# Chapter 12 - Thrusting Against the Quantum Vacuum

Notes by David A Roffman on Chapter 12 of

FRONTIERS IN PROPULSION SCIENCE

Chapter by G. Jordan Maclay (Proffesor Emeritus, University of Illinois),

Quantum Fields LLC, Richland Center, Wisconsin

Chapter 12 explores how quantum vacuum properties may be applied to propulsion. Quantum electrodynamics (QED) is a theory of how light and matter interact (the photon is the force exchange particle for electromagnetism). It has been verified to 1 to 10 billion. QED predicts that the quantum vacuum (the lowest state of the electromagnetic field) holds a fluctuating virtual photon field. Although vacuum is everywhere, currently very little force can be derived from it.

Most efforts in this area revolve around Casimir forces, which arise due to quantum fluctuations. These forces have recently been used in microelectromechanical systems. The chapter will consider spacecraft that use the vacuum for hypothetical possibilities, not engineering feasibilities. To have effective propulsion, breakthroughs in material, methods, and understanding will be necessary. There are no simple ways to mathematically understand how to achieve success.

The field of quantum mechanics is the key to understanding Casimir forces. This area states that the lowest state is that of the quantum vacuum. Particles and light are both quantized fields that are fully relativistic. Any number of photons can exist, and can be easily transformed into coordinate systems (called Lorentz transformations). In the vacuum, pairs of particles (photons, electron-positron pairs, etc.) appear and disappear instantaneously (virtual pairs). Fluctuating electromagnetic fields, which composed the vacuum, are quantized. The vacuum is similar to Heisenberg’s Uncertainty Principle, where momentum and position continually oscillate in certainty. Note: Heisenberg’s Uncertainty Principle Δ*P**Δ*x *≥ * h*/2 where Δ

*P*is the uncertainty in the momentum and Δ

*x*is the uncertainty of the position. In the lowest state, the oscillator is still vibrating, with an energy ½

*The Δx and ΔP are actually standard deviations.*~~ h~~ω.

A zero-point electromagnetic field is an isotropic fluctuating electromagnetic field that occurs in a particle field, and is present everywhere at zero K with all electromagnetic sources removed. Fluctuations affect all things in the universe. This energy comes from virtual photons of energy. For the quantum vacuum, frequencies that correspond to less than 10^{-34} m (Planck length) are ignored. Energy is predicted to exist in the 10^{114} J/m^{3} range. However, real results have shown it to be **hundreds of orders of magnitude less**. This is the greatest discrepancy in scientific history. Some solutions to this cosmological constant problem have been renormalization, super-symmetry, string theory, and quintessence. In this system, real photons have less energy than virtual photons.

Casimir forces were predicted by Heindrick Casimir in 1948. An important note is that modes with frequencies greater than the plasma frequency aren’t really affected by metal surfaces due to transparency of metal at those levels. To not have infinite quantities, the finite change in energy of the vacuum due to surfaces must be computed. These forces can act differently for differently shaped formations. For a cube or sphere, Casimir forces jut outward. However, for a rectangular cavity, the forces may be outward, inward, or zero. For application to space travel, it is hoped that by transferring energy (arising from radiation pressure) from virtual photons to surfaces, net propulsion can be generated.

The dynamic Casimir effect has parallel plates that should move rapidly, and that can cause an excited state of the vacuum between the plates (this causes the creation of real photons). Unfortunately, this has yet to be observed through experimentation. A vibrating mirror could be used here for space propulsion.

Even though the Casimir effect is well known, there are still alternative explanations. The observed effects could just be derivatives of Van der Waals forces. They could also be interpreted in terms of source fields.

Despite all of our knowledge, this field, like many others, has limitations on what can be calculated. Parallel plate geometry (almost sphere-flat plate geometry) has been the only for which results have been calculated. Other surfaces are too difficult to calculate. Right angles provide a real source of trouble. Properties of binding energies are typically ignored.

The force wasn’t accurately measured until 1998. Typically measurements are made by having one surface flat, and the other curved. Recent work has confirmed effects and predictions for finite conductivity, surface roughness, temperature, and uncertainty in dielectric functions.

