Abstract
It is often said that the world is explained by laws of nature together with initial conditions. But does that mean initial conditions don’t require further explanation? And does the explanatory role played by initial conditions entail or require that time has a preferred direction? This chapter looks at the use of the ‘initialness defence’ in physics, the idea that initial conditions are intrinsically special in that they don’t require further explanation, unlike the state of the world at other times. Such defences commonly assume a primitive directionality of time to distinguish between initial and final conditions. Using the case study of the time-asymmetry of thermodynamics and the so-called ‘past hypothesis’—the hypothesis that the early universe was in a state of very low entropy—, I outline and support a deflationary account of the initialness defence that does not presuppose a basic directionality of time, and argue that there is a relevant explanatory asymmetry between initial conditions and the state of systems at other times only if certain causal conditions are satisfied. Hence, the initialness defence is available to those who reject a fundamental direction of time.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
See Farr (2020).
- 2.
See Baras and Shenker (2020) for a recent assessment of the dialectic between Price and Callender, and what it means to explain the low-entropy past.
- 3.
There exist many different statements of the second law (see Uffink 2001), and many different definitions of entropy (see Maroney 2009). As Price (2002) notes, the precise version of the second law, and the definition of ‘entropy’ are relatively inessential to the issue of the relation between time direction and thermodynamics. The example of the wine glass is sufficient to illustrate the kind of time asymmetry with which this chapter is concerned.
- 4.
There are two main approaches to statistical mechanics, owing to the work of Boltzmann and Gibbs respectively. I shall work within the Boltzmannian framework. Gibbsian statistical mechanics (Gibbs 1902) is distinct from Boltzmannian statistical mechanics in a number of ways. The Gibbsian approach is characterised by considering an ensemble of systems, each with slightly different microscopic states. As Frigg (2009) notes, both approaches are widely used within the literature but generally for different purposes: the Gibbsian approach is used in practice (i.e. experiments); the Boltzmannian approach is used in consideration of foundational issues (e.g. philosophical issues concerning the reduction of thermodynamics to statistical mechanics). See Wallace (2020) and Robertson (2020, 2021) for recent defences of the Gibbsian approach.
- 5.
In order for a point in phase space to play this role, the phase space must have the right dimensionality. The state of a one-particle system is provided by two quantities: the position and the momentum of the particle. If the particle is in a three-dimensional physical space, then its position and momentum each have coefficients in each spatial dimension: the position is provided by the triple (q x, q y, q z) corresponding to its location in each spatial dimension (x, y and z); and the momentum is provided the triple (p x, p y, p z). Thus, for a one-particle system, the phase space has 6 dimensions—three for position; three for momentum—such that each point in this space denotes a unique set of position and momentum values, with the entire space covering every possible state of the one-particle system.
- 6.
This assumption is one of the central problems concerning Boltzmannian statistical mechanics—see Sklar (2006) for a survey. The justifiability of Boltzmannian microcanonical probability distribution has historically concerned Liouville’s Theorem (which holds that regions of phase space of fixed energy are invariant under Hamiltonian evolution) and the Ergodic Hypothesis. See Frigg (2008) for a discussion of the relation between the ergodic hypothesis and Boltzmannian statistical mechanics.
- 7.
Frigg and Werndl (2011) argue that a weaker property that of ergodicity—‘epsilon ergodicity’—is sufficient for Boltzmannian statistical mechanics and avoids the problems of the KAM and Marcus-Meyer theorems.
- 8.
The status of the ergodic hypothesis has been the subject of a particularly massive literature that does not concern us in the present chapter. See Sklar (1993, ch. 5) for a review.
- 9.
A normal microstate for a system in equilibrium is one that stays in equilibrium (in both temporal directions).
- 10.
However, this remark is not elaborated on in much detail by Boltzmann, and he elsewhere entertained the hypothesis that the low entropy past is simply the result of a large fluctuation from thermal equilibrium made probable by the universe being significantly older than standard cosmological models assume, and for the most part in thermal equilibrium.
- 11.
Though it should be used that Penrose’s calculation is in the context of black hole thermodynamics, using Bekenstein–Hawking entropy rather than Boltzmann entropy.
- 12.
Indeed, Maudlin (2007, p. 126, fn. 11) describes his own position as a ‘B-series theory’ as opposed to a ‘C-series theory’, fitting with the B/C-theory distinction I’ve set out.
- 13.
Here, a ‘future’ state is simply the Past State described in negative time.
- 14.
Reichenbach’s principle of parallelism of entropy increase: ‘In the vast majority of branch systems, the directions toward higher entropy are parallel to one another and to that of the main system’ (Reichenbach 1956, p. 136). Equivalently, the directions towards lower entropy are also parallel.
- 15.
Maudlin (2007, 172).
- 16.
Both Maudlin (2007, p. 3 & p. 107).
- 17.
Recall that the ‘Future State’ is the hypothetical maximal entropy state in our distant future.
References
Albert, D. Z. (2000). Time and chance. Massachusetts: Harvard University Press.
Baras, D., & Shenker, O. (2020). Calling for explanation: The case of the thermodynamic past state. European Journal for Philosophy of Science, 10(3), 1–20
Boltzmann, L. (1967). On Zermelo’s paper “On the mechanical explanation of irreversible processes”. In S. Brush (Ed.), Kinetic theory. Irreversible processes (Vol. 2). Pergamon.
