We consider the problem of uniqueness of certain simultaneity structures in flat spacetime. Absolute simultaneity is specifiled to be a non-trivial equivalence relation which is invariant under the automorphism group Aut of spacetime. Aut is taken to be the identity-component of either the inhomogeneous Galilei group or the inhomogeneous Lorentz group. Uniqueness of standard simultaneity in the first, and absence of any absolute simultaneity in the second case are demonstrated and related to certain group theoretic properties. Relative simultaneity with respect (...) to an additional structure X on spacetime is specified to be a non-trivial equivalence relation which is invariant under the subgroup in Aut that stabilises X. Uniqueness of standard Einstein simultaneity is proven in the Lorentzian case when X is an inertial frame. We end by discussing the relation to previous work of others. (shrink)

David Malament's (1977) well-known result, which is often taken to show the uniqueness of the Poincare-Einstein convention for defining simultaneity, involves an unwarranted physical assumption: that any simultaneity relation must remain invariant under temporal reflections. Once that assumption is removed, his other criteria for defining simultaneity are also satisfied by membership in the same backward (forward) null cone of the family of such cones with vertices on an inertial path. What is then unique about the Poincare-Einstein convention is that it (...) is independent of the choice of inertial path in a given inertial frame, confirming a remark in Einstein 1905. Similarly, what is unique about the backward (forward) null cone definition is that it is independent of the state of motion of an observer at a point on the inertial path. (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)

The question whether distant simultaneity has a factual or a conventional status in special relativity has long been disputed and remains in contention even today. At one point it appeared that Malament had settled the issue by proving that the only non-trivial equivalence relation definable from causal connectability is the standard simultaneity relation. Recently, however, Sarkar and Stachel claim to have identified a suspect assumption in the proof by defining a non-standard simultaneity relation from causal connectability. I contend that their (...) critique is based on a misunderstanding of the criteria for the definability of a relation, a misunderstanding that Malement's original treatment helped to foster. There are in fact a variety of notions of definability that can be brought to bear. They all, however, require a condition that suffices to secure Malament's result. The non-standard relation Sarkar and Stachel claim to be definable is not so definable, and, I argue, their proposal to modify the notion of “causal definability” is misguided. Finally, I address the relevance of Malament's result to the thesis of conventionalism. (shrink)

In 1977, David Malament proved the valuable technical result that the simultaneity relation of standard synchrony $\epsilon=\frac{1}{2}$ with respect to an inertial observer O is uniquely definable in terms of the relation κ of causal connectibility. And he claimed that this definability undermines my own version of the conventionality of metrical simultaneity within an inertial frame.But Malament’s proof depends on the imposition of several supposedly “innocuous” constraints on any candidate for the simultaneity relation relative to O. Relying on Allen I. (...) Janis’s 1983 challenge to one of these constraints, I argue that Malament’s technical result did not undermine my philosophical construal of the ontological status of relative metrical simultaneity. Furthermore, I show that (a) Michael Friedman’s peremptorily substantivalist critique of my conception, which Malament endorses, is ill-founded, and (b) if Malament had succeeded in discrediting my own conventionalist version of metrical simultaneity, he would likewise have invalidated Einstein’s pioneering version of it. (shrink)