According the many worlds-interpretation (MWI) of quantum mechanics, following a decision with possible outcomes $A$ and $B$, with respective probabilities $p_A=P(A)$ and $p_B=P(B)$, a proportion $p_A$ of the universes branching from the decision point have $A$ occurring, while $p_B$ have $B$ occurring. That is, following the decision's outcome there are two families of universes, $U_A$ and $U_B$, sharing the decision point in their past and occurring in proportions $p_A$ and $p_B$.

If I understand the arguments correctly, where a given person's pre-event conciseness, $c_i$, "ends up" — that is, the kind of universe they will perceive continuity with following the event — is random: for all consciousnesses $c_i$ present in the single universe before the event, the probability that $c_i$ ends up in a post-event kind of universe where a given event has occurred is

$$P(c_i \in U_A) = \sum\limits_{u_k \in U_A}{P(c_i \in u_k)} = P(A)$$ $$P(c_i \in U_B) = \sum\limits_{u_k \in U_B}{P(c_i \in u_k)} = P(B)$$

for all specific post-event universes $u_k \in U_A \cup U_B$, and all pre-event consciousnesses $c_i$.

But what is the relationship between the specific universes where two pre-event consciousness end up? Is it the case that all pre-event consciousnesses end up in the same post-event universe:

$$P(c_j \in u_k\mathbin{\vert} c_i \in u_k) = 1$$

Is it even the case that they end up in the same kind of universe, e.g. that

$$P(c_j \in U_A\mathbin{\vert} c_i \in U_A) = 1$$

Or is all that can be said that

$$P(c_j \in u_k\mathbin{\vert} c_i \in u_k) = P(c_j \in u_k) = P(c_i \in u_k)$$

which is some unknown (presumably vanishingly small) probability.

If the latter — if where consciousnesses end up is uncorrelated — then isn't it the case that after any finite time following the any "decision", consciousnesses that experienced the same shared universe prior to the decision will perceive different ones. Won't consciousness that are together now end up scattered across multiverses after a short time?

  • $\begingroup$ It is hard to understand you. By consciousness, do you mean a recording of a measurement result? I believe that you don't think that presence of human beings is relevant - it may be an apparatus that records the measurement outcome. Next, what is "everybody else's consciousness"? Who are these "everybody else"? Other observers, or apparatuses? $\endgroup$ – Sofia Nov 17 '14 at 21:53
  • $\begingroup$ @Sofia: 'Consciousness' may be the wrong word. What I'm trying to get at is this: I will experience some outcome. According to the MWI there are other (new) "mes" that will experience other outcomes. All these "mes" are distinguished by the outcomes they (we?) experience; but only one will be the same as the "me" before the outcome. $\endgroup$ – orome Nov 17 '14 at 22:32
  • $\begingroup$ @Sofia: (Bear with me.) The same is true for all other individuals (not-mes): only one will correspond to a "consciousness" before the outcome. Clearly there will be a "version" of every other person that will experience "my" outcome along with me. My question is: will all of those versions be the same as the ones that were with me before the outcome? $\endgroup$ – orome Nov 17 '14 at 22:33
  • $\begingroup$ Tell me, each individual (or recording apparatus) lives (is present) in another universe? All these universes exist independently of the preparation of the wave-function to be tested, or they appear only when the measurement is performed? My logic says that if many universes exist, an experiment done by a human being won't change the structure of the world - we are not GOD to create universes. They have to be there much before we, the humans, appeared on the earth. So, when do/did appear these universes? $\endgroup$ – Sofia Nov 17 '14 at 23:46
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    $\begingroup$ "only one will correspond to a "consciousness" before the outcome." This is wrong. All consciousness that shares a history correspond to the one before the branch point $\endgroup$ – user56903 Nov 21 '14 at 12:16

If we consider (for several consciousnesses) one event, behaving like a binary quantum measurement, then the former. If we believe that quantum states possess some objectivity, then probabilities of A and B are expected to be the same for all observers. Generally, such “correlations” were the main feature of Everett’s thesis, that expressed in the language of quantum states the thing known as conditionality (conditional probabilities) in probability theory. This trivial case can be expressed as decomposition of a Hilbert space of states: $$ {\mathcal H} = {\mathcal H}_A \oplus {\mathcal H}_B\,, $$ and resulting probabilities are $$ P(A) =\,∥Ψ_A∥^2,\quad P(B) =\,∥Ψ_B∥^2, $$ where $Ψ_A$ and $Ψ_B$ are orthogonal projections of the original state vector $Ψ∈{\mathcal H}$ to subspaces ${\mathcal H}_A$ and ${\mathcal H}_B$ respectively.

For a composite quantum system this “correlated” splitting is implemented as a measurement on an entangled state. A simple example of that is an EPR experiment.

Update: a “correlated” splitting means: the A-version of a consciousness interacts only with A-versions of (other) consciousnesses. The same for B-versions. In other words: there are (almost) no ultimations where A-versions interact with B-versions. “A says B” is a zero-probability event. The sample space is divided to A and B parts (save for measure 0).

But if decision-making has another underlying mechanism (than quantum measurements), then Ī do not know the answer.

  • $\begingroup$ Thanks. That helps me focus the question better (see updated question). I understand that all individuals must see the same a priori probability of ending up in a universe where a given event has occurred. What I'm trying to get at is whether any two given pre-event consciousnesses (in the single pre-event universe) end up in the same post event universe, or even in the same kind of post-event universe. $\endgroup$ – orome Nov 21 '14 at 16:53
  • $\begingroup$ @raxacoricofallapatorius: the scenario Ī described is splitting one pre-event reality (“universe” in your parlance) in two. Both choices “exist” in the multiverse (are physical), but their probability can be different. “Probability” is just a piece of measure theory; it doesn’t imply exactly one event has “really” to happen and that the multiverse missing all alternatives. $\endgroup$ – Incnis Mrsi Nov 21 '14 at 17:05
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    $\begingroup$ Ī updated the text to explain better what does a “correlated” split mean. $\endgroup$ – Incnis Mrsi Nov 21 '14 at 17:24
  • $\begingroup$ It sounds like what I feared is unavoidable: I need to learn measure theory! $\endgroup$ – orome Nov 21 '14 at 18:09

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