Abstract

While the relation between visualization and scientific understanding has been a topic of long-standing discussion, recent developments in physics have pushed the boundaries of this debate to new and still unexplored realms. For it is claimed that, in certain theories of quantum gravity, spacetime ‘disappears’: and this suggests that one may have sensible physical theories in which spacetime is completely absent. This makes the philosophical question whether such theories are intelligible, even more pressing. And if such theories are intelligible, the question then is how they manage to do so. In this paper, we adapt the contextual theory of scientific understanding, developed by one of us, to fit the novel challenges posed by physical theories without spacetime. We construe understanding as a matter of skill rather than just knowledge. The appeal is thus to understanding, rather than explanation, because we will be concerned with the tools that scientists have at their disposal for understanding these theories. Our central thesis is that such physical theories can provide scientific understanding, and that such understanding does not require spacetimes of any sort. Our argument consists of four consecutive steps: (a) We argue, from the general theory of scientific understanding, that although visualization is an oft-used tool for understanding, it is not a necessary condition for it; (b) we criticise certain metaphysical preconceptions which can stand in the way of recognising how intelligibility without spacetime can be had; (c) we catalogue tools for rendering theories without a spacetime intelligible; and (d) we give examples of cases in which understanding is attained without a spacetime, and explain what kind of understanding these examples provide.

Highlights

  • The debate over the indispensability of representing physical systems in space and in time is an old one

  • A physicist like Schrödinger, who worked at the forefront of the modern revolution in physics, used the idea of the necessity of spatial and temporal representations for our grasping of the phenomena to argue for the superiority of his own explicitly spatiotemporal wave mechanics—criticising the lack of Anschaulichkeit of Heisenberg’s abstract matrix mechanics

  • The contextual theory of scientific understanding explains his preference for direct spatiotemporal visualization by showing how it functions as a conceptual tool that enhances the intelligibility of quantum theory; that is, it facilitates the use of the theory in constructing explanatory models of phenomena

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Summary

Introduction

The debate over the indispensability of representing physical systems in space and in time is an old one. Kant turned space and time into ‘forms of intuition’ (Anschauungsformen), stressing even more the necessity of the spatial and temporal representations for our grasping of the phenomena This was not merely a philosophical debate divorced from scientific issues: late nineteenth- and early twentieth-century scientific developments, from Poincaré’s conventionalism and Einstein’s two theories of relativity to quantum mechanics, challenged the view that space and time—whether a priori concepts of the mind, or some kind of ultimate foundation of reality—are entities which are fixed once and for all. The new theories of gravity which we are referring to here are theories of quantum gravity, which are concerned with the fabric of spacetime itself, and the claim often made is that this very fabric ceases to be a fundamental entity: there is ‘no spacetime’ at the fundamental level This prompts the philosophical question of whether such theories without a spacetime, which are inherently unvisualizable, can be intelligible at all, and whether they can provide us with understanding of the phenomena.

Can ‘theories without a spacetime’ provide scientific understanding?
What is scientific understanding and how can it be attained?
Rejecting metaphysical apriorism
The ‘Spacetime Wars’: debates over scientific understanding?
Emergence of spacetime in quantum gravity
The problem of spacetime as a problem of understanding
How theories without a spacetime can be made intelligible
Cataloguing the tools
Visualization via effective spacetimes
Effective spacetimes in theories with spacetime
Effective spacetimes in theories without a spacetime
Physics in the abyss: no spacetime and no visualization
Interpretation and the intelligibility of theories without a spacetime
Summary and conclusion
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