Most physics theories are deterministic, with the notable exception of quantum mechanics which, however, comes plagued by the so-called measurement problem. This state of affairs might well be due to the inability of standard mathematics to “speak” of indeterminism, its inability to present us a worldview in which new information is created as time passes. In such a case, scientific determinism would only be an illusion due to the timeless mathematical language scientists use. To investigate this possibility it is necessary (...) to develop an alternative mathematical language that is both powerful enough to allow scientists to compute predictions and compatible with indeterminism and the passage of time. We suggest that intuitionistic mathematics provides such a language and we illustrate it in simple terms. (shrink)

Mark Hinchliff concludes a recent paper, "The Puzzle of Change," with a section entitled "Is the Presentist Refuted by the Special Theory of Relativity?" His answer is "no." I respond by arguing that presentists face great difficulties in merely stating their position in Minkowski spacetime. I round up some likely candidates for the job and exhibit their deficiencies.

I examine the issue of persistence over time in thecontext of the special theory of relativity (SR). Thefour-dimensional ontology of perduring objects isclearly favored by SR. But it is a different questionif and to what extent this ontology is required, andthe rival endurantist ontology ruled out, by thistheory. In addressing this question, I take theessential idea of endurantism, that objects are whollypresent at single moments of time, and argue that itcommits one to unacceptable conclusions regardingcoexistence, in the context of SR. (...) I then propose anddiscuss a plausible account of coexistence forperduring objects, which is free of these defects. This leaves the endurantist room for some maneuvers. I consider them and show that they do not really helpthe endurantist out. She can accommodate the notionof coexistence in the relativistic framework only atthe cost of renouncing central endurantist intuitions. (shrink)

Are probabilism and special relativity compatible? Dieks argues that they are. But the possible universe he specifies, designed to exemplify both probabilism and special relativity, either incorporates a universal “now”, or amounts to a many world universe, or fails to have any one definite overall Minkowskian-type space-time structure. Probabilism and special relativity appear to be incompatible after all. What is at issue is not whether “the flow of time” can be reconciled with special relativity, but rather whether explicitly probabilistic versions (...) of quantum theory should be rejected because of incompatibility with special relativity. (shrink)

In his recent article On Relativity Theory and Openness of the Future (1991), Howard Stein proves not only that one can define an objective becoming relation in Minkowski spacetime, but that there is only one possible definition available if one accepts certain natural assumptions about what it is for becoming to occur and for it to be objective. Stein uses the definition supplied by his proof to refute an argument due to Rietdijk (1966, 1976), Putnam (1967) and Maxwell (1985, 1988) (...) that Minkowski spacetime leaves no room for objective becoming whatsoever. However, Stein's proof does not seem to go far enough. By considering only what events have become from the standpoint of any given event, Stein's uniqueness proof fails from the outset to allow for a more general kind of becoming whereby it is understood to occur from the standpoint of events on the particular worldlines followed by observers. This suggests that there may, after all, be more than one way to define objective becoming in Minkowski spacetime once each observer's worldline is allowed to figure in the definition. This suspicion is further aroused by two recent proposals for objective, worldline-dependent becoming due to Peacock (1992) and Muller (1992) who advocate ways of defining becoming that are not equivalent to the definition Stein's uniqueness proof delivers. Nevertheless, we show that Stein's uniqueness proofcan be extended in a natural way to cover this more general kind of becoming, provided one does not enrich standard Minkowski spacetime by privileging certain sets of worldlines over others in an unwarranted manner. Thus we aim to reinforce Stein's point that standard Minkowski spacetime does make room for objective becoming, but in essentially only one way, despite arguments and proposals to the contrary. (shrink)

