The classical quantity momentum is proportional to the spacelike rate of change of phase of a quantum mechanical amplitude. The classical quantity energy is proportional to the timelike rate of change of the phase. The factor of proportionality is Planck's Constant h. We represent a moving object as a superpostion of waves, a wave train or wavegroup. The probability that we will find the object represented by the wavegroup, e.g. an electron, is the absolute square of its amplitude, so the object classically moves at the group velocity. The group velocity is:(adsbygoogle = window.adsbygoogle || []).push({});

V_{g}=pC^{2}/E=kC^{2}/ω

where p=momentum, E=rest energy, k=wavenumber and ω=frequency and C the speed of light,

so that inertia is m=E/C^{2}classically or

i= ω/C^{2}quantum mechanically

As long as we don't change the rest energy or total momentum (wavenumber or total frequency) of a wavegroup it will continue to propagate in a straight, unaccelerated line. The property of inertia arises from the combination of quantum mechanics and special relativity, no deep mystery there.

And that's the modern view.

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# Inertia and momentum, the modern view.

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