Carl Hoefer

Energy conservation in GTR

Abstract The topics of gravitational field energy and energy-momentum conservation in General Relativity theory have been unjustly neglected by philosophers. If the gravitational field in space free of ordinary matter, as represented by the metric g ab itself, can be said to carry genuine energy and momentum, this is a powerful argument for adopting the substantivalist view of spacetime. This paper explores the standard textbook account of gravitational field energy and argues that (a) so-called stress-energy of the gravitational field is well-defined neither locally nor globally; and (b) there is no general principle of energy-momentum conservation to be found in General Relativity. I discuss the nature and justification of the zero-divergence law for ordinary stress-energy, and its possible connection with the failure of General Relativity to realise Machs principle.

Determinism and Chance from a Humean Perspective

On the face of it ‘deterministic chance’ is an oxymoron: either a process is chancy or deterministic, but not both. Nevertheless, the world is rife with processes that seem to be exactly that: chancy and deterministic at once. Simple gambling devices like coins and dice are cases in point.2 On the one hand they are governed by deterministic laws – the laws of classical mechanics – and hence given the initial condition of, say, a coin it is determined whether it will land heads or tails when tossed.3 On the other hand, we commonly assign probabilities to the different outcomes of a coin toss, and doing so has proven successful in guiding our actions. The same dilemma also emerges in less mundane contexts. Classical statistical mechanics assigns probabilities to the occurrence of certain events – for instance to the spreading of a gas that is originally confined to the left half of a container – but at the same time assumes that the relevant systems are deterministic. How can this apparent conflict be resolved?

Einstein's struggle for a Machian gravitation theory

Abstract The story of Einsteins struggle to create a general theory of relativity, and his early discontentment with the final form of the theory (1915), is well known in broad outline. Thanks to the work of John Norton and others, much of the fine detail of the story is also now known. One aspect of Einsteins work in this period has, however, been relatively neglected: Einsteins commitment to Machs ideas on inertia, and the influence this commitment had on Einsteins work on general relativity from 1907 to 1918. In this paper published writings and archival material are examined, to try to reconstruct the details of Einsteins thinking about inertia and gravitation, and the role that Machs ideas played in Einsteins crucial work on the general theory. By the end, a clear picture of Einsteins conceptions of Machs ideas on inertia, and their philosophical motivations, will emerge. Several surprising conclusions also emerge: Einsteins desire for a Machian gravitation theory was the central force driving his work from 1912 to 1915, keeping him going despite numerous frustrating setbacks; Einsteins continued commitment to Machs ideas in 1916–1917 kept him at work trying various strategies of modification of the field equations, in order to exclude anti-Machian solutions (including the addition of the cosmological constant in 1917); and as late as early 1918, Einstein was ready to call the whole General Theory a failure if no way of squaring it with Machs ideas on inertia could be found. But by 1920 Einstein advocated a view that granted spacetime (under the name ‘ether’) independent existence with physical qualities of its own, a complete break with his earlier Machian views.

Kant's hands and Earman's pions: Chirality arguments for substantival space

This paper outlines a new interpretation of an argument of Kants 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. Kants 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 Kants 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 Kants 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.

Freedom from the Inside Out

Since the death of strong reductionism, philosophers of science have expanded the horizons of their understandings of the physical, mental, and social worlds, and the complex relations among them. To give one interesting example, John Dupre has endorsed a notion of downward causation : ‘higher-level’ events causing events at a ‘lower’ ontological level. For example, my intention to type the letter ‘t’ causes the particular motions experienced by all the atoms in my left forefinger as I type it. The proper explanation of the motions of an atom at the tip of my forefinger primarily involves my intentions, rather than (for example) the immediately preceding motions of other nearby atoms, or any other such particle–level events.

Introduction: space–time and the wave function

All the papers in this special issue deal with the questions of what the wave function represents and what the implications of quantum realism are in relation to our conception of space. These questions were the basis of the discussions that took place over two conferences which, under the title of Space–time and the wave function, were held in Barcelona in April 2013 and May 2014. The papers that are included here—or preliminary versions of them—were presented and discussed at those conferences