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Alek Westover 745 words

Introduction

In this essay I will argue that the Everett interpretation (EI) of QM provides a good interpretation of chances. The primary reason why I think EI gives a good interpretation of chances is that, as a theory of reality, I consider the EI superior to the Copenhagen interpretation because it does not need to tack on a mysterious “collapse” postulate. In the rest of this essay, I’ll argue for another reason why EI gives a good interpretation of chances --- namely, that the EI gives simple and compelling answers to the following questions:

• What should I expect to happen when I perform a measurement?
• How should I act in the face of uncertainty?

The Everett interpretation of QM states that, if I have a system , and then Alek observes this system, then the system evolves to

There is no collapse of the wave function: it always evolves deterministically. Note that more formally, states are factors of the universal wave function. When we say “If Alek measures , he will observe with probability ”, we mean mathematically that the measure of the original state splits into an -fraction measure on “Alek observes 0” and a -fraction measure on “Alek observes 1”.

Making sense of credences over measurement outcomes

On the EI, the statement “Alek observes with probability ” is technically false. EI instead says: the fraction of “Aleks” that observe a is . You can visualize this by imagining having a population of Aleks initially, and this splitting into Aleks that observe and Aleks that observe . If I were one of the Aleks before performing the experiment, then I don’t know if I will end up as one of the Aleks that observes a or a , but I do have a probability distribution over these two outcomes. This is the first way to make sense of chances under the EI --- as an observer you are unsure which branch of the multiverse you will end up in.

Acting in the face of uncertainty

The EI also gives a simple and reasonable answer to the question of “how should I act under uncertainty” that happens to match exactly with the classical interpretation of chances!

First, let’s take the perspective of a particular observer, who I’ll call Tarushii. Suppose that Tarushii can take a bet on the outcome of the measurement of , and is given odds. Should she take the bet? Classically we’d say that the answer is yes iff the ratio is at least . I claim that the EI also supports this conclusion. Why? Well, because generally Tarushii should care (approximately) equally much about the different successors of herself --- the “Tarushiis who observe ” and the “Tarushiis who observe ”, because these successors are pretty similar. Of course in some cases, Tarushii might care about these two successors differently. So really when talking about bets you should calibrate the odds of the bet so that Tarushii is ambivalent over the measurement outcome.

Finally, let’s take an impersonal perspective. When thinking classically about what the moral way to act is, a theory that I find compelling (but which is impractical to implement exactly) is:

Under EI the future is no longer randomized, but instead branches into different possible futures, with different measures. But mathematically we will get the same exact expression! The probabilities of different world states are simply replaced with the weight of the multiverse branch corresponding to that state. In other words, the EI does not imply that you should take different actions than you would with a classical random interpretation of the future, at least if you thought the right way to take actions was the one I described above.

Summary

In summary, I have shown that the EI gives simple and intuitive ways to make sense chances. The simplicity and power of the EI makes it a compelling interpretation of reality.