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In quantum physics, particles are also waves. Larger particles have shorter wave lengths, and macroscopic objects have extremely short wave lengths so that the wave aspect can be ignored, and classical physics works fine at those levels. The bigger the object, the shorter the wave length.

So: What is the wave length of the biggest "object" of all: the universe? Has this ever been calculated? Does it have any meaning to talk about wave lengths at those levels?

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The fact that you had to put quotes around object suggests that this question probably doesn't make any sense. First, the the universe may be unbounded, and second, it probably doesn't make sense to think of the universe as an object at all. –  Brandon Enright May 24 '13 at 19:40
    
Even if the universe is finite, it doesn't make sense to talk about its total momentum. There's a good discussion of this in Misner, Thorne, and Wheeler, p. 457. –  Ben Crowell May 24 '13 at 20:17

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The wave description is an approximation to whatever the underlying reality is, and it only applies in some circumstances. I'm sure you heard of wave/particle duality i.e. the fact that objects behave as waves in some circumstances and particles in others. This means that while the wave description can be an excellent description in some circumstances it is a very poor description in others.

In particular once the wavelength approaches the physical size of the object we cannot usefully treat the object as a single wave. Once the wavelength, and hence the resolution, of the wave falls below the size of the object its components will start behaving independantly. So for example, once the de Broglie wavelength of a proton falls below its size we need to treat it as a collection of partons not a single object.

This means you could only assign a wavelength to the universe if its wavelength was (considerably) bigger than the universe, which is obviously impossible.

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