Chris Smeenk

The Elusive Higgs Mechanism

The Higgs mechanism is an essential but elusive component of the Standard Model of particle physics. Without it Yang‐Mills gauge theories would have been little more than a warm‐up exercise in the attempt to quantize gravity rather than serving as the basis for the Standard Model. This article focuses on two problems related to the Higgs mechanism clearly posed in Earman’s recent papers (Earman 2003, 2004a, 2004b): what is the gauge‐invariant content of the Higgs mechanism, and what does it mean to break a local gauge symmetry?

Do the Laws of Physics Forbid the Operation of Time Machines

We address the question of whether it is possible to operate a time machine by manipulating matter and energy so as to manufacture closed timelike curves. This question has received a great deal of attention in the physics literature, with attempts to prove no-go theorems based on classical general relativity and various hybrid theories serving as steps along the way towards quantum gravity. Despite the effort put into these no-go theorems, there is no widely accepted definition of a time machine. We explain the conundrum that must be faced in providing a satisfactory definition and propose a resolution. Roughly, we require that all extensions of the time machine region contain closed timelike curves; the actions of the time machine operator are then sufficiently “potent” to guarantee that closed timelike curves appear. We then review no-go theorems based on classical general relativity, semi-classical quantum gravity, quantum field theory on curved spacetime, and Euclidean quantum gravity. Our verdict on the question of our title is that no result of sufficient generality to underwrite a confident “yes” has been proven. Our review of the no-go results does, however, highlight several foundational problems at the intersection of general relativity and quantum physics that lend substance to the search for an answer.

False Vacuum: Early Universe Cosmology and the Development of Inflation

Inflationary cosmology has been widely hailed as the most important new idea in cosmology since Gamow’s pioneering work on nucleosynthesis, or perhaps even since the heady early days of relativistic cosmology in the 1920s. Popular accounts typically attribute the invention of inflation to Alan Guth, whose seminal paper (Guth 1981) created a great deal of excitement and launched a research program. These accounts typically present Guth and a small band of American particle physicists as venturing into untouched territory. More careful accounts (such as Guth’s memoir, Guth 1997) acknowledge that inflation’s central idea, namely that the early universe passed through a brief phase of exponential expansion, did not originate with Guth. Reading this earlier research merely as an awkward anticipation of inflation seriously distorts the motivations for these earlier proposals, and also neglects the wide variety of motivations for such speculative research. Below I will describe several proposals that the early universe passed through a de Sitter phase, highlighting the different tools and methodologies used in the study of the early universe. The early universe was the focus of active research for over a decade before Guth and other American particle physicists arrived on the scene in the late 1970s. The discovery of the background radiation in 1965 brought cosmology to the front page of the New York Times and to the attention of a number of physicists. In his influential popular book The First Three Minutes, Steven Weinberg characterized the effect of the discovery as follows:

Mie's Theories of Matter and Gravitation

Unifying physics by describing a variety of interactions—or even all interactions— within a common framework has long been an alluring goal for physicists. One of the most ambitious attempts at unification was made in the 1910s by Gustav Mie. Mie aimed to derive electromagnetism, gravitation, and aspects of the emerging quantum theory from a single variational principle and a well-chosen world function (Hamiltonian). Mie’s main innovation was to consider nonlinear field equations to allow for stable particle-like solutions (now called solitons); furthermore he clarified the use of variational principles in the context of special relativity. The following brief introduction to Mie’s work has three main objectives.1 The first is to explain how Mie’s project fit into the contemporary development of the electromagnetic worldview. Part of Mie’s project was to develop a relativistic theory of gravitation as a consequence of his generalized electromagnetic theory, and our second goal is to briefly assess this work, which reflects the conceptual resources available for developing a new account of gravitation by analogy with electromagnetism. Finally, Mie was a vocal critic of other approaches to the problem of gravitation. Mie’s criticisms of Einstein, in particular, bring out the subtlety and novelty of the ideas that Einstein used to guide his development of general relativity. In September 1913 Einstein presented a lecture on the current status of the problem of gravitation at the 85th Naturforscherversammlung in Vienna. Einstein’s lecture and the ensuing heated discussion, both published later that year in the Physikalische Zeitschrift, reflect the options available for those who took on the task of developing a new theory of gravitation. The conflict between Newtonian gravitational theory and special relativity provided a strong motivation for developing a new gravitational theory, but it was not clear whether a fairly straightforward modification of Newton’s theory based on classical field theory would lead to a successful replacement. Einstein clearly aimed to convince his audience that success would require the more radical step of extending the principle of relativity. For Einstein the development of a new gravitational theory was intricately connected with foundational prob-

Inflation and the Origins of Structure

Guth (Phys. Rev. D 23:347–56, 1981) provided a persuasive rationale for inflationary cosmology based on its ability to solve fine-tuning problems of big bang cosmology. Yet one of the most important consequences of inflation was only widely recognized a few years later: inflation provides a mechanism for generating small departures from uniformity, needed to seed formation of subsequent structures, by “freezing out” vacuum fluctuations to form classical density perturbations. This paper recounts the historical development of this aspect of inflation and puts it in context of the development of ideas on structure formation in relativistic cosmology, before turning to the comparison between inflation and a competing account of structure formation based on topological defects. One aim is to assess in what sense inflation is empirically tested through its account of the formation of structure, in light of persistent debates among cosmologists regarding whether inflation is “falsifiable.”

Review of Kant’s Construction of Nature

Michael Friedman’s Kant’s Construction of Nature provides a thorough reconstruction of Kant’s Metaphysical Foundations of Natural Science. In this slender volume, published in 1786, Kant used the resources for characterizing experience and cognition developed in the first Critique to account for the central empirical concepts of Newtonian physics. The text is cryptic even by Kantian standards. Kant’s Construction of Nature elucidates the text, with extensive discussion of almost every passage, drawing on detailed knowledge of Kant’s scientific and philosophical context. Friedman’s admiration for Kant animates the text; while acknowledging possible challenges to puzzling or obscure passages, Friedman always provides a careful, often ingenious, Kantian reply. Although some of Friedman’s readings may inspire controversy, Kant’s Construction of Nature clearly sets a new standard for a systematic understanding of the text and its central arguments. In doing so, it considerably augments Friedman’s influential case in favor of reading Kant in light of his engagement with natural philosophy. Although I lack the space and expertise to explore the matter fully here, Friedman’s reading of Metaphysical Foundations of Natural Science will open up new lines of discussion regarding the Critique, much as his earlier Kant and the Exact Sciences has influenced subsequent scholarship.