Philosophy · Contested
Roger Penrose's Argument from the Universe's Extraordinarily Low Initial Entropy
Roger Penrose has calculated that the entropy of the universe's initial state was extraordinarily low, corresponding, by his estimate, to a probability of roughly one part in ten to the power of ten to the power of 123, a figure some philosophers and scientists argue constitutes evidence requiring explanation beyond chance under a purely naturalistic framework, though the significance of this fact is itself contested.
The evidence explained
In The Road to Reality (2004) and elsewhere, Roger Penrose calculates, using the Bekenstein-Hawking formula for the entropy of black holes applied to the phase-space volume associated with possible initial conditions of the universe, that the actual initial state of the universe occupied an inconceivably small region of the total space of possible initial conditions consistent with our current physical laws, corresponding to what Penrose describes as odds of roughly 1 in 10^(10^123), a number so large that Penrose himself notes ordinary numerical notation is essentially useless for expressing it meaningfully.
Penrose himself, notably, is not a theist and does not use this calculation to argue for God; rather, he treats it as posing a serious unsolved problem for physical cosmology, arguing that any adequate cosmological theory needs to explain why the universe's initial entropy was so improbably low given the enormously larger phase space of possible high-entropy initial states, a problem he has proposed his own Conformal Cyclic Cosmology partly to address, quite apart from any theological application of the figure.
Philosophers of religion, including Robin Collins, have taken up Penrose's low-entropy calculation as one line of evidence within a broader cumulative fine-tuning argument, arguing that on a naturalistic framework without additional explanatory resources, such an extraordinarily improbable initial condition is more surprising, and thus more in need of explanation, than it would be on a theistic framework in which a purposive agent might be expected to select conditions suitable for the emergence of a life-permitting, structured universe, an application of Bayesian reasoning about comparative likelihoods under competing hypotheses.
Critics of this theological application, including some philosophers of physics, note first that Penrose's own preferred explanation is a naturalistic cosmological model rather than a theistic one, second that appeals to prior probability calculated over a phase space may not be methodologically appropriate for a unique, non-repeatable event like the universe's origin, since probability calculations of this kind are more straightforwardly applicable to repeatable trials, and third that some multiverse or eternal-inflation cosmological proposals could, if correct, offer alternative naturalistic explanations for observed initial conditions through observation-selection effects, though such proposals bring their own well-known theoretical and evidential difficulties.
What it does show
- • The universe's initial low-entropy state occupied an extraordinarily small region of possible initial conditions by Penrose's own widely cited calculation, a fact requiring some form of explanation under any cosmological framework.
- • The fine-tuning argument's proponents have found in Penrose's independent, non-theologically-motivated calculation a scientifically grounded data point for cumulative case arguments regarding the universe's improbable initial conditions.
What it does not show
- • It does not, on Penrose's own view, favor theism, since Penrose proposes his own naturalistic cosmological model to address the very problem he identifies.
- • It does not settle the methodological debate over whether probability calculations over a phase space are appropriately applied to a singular, non-repeatable cosmic origin event.
- • It does not rule out that future naturalistic cosmological models, including multiverse proposals, could offer alternative explanations for the observed low entropy.
Primary sources and literature
- Roger Penrose, The Road to Reality (2004), section 27.13Primary source for the low-entropy probability calculation.
- Robin Collins, 'The Teleological Argument,' in The Blackwell Companion to Natural Theology (2009)Philosophical application of Penrose's calculation within a cumulative fine-tuning argument.
- Sean Carroll, From Eternity to Here (2010)Naturalistic physicist's extended discussion of the low-entropy problem and proposed naturalistic solutions.
Where scholars disagree
There is little dispute about Penrose's basic calculation as a description of the phase-space improbability of the observed initial conditions; there is substantial dispute over its proper theological or naturalistic interpretation, and Penrose himself favors a naturalistic explanatory approach.
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 Blackwell Companion to Natural Theology — William Lane Craig and J. P. Moreland (eds.)
The reference volume: long, technical chapters defending each major theistic argument, with the best statements of the cosmological, fine-tuning, moral, and ontological arguments.
Five Proofs of the Existence of God — Edward Feser
Classical (Aristotelian, Neo-Platonic, Thomistic) arguments defended in analytic form, with sustained attention to what the conclusions do and do not establish.
The Miracle of Theism — J. L. Mackie
The best twentieth-century atheist engagement with the theistic arguments; read it to see which objections actually bite.
Arguing About Gods — Graham Oppy
A rigorous skeptical assessment arguing that no theistic argument succeeds as a proof; the standard opposing benchmark.
The Existence of God — Richard Swinburne
Builds a cumulative probabilistic case rather than a single deductive proof — useful for seeing how arguments combine.