It has been repeatedly argued, most recently by Nicholas Maxwell, that the special theory of relativity is incompatible with the view that the future is in some degree undetermined; and Maxwell contends that this is a reason to reject that theory. In the present paper, an analysis is offered of the notion of indeterminateness (or "becoming") that is uniquely appropriate to the special theory of relativity, in the light of a set of natural conditions upon such a notion; and reasons (...) are given for regarding this conception as (not just formally consistent with relativity theory, but also) philosophically reasonable. The bearings upon Maxwell's program for quantum theory are briefly considered. (shrink)

1. Introduction. David Malament has described a natural and satisfying resolution of the traditional problems of Newtonian cosmology—natural in the sense that it effects the escape by altering Newtonian gravitation theory in a way that leaves its observational predictions completely unaffected. I am in full agreement with his approach. There is one part of his account, however, over which Malament has been excessively modest. The resolution requires a modification to Newtonian gravitation theory. Malament presents the modification as so straightforward as (...) to be automatic. This trivializes the crucial postulate, which I shall call the “relativity of acceleration.” It is a significant physical statement in its own right and requires careful justification. Moreover the postulate proved easy to overlook for decades of discussion of the paradox. It really only becomes natural from the perspective of the newer geometric methods Malament exploits. There the postulate has become a commonplace. My purpose here is to develop the following: While Newtonian cosmology can be repaired satisfactorily, in its traditional form it remains deeply troubled. These troubles can be expressed most vividly as the paradoxical contradictions indicated below. They persist in both the integral and differential formulations of Newtonian gravitation theory. Malament's careful geometric treatment is necessarily dense. By taking some liberties with precision, his core result can be expressed in a far simpler form. Attempts to avoid the resolution Malament describes do lead to disaster. Therefore this episode can be inverted and used as the strongest extant argument for the relativity of acceleration in Newtonian gravitation theory. (shrink)

In this essay, I examine the curved spacetime formulation of Newtonian gravity known as Newton–Cartan gravity and compare it with flat spacetime formulations. Two versions of Newton–Cartan gravity can be identified in the physics literature—a ‘‘weak’’ version and a ‘‘strong’’ version. The strong version has a constrained Hamiltonian formulation and consequently a well-defined gauge structure, whereas the weak version does not (with some qualifications). Moreover, the strong version is best compared with the structure of what Earman (World enough and spacetime. (...) Cambridge: MIT Press) has dubbed Maxwellian spacetime. This suggests that there are also two versions of Newtonian gravity in flat spacetime—a ‘‘weak’’ version in Maxwellian spacetime, and a ‘‘strong’’ version in Neo-Newtonian spacetime. I conclude by indicating how these alternative formulations of Newtonian gravity impact the notion of empirical indistinguishability and the debate over scientific realism. r 2004 Elsevier Ltd. All rights reserved. (shrink)

The thesis of the conventionality of simultaneity in the special theory of relativity has been the subject of controversy for over fifty years Unfortunately, debates about this thesis have sometimes been marred by a failure to clearly distinguish different conventionalist theories. In my dissertation I evaluate, clarify, and carefully distinguish a number of different conventionalist theories, and thus clear up some of the confusion surrounding the thesis of the conventionality of simultaneity . In particular, I examine the following conventionalist theories. (...) ;According to the definitional theory of principles, there are some important scientific "laws" which apparently state facts, but which in reality are true by definition. I show that the most notable attempts, to establish that some important scientific laws were actually "definitions in disguise" were not successful. ;According to the theory of conventional reference, there are some words which have meanings which do not uniquely determine their respective references. For example, Reichenbach claimed that the meaning of "simultaneity" did not uniquely determine its reference. I show in my dissertation that if Reichenbach were correct about the meaning of "simultaneity" then his argument would be sound, but that there are good reasons for doubting the correctness of Reichenbach's views about the meaning of "simultaneity". ;Closely related to the theory of conventional reference was Reichenbach's theory of coordinative definitions. According to the theory of coordinative definitions, if a word's meaning failed to uniquely determine its reference, some sentences in the theory must be used solely to fix the reference of the word. Reichenbach proposed a coordinative definition of "simultaneity", but I argue in my dissertation that even if one accepts Reichenbach's views about the meaning of "simultaneity", his views about the coordinative definition of "simultaneity" are not substantiated. ;According to the theory of intertranslatability, there are apparently incompatible scientific theories which nonetheless "say the same thing", in some intuitive sense. Such theories are said to be intertranslatable. For example, according to Winnie there are theories which seem to be incompatible with the standard version of the special theory of relativity, but which are actually intertranslatable with it. After examining a number of proposed criteria for intertranslatability, I select an adequate one. I use this criterion to show that Winnie's claim is true, but trivial, since the proposed "alternatives" to the standard version of the special theory of relativity are merely the same covariant theory expressed in different coordinate systems. ;Finally, according to the theory of conventional relations, there are some relations which are conventional because they are not intrinsic . Malament demonstrated that if symmetric causal connectability is the only intrinsic spacetime relation, then standard simultaneity is not a conventional relation, but every non-standard simultaneity relation is conventional. I demonstrate that if an asymmetric causal connectability relation is intrinsic, then not only is standard simultaneity not conventional, there are also an infinitude of non-conventional non-standard simultaneity relations. (shrink)

Much controversy surrounds the question of what ought to be the proper definition of 'singularity' in general relativity, and the question of whether the prediction of such entities leads to a crisis for the theory. I argue that a definition in terms of curve incompleteness is adequate, and in particular that the idea that singularities correspond to 'missing points' has insurmountable problems. I conclude that singularities per se pose no serious problem for the theory, but their analysis does bring into (...) focus several problems of interpretation at the foundation of the theory often ignored in the philosophical literature. (shrink)