• Phasewraith – Aharonov–Bohm Effect Physics T-Shirt – white
  • Phasewraith – Aharonov–Bohm Effect Physics T-Shirt – male model, black
  • Phasewraith – Aharonov–Bohm Effect Physics T-Shirt – flat lay, black
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PhasewraithAharonov–Bohm Effect

Phasewraith – Aharonov–Bohm Effect Physics T-Shirt

$29.99 USD
$29.99 USD
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Color
White · Black
Size
S–5XL
Made
To order · shipping times

Can a magnetic field affect an electron that never touches it? Phasewraith guides two electron paths around a sealed solenoid. The field is zero on both paths, but the magnetic flux inside shifts the phase between them, and the interference fringes move. Aharonov and Bohm predicted this in 1959, showing that potentials matter in quantum mechanics. Pixel-art unisex tee; equation, symbols and sources in the physics panel below.

Color
Size

Size guideS–5XL · inches

Details

Size & fitS–5XL

Unisex heavy cotton (Gildan 5000), classic fit.

SizeWidthLengthSleeve
S182815.1
M202916.5
L223018
XL243119.5
2XL263221
3XL283322.4
4XL303423.7
5XL323525

Measurements in inches, ±1.5 in tolerance.

ShippingFree US

Free US shipping · $10 flat shipping outside the US. Printed to order for you.

Delivery times & where we ship

Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

Full refund & replacement policy

The physics

Phasewraith never touches the electrons. Two paths pass either side of a sealed solenoid, where the magnetic field is exactly zero, and still the fringes on the screen behind move.

In 1959 Yakir Aharonov and David Bohm showed why: in quantum mechanics a charged particle picks up a phase from the vector potential A, not just from the field B. Round a loop, the phase difference equals the charge times the enclosed flux, divided by ħ.

Akira Tonomura's group confirmed it in 1986 with the field fully shielded inside a superconducting toroid. Never touched. Still shifted.

Equations

\[\Delta\varphi = \frac{q}{\hbar}\oint_C \mathbf{A}\cdot d\boldsymbol{\ell} = \frac{q\,\Phi_B}{\hbar}\]
\[\mathbf{B} = \nabla\times\mathbf{A} = 0 \;\text{on both paths}\]
SymbolMeaningUnit
\(\Delta\varphi\) phase difference between the two electron paths \(\mathrm{rad}\)
\(q\) charge of the particle (electron: -e) \(\mathrm{C}\)
\(\hbar\) reduced Planck constant \(\mathrm{J·s}\)
\(\mathbf{A}\) magnetic vector potential \(\mathrm{T·m}\)
\(C\) closed loop formed by the two paths \(\mathrm{–}\)
\(\Phi_B\) magnetic flux enclosed by the loop (inside the solenoid) \(\mathrm{Wb}\)
\(\mathbf{B}\) magnetic field \(\mathrm{T}\)

Sources

  1. Aharonov & Bohm (1959) Significance of Electromagnetic Potentials in the Quantum Theory, Phys. Rev. 115, 485
  2. Tonomura et al. (1986) Evidence for Aharonov-Bohm effect with magnetic field completely shielded from electron wave, Phys. Rev. Lett. 56, 792
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