Question about the De Broglie Hypothesis

[atyy]

thanks I think I've got it now. But this got me thinking: how can wavepackets produce electron diffraction? The only way I see electron diffraction occurring is if the wave is smeared out across a big space. It seems awkward to apply path difference formulas in a double slit experiment to a localised wave packet.

Is it correct if I say that electron diffraction only occurs when the momentum is really really well defined and the wave is non-localised? This makes sense I think.

The electron and the baseball are both wave packets, so both have some distribution in real space as well as some distribution in momentum or wavelength space. In some cases we model an object as having an exact location in real space (eg. the baseball), in other cases we model an object as having an exact location in wavelength space (eg. the electron for diffraction), but both are approximations because the wave packet is not exactly localized in either position or momentum space. That is the uncertainty principle. Which approximation you use depends on your application, and again you can estimate how good your approximation is via jtbell's exercise.

 

[vanhees71]

The point is that the baseball is a macroscopic object. You are looking in a much more coarse-grained point of view at it. To claim a macroscopic body has a certain position and momentum, you need a very much lower accuracy than it is constrained by the Heisenberg uncertainty principle.

On the other hand there's no principle "cut" between quantum and classical behavior. This is claimed by (some flavors of) the Copenhagen interpretation. For the experimentalist, it's only way more difficult to experimentally realize situations, where quantum behavior can be observed the more macroscopic an object becomes. There are some examples for such experiments. Well known is the double slit experiment with Bucky Balls (molecules made of 60 carbon atoms, which I'd call mesoscopic not macroscopic at best), where you can even tune the decoherence by just getting them at a higher temperature. To investigate quantum behavior you have to cool them down; heating them a bit up, the thermal radiation of pretty long-wave photons is enough to make the behave classical FAPP.

Decoherence is a very efficient mechanism, and for me it's a very satisfying explanation for the fact that most of our everyday experience looks as if classical physics is valid.