On Tue, Feb 18, 2025 at 12:00 PM Quentin Anciaux <[email protected]> wrote:
> Bruce, > > Consider the following thought experiment, which directly parallels MWI > and illustrates why your argument assumes what it tries to prove. > > Imagine we have a machine that can perfectly duplicate an observer, just > as MWI implies happens during quantum measurements. The experiment works as > follows: > > 1. The observer enters a sealed box. > > 2. Inside the box, they are duplicated into 10 copies. > > 3. Each duplicate is placed in an identical room with only one visible > difference: > > One of them sees a 0 written on the wall. > > Nine of them see a 1 written on the wall. > > 4. The observer, upon exiting the box, can only report what they > personally experienced. > > > > At each step, both events (seeing 0 and seeing 1) occur—so in a naive > branch-counting view, after trials, we should get total sequences. However, > the key insight is that these sequences are not equiprobable because the > number of observers seeing each outcome is different at each step. > That is not true. Each observer sees only one sequence of ones and zeros. The fact that there are more sequences with zeros does not mean that there are more observers on such sequences -- there is still only one observer on each sequence, even if there are many sequences with similar numbers of zeros/ones. After many trials, the vast majority of observer sequences will contain > approximately 90% ones and 10% zeros, despite every individual trial having > both outcomes. The reason is simple: there are exponentially more observers > who experienced the outcome "1" than those who experienced "0". > So what? You are assuming that the observers know the Born probability before they start, and that they each assume that they are typical, so are seeing what the majority of others see. But this is not the case. Each observer sees only his/her own data. They see r zeros and (N - r) ones, say. They estimate a probability of p = r/N of seeing zero. If they assume that this is typical, then they take that to be the Born probability. But they have no way of knowing whether this is the case or not. Recall that in the 2^N binary sequences, all values of r, from 0 to N, are found. If everyone assumes that they are typical, then the estimates of the Born probability will range from 0 to 1, with no one knowing whether or not he/she has the correct estimate. So the observed data (r zeros in this case) is not a reliable estimate of the Born probability, which is a^2. Now, compare this directly to MWI and the Born rule: > > Your argument assumes that all sequences in MWI should contribute equally > to probability estimates, independent of amplitudes. > Each observer has only his/her own observed data to work with. He/she cannot know whether they are typical or not. But this ignores the role of measure—just like in our duplication > experiment, some sequences have far more observers experiencing them than > others. > That is not true. There may be more observers seeing a particular number of zeros (depending on the Born probability). But there is still only one observer on each branch, and one set of data for each observer. The amplitudes of the wavefunction dictate how many copies of an observer > exist in each branch, meaning low-amplitude branches contain exponentially > fewer copies of an observer. > That already assumes the Born rule, which has not yet been agreed. > Consequently, an observer drawn at random from all existing copies will > overwhelmingly experience frequencies aligned with the Born rule, not a > uniform distribution. > And exactly how is an observer to be drawn at random? The best we can have is that each observer assumes (him/her)-self to be typical. And that leads to problems, as we have seen. > By assuming all sequences contribute equally, you implicitly assume that > the amplitude does not matter—which is exactly what needs to be proven, not > assumed. The duplication analogy makes it clear: even with deterministic, > mechanical duplication, sequences are not equiprobable when observer count > is taken into account. > > If your logic were correct, then our duplication experiment should also > result in uniform distributions of 0s and 1s across sequences, which is > clearly false. > No, it would not. It would lead, as I have said, to 2^N sequences, covering all possible binary sequences of length N. The fact that the amplitudes affect observer frequencies is exactly what > leads to Born-rule probabilities in MWI, rather than a naive uniform > distribution. > The amplitudes have no effect. They do not affect observer frequencies on each branch, and do not affect the fact that each observer sees only one set of data. In your duplication example, you have assumed the Born rule at the outset by setting the probabilities to 0.9 and 0.1 for zero and one, respectively. If you do not make this assumption, your example collapses. Bruce -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion visit https://groups.google.com/d/msgid/everything-list/CAFxXSLQ1-UMh40ZXDW9RJgdUw21Je4BRJHa-3Jt5L0DuWZseOw%40mail.gmail.com.
