Distinguishing Our Universe From Other Similar Universes In The Multiverse.

Srednicki and Hartle have raised an interesting concern recently about a limitation on the predictive power of multiverse theories. They observe that in multiverse theories, exact snapshots of our universe happen several times in different places. So if we want to have a physical theory that describes our universe, the one we live in, then the question arises: how can we tell which one it is from all the others?

From the paper:

Theories of our universe are tested using the data that we acquire. When calculating predictions, we customarily make an implicit assumption that our data D₀ occur at a unique location in spacetime. However, there is a quantum probability for these data to exist in any spacetime volume. This probability is extremely small in the observable part of the universe. However, in the large (or infinite) universes considered in contemporary cosmology, the following predictions often hold. 

• The probability is near unity that our data D₀ exist somewhere. 

• The probability is near unity that our data D₀ is exactly replicated elsewhere many times.  An assumption that we are unique is then false.

This paper is concerned with the implications of these two statements for science in a very large universe... 

The possibility that our data may be replicated exactly elsewhere in a very large universe profoundly affects the way science must be done.

In order to solve this problem, the authors propose creating a "xerographic distribution" ξ.  Given the set X of all the similar copies of our universe in the multiverse, this xerographic distribution ξ gives a probability that we are the specific snapsot X_i of that set.

The authors claim that this distribution cannot be derived from the fundamental theory.  The fundamental theory can only predict the structure of the whole universe at large, not which snapshot in it we happen to be.  However, given a certain ξ, we can use Bayes Theorem to test which ξ appears to be most correct, and once that ξ is established, we have now a statistical likelihood hinting at which universe in the whole multiverse is ours.

So, given a fundamental physical theory T and a xerographic distribution ξ, the authors say:

We therefore consider applying the Bayes schema to frameworks (T,ξ). This involves the following elements: First, prior probabilities P(T,ξ) must be chosen for the different frameworks. Next, the... likelihoods P^(1p)(D₀|T,ξ) must be computed. Finally, the... posterior probabilities are given by

The larger these are, the more favored are the corresponding framework.

The authors then go on to give some examples of how this might work and solve issues with Boltzman Brains etc...

So, just to repeat:

1. One glaring problem with multiverse theories is our universe happens several times in several places throughout the multiverse.
2. However, we would like a good physical theory to make predictions about the snapshot we happen to live on.
3. The fundamental theory of the multiverse cannot tell us which snapshot we are.
4. However, creating a xerographic distribution ξ we may be able to put probability estimates of which copy is ours using Bayes Theorem.

Some further thoughts and Questions.  I remind the readers, as crazy of a topic this paper covers, it did get published in a respectable journal: Physical Review D.  However, while reading the paper I had several thoughts come to mind and I would appreciate your own thoughts on these issues:

1. How should we feel about multiverse theories given issues like this arise?
2. Can only tenured professors get away with writing such articles?  IE... if a grad student wrote papers like these will universities take him/her seriously when applying for a faculty position?
3. What is your "exact other" in the "other snapshots" doing right now? :) 

Srednicki, M., & Hartle, J. (2010). Science in a very large universe Physical Review D, 81 (12) DOI: 10.1103/PhysRevD.81.123524