Fine-tuning in the context of Bayesian theory testing
Fine-tuning in physics and cosmology is often used as evidence that a theory is incomplete. For example, the parameters of the standard model of particle physics are “unnaturally” small (in various technical senses), which has driven much of the search for physics beyond the standard model. Of particular interest is the fine-tuning of the universe for life, which suggests that our universe’s ability to create physical life forms is improbable and in need of explanation, perhaps by a multiverse. This claim has been challenged on the grounds that the relevant probability measure cannot be justified because it cannot be normalized, and so small probabilities cannot be inferred. We show how fine-tuning can be formulated within the context of Bayesian theory testing (or model selection) in the physical sciences. The normalizability problem is seen to be a general problem for testing any theory with free parameters, and not a unique problem for fine-tuning. Physical theories in fact avoid such problems in one of two ways. Dimensional parameters are bounded by the Planck scale, avoiding troublesome infinities, and we are not compelled to assume that dimensionless parameters are distributed uniformly, which avoids non-normalizability.
KeywordsProbability Bayesian Fine-tuning
Supported by a grant from the John Templeton Foundation. This publication was made possible through the support of a grant from the John Templeton Foundation. The opinions expressed in this publication are those of the author and do not necessarily reflect the views of the John Templeton Foundation.
- Barrow, J.D., & Tipler, F.J. (1986). The anthropic cosmological principle. Oxford: Clarendon Press.Google Scholar
- Carter, B. (1974). Large number coincidences and the anthropic principle in cosmology. In Longair, M.S. (Ed.) Confrontation of cosmological theories with observational data (pp. 291–298). Dordrecht: D. Reidel.Google Scholar
- Collins, R. (2009). The teleological argument: An exploration of the fine-tuning of the universe. In Craig, W.L., & Moreland, J.P. (Eds.) The Blackwell companion to natural theology. Oxford: Blackwell Publishing.Google Scholar
- Dine, M. (2015). Naturalness under stress. arXiv:1501.01035.
- Glymour, C. (1980). Theory and evidence. Princeton: Princeton University Press.Google Scholar
- Halvorson, H. (2014). A probability problem in the fine-tuning argument, Preprint: http://philsci-archive.pitt.edu/11004/.
- Kolmogorov, A. (1933). Foundations of the theory of probability. Berlin: Julius Springer.Google Scholar
- Linde, A. (2015). A brief history of the multiverse. arXiv:1512.01203.
- Ramsey, F.P. (1926). Truth and probability. In Braithwaite, R.B. (Ed.) The foundations of mathematics and other logical essays (pp. 156–198). London: Kegan, Paul, Trench, Trubner & Co.Google Scholar
- Skilling, J. (2014). Foundations and algorithms. In Hobson, M., et al. (Eds.) Bayesian Methods in Cosmology. Cambridge: Cambridge University Press.Google Scholar
- ’t Hooft, G. (1980). Naturalness, chiral symmetry, and spontaneous chiral symmetry breaking. In ’t Hooft, G., et al. (Eds.) Proceedings of recent developments in Gauge theories of 1979 Cargese Institute. New York: Plenum.Google Scholar
- Wilson, K. (1979). Private communication, cited in L. Susskind. Physical Review D, 2619(1979), 20.Google Scholar
- Yang, R., & Berger, J.O. (1997). A catalogue of noninformative priors, Institute of Statistics and Decision Sciences Discussion Paper, Duke University (http://www.stats.org.uk/priors/noninformative/YangBerger1998.pdf).