# Measurement and the Quantum-Classical Transition

According to Cal Tech physicist Hideo Mabuchi, “Perhaps the strangest legacy of twentieth-century physics is the notion that in our scientific analyses of natural phenomena, we have two very different theoretical models to choose from. Whenever we are concerned with the microscopic workings of atoms, molecules, and elementary particles, it appears that we must appeal to quantum-mechanical descriptions of such physical systems and their behavior. If we focus our attention on macroscopic objects such as planes and baseballs and asteroids, however, we find that we are justified in adopting the perspective of classical (Newtonian) mechanics. These two theories, of quantum and classical physics, could hardly be more different in their basic tenets and ontological principles. And yet we would like to believe that macroscopic objects with their classical phenomenology are really just sensibly sized aggregations of bewilderingly many quantum bits.”

We tip our hats to the physicists and welcome them to the real world of existential indeterminacy. For over a century—and most visibly in the last 25 years—biologists have been required to do just this: move between theoretical models as the perspective upon, or the order of magnitude of, the phenomenon under observation changed. What holds for the cell may or may not hold for the tissue or the organ or the system, to use an example from physiology. But biologists always had a nice excuse: They’re dealing with living, dynamic, and responsive phenomena. Could it be that the real discovery of 21st century physics might parallel this biological truism? Part of what makes today’s discussion of the apparent discrepancy between the classical and the quantum so interesting is the tension that is created by the disjunction between what we know and observe and what we expect as rational and logical. As G.K. Chesterton and C. S. Lewis both observed, the problem is not that the world is rational or irrational; the problem is that the world is almost rational. An example? Well, any alien arriving on the planet Earth might be struck by the obvious bilateral symmetry of its creatures. Two eyes, two ears, two nostrils, two legs, two lungs … but, wait, what about the heart? Not to mention the entire digestive system. It would seem that in the biological realm, as the needs change, so do the rules. Bilateral symmetry is only a rule as long as bilateral symmetry is useful.

Perhaps the same could be said for the quantum and the classical paradigms? Read on to see if this might be the case. Hideo Mabuchi’s column is part of a special series in anticipation of The Science & Ultimate Reality Symposium in Princeton, a symposium in honor of the 90th year of John Archibald Wheeler, a great physicist and teacher of physicists. Mabuchi’s research is in the field of quantum optics and quantum information. A summary of his paper appears below.

—Editor

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Perhaps the strangest legacy of twentieth-century physics is the notion that in our scientific analyses of natural phenomena, we have two very different theoretical models to choose from. Whenever we are concerned with the microscopic workings of atoms, molecules, and elementary particles, it appears that we must appeal to quantum-mechanical descriptions of such physical systems and their behavior. If we focus our attention on macroscopic objects such as planes and baseballs and asteroids, however, we find that we are justified in adopting the perspective of classical (Newtonian) mechanics. These two theories, of quantum and classical physics, could hardly be more different in their basic tenets and ontological principles. And yet we would like to believe that macroscopic objects with their classical phenomenology are really just sensibly sized aggregations of bewilderingly many quantum bits.

Indeed, there should be nothing wrong in principal with describing a macroscopic object such as a baseball by the linear evolution of a density operator on a gigantic quantum state space. But where macroscopic systems are concerned, such a micro description would be prohibitively cumbersome and contain the distraction of a great many irrelevant degrees of freedom. From a modeling point of view, we thus appear to be the beneficiaries of an extraordinarily convenient tendency of quantum mechanics to flow robustly into classical mechanics whenever large numbers of microscopic degrees are freedom are coupled together. This modeling ‘transition’ appears to be remarkably independent of the details of exactly what quantum constituents are interconnected, and on the dynamical details of the interconnections—the aggregate degrees of freedom of macroscopic systems can be relied upon to behave classically (even if the exact values of some parameters can be traced back to essentially quantum origins). As a theoretical physicist, one would really like to elucidate the mathematical structure of this transition and to identify the essential features of quantum mechanics that make it so robust and inevitable.

And what about the experimentalist? When presented with such a scenario, I think one’s natural impulse is to try to find a way to break it. In my chapter for the Wheeler book project, I will describe current and foreseeable efforts to do this in two ways:

1) Quantum information technology—The dream of building a large-scale fault tolerant quantum computer relies on the idea that one can find special ways of interconnecting huge numbers of quantum degrees-of-freedom that circumvent the quantum-classical transition. To what extent do we believe that this idea is sound, and what are the important experimental lines of investigation?

2) Quantum measurement and feedback—If the modeler’s point of view is valid, and classical mechanics can really be obtained as an amazingly robust mathematical approximation to quantum mechanics, it cannot be the case that the measurement postulates are axiomatic for quantum physics. They should instead be derivable as efficient descriptions of the generic physical scenario in which a quantum system of interest is dynamically coupled to a quantum measurement device, and where we only care to describe the dependence of ‘readout’ degrees of freedom on the system’s quantum state. There has of course been a great deal of theoretical work in this direction, which has in recent years given rise to a sophisticated machinery for ‘precise’ modeling of realistic measurement scenarios involving real-time observation of individual quantum systems. How can we formulate experimental tests of this theory, and in what sense can such experiments enhance our understanding of the quantum-classical transition?

The author wishes to acknowledge the profound influence of Christopher Fuchs and John Doyle on his thinking in these matters.