Testing Quantum Mechanics in Curved Spacetime Using Entangled Atomic Clocks

Context:

A new study (PRX Quantum, July 2024) by Jacob Covey, Igor Pikovski, and Johannes Borregaard proposes using entangled atomic clocks to experimentally probe the interface of quantum mechanics and general relativity.

Background of the Problem

Quantum mechanics governs the microscopic world, while general relativity describes gravity and spacetime curvature.
Both theories are successful individually but lack a unified framework, making their reconciliation one of the deepest puzzles in modern physics.

Two Categories of Efforts in Bridging the Gap

Quantum Gravity Approach: Attempts to quantise gravity itself, using hypothetical particles called gravitons.
Curved Spacetime Approach: Examines how ordinary quantum systems behave in pre-existing curved spacetime, without invoking speculative new particles.

Spacetime Curvature and Time Dilation

General relativity shows that massive objects curve spacetime, leading to nonlinear variations in the flow of time.
Example: Time difference between clocks at varying heights is not uniform across distances, providing direct evidence of curvature.

Proposed Experimental Setup

Involves a network of three entangled atomic clocks separated by kilometre-scale elevations.
Uses the W state of quantum entanglement, which is resilient even if one particle is lost.
Atoms: Ytterbium atoms chosen as qubits, with coherence times of ~50 seconds.
Detectable shifts: Frequency changes of ~0.02 Hz due to curvature-induced time dilation.

Significance

Would be the first laboratory probe of spacetime curvature using quantum systems.
Tests foundational principles of quantum mechanics in curved spacetime: unitarity, linearity, and Born rule.
Opens possibilities for future precision detectors of dark matter and gravitational waves.
Marks a shift from only large-scale astronomical observations to controlled laboratory-based quantum-gravity experiments.

Technological Challenges

Entangled states are fragile and sensitive to decoherence.
The proposed setup is currently at the frontier of experimental feasibility.

Quantum Mechanics (QM)

Domain: Microscopic scale (atoms, subatomic particles).
Nature: Probabilistic – describes matter and energy in terms of wave functions.
Key Principles:
- Wave–particle duality (particles act like both waves & particles).
- Uncertainty principle (cannot know both position & momentum exactly).
- Superposition (particles exist in multiple states until measured).
- Entanglement (instantaneous correlations across distances).
Successes: Explains atomic structure, semiconductors, lasers, nuclear interactions, quantum computing.
Limitation: Struggles with describing gravity.

General Relativity (GR)

Domain: Macroscopic scale (planets, stars, galaxies, spacetime).
Nature: Deterministic – describes gravity as the curvature of spacetime caused by mass and energy.
Key Principles:
- Equivalence principle (gravitational mass = inertial mass).
- Spacetime curvature (gravity is not a force but geometry).
- Black holes & gravitational waves (predicted & observed).
Successes: Explains planetary orbits, GPS corrections, expansion of universe, black holes.
Limitation: Breaks down at quantum scale (e.g., inside black holes, singularities).