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ForceShift

Weak Nuclear Force / Quantum Tunneling Physics

\[T \approx e^{-2\kappa L}, \qquad \kappa = \frac{\sqrt{2m(V_0 - E)}}{\hbar}\]
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A wall you cannot climb is not always a wall you cannot cross. Tunneling lets a quantum particle cross a barrier it could not climb classically. It drives alpha decay and aids solar fusion. ForceShift wears it in pixel art on a unisex tee. The physics panel below has the equation, every symbol and the sources.

Color
Size

Size guide S–5XL · inches

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.

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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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

ForceShift does not break the wall. The wall was never quite solid.

A classical ball without the energy to clear a hill rolls back, every time. A quantum particle is a wave, and a wave meeting a barrier it cannot climb does not stop dead at the edge. Inside the barrier it dies away exponentially, and if the barrier is thin enough, a little of it is still there on the far side. That remnant is the chance of getting through. The formula on this page is the standard estimate: the probability falls as e to the power minus twice the barrier width times κ, where κ grows with the square root of the particle's mass and of the energy it is short.

The exponent makes tunnelling touchy. In 1928 George Gamow, and independently Ronald Gurney and Edward Condon, used it to explain alpha decay: the alpha particle is trapped inside the nucleus behind an electric barrier it cannot climb, and leaks out. Compare: polonium-212 releases about 8.95 MeV and has a half-life of 294 nanoseconds. Thorium-232 releases about 4.08 MeV and has a half-life of 14 billion years. A little over twice the energy; about twenty-four orders of magnitude faster. The energy sits inside an exponent.

The Sun runs on the same trick. Its core, about 15.7 million kelvin, is far too cool for two protons to climb over their electric repulsion. They tunnel through it. Then, in a rare few encounters, the weak force turns one proton into a neutron, making deuterium: the first step of the Sun's fusion chain. Tunnelling gets them close; the weak force makes it count.

The scanning tunnelling microscope, recognised by the 1986 Nobel Prize, maps single atoms the same way.

ForceShift does not push harder. They are never entirely on one side.

Equations

\[T \approx e^{-2\kappa L}, \qquad \kappa = \frac{\sqrt{2m(V_0 - E)}}{\hbar}\]
Symbols
SymbolMeaningUnit
\(T\) transmission probability \(\mathrm{1}\)
\(\kappa\) decay constant inside the barrier \(\mathrm{m⁻¹}\)
\(L\) barrier width \(\mathrm{m}\)
\(m\) particle mass \(\mathrm{kg}\)
\(V_0\) barrier height \(\mathrm{J}\)
\(E\) particle energy \(\mathrm{J}\)
\(\hbar\) reduced Planck constant \(\mathrm{J·s}\)