Quantum mechanics has a concept called a “wave function.” It’s incredibly important because it holds all the measurable information about a particle (or group of particles) within it. In practice, the wave function describes a set of probabilities that change in time. When we make a measurement, we are really poking at the wave function, causing these probabilities to collapse and take on a definite value. The value that the wave function predicts is determined by the relative probabilities of all the possible measurement results.
But physically, the wave function is problematic. It is often possible to figure out the physical meaning of a symbol in an equation by looking at the physical units you would use to measure it. A quick examination of the wave function shows that the units of the wave function don’t make a great deal of sense. To avoid a mental hernia, physicists tell each other that the wave function is a useful calculation tool, but only has physical relevance in terms of statistics, rather than having some concrete existence. In other words, it’s not really “real.”
Until now, we have taken comfort from the idea that, real or not, the results from the wave function would be the same. So no worries, right? Quite possibly wrong. In a paper posted on the arXiv, a trio of researchers has shown that you can’t have it both ways; a purely statistical wave function will not always give the same results as a wave function with real physical significance.
There’s a long, long history of puzzled physicists showing that the wave function must be a bizarre object. Quantum entanglement is a direct result of the properties of the wave function, for instance, and entanglement envisions particles separated by a vast gulf of space being, apparently, in instantaneous contact with each other. According to the rules of quantum mechanics, if I measure the spin of one of a pair of entangled particles, then that measurement automatically and instantaneously sets the spin of the other… even if it’s on the opposite side of the Universe.
Such findings were only theoretical in nature until the 1980s. Since then, we have confirmed that entanglement is possible and have attempted to measure the speed with which the wave function collapse travels between entangled particles. The answer is: it’s fast. Much faster than the speed of light (or neutrinos). The conclusion seems to be that the bizarre consequences of the wave function are real. But is the wave function itself “real” in any traditional sense?
The only way to figure this out is to create a situation where the wave-function-as-a-statistical-object produces a different experimental result than the wave-function-as-a-real-object. Until now, this has proved to be elusive. But, by considering the consequences of joint measurements on independently prepared objects, the researchers have shown that it’s possible for the statistical and real versions of the wave function to produce different results.
Read the rest of this interesting article here The quantum wave function might be real