Callender, C. (2004a). Measures, explanations and the past: Should ‘special’ initial conditions be explained? British Journal for Philosophy of Science, 55(2), 195–217.
Callender, C. (2004b). There is no puzzle about the low entropy past. In C. Hitchcock (Ed.), Contemporary debates in philosophy of science (pp. 240–256). Oxford: Blackwell Publishing.
Clausius, R. (1864). Abhandlungungen über die mechanische Wärmetheorie (Vol. 1). Braunschweig: F. Vieweg.
Farr, M. (2020). C-theories of time: On the adirectionality of time. Philosophy Compass, 15(12), e12714.
Farr, M. (2022). Conventionalism about time direction. Synthese, 200(1), 1–21. https://doi.org/10.1007/s11229-022-03540-1
Farr, M. (2022). Perceiving direction in directionless time. In K. M. Jaszczolt (Ed.), Understanding human time. Oxford University Press.
Feynman, R. P., Morinigo, F. B., & Wagner, W. G. (1971). Feynman Lectures on Gravitation (Vol. 13). Pasadena, CA: California Institute of Technology.
Frigg, R. (2008). A field guide to recent work on the foundations of statistical mechanics. In D. Rickles (Ed.), The Ashgate companion to contemporary philosophy of physics, Chapter 3 (pp. 99–196). London: Ashgate.
Frigg, R. (2009). What is statistical mechanics? In C. Galles, P. Lorenzano, E. Ortiz, & H. J. Rheinberger (Eds.), History and philosophy of science and technology. Encyclopedia of Life Support Systems (Vol. 4). Eolss: Isle of Man.
Frigg, R., & Werndl, C. (2011). Explaining thermodynamic-like behavior in terms of epsilon-ergodicity. Philosophy of Science, 78(4), 628–652.
Gibbs, J. W. (1902). Elementary principles in statistical mechanics. Woodbridge: Ox Bow Press.
Gold, T. (1966). Cosmic processes and the nature of time. In R. G. Colodny (Ed.), Mind and cosmos (pp. 311–329). Pittsburgh: University of Pittsburgh Press.
Hausman, D., & Woodward, J. (1999). Independence, invariance and the causal Markov condition. The British Journal for the Philosophy of Science, 50(4), 521–583.
Maroney, O. (2009). Information processing and thermodynamic entropy. In E. N. Zalta (Ed.), The Stanford encyclopedia of philosophy (Fall 2009 ed.).
Maudlin, T. (2007). The metaphysics within physics. Oxford: Oxford University Press.
McTaggart, J. M. E. (1908). The unreality of time. Mind, 17(68), 457–474.
Penrose, R. (1989). The emperor’s new mind: Concerning computers, minds, and the laws of physics. Oxford: Oxford University Press.
Price, H. (1996). Time’s arrow and Archimedes’ point: New directions for the physics of time. Oxford: Oxford University Press.
Price, H. (2002). Boltzmann’s time bomb. The British Journal for the Philosophy of Science, 53(1), 83–119.
Price, H. (2004). On the origins of the arrow of time: Why there is still a puzzle about the low-entropy past. In C. Hitchcock (Ed.), Contemporary debates in philosophy of science (pp. 219–239). Oxford: Blackwell Publishing.
Reichenbach, H. (1956). The direction of time. Berkeley: University of California Press.
Robertson, K. (2020). Asymmetry, abstraction, and autonomy: Justifying coarse-graining in statistical mechanics. The British Journal for the Philosophy of Science, 71(2), 547–579.
Robertson, K. (2021). In search of the holy grail: How to reduce the second law of thermodynamics. The British Journal for the Philosophy of Science, Online first.
Sklar, L. (1993). Physics and chance: Philosophical issues in the foundations of statistical mechanics. Cambridge: Cambridge Univ Press.
Sklar, L. (2006). Why does the standard measure work in statistical mechanics? In V. F. Hendricks, K. F. Jörgensen, J. Lötzen, & S. A. Pedersen (Eds.), Interactions. Boston studies in the philosophy and history of science (Vol. 251, pp. 307–320). Springer Netherlands. https://doi.org/10.1007/978-1-4020-5195-1-10
Uffink, J. (2001). Bluff your way in the second law of thermodynamics. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 32(3), 305–394.
Wallace, D. (2011). The logic of the past hypothesis. PhilSci Archive. http://philsci-archive.pitt.edu/8894/
Wallace, D. (2020). The necessity of Gibbsian statistical mechanics. In V. Allori (Ed.), Statistical mechanics and scientific explanation: Determinism, indeterminism and laws of nature, Chapter 15 (pp. 583–616). World Scientific.
Wigner, E. P. (1995). Events, laws of nature, and invariance principles. In Philosophical reflections and syntheses (pp. 321–333). Springer.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Farr, M. (2022). What’s so Special About Initial Conditions? Understanding the Past Hypothesis in Directionless Time. In: Ben-Menahem, Y. (eds) Rethinking the Concept of Law of Nature . Jerusalem Studies in Philosophy and History of Science. Springer, Cham. https://doi.org/10.1007/978-3-030-96775-8_8
Download citation
DOI: https://doi.org/10.1007/978-3-030-96775-8_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-96774-1
Online ISBN: 978-3-030-96775-8
eBook Packages: Religion and PhilosophyPhilosophy and Religion (R0)