• Twissa & Hanbra Hanbury Brown–Twiss Effect pixel-art physics T-shirt, white tee, front view

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Twissa & Hanbra

Hanbury Brown–Twiss Effect Physics

\[g^{(2)}(\tau) = \frac{\langle I(t)\,I(t+\tau)\rangle}{\langle I\rangle^{2}}\]
$29.99 USD
$29.99 USD
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Size guide S–5XL · inches

Twissa and Hanbra stand back to back at their searchlight dishes under Sirius. Their photons like to bunch.

The Physics

Correlating the intensity flickers at two separate detectors measures the coherence of light, and from it the angular size of a star. For thermal light the correlation at zero delay is 2 (bunching), for ideal laser light it is 1, and for single-photon sources it is below 1 (antibunching, a purely quantum effect).

g⁽²⁾(τ) = ⟨I(t) I(t+τ)⟩ / ⟨I⟩²

  • g⁽²⁾(τ): normalised intensity correlation (dimensionless)
  • I: light intensity (W/m²)
  • t: time (s)
  • τ: delay between detectors (s)

R. Hanbury Brown and R. Q. Twiss measured Sirius with two searchlight mirrors (Nature, 1956): angular diameter 0.0068″ ± 0.0005″.

Honest caveat: The value 2 is the ideal for a single polarisation of thermal light; it is not what their 1956 electronics measured.

On the shirt

Front: Twissa & Hanbra, the pixel-art character, with the title. Back: the g⁽²⁾ definition, thermal, laser and single-photon values, the Sirius result and the 1956 paper. Printed on a unisex tee.

Shipping calculated at checkout by destinationMade to order, ships in 2–5 business days

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

För skalans skull: storlek M är 20 in (50.80 cm) bred, ungefär 3.143 × 1034 Plancklängder (lP = 1.616255 × 10−35 m). Ett måttband går snabbare.

Measurements in inches, ±1.5 in tolerance.

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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

We stand back to back at two searchlight mirrors, pointed at Sirius. We never compare the light's phase. We only multiply the flickers of intensity each of us records and average them.

For thermal light like starlight, those flickers are correlated when we are close together and the delay is short. In the ideal case, for one polarisation, the correlation at zero delay is 2: photons arrive bunched. Ideal laser light gives 1. A true single-photon source gives less than 1, antibunching, which has no classical explanation.

In 1956 Robert Hanbury Brown and Richard Twiss used this to measure the angular diameter of Sirius: 0.0068″ ± 0.0005″, a probable error. Their electronics did not see the full value of 2; that figure is the ideal. Many physicists first thought the effect could not exist. It now underpins quantum optics.

Equations

\[g^{(2)}(\tau) = \frac{\langle I(t)\,I(t+\tau)\rangle}{\langle I\rangle^{2}}\]
\[\text{thermal: } g^{(2)}(0) = 2, \quad \text{laser: } g^{(2)}(0) = 1, \quad \text{single photons: } g^{(2)}(0) < 1\]
SymbolMeaningUnit
\(g^{(2)}(\tau)\) normalised intensity correlation \(\mathrm{1}\)
\(I\) light intensity \(\mathrm{W/m²}\)
\(t\) time \(\mathrm{s}\)
\(\tau\) delay between the two detectors \(\mathrm{s}\)
\(\langle\ \rangle\) time average \(\mathrm{1}\)

Sources

  1. Hanbury Brown & Twiss (1956) A Test of a New Type of Stellar Interferometer on Sirius, Nature 178, 1046
  2. Loudon (2000) The Quantum Theory of Light, 3rd ed., Oxford University Press, ch. 3 and 6
  3. Kimble, Dagenais & Mandel (1977) Photon Antibunching in Resonance Fluorescence, Phys. Rev. Lett. 39, 691

Field notes

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