Classical vs quantum
It is a strange thing. Why the obsession with something that in the end comes down to a rather artificial distinction. Nature is the way it is. There is no dualism in nature. The distinction we make between classical and quantum is just an artifact of the theoretical model we build to understand nature. Or is it?
Well there is a history. It started with Einstein’s skepticism about quantum mechanics. Together with some co-workers, he eventually came up with a very good argument to justify the idea that quantum mechanics must be incomplete. At least, it seemed like a good argument until it was eventually shown to be wrong. It was found that the idea that quantum mechanics is incomplete and needs some extra hidden variables does not agree with experimental observations. The obsession with the distinction between what is classical and what is quantum is a remnant of this debate that originated with Einstein.
Today, we have a very successful formalism, which is simply called quantum mechanics, and can be used to model quantum phenomena. Strictly speaking, there are different versions of the quantum mechanics formalism, but they are all equivalent. The choice of specific formalism is usually based on convenience and personal taste.
Though Einstein’s issues with quantum mechanics may have been resolved, the mystery of what it really means remains. Therefore, many people are trying to probe deeper to find out why quantum mechanics works the way it does. However, despite all the probing, nothing seems to be discovered that disagrees with the quantum mechanics formalism, which is by now almost a hundred years old. The strange concepts, such as entanglement, discord, and contextuality, that have been distilled from quantum physics, turn out to be aspects that are already built into the quantum mechanics formalism. So, in effect all the probing merely comes down to an attempt to understand the implications of the formalism. We do not uncover any new physics.
But now a new understanding is rearing it ugly head. It turns out that the quantum mechanics formalism is not only successful for situation where we are clearly dealing with quantum physics. It is equally successful in situations where the physical phenomena are clearly classical. The consequence is that many of the so-called quintessential quantum properties, are actually properties of the formalism and are for that reason also present in cases where one can apply the formalism to classical scenarios.
I’ll give two examples. The one is the celebrated concept of entanglement. It has been shown now that the non-separability, which signals entanglement, is also present in classical optical fields. The difference is, in classical field it is restricted to local properties and cannot be separated over a distance as in the quantum case. This classical non-separability display many of the features that were traditionally associated with quantum entanglement. Many people now impose a dogmatic restriction on the use of the term entanglement, reserving it for those cases where it is clearly associated with quantum phenomena.
It does not serve the scientific community well to be dogmatic. It reminds us of the dogmatism that prevailed shortly after the advent of quantum mechanics. For a long while, any questioning of this dogma was simply not tolerated. It has led to a stagnation in progress in the understanding of quantum physics. Eventually, through the work of dissidents such as J. S. Bell, this stagnation was overthrown.
The other example is where certain properties of quasi-probability distributions are used as an indication of the quantum nature of a state. For instance, in the case of the Wigner distribution, any presence of negative values in the function is used as such an indication of it quantum nature. Nothing prevents one from using the Wigner distribution for classical fields. One can for instance consider the mode profiles of classical optical beams. Some of these mode profiles produce Wigner distributions that take on negative values at certain points. Obviously, it would be misleading to use this as a indication of a quantum nature. So, to avoid this situation, one needs to impose the dogmatic restriction that one can only used this indication in those cases where the Wigner distribution is computed for quantum state. But then the indication becomes somewhat circular, doesn’t it?
It occurs to me that the fact that we can use the quantum mechanics formalism in classical scenarios provides us with an opportunity to question our understanding of what it truly means to be quantum. What are the fundamental properties of nature that indicates scenarios that can be unambiguously identified as quantum phenomena? Through a process of elimination we may be able to arrive at such unambiguous properties. That may help us to see that the difference between the quantum nature of things and the classical nature of things is perhaps not as big as we thought.