- #1

- 18

- 2

**So my question is, can the MWI state the born rule as a postulate (without deriving) and still be a coherent interpretation of probability?**

The most famous argument against this notion is by Meir Hemmo.http://users.ox.ac.uk/~everett/docs/Hemmo Pitowsky Quantum probability.pdf

"We have made a full circle. In the many worlds theory the Born probability rule cannot be derived from the non-probabilistic part of quantum mechanics, with or without (the non probabilistic part of) rational decision theory.17 And the reason for this, as we just saw, boils down to the familiar problem we began with, namely that the branching is unrelated to the quantum mechanical probability. But, the problem goes even deeper. Not only is it the case that the Born probability cannot be derived in the many worlds theory, but also it is unintelligible to postulate as an additional empirical hypothesis any probability rule of the form: the probability of an observer to find herself on a post measurement branch is equal to the square of the amplitude of that branch in the universal quantum state.18 To see why, let us backtrack a bit and consider what it would mean to identify the quantum measure with probability in the many worlds theory as above. No matter how we understand probability (i. e. as measuring degrees of belief, limiting relative frequency, chance), if probability is supposed to do its job, it must be related at least a-posteriori to the statistical pattern in which events occur in our world in such a way that the relative frequencies that actually occur in our world turn out to be typical. We take this as a necessary condition on whatever it is that plays the role of probability in our physical theory. Now, the quantum probability rule cannot satisfy this condition in the many worlds theory (nor can any other non-trivial probability rule), since in this theory the dynamics logically entails that any combinatorially possible sequence of outcomes occurs with complete certainty, regardless of its quantum probability. As we argued in the previous sections, nothing in the unitary dynamics of the quantum state picks out the Born probability as related in such a way to the frequencies that occur in the worlds, and there are no other features of the many worlds theory which might pick out the Born probability in this sense as opposed to any other ‘probability’ rules. Even for agents like us, who observed up to now finite sequences which a-posteriori seem to conform to the quantum probability, adopting the quantum probability as our subjective probability for future action is completely arbitrary, since there are future copies of us who are bound to observe frequencies that don’t match the quantum probabilities. We know now and with certainty that for some of our future copies the quantum probability rule will turn out to be false. So, if we believe that the many worlds theory is true, it will be utterly irrational for us to adopt the quantum probability rule as our subjective probability for future action (nor any other non-trivial probability rule). Viewed in this way, it is not even clear that rational decision theory is applicable in the many worlds theory.

For these reasons we believe that in quantum mechanics the only way in which the subjective probabilities of observers could be guided by the quantum mechanical probabilities is by adding to the dynamics in the theory a genuine stochastic process. This can be done either by injecting chances into the dynamics (as in collapse theories) or by adding to the theory some stochastic (chance) process over and above the unitary dynamics of the state. However, as to the latter possibility, we have argued in our (2003) that it seems inevitable that adding a stochastic dynamics for the worlds or for the minds over and above the dynamics of the quantum state (e. g. of the kind proposed by Albert and Loewer (1988) in their many minds theory) would turn the many worlds theory into a hidden variables theory of a sort, in which subsets of branches (or minds) have quantitative properties that transcend, and cannot be inferred from quantum theory itself."

So taking account the argument above, can the MWI state the born rule as a postulate (without deriving) and still be a coherent interpretation of probability?