Science and our big questions

John O. Campbell

Science is our evidence based method of answering questions concerning the nature of reality and the other 'big questions' which have always been on the human mind. I have long been captivated by the drama of this unfolding story. A trusted aide in this quest has been a subscription to Scientific American magazine. When the December 2012 edition arrived I quickly selected the first article I would read; one titled 'The Unquantum Quantum'. The bi-line for the article is: 'Contrary to the conventional wisdom of quantum mechanics, the physical world may be continuous after all - more analog than digital'

The article traces the history of scientific thought on the ultimate nature of reality as fluctuating between discrete and continuous models. Some early Greeks speculated matter was composed of discrete atoms, Newton endorsed the continuous, the modern atomic theory indicated the discrete as did Bohr in his early version of quantum theory but then the quantum wave equation of Schrodinger seemed to describe a continuous reality. The author of the Scientific American article comes down on the side of the continuous.

One might come away from this shaking their head at the fickleness of science but that would be a mistake. Each flip-flop in this succession actually provided a new depth of knowledge. Greek ideas of atomism were based on scant evidence, Newton provided continuous laws of motion to which the calculus applied, modern atomism explained the periodic table and quantum theory remains the most exquisitely accurate theory in the history of science.

Still one might suspect, given the perseverance of the apparent discrete/continuous duality, that it is a false dichotomy and that its solution may resemble the solution to the nature/nurture debate; it is best thought of as two faces to the same coin.

A couple of recent papers in the foundations of quantum theory by Muller and Masanes shed new light on this question and may have finally provided a near complete explanation:

1) Information-theoretic postulates for quantum theory

2) A digital approach to quantum theory 

These papers have had high impact within the physics community and have stimulated a number of further papers. One paper in particular (Are quantum states real?) by Lucien Hardy of Perimeter Institute may be of importance. It demonstrates that, given some reasonable assumptions, the wave function of quantum states must describe actual states of reality. It may go a long way in clarifying in what sense quantum theory describes the actual world; an issue which has plagued quantum theory for over a century.

The resolution described in the M&M paper to the discrete vs. continuous conundrum is that reality is both. However the paper brings clarity, perhaps for the first time, to the relationship between them. 

Quantum theory is important to anyone wishing to understand how the world works as at bottom information exchange between entities only occurs as a quantum process; via one of the four fundamental forces of physics. All other ways in which one entity may be affected by another are merely different organizations of information exchange at this fundamental quantum level .

For example the information of the world we gain from sight is at bottom due to a quantum interaction between photons from our environment and receptor molecules in our retinas. This is a general principle and not restricted to humans; it is not an anthropocentric phenomena. Any entity can only be affected by another via a quantum interaction. 

The Muller and Masanes (M&M) papers go to the heart of information exchange. Quantum theory is necessary to describe systems that are between interactions; when they are not exchanging information with their environments. The information that may be exchanged between quantum systems is only a small subset of the system's full description. Some theories put this in a Darwinian context: only a small subset of the information describing the system can survive the exchange.

The portion of information which is exchanged forms classical reality. Classical reality is the sum total of the effects which one quantum system has on another  and this basic discontinuity between a full quantum description and the information which can be transferred between systems is the basic discontinuity between quantum and classical realities.

The M&M papers show that the transition from quantum to classical involves a restriction on the quantum information which may survive and that the continuous evolution of quantum states is approximated as a succession of discrete states in classical reality. This transition from continuous to discrete involves a transition in logic; from quantum logic to the classical logic of probability theory. Thus the fundamental relationship between the continuous and the discrete at the basis of reality is revealed. 

M&M show that quantum theory belongs to a generalized set of theories which has only two members: quantum theory and probability theory. This may seem puzzling as quantum theory is a branch of physics and probability theory is a branch of mathematics. A possible resolution is to shift our view and consider probability theory as a branch of physics; the physics of knowledge.

To motivate this shift we might consider that the exchange of information between quantum systems provides them with a form of knowledge of each other. This is evidence based knowledge provided by actual information received. As all information exchange is at bottom exchanges between quantum systems we must understand all evidence based knowledge in a similar manner. 

Science is the form of evidence based knowledge most accessible to us and shares a deep relationship with probability theory. Indeed E.T. Jaynes titled his great textbook 'Probability Theory: the logic of science'. The M&M paper suggest we must consider probability theory in an even more general sense, as the logic of classical reality; as the logic by which the universe comes to know itself and that science is but a recent rediscovery of this ancient, timeless process.