= Charge-sign ambiguity of a curved track
A photograph records a path but supplies no arrow of <time>. The <Lorentz force> depends on $q\mathbf v\times\mathbf B$: reversing both <electric charge> and direction of travel leaves the spatial bending compatible with the same path. Thus a particular arc can represent a <Positron> travelling one way or an <Electron> travelling the other. Knowing the <magnetic field>'s polarity is necessary but insufficient. <Gravity> does not justify assuming that every <cosmic ray> track travels downward.
The <lead> plate adds a physical ordering. For a single particle crossing a passive absorber without an accelerating interaction, the outgoing <momentum> is smaller, so the outgoing <gyroradius> is smaller in the same <magnetic field>. The less curved segment comes first. Once this direction is assigned, the <cross product> in the <Lorentz force> determines the sign of <electric charge>. For the convention below, $\mathbf B=B\widehat{\mathbf z}$ points out of the page; at upward <velocity> $\mathbf v=v\widehat{\mathbf y}$, $\mathbf v\times\mathbf B=vB\widehat{\mathbf x}$. Bending to the right therefore means positive <electric charge>.
\Image[/positron-track-direction-plate.png]
{title=Loss of <momentum> in <lead> resolves the <charge-sign ambiguity of a curved track>}
{description=Original ideal planar teaching diagram with chosen radii $10\,\mathrm{cm}$ and $5\,\mathrm{cm}$ in a $1\,\mathrm T$ <magnetic field>. Dots denote <magnetic field> out of the page. The plate thickness is schematic; each gas segment is a <circle>, with negligible loss of <kinetic energy> in the gas. The right panel shows two interpretations of the same unarrowed arc. This is a synthetic diagram, not a historical photograph or a fit to Anderson's data.}
<Magnetic forces do no work>: the change of <kinetic energy> occurs through interaction with the material, not through the bending <magnetic field>. The ideal construction suppresses <multiple scattering>, <kinetic energy> fluctuations, and loss of <kinetic energy> in the gas. In an actual analysis one compares arcs away from the plate and allows a change of tangent from <multiple scattering>; one cannot interpret every kink as a change of <electric charge>. Short visible arcs, uncertain projection and small bending also limit a determination of <magnetic rigidity>.
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