• Vacuumancer – Lamb Shift physics T-shirt
  • Vacuumancer – Lamb Shift physics T-shirt
  • Vacuumancer – Lamb Shift physics T-shirt
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VacuumancerLamb Shift

Vacuumancer – Lamb Shift Physics T-Shirt

$29.99 USD
$29.99 USD
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Can empty space move an energy level? Dirac’s theory gave hydrogen’s 2S½ and 2P½ the same energy, but in 1947 Lamb and Retherford measured 2S½ about 1057 MHz higher. Bethe showed most of it is the electron’s self-energy in vacuum fluctuations; virtual pairs add only a little. It helped launch quantum electrodynamics. 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

Dirac's theory says the 2S and 2P½ levels of hydrogen have exactly the same energy. In 1947 Willis Lamb and Robert Retherford measured them with microwaves and found them about 1057 MHz apart.

The gap comes from nothing: the electron is jostled by vacuum fluctuations of the electromagnetic field. Hans Bethe estimated the shift on a train ride that same year, and the calculation launched modern quantum electrodynamics.

Vacuumancer plays the empty space between the levels. 1057 MHz of nothing.

Equations

\[\Delta\nu\left(2S_{1/2} - 2P_{1/2}\right) \approx 1057.8\ \text{MHz}\]
\[\Delta E_{n,\ell=0} \approx \frac{4\,\alpha^{5} m_e c^{2}}{3\pi n^{3}}\,\ln\frac{m_e c^{2}}{\langle E\rangle}\]
SymbolMeaningUnit
\(\Delta\nu\) frequency splitting between the 2S_{1/2} and 2P_{1/2} levels of hydrogen \(\mathrm{Hz}\)
\(\Delta E_{n,\ell=0}\) upward shift of an s level (Bethe's non-relativistic estimate, Z = 1) \(\mathrm{J}\)
\(\alpha\) fine-structure constant \(\mathrm{–}\)
\(m_e\) electron mass \(\mathrm{kg}\)
\(c\) speed of light \(\mathrm{m/s}\)
\(n\) principal quantum number \(\mathrm{–}\)
\(\langle E\rangle\) average atomic excitation energy (Bethe's cut-off) \(\mathrm{J}\)

Sources

  1. Lamb & Retherford (1947) Fine Structure of the Hydrogen Atom by a Microwave Method, Phys. Rev. 72, 241
  2. Bethe (1947) The Electromagnetic Shift of Energy Levels, Phys. Rev. 72, 339
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