I argue that Norton & Earman's hole argument, despite its historical association with General Relativity, turns upon very general features of any linguistic system that can represent substances by names. After exploring various means by which mathematical objects can be interpreted as representing physical possibilities, I suggest that a form of essentialism can solve the hole dilemma without abandoning either determinism or substantivalism. Finally, I identify the basic tenets of such an essentialism in Newton's writings and consider how they can (...) be updated to apply to the case provided by General Relativity. (shrink)

This paper considers the implications for the relational-substantival debate of observations of parity nonconservation in weak interactions, a much neglected topic. It is argued that 'geometric proofs' of absolute space, first proposed by Kant (1768), fail, but that parity violating laws allow 'mechanical proofs', like Newton's laws. Parity violating laws are explained and arguments analogous to those of Newton's Scholium are constructed to show that they require absolute spacetime structure--namely, an orientation--as Newtonian mechanics requires affine structure. Finally, it is considered (...) how standard relationist responses to Newton's argument might respond to the new challenge of parity nonconservation. (shrink)

This paper outlines a new interpretation of an argument of Kant's for the existence of absolute space. The Kant argument, found in a 1768 essay on topology, argues for the existence of Newtonian-Euclidean absolute space on the basis of the existence of incongruous counterparts (such as a left and a right hand, or any asymmetrical object and its mirror-image). The clear, intrinsic difference between a left hand and a right hand, Kant claimed, cannot be understood on a relational view of (...) space - for in terms of the spatial relations of their parts, there is no difference to be found. Kant's argument has been interpreted by, among others, Graham Nerlich (in 1973, Hands, Knees and Absolute Space, The Journal of Philosophy). I briefly discuss Nerlich, and then offer a different reconstruction of the argument, one that appears to be closer to Kant's text. The reconstruction, however, essentially involves ascription of primitive identity to parts of space. Comparing the Kantian absolutist account of incongruous counterparts using primitive identity to the correct relationist account, I conclude that the absolutist account pays a heavy metaphysical price, without buying any genuine explanatory advantage over the relationist. I go on to examine recent suggestions that parity-non-conservation phenomena in quantum physics allow a stronger version of Kant's challenge to relationism. On closer examination, it turns out that here too the absolutist or substantivalist must be appealing to space parts with primitive identity in order to claim an advantage over relationists; and here too, I argue the substantivalist story really has no advantage over the correct relationist account. (shrink)

The traditional absolutist-relationist debate is still clearly formulable in the context of General Relativity Theory (GTR), despite the important differences between Einstein's theory and the earlier context of Newtonian physics. This paper answers recent arguments by Robert Rynasiewicz against the significance of the debate in the GTR context. In his (1996) (‘Absolute vs. Relational Spacetime: An Outmoded Debate?’), Rynasiewicz argues that already in the late nineteenth century, and even more so in the context of General Relativity theory, the terms of (...) the original Descartes–Newton–Leibniz dispute about space are not to be found. Nineteenth-century ether theories of electromagnetism, and the metric field of GTR, he claims, do not lend themselves to being interpreted clearly as either absolute space à la Newton, or relational structures à la either Descartes or Leibniz. I argue that, while in some imaginable theories Rynasiewicz's claim that the classical debate dissolves would be correct, in fact in the most important historical theories he discusses, this is not the case. In particular, I argue that in both Lorentz's ether theory and General relativity theory, there is a clear and compelling way to establish connections to the classical absolutist-relationist disputes, and that in both these theories it is the absolutist position that is prima facie victorious. To support my arguments and give a clear overview of the whole debate, I end by offering definitional sketches of relationism and absolutism (substantivalism) about spacetime in the context of contemporary physics. The sketches show the clear connections between these views today and their ancestors in Newton and Leibniz. But at the same time, they indicate how both views are not just claims about existing physical theories, but rather also bets about how future physics will clarify the ontological picture. (shrink)

An Introduction to Quantum Field Theory is a textbook intended for the graduate physics course covering relativistic quantum mechanics, quantum electrodynamics, and Feynman diagrams. The authors make these subjects accessible through carefully worked examples illustrating the technical aspects of the subject, and intuitive explanations of what is going on behind the mathematics. After presenting the basics of quantum electrodynamics, the authors discuss the theory of renormalization and its relation to statistical mechanics, and introduce the renormalization group. This discussion sets the (...) stage for a discussion of the physical principles that underlie the fundamental interactions of elementary particle physics and their description by gauge field theories. (shrink)

INTRODUCTION TO THE ARGUMENT OF 1768 Some ordinary facts about the world we live in can be readily explained by other ordinary facts. One can, for example, explain the fact that when we are facing north the sun rises on the right and ...

"First Published in 1999, Routledge is an imprint of Taylor & Francis, an informa company.".

We discuss the relationship between the interpretative problems of quantum gravity and those of general relativity. We argue that classical and quantum theories of gravity resuscitate venerable philosophical questions about the nature of space, time, and change; and that the resolution of some of the difficulties facing physicists working on quantum theories of gravity would appear to require philosophical as well as scientific creativity.

John Earman and John Norton have argued that substantivalism leads to a radical form of indeterminism within local spacetime theories. I compare their argument to more traditional arguments typical in the Relationist/Substantivalist dispute and show that they all fail for the same reason. All these arguments ascribe to the substantivalist a particular way of talking about possibility. I argue that the substantivalist is not committed to the modal claims required for the arguments to have any force, and show that this (...) naturally leads to an alteration in the way determinism is characterized for local spacetime theories. (shrink)

Consider your right hand and a mirror image duplicate of it. Kant calls such pairs incongruent counterparts. According to him they have the following puzzling features. The relation and situation of the parts of your hand with respect to one another are not sufficient to distinguish it from its mirror duplicate. Nevertheless, there is a spatial difference between the two. Turn and twist them how you will, you cannot make one of them occupy the exact boundaries now occupied by the (...) other. In his 1768 paper, ‘Concerning the Ultimate Foundations of the Differentiation of Regions in Space’, Kant uses these claims to argue against relational accounts of space and goes on to argue that the difference between incongruent counterparts depends on a relation to absolute space as a whole. In his 1770 Inaugural Dissertation he argued that this difference could not be captured by concepts alone but required appeal to intuition. In the Prolegomena (1783) and again in the Metaphysical Foundations of Natural Science (1786) Kant appealed to these puzzling features of incongruent counterparts to support his transcendental idealism about space. (shrink)

Kant seems to have been the first to notice that there is something peculiar about the difference between right and left, but he failed to say exactly what the peculiarity is. His clearest account of the matter is in his inaugural lecture (see Bibliography at the end of the paper): We cannot describe [in general terms] the distinction in a given space between things which lie towards one quarter, and things which are turned towards the opposite quarter. Thus if we (...) take solids which are completely equal and similar but incongruent, such as the right and left hands . . . . although in every respect which admits of being stated in terms intelligible to the mind through a verbal description they can be substituted for one another, there is yet a diversity which makes it impossible for their boundaries to coincide. (shrink)