Shearing the vacuum - quantum friction
J B Pendry
Abstract and summary · read the original at the source
In one page
John Pendry, at Imperial College London, asks a question with no obvious answer. Take two perfectly smooth, perfectly clean surfaces, hold them a little apart in vacuum at absolute zero, and slide one past the other. Nothing touches, nothing is rough, nothing wears away. Is there friction? Pendry finds there is, and it is not a curiosity-sized effect. Each surface sits inside a cloud of zero-point electromagnetic fluctuations. Set one moving and its reflection coefficient becomes lopsided along the direction of travel, because the two Doppler-shifted waves reflect differently. The surfaces then trade virtual photons asymmetrically, and that trade carries momentum across the gap — which is what friction is. For a semi-metal at an atomic separation, sheared at a metre per second, he estimates about three thousand newtons per square metre of true contact area, roughly three newtons per square metre once you allow for how little of two pressed surfaces actually touches. Everyday magnitudes, from empty space.
Why it matters hereChapter 2’s claim that the vacuum is a structured medium is at its strongest where the medium does mechanical work, and this is that case: momentum crossing an empty gap and slowing a moving surface. Chapter 5 gets the image it needs from Pendry’s own remark that the simplest case gives exactly the friction the vacuum would produce if it behaved as a viscous fluid — and the companion survey by Kardar and Golestanian is on this site at /library/stm-e10394fe7e.
What it claims
01Two perfectly smooth featureless surfaces at zero temperature, defined only by their dielectric functions and never in contact, do experience friction when sheared past one another, and the effect is large enough to compare with other contributions to everyday friction.Abstract; Section 8, conclusions
Published and peer-reviewed02The mechanism is an asymmetric exchange of virtual photons: motion makes a surface’s reflection coefficient lopsided along the direction of travel, because in the surface’s own rest frame the two incident waves are Doppler shifted in opposite senses and so reflect differently.Section 1, introduction; Figure 2
Published and peer-reviewed03The friction depends solely on the surfaces’ reflection coefficients to electromagnetic waves, and the formula is the van der Waals expression with the imaginary rather than the real part of the response — so a loss process must be operating in both surfaces for any friction to exist.Section 5, opening observations; Section 5.1, Equation 54
Published and peer-reviewed04For a constant dielectric function the force is proportional to shear velocity and falls as the fourth power of separation — the form friction would take if the vacuum behaved as a viscous fluid — and it never decays exponentially, because the interaction between the surfaces is carried by a massless particle, the photon.Section 5.1, Equations 53 and 54
Published and peer-reviewed05For a semi-metal at a separation of about one ten-billionth of a metre and a shear velocity of one metre per second, the estimated frictional force is about 3 times 10 to the third newtons per square metre, falling to roughly 3 newtons per square metre once the small fraction of area in true intimate contact is allowed for.Section 5.2, Equations 59 to 62
Published and peer-reviewed06Smooth sheared surfaces cannot emit free light: the frequency is bounded by the shear velocity times the wavevector parallel to the surface, which keeps it in the gigahertz range, and escape into a transparent dielectric would need a permittivity larger than the square of light speed over shear speed. Rough surfaces, outside the scope of the paper, may emit — and that is the measurement left open.Section 7, Equations 70 to 73; Section 8, conclusions
What to watch
Read it · abstract
Abstract
We consider two perfectly smooth featureless surfaces at T=0, defined only by their respective dielectric functions, separated by a finite distance, and ask the question whether they can experience any friction when sheared parallel to their interface. We find large frictional effects comparable to everyday frictional forces provided that the materials have resistivities of the order of 1 mΩ and that the surfaces are in close proximity. The friction depends solely on the reflection coefficients of the surfaces to electromagnetic waves and its detailed behaviour with shear velocity and separation is dictated by the dispersion of the reflectivity with frequency.
The way in
https://doi.org/10.1088/0953-8984/9/47/001Licence checked directly. The published article is free to read at the publisher but carries no Creative Commons statement, and the preprint on arXiv as cond-mat/9707190, version 2 filed 21 July 1997, sits under arXiv’s assumed licence for submissions of 1991 to 2003, which does not grant redistribution. So this page carries the summary, the claims and the author’s own abstract, and sends the reader to the source. Published as Journal of Physics: Condensed Matter 9, 10301–10320 (1997), report number CMTH/9697/17, from the Blackett Laboratory, Imperial College, London. The summary, the claims and the locators below were written from the full author text. One typesetting note: the ohm symbol in the abstract’s resistivity figure is mangled in the machine-readable preprint and is restored here as printed.
How to cite it
J B Pendry (1997) Shearing the vacuum - quantum friction. doi:10.1088/0953-8984/9/47/001
Where it sits in the curriculum