Entanglement of quantum clocks through gravity.

Area of Science:

• Quantum Gravity
• General Relativity
• Quantum Mechanics
• Spacetime Physics

Background:

• Classical general relativity models spacetime with ideal, non-interacting clocks.
• Operational definitions of time require physical clocks obeying physical laws.
• Reconciling general relativity and quantum mechanics is a major challenge in theoretical physics.

Purpose of the Study:

• To investigate the implications of combining general relativity and quantum mechanics for physical timekeeping.
• To determine if operational time definitions are consistent with both theories.
• To explore the quantum gravitational effects on time measurement.

Main Methods:

• The study theoretically analyzes the gravitational interaction between physical clocks based on general relativistic mass-energy equivalence.
• It incorporates quantum mechanical principles, specifically the superposition of energy eigenstates, affecting the spacetime metric.
• Entanglement dynamics between clocks due to relativistic time dilation are mathematically derived.

Main Results:

• Physical clocks, when considered within both general relativity and quantum mechanics, exhibit gravitational interactions.
• Quantum superposition leads to a non-fixed spacetime metric background.
• Clocks become entangled via time dilation, causing decoherence and rendering single-clock time measurements ill-defined.

Conclusions:

• The idealized notion of time in general relativity is a classical approximation.
• A consistent theory of quantum gravity suggests that time, as measured by individual physical clocks, is not fundamentally well-defined due to entanglement.
• The classical relativistic concept of time emerges in the macroscopic, classical limit of numerous interacting clocks.