Abstract
In his 1956 book ‘The Direction of Time’, Hans Reichenbach offered a comprehensive analysis of the physical ground of the direction of time, the notion of physical cause, and the relation between the two. I review its conclusions and argue that at the light of recent advances in physics Reichenbach analysis provides the best account for the physical underpinning of these notions. I integrate results in cosmology, and on the physical underpinning of records and agency into Reichenbach’s account, and discuss which questions it leaves open.
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Notes
This makes sense in the Newtonian approximation, where a time variable can be globally defined. It also makes sense in special and general relativistic physics, since—at least in the currently accessible spacetime region—the pseudo-Riemannian metric is time orientable. This article does not consider the properties of nature beyond the approximation where quantum gravitational phenomena can be disregarded.
The idea that a preferred direction of time might be intrinsic to time itself, independently from the irreversible thermodynamic phenomena, and is only revealed by these phenomena, is discussed and criticized in Sect. 9.
Given macroscopic variables An, the entropy of a system is defined also for a microstate s away from equilibrium. This can be done in terms of the phase-space volume where An = An(s).
Dissipation is used in the conversion of oscillatory (non-oriented) motion into monotonic (oriented) motion. Hence the duration of a time interval is determined by the mechanical device, but the direction of the passage of time is measured by the dissipation.
Some authors appropriately distinguish the second principle of thermodynamics, which states whether a thermodynamic process is possible, from an ‘Equilibrium Principle’ (Harvey 2001) or ‘Equilibration Principle’ (Wayne 2021), which states that systems spontaneously attain their equilibrium state. Strictly speaking, this is not what we see around us: systems do spontaneously move towards higher entropy states, but they mostly get trapped into metastable states, during the time scale we observe them.
An example of these attempts is the idea that it is the smoothness of the geometry that provides the low entropy of the universe relevant to account for the observed arrow of time (Penrose 1979). The problem with this idea is that if this was the case, a universe where the only dynamical part of the gravitational field was a(t), and matter interacted gravitationally via a Newtonian interaction only, would have no arrow of time, contrary to what the analysis of this model shows.
I am not referring to inflation here.
This is a fact which ultimately might be relevant (Carroll and Chen 2004), but not at this stage of the discussion. I will return to this point later on.
This remains true in an appropriate sense even in ‘deterministic’ interpretations such as ‘Bohmian’ or ‘Many Worlds’, because the total state that evolve deterministically is in principle inaccessible to us. Hence our best predictions remain probabilistic even within these interpretations.
But of course any agent is also a physical system like any other. As such, it does not necessarily need to be seen as a ‘free’ agent. A complex system with a rich internal dynamics can be considered as an agent, as we do with humans, and can be analysed at many different levels, in terms of the combination of factors determining its behaviour, including its mechanics, its memories, the external influence, and much more.
I thank an anonymous referee for pointing out this issue.
It is beautifully put in (Price 2007 264): “this view […] requires a deep link between the mental, on the one hand, and some deep and fundamental time-asymmetric aspect of physical reality, on the other—without the time-asymmetry concerned being manifest at intermediate levels!”.
A point nicely argued for instance is (Stein 2021).
The phase space is a modal notion; hence this is a potential, not an actual, infinity.
I return to Penrose’s suggestion that our universe is ‘special’ because its geometry is smooth, while ‘most’ geometries are crumpled (Penrose 1979). This is a brilliant suggestion, but—again—it does not seem to me to work. If this was the source of the arrow of time, then there would be no arrow of time in the approximation where the geometry remains smooth. And yet there is.
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This study was supported by John Templeton Foundation (Grant No. ID#62312).
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Rovelli, C. Back to Reichenbach. J Gen Philos Sci (2024). https://doi.org/10.1007/s10838-024-09680-x
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DOI: https://doi.org/10.1007/s10838-024-09680-x