Light can bounce off light by exchanging virtual charged particles! This gives nonlinear corrections to Maxwell’s equations, even in the vacuum—but they’re only noticeable when the electric field is about 1018 volts/meter or more. This is an enormous electric field, able to accelerate a proton from rest to Large Hadron Collider energies in just 5 micrometers!
In 2017, light-on-light scattering was seen at the LHC when they shot lead ions past each other:
Direct evidence for light-by-light scattering at high energy had proven elusive for decades, until the Large Hadron Collider (LHC) began its second data-taking period (Run 2). Collisions of lead ions in the LHC provide a uniquely clean environment to study light-by-light scattering. Bunches of lead ions that are accelerated to very high energy are surrounded by an enormous flux of photons. Indeed, the coherent action from the large number of 82 protons in a lead atom with all the electrons stripped off (as is the case for the lead ions in the LHC) give rise to an electromagnetic field of up to 1025 volts per metre. When two lead ions pass close by each other at the centre of the ATLAS detector, but at a distance greater than twice the lead ion radius, those photons can still interact and scatter off one another without any further interaction between the lead ions, as the reach of the (much stronger) strong force is bound to the radius of a single proton. These interactions are known as ultra-peripheral collisions.
But now people want to see photon-photon scattering by shooting lasers at each other! One place they’ll try this is at the Extreme Light Infrastructure.
In 2019, a laser at the Extreme Light Infrastructure in Romania achieved a power of 10 petawatts for brief pulses — listen to the announcement for what means!
I think it reached an intensity of 1029 watts per square meter, but I’m not sure. If you know the intensity in watts/square mete of a plane wave of light, you can compute the maximum strength of its electric field (in volts/meter) by
where is the permittivity of the vacuum and is the speed of light. According to Dominik Wild, = 1029 watts per square meter gives 1016 volts/meter. If so, this is about 1/100 the field strength needed to see strong nonlinear corrections to Maxwell’s equations.
In China, the Station of Extreme Light plans to build a laser that makes brief pulses of 100 petawatts. That’s 10,000 times the power of all the world’s electrical grids combined—for a very short time! They’re aiming for an intensity of 1028 watts/square meter:
• Edwin Cartlidge, Physicists are planning to build lasers so powerful they could rip apart empty space, Science, January 24, 2018.
The modification of Maxwell’s equations due to virtual particles was worked out by Heisenberg and Euler in 1936. (No, not that Euler.) They’re easiest to describe using a Lagrangian, but if we wrote out the equations we’d get Maxwell’s equations plus extra terms that are cubic in and .
For more, read these:
• Wikpedia, Schwinger limit.
• Wikpedia, Schwinger effect.
The Schwinger limit is the strength of the electric (or magnetic) field where nonlinearity due to virtual charrged particles becomes significant. They’re about
where is the electron charge and is Planck’s constant. For more see page 38 here:
• David Delphenich, Nonlinear electrodynamics and QED.
The Schwinger effect is when a very large static electric field ‘sparks the vacuum’ and creates real particles. This may put an upper limit on many protons can be in an atomic nucleus, spelling an end to the periodic table.