by Prof. Sudip Patra
Since the advent of quantum mechanics in 1920s, there have been numerous battles of ideas among great minds on what should be the right interpretation of the theory. What is the picture of reality that this novel theory presents us? Or is it that we should ‘shut up and calculate’? Well, till now there have been no resolution of conflicts, and roughly the following schools of thoughts have emerged:
- Copenhagen School: Neils Bohr, being the most vocal advocate of this school, believed in the so called collapse of the wave function by measurement. The school believes that when there is no measurement, an isolated quantum state evolves deterministically based on the Shrodinger wave equation, also known as the unitary transformation. However, it is the act of measurement which reduces the superposition state into one of its component (Eigenvalue), and this is how the classical world emerges around us. Just think of while you are not looking at the moon, the moon is in a superposition of many possible states, and such a superposition evolves over time perfectly deterministically. However, as soon as you look at her, she collapses in to one of such Eigen states.
Quantum physicists can only measure the probability of obtaining one of such states, it is thus inherently a probabilistic model, unlike classical physics where probability is used only if the experimenter lacks knowledge of initial state of the system. Certainly this picture was, and still is not liked by all in the trade. Famously, Einstein attempted many a time to falsify such a picture, with mixed success. Any way this school remains as the orthodox quantum mechanics, as we know today in standard text books.
- Hidden Variable School: Spear headed by David Bohm and other theoreticians this school of thought believed that quantum description (the wave function description of a state, well such a wave function is far from a physical wave function. It can be thought as a probability wave after Max Born, and till date there are lots of arguments on what this description means, whether this is ontic or epistemic?) of a system is incomplete, and there are some hidden parameters which actually are required to be understood to make sense of the measurements. Till date there have been numerous attempts to prove this position, but with no true success.
- Many World School: Perhaps the most radical school, which based on works of Everret, Wheeler and others, proposed that while measurements are done (here we should not bring in consciousness as the only way of measuring things. For example, some kind of interaction of an isolated quantum system with environment can also qualify as a measurement, which is the new theory of so called atmospheric decoherence), there is actually no collapse of the superposition state at all. All the Eigen values of the state are realized and they all evolve over time, but in different parallel universes! So as I am writing this article, and as you are hopefully reading this article, there are many universes where something totally different is happening with this article, and everything is happening now! (certainly the concept of NOW is a confusing concept in space time, but say we oversimplify this a bit).
All other models revolve around these extremes. However, the masterstroke of quantum theory is that the predictions are immaculate, at times as accurate as 16 decimal places. It is this precision that makes quantum theory very special, and un put down able.
Now we come to the application of quantum theory in social science. As in the earlier articles I have tried to provide the exciting new field, the interpretation of such an application is also a daunting task. I think this is an open problem, and social scientists, psychologists, philosophers, economists, everyone is welcome to contribute to it.
We know that there are some very intriguing works by Penrose, Hamerhoff and others which speculate whether there is a physical quantum theory of brain. In other words, we are finding excellent results by applying quantum modeling in social sciences may well be grounded in the fact that we all are quantum computers. However, there are many criticisms of this position. For example, Max Tegmark of MIT, a well known cosmologist, has famously criticized this theory by remarking that brain is too hot a place to sustain quantum effects.
Hence, as of now, we, who apply quantum modeling in economics/finance/decision making at large, want to subscribe to the black box view of brain. We would rather take an operational position as of now, but there is no doubt that tomorrow can be very different!
Who knows maybe it’s your turn next in this brave new world?
Professor Sudip Patra is an Assistant Professor of Management Practice at O.P. Jindal Global University . His research interest encompass dividend signaling theory under information asymmetry, game theory for applied corporate finance, econometric modeling, and allied areas.
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