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Quantum Physics

Reduced mass μ

Reduced mass μ is used throughout physics and engineering as a correction ‘factor’ for interacting particles whose interaction affects the centre of mass. It is given by

where m is the mass of the particle and M is the mass of the particle it interacts with. For example, the reduced mass μe of an orbital electron is given by

where me is the mass of the orbiting electron and mp is the mass of the proton. This is due to their mutual interaction given by Newton’s Third Law of Motion, which causes the two to rotate about a mutual origin of orbit, instead of at the centre of mass of either one of the particles.

Multiple bodies

The reduced mass mN of N mutually interacting bodies is given by

where mn is the mass of the nth body.

Relativistic correction

See posts about special relativity.

The reduced mass often sees an additional relativistic correction, given for N bodies by

since mrel = γm for a rest mass m. Note that γn is the Lorentz factor for the nth body travelling at velocity vnc, defined such that

For only two bodies, this simply becomes

Max Factor’s Beauty Micrometer, 1934
In the 1930′s, make-up legend Max Factor came up with an ingenious invention combining phrenology, cosmetics and a withering pseudo-scientific analysis of a woman’s physical flaws, This “Clockwork Orange” style device analyzes facial ugliness. As the article which contains this image explains:

“Flaws almost invisible to the ordinary eye become glaring distortions when thrown upon the screen in highly magnified images… the device, remotely resembling a baseball mask, fits over the head and face with flexible metal strips which conform closely to the various features. The strips are held in place by set screws, allowing for 325 possible adjustments. If, for instance, the subject’s nose is slightly crooked — so slightly, in fact, that it escapes ordinary observation — the flaw is promptly detected by the instrument and corrective makeup is applied by an experienced operator.”