Historical research guide · 0743 · 2025
Thermal Effects in the Casimir Torque between Birefringent Plates
Benjamin Spreng · Jeremy N. Munday
In one minute
Benjamin Spreng and Jeremy Munday, at the University of California, Davis, work out what temperature does to the Casimir torque. Two plates held a fraction of a micrometre apart feel the Casimir force, the pull the vacuum’s own fluctuations exert on them; if the plates are birefringent — crystals whose optical response depends on direction — those same fluctuations also try to twist the two into alignment. That twist has been measured in the laboratory once. Spreng and Munday add the thermal part of the fluctuation spectrum, which nobody had done for the torque, and find that it works against the quantum part rather than adding to it: for barium titanate at room temperature the torque falls by about 99.5 percent, a factor of two hundred, where the same thermal correction trims the ordinary Casimir force between metal plates by only about a third. Temperature also bends the torque away from its textbook angle dependence and, for two unlike crystals, can reverse which way it turns.
Connection
Chapter 2 rests on the vacuum being a real, structured medium, and the Casimir torque is its second mechanical signature: not only a pull between surfaces but a twist, sensitive to the direction the material faces. This paper says how strongly the thermal part of the spectrum fights the quantum part, which is exactly the design knob chapter 6 cares about — cool the apparatus and the vacuum torque grows while the Brownian noise shrinks, or hold the gap fixed and change the temperature to flip which way the vacuum turns your plate. The authors’ review of the field is on this site at /library/stm-58df236cfb.
From the source
Thermal fluctuations exert a Casimir torque that counteracts the torque coming from quantum vacuum fluctuations, so raising the temperature diminishes rather than adds to the twist: between two barium titanate plates at 300 kelvin the torque is reduced by up to about 99.5 percent, roughly a two-hundred-fold reduction, and the ratio of the 300-kelvin torque to the zero-temperature torque bottoms out near 0.005.Abstract; Figure 1(c) and 1(d)
The reduction is far larger than the corresponding thermal correction to the Casimir force between isotropic surfaces, where the same ratio is about 0.69 for two metallic plates and about 0.76 for a sphere and a plane — so lowering the temperature raises the torque signal while lowering the Brownian noise, which favours low-temperature experiments for precise Casimir torque measurements.Paragraph following Figure 1(d), citing references 5 to 7
The torque follows a one-over-distance-cubed power law at zero temperature and crosses over to a one-over-distance-squared law, linear in temperature, once the separation exceeds the thermal wavelength of about 7.6 micrometres at 300 kelvin, where only the zero-frequency Matsubara term survives and only the polarisation-preserving element of the reflection matrices contributes.Figure 1(c); Equations 2, 5 and 6
For strongly birefringent plates the torque no longer follows the sine-of-twice-the-twist-angle dependence known for weakly birefringent ones: at room temperature and 10 micrometre separation the angle of maximum torque shifts well below 45 degrees, and the deviation grows both at separations beyond the thermal wavelength and at short separations.Figure 2(a) and 2(b)
In a pair of unlike birefringent plates the torque reverses direction at a separation that itself depends on temperature — 1.17 micrometres at zero temperature and 1.87 micrometres at 300 kelvin for barium titanate against calcium carbonate — so at a fixed gap of 1.7 micrometres the torque can be tuned from 24 femtonewton-metres per square metre at 100 kelvin to minus 12 at 400 kelvin by changing temperature alone, which the authors offer as a guide for designing a separation sensor read out through the Casimir torque.Figure 4(a) and 4(b); closing paragraph before the summary
The Casimir torque has been verified experimentally only once, between a birefringent plate and a liquid crystal, and a recent self-alignment result on triangular platelets did not reach quantitative agreement with theory; the torque magnitudes computed here for barium borate against barium titanate lie within the range of an already proposed Casimir torque experiment, which is where the thermal prediction would be tested.Introduction, citing references 18 and 19; closing paragraph, citing reference 25
The way in
https://doi.org/10.1103/32gq-dbmsHow to cite it
Benjamin Spreng, Jeremy N. Munday (2025) Thermal Effects in the Casimir Torque between Birefringent Plates doi:10.1103/32gq-dbms