Illustrated Physics
physics, drawn
Concept

Penning trap — where it appears

A device that holds a charged particle with a strong uniform magnetic field and a weak electric field, so that it circles at its cyclotron frequency qB/2πm. Comparing two ions' frequencies in one trap gives the ratio of their masses to parts in 10¹¹.

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

No beam is narrow enough and wide enough at once. Three lengths at the far end of a Stern-Gerlach magnet 10 centimetres long with a gradient of 1000 tesla a metre, against the width of the beam entering it, for an electron at 100 electronvolts. The spin splitting is a horizontal line at 2.9e-6 metres: it does not depend on the beam's width. The Lorentz blurring rises in proportion to the width, because the field a particle sees depends on where in the beam it is, and the divergence-free condition ties a gradient in one component to a gradient in another. It overtakes the splitting at 1.0e-9 metres. Narrower than that and diffraction has already spread the beam by 3.9e-3 metres, which is larger still. There is no width at which the splitting is the largest of the three, and the magnet's length and gradient cancel out of the comparison entirely — so no magnet helps.

The experiment that defines spin and cannot be done on it

A Stern–Gerlach magnet separates magnetic moments and is how spin was discovered. It cannot be made to work on a free electron, and the obstruction is not the apparatus: the field gradient that splits the beam also deflects the charge by an amount that varies across it, and the ratio of the splitting to that blurring comes out as the de Broglie wavelength over the beam width — with the magnet's length and gradient cancelling exactly.

quantum · Spin A mass that goes missing as light. For six captures of a slow neutron — ¹H to ²H, ¹²C to ¹³C, ⁵⁶Fe to ⁵⁷Fe, ²⁸Si to ²⁹Si, ³⁵Cl to ³⁶Cl and ³²S to ³³S — the mass that disappears, the atom plus the neutron less the atom formed, in thousandths of an atomic mass unit, against the energy released as gamma rays, in MeV, both computed from the tabulated atomic masses. All six lie on the line Δm = E/c², whose slope is one atomic mass unit per 931.494 MeV: ¹H → ²H loses 2.388 mu and releases 2.225 MeV; ¹²C → ¹³C loses 5.310 mu and releases 4.946 MeV; ⁵⁶Fe → ⁵⁷Fe loses 8.208 mu and releases 7.646 MeV; ²⁸Si → ²⁹Si loses 9.097 mu and releases 8.474 MeV; ³⁵Cl → ³⁶Cl loses 9.211 mu and releases 8.580 MeV; ³²S → ³³S loses 9.277 mu and releases 8.642 MeV. Drawn this way the line is a definition — the energies were computed from the masses. The experiment of 2005 measured the two quantities for silicon and sulphur independently, the masses as frequencies and the energies as angles, and asked whether they still fell on it.

The test of mass and energy that needs a ruler

The most direct test of E = mc² weighed two silicon atoms and measured a gamma ray. A silicon-28 nucleus that captures a slow neutron becomes silicon-29 and loses three ten-thousandths of its mass as gamma rays; weigh both atoms in a trap where they circle a magnetic field, measure the gamma rays by the angle at which a silicon crystal diffracts them, and the two sides agree to four parts in ten million. What the comparison needed is the interesting part: the recoil of the atom, a correction four hundred times larger than the precision, computed from the momentum relativity gives to light; angles of a few hundred picoradians; and a chain of constants tying a frequency and a ruler to the same number.

relativity · Mass-energy

Named alongside it

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

Atomic mass unitBeamBinding energyBohr magnetonBragg diffractionComplementarityDe broglie wavelengthDiffractionThe Lorentz forceMagnetic momentE = mc²Measurement

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