Institutionalizing Quantum Gravitational Research

This chapter describes the establishment of such a quantum gravity-friendly environment that enabled it to go out into the world on its own, somewhat less dependent on other areas of physics. It is more concerned with the development of basic infrastructure. The focus is on private philanthropy and the reasons behind a mid-century surge in funding for gravitational and quantum gravitational physics, which themselves are centered around the establishment of the Institute of Field Physics.

“Prehistoric” Quantum Gravity

In this chapter we examine the very earliest work on the problem of quantum gravity (understood very liberally). We show that, even before the concept of the quantization of the gravitational field in 1929, there was a fairly lively investigation of the relationships between gravity and quantum stretching as far back as 1916, and certainly no suggestion that such a theory would not be forthcoming. Indeed, there are, rather, many suggestions explicitly advocating that an integration of quantum theory and general relativity (or gravitation, at least) is essential for future physics, in order to construct a satisfactory foundation. We also see how this belief was guided by a diverse family of underlying agendas and constraints, often of a highly philosophical nature.

The Problem of Quantum Gravity: From Feelings to Phenomena

This chapter provides a simple, schematic introduction to the problem of quantum gravity. The problem of quantum gravity spent much of its earliest history at the mercy of wider changes with respect to the ingredient theories, general relativity and quantum theory. Even once those theories settled down, quantum gravity remained firmly detached from experiments. This situation has only recently changed and promises to offer new phenomena to test proposed solutions to the problem which will enable us to make firmer statements about the more physical implications of these proposed solutions. However, we see that we may still face a problem of polysemicity stemming from the very differing interpretations and formulations that the ingredient theories allow, as well as differing motivations for pursuing quantum gravity.

Quantum Gravity as a Resource

This chapter focuses on the central motivation for much of what can be labeled ‘quantum gravity’ in the earliest phases of research, namely that it provides a potentially abundant resource for curing problems in quantum field theory. While it was rare to have fully worked out examples along these lines, it provided a much needed impetus to the study of quantum gravity at a time when there were few other reasons to bother with it. The primary problem was the ubiquitous divergences, which proved extremely stubborn and worrying to field theorists. Not all of the approaches were looked at involved gravitation directly, however, and focused more on ways of generating a discrete structure (with a minimal length or maximum energy) that would provide a physical cutoff, thus grounding a finite theory. These filtered through into gravitational research only later than our timeframe, in a variety of ways, including the small scales necessarily reached in gravitational collapse.

On Writing a History of Quantum Gravity

This chapter describes some of the special challenges and novelties facing historical research in quantum gravity. Though often looked at with wry amusement when mentioned in the same breath, “history” and “quantum gravity” fit remarkably well together. Not only is there more than enough in chronological terms, the episodes are closely intertwined with other important developments in the life histories of the ingredient theories, quantum theory and general relativity. However, there are also more sociologically interesting aspects having to do with the emergence of a community of quantum gravity scholars, itself piggybacking on the availability of funding sources. Finally, we note the special status of quantum gravity, historiographically speaking, as a rare case of a field of research with more than a century of history behind it, including within it various rejections and selections of results, and yet which has as yet no experiments of its own, and no final endpoint from which to interpret the past.

Geon Wheeler

This chapter focuses on John Wheeler’s work on geons and geometrodynamics which would lead to many concepts and results that would be of importance to quantum gravity research - these projects, initially, were rather old fashioned, harking back to the classical ‘unified field theory’ work of Einstein. Moreover, we find that this work that we now tend to think of as foundational in quantum gravity---e.g., we often think of ‘quantum geometrodynamics’ as just another phrase for ‘quantum gravity’---had its roots firmly embedded in the quest for understanding the elementary particles. It wasn’t until after 1957 that Wheeler began to look seriously at general relativity and quantum gravity independently from concerns in particle physics, and this shift in fact coincides with a more general trend to treat gravitational physics as a worthwhile field in its own right.

Forming the Canon

This chapter charts the early development of the canonical quantum gravity (that is, the quantization of the gravitational field in Hamiltonian form). What we find in this period include: the establishment of a procedure for quantizing in curved spaces; the first expressions for the Hamiltonian of general relativity; recognition of the existence and importance of constraints (i.e. the generators of infinitesimal coordinate transformations); a focus on the problem of observables (and the realisation of conceptual implications in defining these for generally relativistic theories), and a (template of a) method for quantizing the theory. Although it commenced relatively early, the canonical approach was slow in its subsequent development. This had two sources: (1) it required the introduction of tools and concepts from outside of quantum gravity proper (namely, the constraint machinery and the parameter formalism); (2) by its very nature, it is highly rigorous in a conceptual sense, demanding lots of groundwork to be established, in terms of the structure of physical observables, before the actual issue of quantization can even be considered. Work was further complicated by the fact that these two sources of difficulty happened to be entangled. Particular emphasis is placed on the parameter formalism of Paul Weiss.

Another Field to the Pot

This chapter focuses on the impact of field quantization methods on the problem of quantum gravity. It is shown that much work after 1930 until mid-century was an exercise in ‘exploring the consequences’ of the Heisenberg-Pauli theory of quantum electrodynamics: understanding the symmetries and the divergences, and attempting to find ways of dealing with both. The goal was very much to treat all fields in much the same way, and so one could also envisage learning about one field from another. However, there was a separate track, superficially similar, though issuing from a desire to have a theory of gravitation more in line with the rest of physics, and in particular one not involving the difficulties of curved, dynamical spacetime. The interaction representation and a desire for a manifestly covariant description played a crucial role in the development of such approaches, and involved a curious borrowing of concepts often associated with canonical approaches. An apparently orthogonal approach developed alongside these later manifestly covariant approaches, involving a hybrid approach retaining a classical gravitational field, albeit still coupled to quantized sources through the Einstein field equations. These were done largely to avoid complications, however, and the conceptual consequences, though hinted at, were not further explored.

The Shock of the New

In this chapter, we show how the newest developments in quantum mechanics of the late 1920s were very quickly compared with general relativity, with attempts made to demonstrate their mutual coherence. This involved focusing on the basic mathematical structures that formed the first concrete representations of quantum mechanical systems. The aim was structural harmonisation, rather than quantization. Likewise, we will find that conceptual debates, especially having to do with measurement and the uncertainty relations, as well as new cosmological discoveries (based on applications of general relativity) were also quickly compared, often with surprising results such as explanations of discreteness and predictions of particle production in curved spaces. We see two primary motivations pushing this research forward: coherence (into which the more formal approaches also fit) and utility (that is attempting to gain a better grip on the quantum theory).