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There are some interesting statistical thought experiments related to observers and the Anthropic Principle such as the Doomsday Argument formulated by a physicist Brandon Carter and later improved by others, e.g. Nick Bostrom.

The many-worlds interpretation of quantum mechanics has a radical impact on these considerations because each Everettian branching creates many new worlds some % of which have their own observers, adding to the total count of observers.

Recently I was wondering - in similar way to how the Doomsday Argument asserts that subjectively you are most likely to find yourself somewhere "in the middle" of all observers which will ever have existed - is there some way to deduce likelihoods (relative count) of possible future lives in a MWI universe, for example depending on their length?

Consider all possible future lives branching out from a specific point in one's life, e.g. birth. Now sort all of them based on their length. Some will be very short, some longer, some very long. In a population of different people lengths of these lives would follow some typical survival-rate curve. However, because of the huge world-branching factor in a quantum multiverse - it would seem that the longer lives would actually be far more numerous than the short ones because the longer they last the more "survival branches" they could produce. Intuitively I would say that the longest possible life would be the most likely/numerous one of all, possibly resulting in something similar to "quantum immortality". But how can this be proven formally? What mathematical methods can be used to approach this problem?

And would this assertion hold in the extremes? For example a 30-year-old person has a much higher probability of surviving until 40 than a 110-year-old has surviving until 120, much less a 120-year-old until 130. Lets say 50% vs 0.01% vs 0.00001%, creating respective relative counts of survival branches.

Another aspect to consider is that maybe it would be better to count individual "observer moments" as units in the statistics instead of whole lives. In that case the longer lives might have another advantage over the short ones because they have more moments for an observer to "find themselves in".

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In thinking of the MWI it is critical to consider the measure-of-reality (amplitude squared, Born rule) of observers, not their "number". The fraction of reality containing such long-lived observers is tiny, so that they are highly unlikely. The probability of you living to very old age in the MWI is the same as the probability of you living to very old age in a single-universe Copenhagen universe - it has to be, they are both interpretations of the same theory.

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  • $\begingroup$ Thanks! Will read up on the Born rule. But I thought that in MWI the probability that some specific state is observed comes from the relative count of the worlds with such state. But that all actually exist. Lets say there is an observer observing a single particle. After the observation there would be many worlds each with a new observer having observed a specific state. And the relative count of these worlds would correspond to the probability distribution. Statistically the observer would be more likely to find themselves in some of the more numerous worlds. Is this view incorrect? $\endgroup$ – kyjo Jul 18 at 1:58
  • $\begingroup$ But that's actually a good point about the compatibility of the different interpretations. Makes me wonder if it's actually true. MWI seems to suggest some very weird (woo woo) conclusions such as the "quantum immortality" thing. When you consider the Schrodinger's experiment from the pov of the cat, the cat will subjectively always survive because both worlds actually exist: the one where the cat is gets poisoned and the one where it survives. No idea how to explain this in terms of the Copenhagen interpretation. Extreme luck? :) $\endgroup$ – kyjo Jul 18 at 2:05
  • $\begingroup$ You need to determine the relative count of worlds, yes, but there are infinite "copies" of each world. The "relative amount" of each world is essentially its probability in the Copenhagen interpretation. And in regards to the cat - yes, extreme luck! There is a small, tiny change, the cat will get lucky; just like there is a small, tiny part of reality that corresponds to this possibility in the MWI. $\endgroup$ – PhysicsTeacher Jul 18 at 4:29
  • $\begingroup$ I think I see my mistake now. I used two different definitions of observer at once. I discarded the "dead" branches from the stats, i.e. the worlds where the observer is dead as a macroscopic life-form. However even such worlds would still continue to branch out same as the "macroscopic-survival" ones, so when we come to some point in time, lets say the 130-year mark, there will be many more words which branched out from shorter lives than those where the person is still alive at that age - probably matching the survival rate expected in a Copenhagen universe. $\endgroup$ – kyjo Jul 18 at 8:44
  • $\begingroup$ You are still counting observers rather than factions of reality. Consider an observer splitting into two: its state becomes $\sqrt{\frac{1}{3}} |1\rangle + \sqrt{\frac{2}{3}} |2\rangle$. And under Copehagen the state is measured, giving two options: 1 or 2. According to your count, 50% of the worlds are in state 1, which does not correspond to Copenhagen (and experimental) probabilities. According to the MWI, there are infinitely many copies of each world, so that 1/3 of them include 1, thus getting the correct (1/3) probability. $\endgroup$ – PhysicsTeacher Jul 18 at 10:19

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