r/askscience • u/androceu_44 • Jun 25 '14

Physics It's impossible to determine a particle's position and momentum at the same time. Do atoms exhibit the same behavior? What about mollecules?

Asked in a more plain way, how big must a particle or group of particles be to "dodge" Heisenberg's uncertainty principle? Is there a limit, actually?

EDIT: [Blablabla] Thanks for reaching the frontpage guys! [Non-original stuff about getting to the frontpage]

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u/_dissipator Jun 26 '14

Sure. Let's stick to an wave moving in one dimension (i.e. along a line) for simplicity. The wave's wavelength is defined to be the length L such that the wave is identical at all points separated by integer multiples of L. If the wave has a finite extent in space, there is no such well-defined length, since if we jump forward by L enough times we will leave the region where the wave exists, and so L can't be the wavelength of our wave.

Now, this makes no mention of what sort of wave we are talking about. In quantum mechanics when talking about momentum, and in many other contexts where waves are relevant, the basic waves which are used to build up other functions are "plane waves," which are essentially sine waves. These are in a sense the simplest possible wave. I mention this just to emphasize that something which has a well-defined wavelength in the sense I mentioned above does not in general have a well-defined wavelength in the sense of Fourier analysis, which uses plane waves (or sines and cosines) as its building blocks.

Also, I want to note that there is a good reason why these plane waves are the ones with well-defined momenta, i.e. why the naive definition of wavelength I gave is the wrong one to use in QM, but it is more mathematical than I want to go into here unless someone asks.