Quantum friction — the vacuum as a shear medium

Why the library suggests it

Nothing touches, and the gap still drags. Set the separation and the sliding speed, and watch the drag fall by four decades for every decade of distance.

The shear plot

Two surfaces slide past each other in vacuum, never touching. Pendry's scaling says the drag between them is proportional to the sliding speed and falls as the fourth power of the separation — the law a viscous fluid would obey. Move the separation and the speed, and read the shear stress off the curve. The curve passes through the one number he published, and through nothing else.

Which area the stress is spread over

The true contact area — the part that genuinely comes closeThe whole pressed area — what an instrument would weigh

At this setting

Separation between the surfaces

0.1

Sliding speed

1

Return to Pendry's setting

• The scaling carried through that estimate
• Pendry's published estimate

Shear stress:

3E3 Pa

Force on one square centimetre:

3E-1 N

Against the published estimate:

1E0 ×

At this setting: This is the stress on the area that actually comes close. Pendry's figure of about three thousand newtons per square metre is an everyday pressure — and it applies only where two surfaces genuinely approach.

The companion review reaches vacuum drag by a different route — an oscillating boundary rather than a sliding one — and gets an effective shear viscosity growing as the fourth power of frequency, with the lost energy leaving as real photons. Different motion, different law; the same vacuum pushing back.

Shearing the vacuum — quantum friction (Pendry, 1997) · The “friction” of vacuum, and other fluctuation-induced forces (1999) · Near-field radiative heat transfer in many-body systems (2021)

John Pendry showed that a moving surface has a lopsided reflection coefficient along its direction of travel, so the two surfaces trade virtual photons asymmetrically and momentum crosses the gap; for a semi-metal at atomic separation sheared at a metre per second he estimates about three thousand newtons per square metre of true contact area, or roughly three newtons per square metre once you allow for how little of two pressed surfaces actually touches (Shearing the vacuum — quantum friction, 1997). Pendry's own remark is the one that matters here: the simplest case gives exactly the friction the vacuum would produce if it behaved as a viscous fluid. The companion survey of fluctuation-induced forces is The "friction" of vacuum, and other fluctuation-induced forces (1999).

The experiment or build

The measurement has never been made cleanly because contamination and real contact swamp it. Two routes are now open that were not in 1997. First, use the near-field radiative heat-transfer geometry, where a nanometre gap carries a flux almost five orders of magnitude above the black-body limit and the same fluctuational electrodynamics applies (Near-field radiative heat transfer in many-body systems, 2021). Second, use the patterned surfaces of the geometry card above to change the predicted drag by a known factor while leaving every contaminant unchanged. The settling measurement is the shear force per unit area against sliding velocity, at fixed separation, with the force changing by the predicted factor when only the surface pattern changes. A drag that tracks geometry is a drag that came from the field.