What proof did Louis De Broglie have in saying that all matter moves as waves in space?

Answer 1

Louis de Broglie first hypothesized that matter have wave-like properties in 1923, advancing wave-particle duality. Experimental confirmation of this wave-particle duality didn't happen until the Davidson-Germer experiments of electron diffraction in 1927, showing that electrons of the same predicted wavelengths as x-rays diffracted in the same way from a crystalline nickel target. This is normal, one gets a hunch based on prior experiments, forms a hypothesis, works out the mathematics behind it, make some predictions, and see if later experiments confrim them.

Answer 2

Experiments showing defraction patters of electrons confirmed the assumption and the extrapolation to everything else just follows. Experimenst on large slowly moving particles has confirmed even that part of it.

http://en.wikipedia.org/wiki/De_Broglie_hypothesis