• Neutrina Fade Neutrinos pixel-art physics T-shirt, black tee, front view

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Neutrina Fade

Neutrino Ghost Matter Physics

\[\cos\theta_C = \frac{1}{n\beta}\]
$29.99 USD
$29.99 USD
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Size guide S–5XL · inches

Right now, tens of billions are passing through your thumbnail. About 65 billion solar neutrinos cross each square centimetre every second. Pauli proposed them in 1930; Cowan and Reines caught one in 1956. Neutrinos change flavour as they travel, which is only possible if they have mass. We see them through the Cherenkov light of the electrons and muons they knock loose. Neutrina Fade on a pixel-art unisex tee; equation, symbols and sources in the panel below.

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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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The physics

A charged particle moving through water faster than light moves in water gives off a cone of blue Cherenkov light, at an angle set by its speed and the refractive index. Neutrino detectors see this glow from the particles that neutrinos knock loose, and the second formula describes how neutrinos change flavour as they travel.

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

\[\cos\theta_C = \frac{1}{n\beta}\]
\[P_{\nu_a\to\nu_b} = \sin^{2}(2\theta)\,\sin^{2}\!\left(\frac{\Delta m^{2}c^{4}L}{4\hbar c E}\right)\]
SymbolMeaningUnit
\(\theta_C\) Cherenkov cone angle of light from the charged secondary particle (e.g. electron or muon) a neutrino interaction produces, not the neutrino itself \(\mathrm{rad}\)
\(n\) refractive index of medium \(\mathrm{1}\)
\(\beta\) speed of that charged secondary particle / 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 \(\mathrm{m/s}\)

Sources

  1. Encyclopaedia Britannica — Neutrino
  2. Encyclopaedia Britannica — Cherenkov radiation
  3. NobelPrize.org — The Nobel Prize in Physics 1958 (Cherenkov, Frank, Tamm)
  4. Cowan, Reines et al. (1956) Detection of the Free Neutrino: a Confirmation, Science 124, 103
  5. NobelPrize.org — The Nobel Prize in Physics 1995 (Perl, Reines)
  6. Super-Kamiokande (1998) Evidence for Oscillation of Atmospheric Neutrinos, PRL 81, 1562
  7. SNO (2002) Direct Evidence for Neutrino Flavor Transformation, PRL 89, 011301
  8. NobelPrize.org — The Nobel Prize in Physics 2015 (neutrino oscillations)
  9. PDG 2024 review — Neutrino masses, mixing and oscillations
  10. NASA NSSDCA — Sun Fact Sheet (mass, central temperature; Earth comparison)

Source Frank, I.; Tamm, I. (1937). Coherent visible radiation of fast electrons passing through matter. Doklady Akademii Nauk SSSR 14, 109. Reprinted in Usp. Fiz. Nauk 93, 388–393 (1967),doi.org/10.3367/UFNr.0093.196710o.0388

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