• Casimira pixel-art physics sticker – Casimir effect, two plates pulled together
  • Casimira pixel-art physics sticker on a laptop
  • Casimira pixel-art physics sticker on a water bottle
1 3

CasimiraCasimir EffectSticker

Casimira – Casimir Effect Physics Sticker

$6.99 USD
$6.99 USD
Sale Sold out
Shipping calculated at checkout. Free US shipping · $10 flat shipping outside the US.
Size
3" × 3"
Surface
White
Made
To order · shipping times

Can empty space pull mirrors together? Two uncharged, parallel conducting plates a gap d apart attract with a pressure of π²ħc/(240 d⁴), about 1.3 millipascals at 1 µm. Hendrik Casimir predicted it in 1948, and Lamoreaux measured it in 1997. Whether it shows vacuum energy is debated, since Jaffe derived it without that picture in 2005. A 3" pixel-art sticker; equation, symbols and sources in the physics panel below.

Size
Surface

Free US shipping$10 flat shipping outside the USMade to order, ships in 2–5 business days

Details

Size3″ × 3″

3″ × 3″ kiss-cut sticker.

Shipping

Free US shipping · $10 flat shipping outside the US, whatever's in your order.

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

Casimira stands between two uncharged mirrors and braces them apart, because they pull toward each other.

For ideal parallel conducting plates a gap d apart, the attraction per unit area is π²ħc/(240 d⁴). At d = 1 µm that is about 1.3 mPa; at 100 nm it is 10,000 times larger.

On the sticker the cyan wiggles outside are field modes of every wavelength; between the plates only modes that fit the gap survive (amber). The magenta arrows show the net push inward.

The force has been measured, starting with Lamoreaux in 1997. Calling it a push from vacuum energy is the popular picture; Jaffe (2005) showed it can also be derived without it, so the interpretation is debated.

Nothing pushes in.

Equations

\[\frac{F}{A} = -\frac{\pi^2\hbar c}{240\,d^4}\]
SymbolMeaningUnit
\(F/A\) force per unit area between the plates (negative = attractive) \(\mathrm{Pa}\)
\(\hbar\) reduced Planck constant \(\mathrm{J s}\)
\(c\) speed of light \(\mathrm{m/s}\)
\(d\) gap between the plates \(\mathrm{m}\)

Sources

  1. Casimir, H. B. G. (1948) On the attraction between two perfectly conducting plates, Proc. K. Ned. Akad. Wet. 51, 793
  2. Lamoreaux, S. K. (1997) Demonstration of the Casimir force in the 0.6 to 6 µm range, Phys. Rev. Lett. 78, 5
  3. Jaffe, R. L. (2005) Casimir effect and the quantum vacuum, Phys. Rev. D 72, 021301
  4. Wikipedia, Casimir effect
View full details

Field notes

View all
1 3
View all