Past the Schwinger limit

Heisenberg and Euler could see this milestone on the horizon of extremes, yet I doubt they thought we'd reach it so quickly.

Science moves forward, at least in part, by pursuing extremes — seeking what's faster, hotter, more stable or more accurate than anything before. We take matter apart into ever smaller pieces, slam particles together at ever higher energies, and manufacture telescopic devices that see ever more deeply into space. In chasing such extremes, we often pass milestones, sometimes almost without noticing.

Seventy years ago, Werner Heisenberg wrote a paper with his student Hans Euler in which they explored the nature of quantum corrections to the classical equations of electrodynamics. They showed that these corrections imply the nonlinear behaviour of the electromagnetic field, much as one finds for Maxwell's equations in a nonlinear medium — for light in an optic fibre, for example. In quantum theory, in effect, the vacuum is also a 'medium', as we now take for granted. Indeed, theorists have shown that the vacuum should participate in fascinating effects ranging from the creation of electron–positron pairs, to photons moving along closed paths, or the self-focusing of beams in free space.

Yet until fairly recently, most of these nonlinear peculiarities expected in electrodynamics have remained theoretical fantasies, owing to our inability to produce the extreme conditions required to see them. But with the rapid and continuing advancement of laser technology, researchers are now getting close. We're set to reach the point — seemingly quite soon — where we can literally bring the vacuum to a boil.

Nonlinear effects associated with the vacuum should be important if the field strength is comparable to m_ec²/eλ_e, where λ_e is the electron Compton wavelength. This is the so-called Schwinger limit, developed by Julian Schwinger in 1951, and works out to be 10¹⁸ V m⁻¹. This value is surpassed routinely in supernovae and other astrophysical phenomena, but not yet in the lab. At SLAC in the US and DESY in Germany, free electron lasers now being constructed should reach energy densities pushing 10²⁹ J m⁻³, which implies electric fields of about 10²⁰ V m⁻¹, two orders of magnitude above the Schwinger limit. Even before then, however, the limit may be passed by boosting the capabilities of weaker lasers.

Take the sci-fi-sounding idea of the 'relativistic flying parabolic mirror'. On entering plasma, a powerful laser pulse produces an electric field in its wake, which accelerates electrons — a technique that holds promise for tabletop particle accelerators. But it may also prove useful for boosting the power of laser pulses. Nonlinear effects tend to press the accelerating electrons into dense bunches, and if some of these electrons later meet a counter-propagating laser pulse, they act as a flying mirror — and a relativistic one at that — which should compress the pulse, shift its frequency, and amplify its power. Some teams believe they will be able to use such techniques to blow past the Schwinger limit in the near future.

At that point, we'll be able to see photons scattering off one another and lasers that interact by churning up streams of electrons and positrons. Astrophysics will enter the laboratory in laser-plasma experiments that probe the physics of planetary interiors or the dynamics of supernova shocks. Heisenberg and Euler could see this milestone on the horizon of extremes, yet I doubt they thought we'd reach it so quickly.