Cosmology · Contested
Low-Entropy Initial Conditions and the Arrow of Time
The very low entropy (high order) of the early universe, required to explain the thermodynamic arrow of time we observe, is considered by several physicists to be an extraordinarily improbable initial condition demanding further explanation.
The evidence explained
The second law of thermodynamics states that entropy, a measure of disorder or the number of microscopic arrangements consistent with a system's macroscopic state, tends to increase over time in closed systems. For this to apply consistently to the universe as a whole, and to explain the observed asymmetry between past and future (the 'arrow of time'), the early universe must have started in an extremely low-entropy, highly ordered state, since a system starting near maximum entropy would show no consistent directional change.
Physicist Roger Penrose has calculated, using the entropy associated with gravitational degrees of freedom (related to the smoothness of the early universe as opposed to the clumpiness of a maximum-entropy state dominated by black holes), that the probability of the universe's initial low-entropy state arising by chance among all possible initial states is extraordinarily small, a number Penrose expresses using a double-exponential notation in The Road to Reality (2004), leading him to argue this fine-tuning of initial conditions requires explanation beyond mere chance.
Not all physicists agree with Penrose's framing or his specific probability estimate. Sean Carroll has argued that the appropriate reference class of possible initial conditions and the correct way to assign probabilities to cosmological states are themselves deeply contested issues, and that inflationary cosmology may offer a dynamical mechanism generating the observed low-entropy conditions without requiring a separately fine-tuned initial state, though Penrose has specifically criticized standard inflationary models as not adequately solving this problem and has developed alternative proposals, including his Conformal Cyclic Cosmology.
The debate connects to broader disagreements about whether probability talk is even well-defined for the universe as a single, unrepeated system, since standard probability theory usually presupposes a reference class of comparable cases or a well-defined measure over possibilities, both of which are contested when applied to cosmology as a whole, a concern raised by philosophers of physics such as Craig Callender in discussions of the 'past hypothesis.'
There is no consensus resolution to this problem. Some physicists regard the low entropy of the early universe as a brute, unexplained fact (sometimes called the 'past hypothesis' following David Albert's terminology), others seek dynamical explanations through inflation or alternative cosmological models, and a minority, following Penrose, treat the required fine-tuning as evidence that current cosmological models are incomplete or require significant revision.
What it does show
- • The early universe's entropy must have been extremely low relative to available phase space to account for the observed thermodynamic arrow of time.
- • Some physicists, notably Penrose, calculate this initial condition as extraordinarily improbable under standard probability assumptions.
- • The problem has motivated serious alternative cosmological proposals, including Penrose's Conformal Cyclic Cosmology.
What it does not show
- • It does not establish that any specific probability calculation over cosmological initial conditions is well-defined or uncontested.
- • It does not show that inflationary cosmology fails to provide a dynamical explanation; this is itself disputed among physicists.
- • It does not, by itself, license conclusions about design or purpose behind the initial conditions; this is a separate philosophical inference some draw and others reject.
Primary sources and literature
- Roger Penrose, The Road to Reality (2004), ch. 27-28Original calculation and argument regarding early-universe entropy fine-tuning.
- Sean Carroll, From Eternity to Here (2010)Alternative treatment discussing the past hypothesis and inflationary explanations.
- David Albert, Time and Chance (2000)Philosophical framing of the 'past hypothesis' regarding low initial entropy.
- Craig Callender, 'Thermodynamic Asymmetry in Time,' Stanford Encyclopedia of PhilosophySurvey of philosophical issues in defining probability over cosmological states.
Where scholars disagree
Physicists disagree over whether the low entropy of the early universe requires special explanation, can be explained dynamically (e.g., via inflation), or should be accepted as a brute unexplained boundary condition.
For further study
Primary and secondary sources on both sides of this question. Reading the strongest opposing case is part of the work, not a concession.
The Beginning of the Universe — Alexander Vilenkin (Many Worlds in One)
A cosmologist on why classical spacetime appears to have a beginning, in his own words rather than filtered through apologetics.
The Kalam Cosmological Argument (2 vols.) — Paul Copan and William Lane Craig (eds.)
The scholarly state of the debate on both the philosophical and physical premises.
A Universe from Nothing — Lawrence Krauss
The best-known attempt to make cosmic origins require no cause; note carefully what 'nothing' means in it.
The Big Picture — Sean Carroll
A leading physicist's naturalistic account of reality, including his direct replies to fine-tuning arguments.