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ρM=ℏ/(2mec)≈1.931×10−13 m\rho_M = \hbar/(2m_ec) \approx 1.931\times10^{-13}\ \mathrm{m}

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A number makes the scale concrete without pretending to describe an experiment. Take a spin-one-half wavepacket of electron mass, S = ℏ\hbar/2 , so that ρM\rho_M = ℏ\hbar/(2mem_ec) ≈\approx 1.931×\times10^{-13}\ m\mathrm{m} , essentially half the electron’s reduced Compton wavelength. Boost it transverse to its own spin at β\beta = v/c = 0.6 . The exact centroid shift between the rest-frame observer and the boosted observer is

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ρM=ℏ/(2mec)≈1.931×10−13 m\rho_M = \hbar/(2m_ec) \approx 1.931\times10^{-13}\ \mathrm{m}

Equation 56 · Evolutionary Physics

The Atlas That Refuses to Close

This equation gives an approximation: it relates the quantities while allowing an approximation.

A number makes the scale concrete without pretending to describe an experiment. Take a spin-one-half wavepacket of electron mass, S = ℏ\hbar/2 , so that ρM\rho_M = ℏ\hbar/(2mem_ec) ≈\approx 1.931×\times10^{-13}\ m\mathrm{m} , essentially half the electron’s reduced Compton wavelength. Boost it transverse to its own spin at β\beta = v/c = 0.6 . The exact centroid shift between the rest-frame observer and the boosted observer is

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