mathematical structures required to define spacetime itself. The conformal compactification eliminates the metric, tangent spaces, vectors, affine structure, and curvature, leaving behind a picture whose meaning depends entirely on prior knowledge of the full spacetime. The diagram does not contain null cones, causal relations, or vector structure; it only marks where such features existed before being stripped away. Treating the diagram as if it preserved geometry or causality introduces internal inconsistencies, because the abstraction no longer obeys invariance, covariance, or the logical coherence required of a legitimate physical representation. Its apparent explanatory power arises from projecting the original metric back onto a picture that no longer contains it. A Penrose diagram is therefore not a selfcontained model of spacetime but a symbolic sketch of causal type, meaningful only through external assumptions about the underlying geometry.