Modern interpretation of wave-particle duality As far as I understand, in the early days of quantum theory there was quite a lot of debate over how to interpret what it meant for a quantum mechanical object to exhibit both wave-like and particle-like properties. 
Is it correct to say that the modern interpretation (as in the one arrived at at the end of the original construction of quantum mechanics) is that there is an intrinsic uncertainty in the measurement of properties of a quantum mechanical object, such as its position, momentum, etc. As such one can at best describe the state that it is in by a wave function that encodes all the statistical information about the possible values of its observables. Hence there is no wave-particle duality - the wave-like properties arise due to the intrinsic uncertainty arising in the measurements of a particles physical observables.
Is something like this a correct understanding at all?
 A: It probably depends what interpretation of quantum physics you subscribe to. That sounds approximately right for the Copenhagen interpretation, in which you aren't allowed to analyze where the wave function comes from.
For those who appreciate more what de Broglie, Einstein, Bell and others have put into quantum physics, there's always the interpretation that a real, physical system underlies the probabilistic description, a system with a localized component (particle) interacting with a non-localized one (waves). In this case the wave-like properties really do come from the wave part and the particle-like properties from the particle part. See bouncing droplets, for example: https://www.youtube.com/watch?v=nmC0ygr08tE, http://math.mit.edu/~bush/wordpress/wp-content/uploads/2015/08/Bush-PHYSICS-TODAY2015.pdf
A: I think what you wrote is fine, and interpretation matters a lot to answer this question. However, I think the notion of "wave particle duality" is still meaningful. There are two ways a wave function can evolve, via time evolution given by the Schrodiner equation, or randomly via external measurement. When not being measured, a particle obeys the wave equation. When it's position is measured, it is found all in one place, as a pointlike Dirac delta function. The word "wave" in "wave particle duality" refers to the deterministic wave, while the word "particle" refers to the random measured particle.
