Louis de Broglie's "mechanical analogy" for de Broglie vibrations and wavelength
De Broglie's original paper (his thesis actually) is seldom read for two reasons:
Most people do not realize that de Broglie vibration is the funcamental parameter, and that:
- Only the first section on the waves of free particles remained popular after Schrodinger's paper appeared the following year.
- It was not translated into English until nearly 80 years later. You can find this translation at https://www.relativitycalculator.com/pdfs/On_Theory_Quanta.pdf
De Broglie gave a verbal description of a "mechanical analogy" of his waves. The purpose of this web page is to present animated drawings of this description for stationary and moving particles. For further information, you can view a pre-review copy of a paper on Common pedagogical issues with de Broglie waves: moving double slits, composite mass and clock synchronization. To view the animations, click on one of the images below. De Broglie's description:
- de Broglie "waves" are an artifact of the effect of the Lorentz transform on time, creating clock skew, even at slow speeds
- de Broglie "frequency" really does transform in the ordinary relativistic way, but it seems higher because we observe the spatially distributed wave, i.e. we are looking at an array of clocks, not just one clock.
Our theorem teaches us, moreover, that this wave represents a spacial distribution of phase, that is to say, it is a "phase wave." To make the last point more precise, consider a mechanical comparison, perhaps a bit crude, but that speaks to one's imagination. Consider a large, horizontal circular disk, from which identical weights are suspended on springs. Let the number of such systems per unit area, i.e., their density, diminish rapidly as one moves out from the centre of the disk, so that there is a high concentration at the centre. All the weights on springs have the same period; let us set them in motion with identical amplitudes and phases. The surface passing through the centre of gravity of the weights would be a plane oscillating up and down. This ensemble of systems is a crude analogue to a parcel of energy as we imagine it to be.