The Logical Origin of Spacetime Continuity

By the very definition of a necessary condition, the Principle of Relativity follows directly, compelling fundamental Lorentz invariance with no exceptions. Thus, spacetime must be continuous.

An independent argument aligns: were spacetime discrete, no observer’s apparatus—itself embedded within that spacetime—could ever probe it, for finer resolution would demand manipulation of entities smaller than spacetime atoms, a manifest logical impossibility.

Hence, such discreteness remains unobservable in principle and is thereby equivalent to non-existence.

A widespread misconception holds that each observer’s resolution limit implies universal Planck-scale discreteness. The opposite is true: precisely because spacetime is continuous, lacking any universal grid, every observer, constrained by their own resolving power, effectively operates within a personal Planck-scale grid.

Sources of this misconception include:

• The assumption that “quantum” necessarily entails discrete spacetime—an opinion devoid of logical or physical necessity.

• The belief that a spacetime continuum demands actual (completed) infinity. In reality, it requires only potential infinity.

Spacetime continuity lies at the foundation of physics. Once secured here, it permits an almost wholly deductive derivation of both special relativity and quantum mechanics.