STM-D-0566Paper1999Published and peer-reviewed

Unusual properties of conductive rectangular cavities in the zero point electromagnetic field: Resolving forward’s Casimir energy extraction cycle paradox

G. Jordan Maclay

Summary and citation · read the original at the source · none found

In one page

Robert Forward had asked a sharp question: could you take energy out of the vacuum for nothing, by walking a conducting box around a closed loop of shapes? G. Jordan Maclay, then Professor Emeritus at the University of Illinois, answers it by looking at what the vacuum actually pushes on. The Casimir force between two plates is settled physics, measured to within five percent. Inside a rectangular box the same field does something less obvious: at one and the same shape, the pressure on one pair of faces can be outward while the pressure on another pair is inward. Forward’s cycle assumed the pressure follows the average energy — that a box holding more energy than open space must push outward everywhere. Detailed field-theory computations show that assumption fails, so real work is done during the cycle and the books balance. Maclay’s closing point is the interesting one: a box whose faces swing between pulling and pushing behaves as if it held a fluid, and might be made to oscillate on its own.

Why it matters hereChapter 6 is about taking energy out of the vacuum, and this is the paper that says what the accounting has to look like: the extraction is real, the free lunch is not, and the difference lives in the geometry. For chapter 2 it is the clearest published demonstration that the vacuum’s stress is not isotropic — the size and the sign of the force depend on the shape of the cavity, not merely on how much energy it holds — which is exactly the handle a Casimir power cell has to grip.

What it claims

01Rigorous field-theoretic computations predict that both the magnitude and the direction of the force due to the ground state of the electromagnetic field depend strongly on the specific geometry, and the force is repulsive in several cases: for a cube the change in vacuum energy density is positive and grows as the side is reduced, while for parallel plates it is negative.Introduction, Table 1
Settled physics
02Using Casimir forces to extract energy from the vacuum is possible from both the experimental and the theoretical viewpoint, following Forward in 1984 and Cole and Puthoff in 1993, and the total energy of the system, including the surface energy, is expected to be conserved in the process.Introduction, third paragraph
Published and peer-reviewed
03For a cavity with two sides equal to one, the Casimir energy is positive for the third side between 0.4 and 3.3, but the average pressure on the square faces and the average pressure on the long faces are both positive only between 0.7 and 1.6; outside that band the two pressures have opposite signs.Abstract; Casimir energy densities and forces in rectangular cavities, Figure 2
Published and peer-reviewed
04Forward’s proposed extraction cycle depends on the implicit assumption that the energy density inside the cavity is approximately isotropic, so that a positive average energy density gives outward forces on every face; the computed stresses show that assumption is not valid for a rectangular cavity whose sides are finite and unequal.Abstract; Forward’s proposed Casimir energy extraction cycle, opening paragraphs
Published and peer-reviewed
05When the forces are computed correctly, net work is actually done while energy is being extracted from the vacuum, and energy is conserved as expected; other cycles for which computations are available were also checked, and in all of them the energy extracted from the vacuum equalled the work done.Forward’s proposed Casimir energy extraction cycle, closing paragraph; Conclusions
Published and peer-reviewed
06Varying the long dimension of a cavity periodically about a value of 1.8 makes the pressure on the four side faces swing between attractive and repulsive, so that the cavity behaves as if it held a fluid; this suggests a cavity designed to oscillate by itself in the vacuum, matched to a mechanical resonance, converting vacuum fluctuation energy into kinetic or thermal energy.Oscillations of walls in rectangular cavities and other phenomena
What to watch

The way in

https://doi.org/10.1063/1.57676LICENCE CHECK. The version of record is Proceedings of STAIF-99, the Space Technology and Applications International Forum, AIP Conference Proceedings pages 968 to 973, published on CD-ROM by the American Institute of Physics, Albuquerque, January 1999; copyright sits with AIP and no Creative Commons statement appears on the publisher record. SOURCE REACHED. The author has posted his own copy of the paper free to read at quantumfields.com, and this sheet’s summary and claims were written from that text, read in full; the locators use the paper’s own section headings. The sheet stays summary-only and sends the reader to the source.

How to cite it

G. Jordan Maclay (1999) Unusual properties of conductive rectangular cavities in the zero point electromagnetic field: Resolving forward’s Casimir energy extraction cycle paradox. doi:10.1063/1.57676

Where it sits in the curriculum

What the vacuum is Energy from the vacuum