Wave-corpuscle duality is usually (and maybe best) illustrated in the famous double-slit experiment, where one lets a beam of particles pass through a wall with two slits to reach a screen, on which an intensity pattern shall be observed. Now if these particles are what every one understands with his daily experience, such as bullets and sands, one gets a pattern displaying all features one can find with bullets. On the other hand, if these particles are light quanta, i.e., photons, a completely different pattern, which is usually called interference pattern, shows up exhibiting all features one may perceive with water waves bypassing two obstacles (e.g., two big stones). If the first pattern prevails over the latter, then one may say this beam behaves more like a beam of particles. And the opposite case corresponds to wave-like behaviors. Now the 'wield' thing is that, the same beam can display both patterns, depending on whether a slit is open or closed !
Common sense would say, a bullet is always a bullet, regardless of the experimental setup. However, the quantum world goes absolutely against one's common sense, since by operating a slit switch without explicitly affecting the gun, the bullets become something else. Were such quantum effect dominant in daily world, one would be able to alter the moon by playing with something on earth. Wield ! Completely wield !
Yes, it is wield relative to common sense, as wield as curved space-time! Einstein said our universe is curved, which is also counter-intuitive. Nevertheless, in spite of their wields, they are elegant. Why ? Because they seem to be the simplest notions one can have to solve all puzzles in their own fields. One can hardly expel them without encountering awkwardness. They have a unique unifying power. In the eyes of theoretical physicists, the elegance of a concept consists largely of its unifying power. Such concept solves not one phenomenon, not two phenomena, but a dozen of seemingly isolated phenomena. In quantum world, it is hard to dispense with wave-corpuscle duality and at the same time explains everything. It is impossible to explain double-slit experiment using a particle-only picture without invoking some very ugly assumptions. It is impossible to dispense with the notion of relativity of simultaneity while at the same time accounting for all fast phenomena.
So, wield and elegant are likely to go hand in hand. Further, what is wield is constantly changing, because our common sense is constantly changing. It is never a good reason to reject an elegant idea just because it is wield !
P.S.: this blog is intrigued by a research presented in PHYS.FORUM, aiming at eradicating wave-particle duality. The author was motivated by this question, 'what goes through the slits ?'. In my opinion, all exiting answers to this question differ as sheerly an issue of semantics. You may use another name of wave-particle duality, but the content remains the same, because, it is at the heart of quantum mechanics.
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