Relativistic Treatment of Entangled Particles

Also read – Boost of a singlet entangled state

1. Lorentz Invariance of Entanglement

Entanglement is a property of the quantum state as a whole. If two particles are entangled in one inertial frame,
they are entangled in all inertial frames.

  • Lorentz transformations (boosts and rotations) are unitary transformations on the Hilbert space.
  • Unitary transformations cannot convert an entangled state into a separable one (or vice versa).

Thus, the fact of entanglement is invariant.

\[
|\Psi^-\rangle = \frac{1}{\sqrt{2}}\Big(|\uparrow\rangle_A|\downarrow\rangle_B – |\downarrow\rangle_A|\uparrow\rangle_B\Big)
\]

A Lorentz boost maps spin states to spin states (through Wigner rotations), but does not turn the state into a separable product.

2. What Does Change With Reference Frame?

While entanglement as such is invariant, the manifestation of correlations can change:

  • Spin and momentum entanglement trade-off: In relativistic treatments, spin and momentum are not independent. A Lorentz boost can “mix” these degrees of freedom (via Wigner rotations).
  • Observable correlations: Measurement outcomes depend on the orientation of detectors. In a boosted frame, the effective measurement axis is rotated relative to the particle’s momentum, so the correlations can appear altered.
  • Accessibility of entanglement: If you “trace out” momentum degrees of freedom (because your detectors don’t resolve them), then in some frames you may see reduced spin entanglement—even though the full state is still entangled.

The full quantum state remains entangled, but how much entanglement you observe in a particular subsystem depends on the frame.

3. Relativity of Simultaneity

  • Entanglement correlations are nonlocal, but they don’t imply causal signaling.
  • Different frames disagree on the time ordering of spacelike-separated measurements, but all observers predict the same joint statistics.
  • This is why the no-communication theorem survives relativity.

4. Research Frontiers

  • Relativistic quantum information: Studies how entanglement is affected by boosts, acceleration, and curved spacetime.
  • Unruh effect: Accelerated observers perceive the vacuum as a thermal bath, which can degrade entanglement.
  • Gravitational backgrounds: In curved spacetime, entanglement entropy can change depending on observer horizons (e.g., black holes, Rindler observers).

✅ Answer in one line

Entanglement itself is Lorentz invariant—if two particles are entangled in one frame, they remain entangled in all—
but the type of entanglement (e.g., spin vs momentum) and the measurable correlations can appear different
to observers in different reference frames.