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Adiabatix
The Adiabatic Invariant / J = ∮p dq Physics
Adiabatix, a white-bearded sage, slowly draws up the string of a glowing pendulum.
The Physics
At the 1911 Solvay conference Lorentz asked what happens to a pendulum if you shorten its string very slowly. Einstein answered: the energy changes, but the ratio of energy to frequency stays the same. Paul Ehrenfest built this into a principle (1916): for slow changes, the action J stays constant. That is why quantum numbers stay put when conditions change gently.
J = ∮p dq
- J: action over one cycle (J·s)
- p: momentum
- q: position coordinate
- ∮: integral over one full oscillation
For a harmonic oscillator J = E/f, which is why the old quantum rule set E = nhf.
Honest caveat: J is only approximately conserved; it holds better the slower the change compared with one period.
On the sticker
Adiabatix pinches a thin string from which a small glowing bob hangs. Printed text: ADIABATIX with the line J = ∮p dq. Pixel-art kiss-cut vinyl sticker, white, in 2″, 3″, 4″ and 6″ sizes.
Shipping calculated at checkout by destinationMade to order, ships in 2–5 business days
Details
Size3″ × 3″
3″ × 3″ kiss-cut sticker.
Shipping
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.
Field notes
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