The aim of this doctoral dissertation is to closely explore the nature of Einstein’s block universe and to tease out its implications for the nature of time and human freedom. Four questions, in particular, are central to this dissertation, and set out the four dimensions of this philosophical investigation: (1) Does the block universe view of time follow inevitably from the theory of special relativity? (2) Is there room for the passage of time in the block universe? (3) Can we (...) distinguish past from future in the block universe? (4) Is there room for human freedom in the block universe? Although the answer of most philosophers would be yes, triple no, my own answer, controversially, is no, triple yes. -/- I thereby challenge the status quo with respect to each of these metaphysical questions, and argue that none of these questions can be answered from looking at physics alone. Physics may constrain our metaphysics, but it certainly does not settle it. What is needed in order to answer these questions, are additional metaphysical assumptions that fall outside the scope of modern physics. My primary goal in this dissertation, therefore, is not to settle the debates on the nature of time and human freedom, but to clarify them by expliciting the metaphysical assumptions that are otherwise left implicit. (shrink)

In a reply to Nicholas Maxwell, Stein has proved that Minkowski spacetime can leave room for the kind of indeterminateness required both by certain interpretations of quantum mechanics and by objective becoming. By examining the consequences of outcome dependence in Bell-type experiments for the co-determinateness of spacelike-related events, I argue that the only becoming relation that is compatible with both causal and noncausal readings of the quantum correlations is the universal relation. This result might also undermine interpretations of quantum mechanics (...) requiring non-epistemically indeterminate states before measurement and hyperplane-dependent wave collapse. (shrink)

Tensism holds that the present moment has a special status that sets it apart from the past and the future, independently of perceivers. One of the main objections to this view has been Einstein’s argument from special relativity, which aims at showing that absolute simultaneity is a myth. We argue that the moving observer in a causal variant of Einstein’s original thought experiment is subject to a temporal illusion. Owing to the analogy of the cases, this casts doubt on the (...) conjectures that there is no privileged frame of reference and that special relativity poses a problem for tensism. (shrink)

Quantum theory predicts that, e.g., in a Stern-Gerlach experiment with electrons the measured spin component $S_Z = \pm \frac{1}{2}$ does not come about by an adjustment at the last moment, a forced “flipping” or “tilting” of the spin (vector), which would imply z-angular momentum exchange between particle and instrument, but will afterward appear to have had the value $\frac{1}{2} or - \frac{1}{2}$ already before the measurement. Because an electron spin cannot have components $ \pm \frac{1}{2}$ in all directions at the (...) same time, the measuring direction has a “privileged” status before the measurement, however we choose that direction, which implies a retroactive effect. A second proof of retroactivity is derived from a special case of the paradox of Einstein, Podolsky, and Rosen. It is strongly suggested by our result that, in essential respects, both Bohr and Einstein were right in their famous controversy about determinism and considering microprocesses “as a whole.”. (shrink)

Richard Arthur and I proposed that the present in Minkowski spacetime should be thought of as a small causal diamond. That is, given two timelike separated events p and q, with p earlier than q, they suggested that the present is the set I+ ∩ I-. Mauro Dorato presents three criticisms of this proposal. I rebut all three and then offer two more plausible criticisms of the Arthur/Savitt proposal. I argue that these criticisms also fail.

First it is proved that, in a deterministic theory, Malus' law requires that, if a photon is successively transmitted by two polarizers with appropriately chosen settings, the first transmission influences a hidden variable (co-) determining the second one. We derive from this that in an ideal EPR experiment (giving the result predicted by quantum mechanics for two correlated photons transmitted by two polarizers with suitably chosen settings) there has to be a nonlocal influence from the “first” transmission interaction to the (...) second. Subsequently we argue that we can abandon determinism as an assumption so that the locality hypothesis is in any case untenable if the predictions of quantum mechanics are all correct. (shrink)

Ever since Quine’s „No entity without identity“ questions about identity and ontology have been closely connected. The present article aims at a survey of ontologies of space and space-time by considering questions such as how to identify places across possible worlds, how to identify places through time, how to identify places across possible worlds in space-time, and how to identify Minkowski events across possible worlds. In the course of considering these questions, the classical debate betwen Leibniz and Clarke and Kant’s (...) systematic contribution to this debate, his famous 1768 article on the distinction between left and right, is scrutinized by means of only recently developed three-dimensional products of modal logics. (shrink)