Abstract
Russell’s dictum that there is no place for causality in fundamental physics has been revitalized in a recent debate. One of the main reasons Russell had for denying a genuine place for causality in physics was that the asymmetry of the causal relation has no counterpart in modern theories of physics because of the symmetry of determination relations as provided by fundamental equations. But there exists a further way of fundamental anchoring of causality. As we argue, despite the time-reversal invariance of fundamental laws it is possible that the solutions of those laws are typically time-asymmetric. In particular, it has been proven that almost all spacetimes that are solutions of the field equations of General Relativity and which allow for a universal “cosmic” time parameter and, furthermore, possess a matter field are time-asymmetric. We show that this result provides a new resource for anchoring the causal asymmetry in physics and thus diminishes the need for epistemic or even anthropocentric foundations of causality.
A first and longer version of this contribution has been published in: Maria Carla Galavotti et al. (eds.): New Directions in the Philosophy of Science, Springer 2014.
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Notes
- 1.
In Sect. 3, we will elaborate on the notion of typicality in connection with the asymmetric behavior of solutions of the field equations of GR.
- 2.
cf. (Castagnino and Lombardi 2009, p. 3).
- 3.
- 4.
cf. (Castagnino and Lombardi 2009, p. 14.) In more technical terms, time-symmetry of a spacetime with respect to a spacelike hypersurface t = tS requires “time-isotropy”, i.e. the existence of a diffeomorphism onto itself which reverses the temporal orientations but preserves the metric and leaves the hypersurface t = tS fixed.
- 5.
Frisch has provided an impressive epistemic account of causality in fundamental physics (cf. Frisch 2012).
- 6.
Castagnino et al. have raised an objection against this reductionist move: The entropy of the universe can only be defined under some physical conditions referring to space-time as a whole, in particular the condition that the space-time allows for a foliation into space-like hyper-surfaces, e.g. there exists a cosmic time (cf. Castagnino et al. 2003, p. 896).
- 7.
- 8.
- 9.
Since the condition of time-orientability guarantees that there is a consistent local time orientation for all points of spacetime, this weaker condition would be sufficient to reduce the class of spacetimes to those that have a unique local time order. But only the stronger condition of the existence of a cosmic time provides a global time function the value of which increases (decreases) along every timelike world line of the universe. Only then we can speak of ‘two directions of time’ for the whole universe.
- 10.
Notice, that Price’s use of the Gold universe as a counterexample to any intrinsic time-asymmetry of the universe relies on his considering the scaling factor as the only parameter characterizing the universe.
- 11.
Spacetimes that have an open but time-symmetric (and not static) topology are open with respect to both past and future. We will not consider them because they require a change in the value of the cosmological constant. But, in the context of classical GR, the cosmological constant is constant in cosmic time. This may not be the case for full blown quantum or string cosmology, but these yet quite speculative accounts are beyond the scope of this paper. In classical GR a contracting spacetime always includes a Big Crunch (cf. Hawking and Ellis 1973). Thus, a spacetime cannot be open with respect to two directions of cosmic time if the spacetime is not static.
- 12.
We follow here the argumentation of (Castagnino and Lombardi 2009, p. 18).
- 13.
We follow here the mathematical procedure of (Castagnino et al. 2003, p. 376f; Castagnino and Lombardi 2009, p. 19 f.). But we will not agree with the view of Castagnino et al., according to which positive local energy flow as constructed in this procedure selects a substantial future direction of time and thus defines a local arrow of time.
- 14.
Here R μν is the Ricci tensor, R the Ricci curvature, Λ is the cosmological constant and g μν the metrical tensor.
- 15.
- 16.
This interpretation appears to be canonical in the context of general relativity, but there are exceptions that show that this understanding of T 0μ is not valid in general. The exceptions come into play by considering quantum effects. Critical points are, for example, the Casimir effect or squeezed vacuum or Hawking-evaporation. (see e.g. Visser 1996; Barceló and Visser 2002).
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Bartels, A., Wohlfarth, D. (2015). How Fundamental Physics Represents Causality. In: Mäki, U., Votsis, I., Ruphy, S., Schurz, G. (eds) Recent Developments in the Philosophy of Science: EPSA13 Helsinki. European Studies in Philosophy of Science, vol 1. Springer, Cham. https://doi.org/10.1007/978-3-319-23015-3_15
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