FOUNDATIONSAUDITEVIDENCE OBSERVATORY
Foundational Physics Primer8 min read

What Is Locality?

“What does it mean for physics to be 'local', and does quantum theory violate Einstein causality?”

Audience:StudentsPhysicistsEngineers
Executive Short Answer

In physics, locality is the principle that an object or event can only be directly influenced by its immediate spatial surroundings, and that no causal influence can propagate faster than the speed of light in vacuum (c). In relativistic quantum field theory (QFT), locality is mathematically enforced by microcausality: field operators at spacelike-separated spacetime points strictly commute ([O(x), O(y)] = 0). Quantum mechanics violates Bell locality (local realism), but strictly respects signal locality (no-signaling).

Key Physical Principles at a Glance

  • •Einstein Locality asserts that what happens in region A cannot instantaneously alter physical reality in spacelike-separated region B.
  • •Signal Locality guarantees that no message or controllable energy can be transmitted faster than c.
  • •Microcausality in QFT guarantees that measurements performed at spacelike separation cannot interfere with one another.
  • •Quantum mechanics is non-local in its correlations (violates Bell locality), but entirely local in its causal signaling.
Mathematical & Physical Formalism

Microcausality in Relativistic Quantum Field Theory

In relativistic quantum mechanics and QFT, physical observables are represented by local operator fields Φ(x). For any two spacetime points x and y that are spacelike separated ((x - y)² < 0), the commutator of any two local observable operators must vanish identically:

[O(x), O(y)] = 0 quad \text{for all } (x - y)^2 < 0
Empirical Validation

Experimental Tests of Causality and Signal Locality

Decades of high-energy particle physics experiments at CERN, Fermilab, and SLAC confirm that relativistic causality holds down to sub-femtometer scales. No faster-than-light signal has ever been observed in any quantum optical, condensed matter, or particle physics experiment.

#11905: Albert Einstein formulates Special Relativity, establishing c as the universal causal speed limit.
#21950s: Development of axiomatic quantum field theory (Wightman axioms, Haag-Kastler algebraic QFT) embedding microcausality as a core axiom.
#31980s: Strict experimental verification of no-signaling in pulsed laser EPR systems.
#42010s: Quantum communication networks confirm signal locality over fiber optic and satellite networks.
Common Misconceptions Debunked

What This Principle Does NOT Mean

Myth:Because Bell's theorem is violated, Einstein's special relativity must be wrong.
Reality:False. Special relativity requires that energy, matter, and controllable signals cannot travel faster than c. Quantum correlations violate classical factorizability, but they do not transmit mass, energy, or information faster than light.
Myth:Spacelike collapse of the wavefunction means an observer in Andromeda can physically shock a particle on Earth.
Reality:False. In relational and operational frameworks, wavefunction collapse is not a mechanical shock wave traveling through space; it is an update of conditional predictive state assignments relative to an accessible record.
Connection to the Measurement Problem

How This Relates to the Measurement Problem

Understanding locality is essential for resolving the Measurement Problem: once we distinguish mechanical causal influences (governed by relativistic microcausality) from relational state updates (governed by conditional access), the appearance of superluminal paradoxes completely dissolves.

Read the Lead Article: The Measurement Problem Solved