Aharonov–Casher Effect

No electric charge. Still a quantum phase.

The Physics

In 1984 Yakir Aharonov and Aharon Casher showed that a neutral particle carrying a magnetic moment acquires a quantum phase when it circles a line of electric charge. It is the electromagnetic dual of the Aharonov–Bohm effect: magnetic moment around charge, rather than charge around magnetic flux. Neutron interferometry first observed it in 1989.

|φ_AC| = |(1/(ħc²)) ∮ (E × μ) · dl|.

For a magnetic moment parallel to the charge line: |φ_AC| = |μλ|/(ħc²ε₀).

• φ_AC: Aharonov–Casher phase (rad).
• μ: particle magnetic dipole moment (J T⁻¹).
• E: electric field (V m⁻¹).
• dl: path element (m); ∮ denotes a closed-loop integral.
• λ: linear charge density (C m⁻¹).
• ħ: reduced Planck constant (J s).
• c: speed of light (m s⁻¹).
• ε₀: vacuum permittivity (F m⁻¹).

Honest caveat: No classical force acts in the ideal configuration. The phase is strictly topological and independent of path shape when the magnetic moment is parallel to the line charge. The overall sign depends on the orientation convention; the equations above give the magnitude. The printed equation uses the approved E × μ convention in SI.

Sources

• Y. Aharonov & A. Casher, “Topological Quantum Effects for Neutral Particles,” Phys. Rev. Lett. 53, 319–321 (1984), doi:10.1103/PhysRevLett.53.319.
• A. Cimmino et al., “Observation of the topological Aharonov–Casher phase shift by neutron interferometry,” Phys. Rev. Lett. 63, 380–383 (1989), doi:10.1103/PhysRevLett.63.380.

On the shirt

Approved physics print block:

“AHARONOV–CASHER EFFECT”

“φ = (1/ħc²) ∮ (E × μ) · dl”

“μ in J/T · E in V/m · φ in rad”

“A neutral particle with a magnetic moment, circling a line of electric charge, picks up a quantum phase — the mirror image of the Aharonov–Bohm effect.”

Printed front and back. Physics. Personified.