Marina Dirac
The Dirac Sea Physics
Size guide S–5XL · inches
Marina Dirac rises from a sea of filled states, and the hole she leaves behind shines like a positive electron.
The Physics
Dirac's equation for a free electron allows negative as well as positive energies, separated by a gap of 2mc². Dirac proposed that every negative-energy state is already filled, so electrons cannot fall into them. An empty state, a hole, would move like a positively charged electron.
(iħ γ^μ ∂_μ − m c) ψ = 0, E = ± √(p²c² + m²c⁴)
- ħ: reduced Planck constant (J·s)
- γ^μ: Dirac matrices (dimensionless)
- ∂_μ: spacetime derivative (1/m)
- m: electron mass (kg)
- c: speed of light (m/s)
- ψ: electron wavefunction
- E: energy (J)
- p: momentum (kg·m/s)
Dirac proposed the sea in 1930 (he first suggested the holes were protons); C. D. Anderson reported the positron in cosmic rays in 1933. The gap is 2m_ec² ≈ 1.022 MeV.
Honest caveat: The sea is a historical picture. Quantum field theory keeps the positron and drops the sea.
On the shirt
Front: Marina Dirac, the pixel-art character, with the title. Back: the Dirac equation, the two energy branches, the 1.022 MeV gap, Anderson's positron and the historical-picture note. 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.
| Size | Width | Length | Sleeve |
|---|---|---|---|
| S | 18 | 28 | 15.1 |
| M | 20 | 29 | 16.5 |
| L | 22 | 30 | 18 |
| XL | 24 | 31 | 19.5 |
| 2XL | 26 | 32 | 21 |
| 3XL | 28 | 33 | 22.4 |
| 4XL | 30 | 34 | 23.7 |
| 5XL | 32 | 35 | 25 |
Ter vergelijking: maat M is 20 in (50.80 cm) breed, ongeveer 3.143 × 1034 Plancklengtes (lP = 1.616255 × 10−35 m). Een meetlint is sneller.
Measurements in inches, ±1.5 in tolerance.
ShippingBy destination
Shipping calculated at checkout by destination. Printed to order for you.
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.
The physics
Equations
| Symbol | Meaning | Unit |
|---|---|---|
| \(\hbar\) | reduced Planck constant | \(\mathrm{J·s}\) |
| \(\gamma^{\mu}\) | Dirac matrices | \(\mathrm{1}\) |
| \(\partial_{\mu}\) | spacetime derivative | \(\mathrm{1/m}\) |
| \(m,\ m_e\) | electron mass | \(\mathrm{kg}\) |
| \(c\) | speed of light, 299 792 458 m/s (exact) | \(\mathrm{m/s}\) |
| \(\psi\) | electron wavefunction (four-component spinor) | \(\mathrm{m^(−3/2)}\) |
| \(E\) | energy | \(\mathrm{J}\) |
| \(p\) | momentum | \(\mathrm{kg·m/s}\) |
Field notes
Alles bekijken-
Fermions vs Bosons: What Is the Difference?
Every particle in nature is either a fermion or a boson. Fermions, like electrons and quarks, have half-integer spin and obey the Pauli exclusion principle. Bosons, like photons, have integer...
Fermions vs Bosons: What Is the Difference?
Every particle in nature is either a fermion or a boson. Fermions, like electrons and quarks, have half-integer spin and obey the Pauli exclusion principle. Bosons, like photons, have integer...
-
Does Erasing Information Cost Energy? Landauer’...
Deleting a file feels free, but physics says erasing information has a minimum cost. Landauer’s principle puts it at kT ln 2 per bit, about 2.9 × 10⁻²¹ joules at...
Does Erasing Information Cost Energy? Landauer’...
Deleting a file feels free, but physics says erasing information has a minimum cost. Landauer’s principle puts it at kT ln 2 per bit, about 2.9 × 10⁻²¹ joules at...
-
How Did Rømer Measure the Speed of Light with Io?
In 1676, at the Paris Observatory, Ole Rømer noticed that eclipses of Jupiter’s moon Io came late when Earth was moving away from Jupiter and early when it was approaching....
How Did Rømer Measure the Speed of Light with Io?
In 1676, at the Paris Observatory, Ole Rømer noticed that eclipses of Jupiter’s moon Io came late when Earth was moving away from Jupiter and early when it was approaching....
