Illustrated Physics
physics, drawn
Concept

Strong field — where it appears

A field strong enough that a particle's motion in it is dominated by quantum and relativistic effects. For electrons the scale is 4.4 × 10⁹ tesla, where cyclotron energy reaches rest energy. Magnetars exceed it, and their radiation shows effects that weaker fields never produce.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

Five rays, and the one that decides which side everything falls on. Light traced past a non-rotating mass at five impact parameters, by integrating the exact null geodesic rather than the weak-field formula. The shaded disc is the horizon and the dashed circle is the photon sphere at three masses. Rays passing closer than 5.196 masses are captured — 2 of the five here — and rays passing further escape, however far they are bent on the way. The two nearest the critical value behave in the most striking way: one wraps 1.06 times round before leaving and the other wraps round before falling in, and between them lies a ray that would circle for ever on the unstable orbit. Far away the same integration reproduces the familiar weak-field deflection: at sixty masses it gives 0.07021 radians against 4M/b = 0.06667, so the strong field and the weak one are one calculation.

The circle light cannot leave

A black hole has three radii and they are all sometimes called its size. The horizon is where nothing can come back from; the photon sphere, half again as far out, is where light can circle and cannot keep circling; and the shadow a distant observer sees is larger than either, because the ray that just escapes was bent on its way out.

astrophysics · Horizons An electron that runs into light and loses its energy to it. The energy of an electron of 511 MeV (γ = 1000) as it passes head-on through a 10-cycle pulse of 0.8 µm light, as a fraction of its starting energy, against the number of laser cycles it has crossed, for normalised field strengths a₀ = 30 and 100: with radiation reaction (solid) and without (dashed). Without it, the electron is shaken sideways while in the light and leaves with exactly the energy it brought, as a plane wave requires. With it, each half-cycle near the pulse's peak radiates away a slice: the electron leaves with 76 per cent of its energy at a₀ = 30 and 22 per cent at a₀ = 100, the rest gone as gamma rays.

The light that takes back an electron's energy

An electron at rest in the most intense laser light ever made feels its own radiation as a force a millionth of the light's push — the textbook reason radiation reaction never matters. Send the electron into the light at nearly the speed of light and the arithmetic turns over. In its own frame the light is stronger by twice its Lorentz factor, the power it radiates grows as the square of that, and a pulse a few tens of femtoseconds long can strip it of most of its energy as gamma rays. That is where the classical theory of a radiating charge, argued over for a century, finally has to answer to experiment — and where it starts to fail for quantum reasons.

relativity · Relativistic dynamics

Named alongside it

The objects these essays reach for when they reach for this one.

Black hole shadowCapture cross-sectionCompton scatteringCritical fieldEffective potentialEvent horizonGravitational lensingImpact parameterLaserLight deflectionThe Lorentz factorNull geodesic

All concepts