Quantum Mechanics is by far the best theory in describing the subatomic world. It is the physics applicable to particles no larger than the size of an atom. Quantum physics has given us the microchip technology, the computers, the cellular phones, medical imaging instruments, laser technology, CD, DVD and bar coding. At the heart of quantum mechanics stands the wave function which is a mathematical function physicists use to calculate the system’s future state with a certain probability. This inherently probabilistic nature of quantum physics has led to long debate on how to interpret the wave function. Mathematically speaking, wave functions are the complete set of solutions of the Schrodinger equation for a given system. It can be used to describe reality whether or not an observer is present to making a “measurement” on the system. Before measurement, the wave function contains all the information about the system and once you want a measurement made on the system, you need an observer or an operator ( Hermitian Operators) to cause a disturbance on the wave function and obtain an element of reality ( state of the system). According to the Copenhagen interpretation of QM, the wave function collapses to one of the states which is the result of the interaction of the observer with the original system and the measurement is purely a probabilistic value determined by squaring the probability amplitude. ( Max Born’s rule). Does the quantum wave function represent reality?
In one perspective, the wave function signifies an element of reality which objectively exists regardless of an observer measuring it. An alternative perspective is that the wave function does not represent reality but instead an observer’s subjective state of knowledge about the underlying reality. One of the greatest physicists, Niels Bohr, supported this alternative view in the Copenhagen interpretation in which the wave function is simply a miraculous mathematical instrument which can be used to calculate the precise probability value when an observer measures the system, results in the collapsing of the wave function. Physicists Roger Colbeck of the Perimeter Institute in Waterloo, Ontario, and Reneto Renner who is based at ETH Zurich, Switzerland, presented their view in favor of the objective reality of the wave function. In their paper, Colbeck and Renner discuss the difference between the two perspectives of the wave function’s probabilistic nature with an analogy.
” A meteorologist giving a prediction about the weather for tomorrow ( like 23% chance of sunny sky or 58% chance of cloudy sky or 20% chance of a storm ), and assuming classical mechanics accurately describing the relevant process so that the weather depends on the initial conditions deterministically. The fact that the prediction is probabilistic is really reflecting a lack of knowledge on the part of the meteorologist on these conditions. In addition, the forecast isn’t an element of reality associated with the atmosphere but rather reflects the subjective knowledge of the forecaster. The second meteorologist with different knowledge may give an alternative forecast. So going back to quantum mechanics, we may question whether the wave function that we assign to a quantum system should be viewed as a subjective object ( the weather forecast) representing the knowledge an experimenter has about the system or the wave function is merely an element of reality of the system ( cloudy sky).”
Colbeck and Renner debated that the wave function of a quantum system completely describes reality and not just some lack of knowledge of the physicists about the reality. They were able to show that a quantum system’s wave function is in one to one correspondence with its ” elements of reality” where the measurement settings are freely chosen and quantum mechanics yields the correct statistical predictions of probabilities at all time. The wave function contains all the elements of reality and that a system’s list of reality includes its wave function, hence a one to one correlation with its elements of reality. For nearly a century physicists have debated about whether the wave function is a real part of the world or just some mathematical tool for the purpose of calculating probabilities. The wave function helps to predict the results of quantum experiments with phenomenal accuracy, but at the same time, it describes a world where particles exhibit fuzziness such as existing in two different places at the same time( quantum entanglement). Erwin Schrodinger indicated that treating wave function as a real entity leads to bizarre situations in which a cat in the box can be both dead and alive until someone opens the box and observes it. Albert Einstein argued that the wave function is simply a mathematical tool representing the lack of knowledge about the status of the poor cat, called ” epistemic interpretation” who once asked,” Do you really believe the moon exists only when you look at it?”
Eric Cavalcanti at the University of Sydney and Alessandro Fedrizzi at the University of Queensland have made a measurement of the reality of the quantum wave function and rule out a large class of interpretation of quantum mechanics to suggest the objective description of the world where the wave function is a part of it: Schrodinger’s cat can indeed be both dead and alive. ” In my opinion, this is the first experiment to place significant bounds on the viability of an epistemic interpretation of the quantum state,” says Matthew Leifer at the Perimeter of Institute in Waterloo, Canada.
In conclusion, which view is correct about the wave function? Is it the objective reality or the subjective state of knowledge of the observer? This is a very interesting question for it calls into the very nature of reality. The wave function and Schrodinger equation act as mathematical models which predict physical phenomenon with incredible accuracy and these mathematical theories provide excellent descriptions about the real world entities. When we say light is a wave, we really mean light exhibits the behavior of a wave so that we can apply Maxwell’s equations to obtain the correct answers, but it doesn’t mean light is a wave. So whether or not a greater reality should be attributed to a quantum wave function depends on how much emphasis we should be placing on some other greater reality such as Magnetic Moment or the exchange of gluons within quark-quark interactions. It could just be something due to the convenience of mathematics that we employ to solving these problems to get to the correct answers and not due to some real physical structures of these wave functions. Since the wave function predicts reality so incredibly accurate and assuming that it continues to do so into the far future, there is really no way to distinguish between these two perspectives of the wave functions. Should we care to find out or simply follow what Richard Feymann once said, ” shut up and just calculate”.