The Agent's Arrow: Reconciling Subjectivity and Scientific Understanding in the Philosophy of Time — Epoche C2
Huw Price's Time's Arrow and Archimedes' Point (1996) advances a claim that is easy to state and easy to misread: the asymmetry of causation — that causes precede effects, that we deliberate about the future and take ourselves able to affect what is to come and not what has been — is not a further asymmetry in the physical world alongside the thermodynamic one, but an artefact of the standpoint from which agents like us describe that world. Price calls the corrective he wants an Archimedean point, a view from nowhen : a description of the temporal structure of the world that does not smuggle in the orientation of the describer. The criticism this essay is written against is that the manoeuvre buys its reconciliation too cheaply, dissolving the objectivity of causal explanation into pragmatic convenience. The reply offered here is that Price's position is not a retreat into subjectivity but a claim of a specific and arguable kind: that one of the asymmetries commonly listed as physical is perspectival, that the remaining ones are objective though contingent, and that the perspectival one is itself explained by the objective ones. Setting it out in that form requires distinguishing several asymmetries that the compressed version of this argument ran together, and withdrawing one claim in it that was not Price's. Five asymmetries, and the distinction that sorts them The first task is to stop speaking of "the" arrow of time, because at least five distinct asymmetries travel under that name and Price's thesis applies to exactly one of them. They are: the thermodynamic asymmetry: the entropy of an isolated macroscopic system does not decrease towards the future; the radiative asymmetry: an accelerating charge's field is described by the retarded and not the advanced solution of Maxwell's equations, though both are solutions; the cosmological asymmetry: the universe expands in one temporal direction and not the other; the epistemic or record asymmetry: we have traces of earlier states and not of later ones; the causal asymmetry: causes are earlier than their effects, counterfactual dependence runs futurewards, and the past is not open to intervention. Cutting across this list is a distinction Price presses harder than most of his predecessors: between an asymmetry that is de jure , written into the dynamical laws themselves, and one that is de facto , arising from contingent boundary conditions imposed on laws that are themselves symmetric under time reversal. A de facto asymmetry is perfectly objective — it is a fact about how the actual world is arranged — but it is not a fact about what is nomologically possible. The distinction matters because the standard microphysical dynamics, classical and quantum alike, is very nearly symmetric under time reversal, so any macroscopic asymmetry must be traced either to that residual violation, which is far too small and too specialised to do the work, or to boundary conditions. The interesting question is therefore never "is this asymmetry real?" but "is it de facto, and if so, which boundary condition supplies it?" Why the thermodynamic arrow needs a boundary condition, and how we know The second task is to see why the thermodynamic arrow is not self-supporting, since this is what makes the causal arrow's status a live question rather than an obvious one. Boltzmann's H -theorem derives monotonic entropy increase for a dilute gas from the collision dynamics plus one extra premise, the Stosszahlansatz , or molecular-chaos assumption: that the velocities of two molecules about to collide are statistically uncorrelated. Josef Loschmidt's objection of 1876 is that the conclusion cannot follow from the dynamics alone, because the dynamics is reversible: for every trajectory along which entropy rises there is a velocity-reversed trajectory, equally permitted, along which it falls. What Loschmidt located is that the asymmetry has been imported through the extra premise, which is applied to the molecules entering a collision and not to those leaving it. The counting that underlies the second law is, taken on its own, entirely symmetric. For a gas of N molecules in a box, the fraction of the phase-space volume in which every molecule lies in the left half is $2^{-N}$, since each molecule independently contributes a factor of one half; for a laboratory sample with $N = 10^{20}$ this is $2^{-N} = 10^{-N \log_{10} 2} \approx 10^{-3.0 \times 10^{19}}$, a number small enough that no observation will ever be made against it. But this measure-theoretic fact says only that low-entropy macrostates occupy vanishingly little of the available volume; it says nothing about direction. Run the same reasoning backwards from a present non-equilibrium state and it delivers the conclusion that the state arose as a fluctuation from a higher -entropy past, since the overwhelming majority of microstates compatible with the present macrostate have that history. That conclusion is false, and its falsity is not a matter of taste: if it were true, every record, memory and photograph would be a chance fluctuation carrying no information about what it purports to record. The repair, which David Albert calls the Past Hypothesis in Time and Chance (2000), is to add as an independent posit that the universe began in a macrostate of extraordinarily low entropy, and to impose a uniform probability measure over the microstates compatible with it. On that package the thermodynamic arrow is de facto and objective: dynamics plus a boundary condition, with no agent's standpoint entering. Boltzmann himself, in the second part of the Vorlesungen über Gastheorie (1898), had already drawn the further inference that in a universe of local entropy gradients, what we call the direction of time in a region is fixed by the direction in which entropy there increases. One claim in the compressed version of this essay must be withdrawn here, since the expansion shows it to be false. That version said that the o