Parallel plate Casimir forces result in an inverse fourth power relationship as the plates change in distance for conducting surfaces. The sticking of micromachined membranes to each other may be caused by these forces. However, for semiconductor surfaces, the equation for force is more complicated. For this situation, it is possible to tune plasma frequency by light, temperature, or voltage. Arnold et al. were able to see an increase in Casimir forces due to light. This has yet to be repeated though.

As for space propulsion, it is possible, but is not efficient. An important fact in this area is that if vacuum energy is independent of craft position, then energy and momentum are constant. The space ship mentioned in the book is that of quantum sails. One would think symmetry of radiation pressure must be broken. Equal virtual photon impacts on both sides of a sail will produce no net force. Different materials on each side of the sail will make no difference. Temperature gradients may, however, may cause a force to be exerted. Invariance of zero-point fluctuations is a precept of the quantum vacuum. If this didn’t exist, then it would be possible to find a universal rest frame for the universe. But if that were true, then special relativity would be false. While it would seem that thermal effects could generate propulsion, causality may throw this pleasant result out. The real question is how to remove energy from the vacuum.

There have been ideas about using negative vacuum energy density to assist in propulsion. This would make negative mass (or so it is hoped). As discussed in earlier chapters, this has repulsive properties, and could provide endless propulsion. However, there has been no negative vacuum energy density ever produced (it is always positive). If success occurs, then it may also be possible to generate wormholes. It may be possible to reduce mass through this approach.

A dynamic system is another possibility for propulsion. The vibrating mirror is one such approach. A mirror is powered to generate radiation. Such a rate of vibration starts at zero, increases, and then returns to zero. The book considers ideal conditions, and efficiency. All photons produced are assumed to fly off in one direction (and not all the over the place). Efficiency is still very low, with a momentum to energy ratio of about 1/c (the speed of light). The following are ignored in this setup: mass change in the craft, radiative mass shifts, fluctuations and divergence issues, and dissipative force that made the mirror vibrate. Based on the dynamic Casimir effect and known science, 10^{-5} photons will emitted per second.

Chapter 12 goes further by proposing a craft that relies 100% on the quantum vacuum. The motor that would power the mirrors could be run off quantum energy. Quantum energy could be collected via perfectly conducting (uncharged) parallel plates. Casimir forces would do work on the plates, and with a reversible isothermal process, success could achieved (mirrors would accelerate). A best-case result of such a rocket would peak at 8 m/s. This is about 10^{3 }fold less than a chemical rocket. While propulsion is possible, an assistive power source would be a good idea to have.

Mirrors could produce a velocity 3 x 10^{-20} m/s^{2}. This is inefficient and slow. Not all hope is lost, as the chapter provides ideas to increase acceleration. A typical response to this problem is to use the dynamic Casimir effect, which hasn’t been proven yet. In 1994, it was predicted (by Law) that a resonant response of the vacuum to an oscillating mirror in a one-dimensional cavity would occur.

If the oscillation frequency is equal to the odd integer multiple of the fundamental optical resonance frequency, then (for the GHz range) it possible to increase acceleration of the theoretical craft by a factor 10^{9 }(to 3 x 10^{-11}). By raising temperature of a 1cm cavity to 290K, it is possible to provide another increase of 10^{3}. This means that after ten years, a velocity of 10m/s is reached (three orders of magnitude less than voyager).

Results are very dependent upon assumptions. The book used plate mass/area and systems liberally. However, for the oscillation amplitudes, conservative estimates were used. To create large amplitudes (for oscillation) it may be necessary to use carbon-nanotubes. Another approach is creating a large gradient of an index of refraction using a plasma front. When the gas and the semiconductor in this approach are viewed, the acceleration of the mirror can be 10^{20} m/s^{2}. There will be Fourier components, and there is still much work to be done in this area. It may also be possible to focus the fluctuations of the vacuum electromagnetic field.

While all this may seem to be great, there is still too much unknown in physics. We still cannot magnify Casimir forces to the macroscopic levels. Complex geometries and facts of interest from them are still all in the dark. There is no consensus for the general outlook and the effects of materials. Numerous tests are needed to find closure on negative mass claims and the dynamic Casimir effect. The only real use of Casimir forces has been in micro and nano-electromechanical systems. There are more possibilities to be discovered here, including quantum torque. Only time will tell if success waits, but miniaturization and progress are expected.