FORUM

By E. Andrew Boyd

By 2007, 50 years after it was submitted as a doctoral dissertation, the “many worlds” interpretation was one of the most widely accepted views of our universe by physicists. And its progenitor, Hugh Everett III, was an operations researcher.

In the mid-1950s, Everett was a graduate student at Princeton working under the direction of physicist John Wheeler. At question was the physical interpretation of quantum mechanical models, which in turn were developed as a result of perplexing experimental results. It seemed as though electrons and other subatomic particles behaved like waves until an experimenter looked at them, at which point they behaved like particles.

Niels Bohr defended what came to be known as the Copenhagen interpretation, an interpretation in which the act of observation actually brought about wave function collapse; that is, subatomic particles really were waves until someone peeked at them, at which point they became particles. This special role of an observer in the physical reality of the universe carries heavy philosophical baggage. Bohr spent much of his later life trying to convince Einstein of the physical reality of the Copenhagen interpretation in what came to be known as the Bohr-Einstein debates. Einstein remained utterly unconvinced to his death, though never offered his own interpretation.

Everett offered a different interpretation. Instead of the wave function collapsing to a single reality – a single particle in a single place – it actually collapsed into all possible realities. The universe we experience is but one of an infinite number of ever increasing universes – just one of “many worlds.”

God Playing Dice

In spite of its own philosophical baggage, the “many worlds” interpretation has numerous advantages over competing interpretations. Most notably it rescues the causal determinism ushered in by Newton. Particles don’t live in a world of possibilities described by a probabilistic wave function, only to randomly show up here or there when we look for them. Instead, they show up everywhere, and we, in our universe, only observe one realization. Einstein would have welcomed the deterministic element of the “many worlds” interpretation – his concern over quantum mechanics was that it “forced God to play dice with the universe.” Whether he would have accepted the interpretation itself is open to debate.

Wheeler was a student of Bohr’s and arranged to introduce Everett’s ideas to Bohr. Everett himself had the opportunity to speak with Bohr on multiple occasions. But Bohr could not be convinced, and Wheeler, concerned over rocking the boat, worked with Everett to reduce his thesis to one-fourth of its original length, removing any remotely controversial passages. The original version didn’t appear in print until 15 years later at the prompting of “many worlds” advocates.

Making little headway with the physics community, Everett turned his attention to the newly emerging field of operations research – a field that was both intellectually challenging and well funded by the U. S. military. Everett finished his thesis in the late-1950s at the height of the Cold War and took a position with the Weapons Systems Evaluation Group, a think tank of Ph.D.s tasked with modeling defensive and offensive nuclear attack plans for the Pentagon. Kill ratios and mutual assured destruction were at the center of Everett’s activities. He once participated in a small, crucial, daylong presentation to Robert McNamara, the influential secretary of defense under John F. Kennedy.

At the same time, Everett was publishing in Operations Research. His first paper, “The Distribution and Effects of Fallout in Large Scale Nuclear Campaigns” (Vol. 7, 1959, pp. 226-248), came directly from work done at the Weapons Systems Evaluation Group with George Pugh. It describes “a method of optimally distributing weapons among large areas in order to maximize radiation casualties.” Shocking as this idea sounds today, Everett and Pugh’s models helped demonstrate that fallout was a greater cause of death than the initial nuclear blasts, something that wasn’t fully appreciated when the nuclear arms race began.

Everett’s second and only other paper found in Operations Research, “Generalized Lagrange Multiplier Method for Solving Problems of Optimum Allocation of Resources” (Vol. 11, 1963, pp. 399-417), discusses an early application of constraint relaxation in optimization. Everett’s primary theoretical contribution was recognizing that constraint relaxation techniques were applicable when the unrelaxed constraint set was arbitrary, not simply the intersection of sets defined by continuously differentiable functions. In essence, Everett helped pave the way for the use of Lagrangian relaxation in the solution of integer programs.

By today’s standards the paper’s development is quite rudimentary. Everett relies on expert knowledge to choose a good set of Lagrange multipliers, provides almost no guidance on iterative techniques for improving the multipliers, and his description of relaxation is clumsy compared to the articulations found in textbooks today. Nonetheless, Everett’s development was novel when it was first published.

Great Pioneer, Genius

Harvey Greenberg, an INFORMS member and professor emeritus at the University of Colorado Denver, was mentored by Everett while Greenberg was still a student at Johns Hopkins. Greenberg remembers Everett as a great pioneer – even a genius – well deserving of recognition by the operations research community. According to Greenberg, Everett introduced the term “gap” in the discussion of generalized Lagrange multipliers. While Everett’s paper references gaps in access to primal solutions that arise as the result of non-convexities, “gap” isn’t used in the well-defined sense of primal/dual problems differing in their optimal values. Nonetheless, as Greenberg points out, Everett had latched onto an initial understanding of the intricacies of generalized Lagrange multiplier methods that wasn’t fully appreciated at the time.

Everett and Greenberg had many discussions about the deeper aspects of generalized Lagrange multiplier methods, leading Greenberg to write a sequence of six articles on the topic in Operations Research between 1970 and 1977. All cited Everett’s 1963 paper, and Greenberg took Everett’s perspective on generalized Lagrange multipliers as his jumping off point in “Generalized Penalty Function Concepts in Mathematical Programming” (Operations Research, Vol. 18, 1970, pp. 229-252, with M. Bellmore and J. J. Jarvis).

Arthur Geoffrion, INFORMS Fellow and UCLA professor emeritus, had less direct contact with Everett but also wrote papers based on Everett’s 1963 work. In a paper with Robin Brooks, Geoffrion suggested an explicit method for iteratively updating Everett’s multipliers (“Finding Everett’s Lagrange Multipliers by Linear Programming,” Operations Research, Vol. 14, 1966, pp. 1,149-1,153). Brooks and Geoffrion went so far as to coin the term “Everett’s Condition” in their paper. The name was used for reference purposes rather than to elevate the condition to a state of notoriety. Nonetheless, it’s interesting that Everett’s work was sufficiently well recognized at the time to generate a chain of publications. Everett didn’t leave a long list of his own journal publications, in part due to the secret nature of his work with the Pentagon, in part because he lost interest in the academic endeavor, and in part to keep his successful consulting business ahead of the competition.

In “The Many Worlds of Hugh Everett III: Multiple Universes, Mutual Assured Destruction and the Meltdown of a Nuclear Family” (Oxford, 2010), author Peter Byrne documents the life of Everett through interviews and collected papers provided by Everett’s son. The picture that emerges isn’t pretty – a self-absorbed man of questionable morals who failed as a husband and father, and whose eating, drinking and smoking led to death by a heart attack at age 51. But for his failings, Everett can be counted among the ranks of operations researchers – one who not only helped shape our view of generalized Lagrange multipliers but of the universe itself.

Andrew Boyd (e.a.boyd@earthlink.net) served as executive and chief scientist at an analytics firm for many years.