Classical physics is sufficient to explain the workings of our day to day life. We don’t expect anything out of the ordinary, for instance the act of measuring does not affect the outcome of the measurement. When we buy a black pen, we write on a piece of paper to check if it is indeed a black pen, we don’t expect the act of writing to change the color of the pen. When we go back home and use the pen we expect it to write in black. This phenomena couldn’t explain the workings of subatomic particles.
Quantum physics was born to explain the workings of the subatomic world where measurements and actions are of the order of planks constant (6.626*10-34 m2kg/s). The behaviour of these particles cannot be understood in terms of Newtonian mechanics. Here the very act of measurement defies the state of the system; for example, the act of writing changes the color of the pen and sometimes may even change the length of the pen. To understand the behavior of these particles the pioneers in this field devised a new mathematical language. Quantum physics is a probabilistic study of the outcome of concrete experiments.
Cognitive science deals with the constant dilemma faced by an individual every second of their life. While making a decision we marshal a variety of inputs from various stages of our life. Each decision shapes our life a little and this influences our next decision. We cannot understand the science behind decision making by using the limited framework of classical logic. Quantum approach is suitable to understand the human cognitive behavior as they show similar phenomena.
Classically, it is assumed that a person is always in a fixed state with respect to some judgement. That is, even before they are asked about their opinion on a certain judgement they have a fixed opinion about it. This is certainly not true, till the actual judgement is made, the outcome can only be predicted by assigning a certain probability to all the outcomes. Quantum theory works on the concept of superposition which allows the particle to have a definite potential in all its possible states with a certain probability. This provides room for conflict, ambiguity or uncertainty that people experience every instant.
By asking a judgement question a judgement is created at that particular instant rather than recording the previous property of the system. Similarly, in quantum theory to measure any physical property of a subatomic particle, we send a photon towards it. While the photon measures the property of the particle at that instant, the state prior to that cannot be determined. This logic can demonstrate how the act of questioning the state of a system creates a definite state out of an indefinite state.
When a series of questions are asked, the answer to one question influences the answer for the subsequent questions, hence we cannot assign a joint probability of answers. One of the pioneers in quantum mechanics Werner Heisenberg revolutionized the understanding in quantum mechanics with a famous principle called “Heisenberg’s uncertainty principle” which states that you cannot simultaneously measure the values of a position and momentum (non-commutating) with great precision. This is not a statement about the precision of the instruments used, but talks about the inherent property of the particles. In quantum theory a mathematical model is produced which can probabilistically measure the non-commutative states.
Classical Boolean logic is too restrictive to explain the human judgement. Classical logic implies total probability theory, which is defied by various psychological experiments. Quantum probability suggests that the probability is defined as sub spaces, these subspaces do not obey the classical total probability theory. Quantum probability theory is a generalized probability theory which can encompass the intuitive judgements of human cognition.
Classical probability theory obeys of principle of unicity, here a single sample space is used to exhaustively explain all the events in our world. This doesn’t give room to explain the coexistence of various judgements, measurement incompatibility or measure the non-commutable states. Quantum probability does not require a joint probability of all the events to be set up in the same sample space; this is required to understand the underlying complexity of human cognition.
Finally, in classical analysis of cognitive studies judgements are said to be decomposable such that complete analysis can be done by understanding each constituent part. The concept of quantum entanglement enables the system to be in non-decomposable states such that there can’t be a joint common probability distribution. This gives the system an extreme form of correlation which cannot be explained otherwise.
Given the similarity between the workings of quantum theory and cognitive behavior it is natural for us to use the same mathematical formulation to set up a general framework for human cognition.