Since its development 100 years ago, quantum mechanics has revolutionized our understanding of nature, revealing a bizarre world in which an object can act like both waves and particles, and behave differently depending on whether it is being watched.

In recent decades, researchers exploring this wave-particle duality have learned to measure the relative “wave-ness” and “particle-ness” of quantum objects, helping to explain how and when they veer between wave-like or particle-like behaviors.

Now, in a paper for Physical Review Research, researchers at the Stevens Institute of Technology report an important new breakthrough: a simple but powerful formula that describes the precise closed mathematical relationship between a quantum object’s “wave-ness” and “particle-ness.”