de Broglie wavelength vs. Planck length

[David Cerny]

This is probably more of a physics question: what is the significance of the Planck length in connection with the de Broglie wavelength? If we apply the concept to human-scale objects, the resulting wavelength is often shorter than the Planck length (e.g., p. 12 in the course reader: ). I understand that different quantum mechanics theories do not agree on the exact meaning of the Planck length -- is there some research on its implications for matter waves? For example, does the Planck length constitute the lower limit for the application of de Broglie equations?

[Patrick Chin 1F]

I did some research on it, and it appears Planck length (1.616199(97)×10^−35 m) is several magnitudes smaller than the lengths we can currently measure with our technology, so no, there is no research on its implications for matter waves. But theoretically speaking, as Planck length is the shortest possible length, or the length of space at which our ideas of space-time cease to be valid, it probably does constitute the lower limit for matter waves. In any case, the example from p.12 also says that there are no measurable wavelike properties, and the current definition of "measurable" does not even come close to Planck length. I guess it is safe to assume that the immeasurable wavelengths of human-scale do not break the laws of space-time, and are limited to Planck length.

[stephanie garcia]

how do you know if something has measurable wavelike properties?

[Niharika Reddy 1D]

The size of the wavelength determines whether or not something has measurable wavelike properties. I use the wavelengths in the electromagnetic spectrum as a guide. Since gamma rays (wavelength of about .1 pm, or 10^-13 m) can be detected, moving objects with wavelengths that are about this short, maybe even a little shorter, have measurable wavelike properties. In the course reader example of a moving car, though, the wavelength of 10^-38 m is an example of something that has far too short of a wavelength to have measurable wavelike properties. Hope this helps!