Illustrated Physics
physics, drawn
Concept

Compton wavelength — where it appears

The wavelength h/mc of a particle of mass m, the wavelength of a photon whose energy equals the particle's rest energy: 2.43 picometres for an electron. It sets the shift in wavelength of light scattered off a free electron, and the scale below which a particle cannot be located without creating new ones.

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

The wavelength shift against scattering angle. How much longer a scattered photon's wavelength is, against the angle it scattered through. The shift runs from nothing at 0 degrees to 4.853 picometres straight back, passing through the electron's Compton wavelength of 2.4263 picometres at 90 degrees. Nothing about the incident light or the target material appears anywhere on this axis.

A photon with a momentum, and a collision that proves it

X-rays bouncing off electrons come back with a longer wavelength. How much longer depends on the angle they turned through, and on nothing else — not the incident wavelength, not the target material, not the intensity.

quantum · Photon The readings of the moving clocks along one instant: a wave. The cosine of each moving clock's phase, read along a single laboratory instant, against position in light-periods of the clock, for clocks moving at 0.3c, 0.6c, 0.85c. The readings make a wave whose wavelength, measured from the drawing, is 3.18, 1.33, 0.62 light-periods: c²/(γvν₀), shrinking as the clocks move faster. For a clock that ticks at its rest energy over Planck's constant, ν₀ = mc²/h, that is h/γmv — de Broglie's wavelength, h over the momentum. Nothing about waves was assumed: only clocks, synchronised where they rest, read from a frame in which they move.

The wave a row of moving clocks leaves on an instant

Line up identical clocks, synchronise them where they stand, and send the whole row past a laboratory at a steady speed. On any one laboratory instant the clocks do not agree: the ones further ahead read less, by an amount that grows steadily along the row. The readings form a wave laid out in space, its crests are the moving row's instants, and they sweep along faster than light. Give each clock the frequency of its rest energy and the wavelength is exactly h/p. De Broglie's matter wave began, in 1923, as an argument about the relativity of simultaneity.

relativity · Simultaneity

Named alongside it

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

De broglie wavelengthElastic collisionEnergy conservationGroup velocityThe Lorentz transformationE = mc²Momentum conservationPhase velocityPhotonRelativity of simultaneitySpectrumTime dilation

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