Theory 001/Physics & Matter /Quantum electrodynamics
Vacuum Birefringence Follows the Gradient
The effect is calculated from field strength. The measurement may be dominated by how fast it changes.
Vacuum birefringence in strong magnetic fields is set by the field gradient rather than its peak strength, so a weaker but sharper field should polarise light more than a stronger uniform one.
01The evidence
Quantum-electrodynamic birefringence is predicted to scale with the square of the field, and the fields needed are at the limit of what magnetars provide.
02The tension
Predictions use the peak field, and measurements of polarisation in magnetar emission scatter more than the field estimates can explain. The scatter is attributed to unknown emission geometry.
03The mechanism
The vacuum polarisation that produces birefringence depends on how much the field changes across the photon's path, because the virtual pairs are sensitive to the local curvature of the field rather than to its absolute value.
If the gradient dominates, then a compact source with a steep falloff should produce more polarisation per unit field than an extended source at the same peak, which is a testable ordering.
04What this is not
Peak-field models rank sources by strength. This ranks them by gradient, which predicts a different ordering.
05Predictions
- P1Polarisation should correlate with field gradient better than with peak field.
- P2Compact sources should out-polarise extended ones at equal peak.
- P3The effect should vanish for uniform fields above a threshold.
06Refutation
Polarisation tracking peak field at controlled gradient would restore the standard scaling.
07What it changes
It would change how magnetar polarimetry is interpreted.