Implications for cosmological finetuning

One immediate implication of observation selection theory for cosmologi-cal fine-tuning is that it allays worries that anthropic reasoning is fundamentally unsound and inevitably plagued by paradoxes. It thereby puts the multiverse explanation of fine-tuning on a more secure methodological footing.

A multiverse theory can potentially explain cosmological fine-tuning, provided several conditions are met. To begin with, the theory must assert the existence of an ensemble of physically real universes. The universes in this ensemble would have to differ from one another with respect to the values of the fine-tuned parameters, according to a suitably broad distribution. If observers can exist only in those universes in which the relevant parameters take on the observed fine-tuned values (or if the theory at least implies that a large portion of all observers are likely to live in such universes), then an observation selection effect can be invoked to explain why we observe a fine-tuned universe. Moreover, in order for the explanation to be completely satisfactory, this postulated multiverse should not itself be significantly fine-tuned. Otherwise the explanatory problem would merely have been postponed; for we would then have to ask, how come the multiverse is fine-tuned? A multiverse theory meeting these conditions could give a relatively high conditional probability to our observing a fine-tuned universe. It would thereby gain a measure of evidential support from the finding that our universe is fine-tuned. Such a theory could also help explain why we find ourselves in a fine-tuned universe, but to do this the theory would also have to meet the ordinary crew of desiderata - it would have to be physically plausible, fit the evidence, be relatively simple and non-gerrymandered, and so forth. Determining whether this potential anthropic explanation of fine-tuning actually succeeds requires a lot of detailed work in empirical cosmology.

One may wonder whether these conclusions depend on fine-tuning per se or whether they follow directly from the generic methodological injunction that we should, other things being equal, prefer simpler theories with fewer free variables to more complex theories that require a larger number of independent stipulations to fix their parameters (Ockham's razor). In other words, how does the fact that life would not have existed if the constants of our universe had been slightly different play a role in making fine-tuning cry out for an explanation and in suggesting a multiverse theory as the remedy?

Observation selection theory helps us answer these questions. It is not just that all single-universe theories in the offing would seem to require delicate handpicking of lots of independent variable values that would make such theories unsatisfactory - the fact that life would not otherwise have existed adds to the support for a multiverse theory. It does so by making the anthropic multiverse explanation possible. A simple multiverse theory could potentially give a high conditional probability to us observing the kind of universe we do, because it says that only that kind of universe - among all the universes in a multiverse - would be observed (or, at least, that it would be observed by a disproportionately large fraction of the observers). The observation selection effect operating on the fact of fine-tuning concentrates the conditional probability on us observing a universe like the one we live in. This is illustrated by Fig. 24.2.

Further, observation selection theory enables us to answer the question of how big a multiverse has to be in order to explain our evidence. The upshot is that bigger is not always better [7]. The postulated multiverse would have to be large and varied enough to make it probable that some universe like ours should exist. Once this objective is reached, there is no additional

Fig. 24.2. An observation selection acts like a focusing lens, concentrating conditional probability on a small set of observational parameter values.

anthropic ground for thinking that a theory that postulates an even bigger ensemble of universes is therefore, other things equal, more probable. The choice between two multiverse theories that both give a high probability to a fine-tuned universe like ours existing must be made on other grounds, such as simplicity or how well they fit with the rest of physics.

A multiverse would not have to be large enough to make it probable that a universe exactly like ours should exist. A multiverse theory that entails such a huge cosmos that one would expect a universe exactly like ours to be included in it does not have an automatic advantage over a more frugal competitor. Such an advantage would have to be earned, for example by being a simpler theory. There is, as we noted earlier, no general reason for assigning a higher probability to theories that entail that there is a greater number of observers in our reference class. Increasing the membership in our reference class might make it more likely that the reference class should contain some observer who is making exactly the observations that we are making, but it would also make it more surprising that we should happen to be that particular observer rather than one of the others in the reference class. The net effect of these two considerations is to cancel each other out. All the observation selection effect does is concentrate conditional probability on the observations represented by the observer-moments in our reference class so that, metaphorically speaking, we can postulate stuff outside the reference class 'for free'. Postulating additional stuff within the reference class is not gratis in the same way, but would have to be justified on independent grounds.

It is, consequently, in major part an empirical question whether a multiverse theory is more plausible than a single-universe theory, and whether a larger multiverse is more plausible than a smaller one. Anthropic considerations are an essential part of the methodology for addressing these questions, but the answers will depend on the data.

In its current stage of development, observation selection theory falls silent on problems where the solution depends sensitively on the choice of reference class. For example, suppose a theory implies that the overwhelming majority of all observers that exist are of a very different kind from us. Should these radically different observers be in our reference class? If we do place them in our reference class (or, more precisely, if we place their observer-moments in the same reference class as our own current observer-moments), then a theory that implies that the overwhelming majority of all observers are of that different kind would be contra-indicated by our evidence, roughly because - according to that theory - we should have thought it highly unlikely that we should have found ourselves to be the kind of observer that we are rather than a more typical kind of observer. That is to say, such a theory would be disconfirmed compared to an equally simple theory that implied that a much larger fraction of all observers would be of our kind. Yet if we exclude the other kind of observer from our reference class, our evidence would not count against the theory. In a case like this, the choice of reference class makes a difference to our interpretation of our evidence.

Further developments of observation selection theory would be needed to determine whether there is a unique objectively correct way of resolving such cases. In the meantime, it is a virtue of the methodological framework encapsulated by the Observation Equation that it brings this indeterminacy into the open and does not surreptitiously privilege one particular reference class over potentially equally defensible alternatives.

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