The Casimir Effect: Visualisation · Signals from the Periphery

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Separation

1 µm

Vacuum squeeze

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Force

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Energy in the gap

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CASIMIR · THE NEGATIVE-ENERGY BENCH
two uncharged mirrors, and the vacuum pushes them together
fewer waves fit between than outside
the gap holds less energy than nothing
measured to 1% · the only negative energy ever made
tighten the gap and watch the modes drop out

Part

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Evidence

fact ⇄ what kind of claim · live

The force is real: 5% (1997), 1% (1998), <1% (2000s)

Lamoreaux, Mohideen, Decca · the law this bench computes

MEASURED

Sparnaay 1958: errors near 100%

"not inconsistent" · the whole record for 39 years

MEASURED

At 10 nm the vacuum's squeeze passes one atmosphere

the law extrapolated · roughness and patches rule down here

MODELLED

The gap holds negative energy density

inferred from the measured force · never probed directly

MODELLED

Negative energy is rationed: Ford-Roman inequalities

more negative → smaller and briefer, by theorem

MODELLED

~60 orders of magnitude short of a warp wall

the Ledger prices this bench against INST-12's bill

MODELLED

Drude vs plasma: a factor-of-two thermal dispute

Decca's data prefer the "wrong" model · unresolved

READING

Does the force prove vacuum zero-point energy?

Jaffe 2005: derivable as van der Waals without it · open

READING

View

Experiment · which one do you run?

PREDICTED 1948

▶ One law runs everything here. Tighten the separation and the fourth-power steepens it a thousandfold per decade.

The bench

Separation…

The only dial that matters: P ∝ 1/d⁴. From 10 µm, where the force is hopeless, down to 5 nm, where the extrapolated squeeze passes an atmosphere and no experiment has cleanly gone.

Plate size…

Area only scales the total force and energy; the pressure ignores it. Casimir's worked example used a square centimetre.

Sphere radius…

The sphere-plate geometry every modern measurement actually used. F = 2πR·E/A(d): the proximity-force conversion, good to about d/R.

Temperature…

Thermal photons join the zero-point ones. At 300 K the crossover sits near 4 µm; beyond it the force goes classical, and by how much is the open Drude/plasma dispute below.

Geometry · material · thermal model

Real gold (λp = 136 nm)

Vacuum modes

Force arrows

Labels

Readout · exact from your dials

Vacuum pressure

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In atmospheres

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Force

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Energy in the gap

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Mass-equivalent

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vs the warp bill

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Vs experiment

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What is measured vs modelled here

Measured: the force itself, from Sparnaay's ±100% shrug to Decca's sub-1%, and Chan's MEMS actuation; also Wilson's 2011 photons from the dynamical effect. Modelled: everything this bench prints: the exact ideal law, the disclosed gold and thermal corrections, and above all the negative energy, which is the standard inference from the measured force, not a probed quantity. Reading: whether the force proves vacuum zero-point energy at all (Jaffe says no proof), and which thermal model gold obeys. Both stay open on this screen.

The two corrections, and the dispute

Real gold is not a perfect mirror: wavelengths shorter than its plasma wavelength (136 nm) leak in, and this bench applies a one-line stand-in for the full Lifshitz theory, η = d/(d+λp): about half strength at 136 nm, ~90% at a micron. Heat adds real photons on top of the zero-point ones; in the classical limit the pressure goes to ζ(3)kT/4πd³ for lossless (plasma) metal and exactly half that for lossy (Drude) metal. Gold is lossy, so theory says Drude; Decca's precision data fit plasma. That factor of two has been an open dispute for twenty years, and the seg above hands it to you.

Where this drawing takes liberties

The gap on screen is a log-mapped exaggeration: nanometres drawn at centimetres, or the mirrors would touch. The waves are a schematic of mode counting, a handful of standing waves standing in for a sum over all frequencies and angles; the Modes view says so on its face. The thermal blend between the exact T=0 law and the exact classical limit is this site's smooth interpolation, disclosed here rather than buried. And below ~20 nm every number is the extrapolated law: real surfaces are ruled by roughness and electrostatic patches there, and the verdict line says so when you enter that regime.

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drag = orbit · scroll = zoom · tighten the gap and watch the waves thin out