The Direction of Time

Whether or not time flows, it has a direction: the past and the future are not interchangeable. We remember the past but not the future; causes precede their effects; ice melts in warm water but warm water never spontaneously unmixes into ice and heat; a dropped glass shatters but shards never leap back together. This pervasive anisotropy — the "arrow of time" (Eddington's phrase) — is one of the deepest puzzles in the philosophy of physics, because it sits atop a paradox: the fundamental laws of physics are, with a tiny exception, time-symmetric, drawing no distinction between past and future, yet the world they govern is flagrantly asymmetric in time. Where, then, does the arrow come from?

This page distinguishes the several arrows, states the puzzle of their origin, and sets up the reduction to thermodynamics developed on the thermodynamic arrow page. It presupposes the A/B and passage discussions.

The arrows of time

The temporal asymmetry shows up in many guises. It is a substantive question whether these are one arrow or several, and if one, which is fundamental:

The striking fact is that these arrows all point the same way, which cries out for explanation: either one arrow grounds the rest, or a common cause underlies them all.

The puzzle: symmetric laws, asymmetric world

The dynamical laws are (almost entirely) time-reversal invariant. Newtonian mechanics, electromagnetism, general relativity, and the strong and electromagnetic interactions are all symmetric under $t\to -t$: run any solution backward and you get another valid solution. Reverse all the velocities of the molecules in a glass of warm water and the laws happily permit it to unmix into ice and steam. (The lone fundamental exception is a minuscule T-violation in the weak interaction, tied by the CPT theorem to the observed CP-violation; it is far too small and too special to explain the everyday arrow.)

So the asymmetry we see cannot come from the laws. This is Loschmidt's reversibility objection to any purely dynamical derivation of the Second Law: if the microscopic laws are symmetric, entropy should be as likely to have been higher in the past as to be higher in the future; the microdynamics alone cannot pick a direction. The arrow must come from somewhere else — and the leading answer is boundary conditions, not laws.

The strategy: reduce the arrows to the thermodynamic one

The dominant research programme (Boltzmann, and in philosophy Reichenbach, Grünbaum, Horwich, Price, Albert) seeks to reduce the various arrows to the thermodynamic one, and then to explain that by a cosmological boundary condition. The idea:

• The psychological/epistemic arrow reduces to the thermodynamic. Memory and records are low-entropy traces left by past interactions; forming and preserving a record requires an entropy gradient. We remember the past rather than the future because reliable records correlate with the low-entropy past — this is why the accumulation of memory that underlies the experience of passage runs the way it does.
• The causal arrow plausibly reduces too: the asymmetry of cause and effect, and our ability to influence the future but not the past, track the entropy gradient and the proliferation of correlated traces toward the future (Reichenbach's "fork asymmetry" of common causes).
• The radiative arrow (why outgoing, not incoming, spherical waves) is standardly linked to the same initial conditions rather than to any asymmetry in the wave equation, which admits both retarded and advanced solutions.

If these reductions succeed, the whole family of arrows rests on the thermodynamic arrow, and the origin of time's direction becomes the question: why does entropy increase toward the future?

The deep answer: the Past Hypothesis

Boltzmann's statistical mechanics explains why entropy increases — high-entropy macrostates are vastly more probable, occupying overwhelmingly more of phase space, so a system not already at maximum entropy will almost certainly move toward it. But by the same token entropy should be higher in the past too — the statistics are time-symmetric. To break the symmetry one must add a boundary condition: the universe began in an extraordinarily low-entropy state. This is the Past Hypothesis (Albert's term for Boltzmann's insight): given a low-entropy early universe, entropy has increased ever since, in the only direction it could, and that asymmetry — cosmological in origin — is the source of every other arrow. The direction of time is thus not built into the laws but inherited from a special initial condition of the cosmos.

This pushes the puzzle back to cosmology and raises its own questions — why was the early universe so improbably ordered? — taken up on the cosmology page.

Is the arrow in time itself?

A prior, more metaphysical question: even granting all this, is the asymmetry a feature of time itself, or only of its contents? Two views:

• Intrinsic (anisotropy of time). Time has a built-in direction, an orientation independent of what fills it; the entropy gradient merely lines up with time's own arrow. On this view a temporally reversed world would be genuinely different.
• Reductive (asymmetry of contents). Time itself is isotropic — directionless, like the C-series — and "the direction of time" is entirely constituted by the de facto asymmetric distribution of stuff in it (above all the entropy gradient). "Later" just means "toward higher entropy." Huw Price presses the methodological demand for an "Archimedean" standpoint free of temporal double standards, and argues that most purported explanations of the arrow smuggle in the asymmetry they claim to derive.

The reductive view is the majority position among philosophers of physics: the arrow is grounded in the thermodynamic gradient and the Past Hypothesis, not in an intrinsic orientation of time. But it must answer the worry that some asymmetry — for instance, the direction of the Past Hypothesis itself — looks primitive.

Where this sits

The direction of time is a distinct problem from both passage and tense: a B-theoretic block universe with no flow and no privileged present can still be anisotropic, its two temporal ends objectively different. It is the point where the temporal question most directly meets physics, since the arrow reduces (on the leading view) to the thermodynamic arrow and thence to the cosmological boundary condition of a low-entropy past. It also underwrites the experience of passage, since memory grows along the entropy gradient. The next page turns from the structure of time to the objects in it: how things persist through time — the endurantism/perdurantism debate.