Quantum Gravity and String Theory


A Short Note on the de Broglie Wavelengths of Composite Objects

Authors: James Bonnar

The de Broglie wavelength of an object is inversely proportional to the object's mass and relative velocity multiplied by Planck's constant. A composite object, such as an atom composed of a proton and electron, possesses a total mass and therefore a composite de Broglie wavelength. Mass is simply additive, although the relation for combining de Broglie wavelengths does not seem to have been stated anywhere in the literature. In this paper, we derive the relation for combining the de Broglie wavelengths of an object's component parts into the composite de Broglie wavelength of the object as a whole. In so doing, we discover an interesting fact concerning de Broglie waves -- that they do not undergo ordinary wave interference. In general, when we combine two waves to form a composite wave, the composite wave is the algebraic sum of the two original waves, point by point in space (Superposition Principle). The wavelength of the resultant wave is ordinarily that of the shorter wavelength wave, measured from adjacent crest to trough. De Broglie waves behave differently, the wavelength of the resultant de Broglie wave being the reciprocal of the sum of the inverses of the component wavelengths, multiplied by a factor to correct for relative velocity. De Broglie wave interference is shown to have a geometric analogue in the form of the Crossed Ladders Theorem. The macroscopic conservation of mass is partly accounted for, in particular its additivity, by interpreting the reciprocal sum formula for the resultant wavelength as the truest value.

Comments: 10 Pages.

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Submission history

[v1] 2017-04-26 10:13:48
[v2] 2017-12-16 11:16:22
[v3] 2017-12-16 23:16:39
[v4] 2017-12-17 08:49:18
[v5] 2017-12-19 04:08:51
[v6] 2017-12-20 12:50:26
[v7] 2017-12-22 07:59:03
[v8] 2017-12-22 21:41:17
[v9] 2018-01-12 02:11:21
[vA] 2018-01-12 07:03:57

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