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Color
Black
Size
S–5XL
Made
To order · shipping times
Color
Size

Details

Size & fitS–5XL

Unisex heavy cotton (Gildan 5000), classic fit.

Unisex tee size chart, inches
SizeWidthLengthSleeve
S182815.1
M202916.5
L223018
XL243119.5
2XL263221
3XL283322.4
4XL303423.7
5XL323525

Measurements in inches, ±1.5 in tolerance.

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The physics

Neutrina Fade is passing through you as you read this, about sixty-five billion of her per square centimetre every second, from the Sun alone.

Wolfgang Pauli proposed the neutrino in 1930 to rescue energy conservation in beta decay, where electrons came out with less energy than they should have. He worried he had invented a particle that could never be detected. It took until 1956 for Clyde Cowan, Frederick Reines and colleagues to catch one, using the flood of antineutrinos from a nuclear reactor; Reines shared the 1995 Nobel Prize.

That opening number is a calculation, not a guess. Every helium nucleus made in the Sun's core releases about 26.7 MeV and two neutrinos. Divide the Sun's power output by that energy, double it, and spread it over a sphere the size of Earth's orbit.

Neutrinos are seen only when one, rarely, strikes something. In a tank of water, a struck electron or muon can be knocked out faster than light travels in water, which is about three-quarters of its speed in vacuum. It then emits a cone of blue Cherenkov light, the optical cousin of a sonic boom, at the angle in the first formula: up to about 41 degrees in water.

The second formula is oscillation. A neutrino made as one flavour can be detected as another, with a probability that swings with distance over energy. It can only happen if neutrinos have mass. Super-Kamiokande in 1998 and SNO in 2002 showed it does happen, and the 2015 Nobel Prize followed. Oscillations measure only differences between masses squared. The absolute masses, and whether the neutrino is its own antiparticle, are still open.

Neutrina Fade does not stop. She almost never touches anything, and that is the whole difficulty.

Equations

\[\cos\theta_C = \frac{1}{n\beta}\]
\[P_{\nu_a\to\nu_b} = \sin^{2}(2\theta)\,\sin^{2}\!\left(\frac{\Delta m^{2}c^{4}L}{4\hbar c E}\right)\]
Symbols
SymbolMeaningUnit
\(\theta_C\) Cherenkov cone angle \(\mathrm{rad}\)
\(n\) refractive index of medium \(\mathrm{1}\)
\(\beta\) particle speed / c \(\mathrm{1}\)
\(\theta\) mixing angle (two-flavour approx.) \(\mathrm{rad}\)
\(\Delta m^{2}\) difference of squared neutrino masses (quoted in eV²/c⁴) \(\mathrm{kg²}\)
\(L\) baseline distance \(\mathrm{m}\)
\(E\) neutrino energy \(\mathrm{J}\)
\(\hbar\) reduced Planck constant \(\mathrm{J·s}\)
\(c\) speed of light \(\mathrm{m/s}\)
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