An interesting and ongoing major issue in physics is how to interpret the mathematics of quantum mechanics. Quantum mechanics is a mathematical theory that describes the workings of molecules and atoms, the properties of materials, and basically everything else that happens at these small size scales. Deciding on an interpretation means to decide how nature operates at the most-fundamental level. A recent paper by Matthew F. Pusey, Jonathan Barrett, Terry Rudolph offer a mathematical proof that may partially solve this long-standing riddle at the cost of a mind-boggling interpretation of reality.
Shown above are the wave functions describing an oscillator (like a mass on a spring)
Solutions to the equations of quantum mechanics involve waves, but waves of what? One interpretations has been that these waves represent probabilities for different outcomes of an experimental measurement. The act of measuring collapses this wave function to a definite value for the measurement. What value that measurement yields was completely open to chance, with certain probability for one outcome or another, described by that wave function. According to the authors, the wave function is not simply a statistical tool that reflects our ignorance of the particles being measured, but is physically real. Below is the abstract to the paper.
Quantum states are the key mathematical objects in quantum theory. It is therefore surprising that physicists have been unable to agree on what a quantum state represents. There are at least two opposing schools of thought, each almost as old as quantum theory itself. One is that a pure state is a physical property of system, much like position and momentum in classical mechanics. Another is that even a pure state has only a statistical significance, akin to a probability distribution in statistical mechanics. Here we show that, given only very mild assumptions, the statistical interpretation of the quantum state is inconsistent with the predictions of quantum theory. This result holds even in the presence of small amounts of experimental noise, and is therefore amenable to experimental test using present or near-future technology. If the predictions of quantum theory are confirmed, such a test would show that distinct quantum states must correspond to physically distinct states of reality.