Hey, your response is reasonable as well, and I really do appreciate your reaching out to me. From a mathematical standpoint I totally “get” the notion that you have to account for all possible outcomes of the universal wavefunction and that they are “real”. As you note, a problem MWI has is that people (including many popular press physics books) tend to almost immediately get mystical and start postulating parallel worlds, quantum immortality, etc.
So since you seem to be a nice person, would you indulge me and tell me if I understand the differences in these interpretations correctly or not? I also have one question at the end that maybe is just naïve, but would appreciate somebody knowledgeable telling me about.
Let me begin by setting up a situation and then explaining how I think quantum mechanics works, and then how I think both Copenhagen and MWI interprets the event. Not doing this to be tedious, but rather recognizing that my interpretation could be incorrect and that leads to my questions being nonsensical. So let’s say that you have a sample of a radioactive isotope. The wavefunction can tell you that there is a probability (p) that when you next observe the isotope it will have decayed. You then observe the sample and find out its state at that precise moment.
The Copenhagen interpretation would say that the wavefunction “collapsed” and the state of the system is known with certainty at that moment. Copenhagen does not explain how the collapse happened – that is it specifies no physical mechanism for how the universe decided whether the isotope decayed. Basically it says some things, like radioactive decay, are just actually random/stochastic .
The MWI interpretation would say that the wavefunction bifurcated at that point and we just happen to be along one branch of the two (or more I suppose) paths that the wavefunction could have taken, but that the other branch is still “real” in some sense (and this is where the mysticism seems to come in.) Critically, I think, is that even though the other branch is still “real” it does not affect future probabilities along the branch we are on. That is, if we observe our sample and find that we are on the path where it did decay, the path where it did not decay – and future probabilities along that path – is no longer relevant to our world. They big difference (I think) is that in MWI the universe never has to decide how to determine whether the isotope decayed or not. Along one branch it did and along another branch it did not, and “I” exist along both paths and observe the relevant outcome on both paths. There is an illusion that the universe did decide because of my own observational bias of only seeing the path I am currently on.
It seems like the main difference between the two theories is whether or not stochastic processes (like radioactive decay) are truly stochastic or not. In Copenhagen we assume that the universe really did have a purely random element to it which actually decided whether the sample decayed. MWI says fundamental randomness is an illusion – the probability of following a given path is completely deterministic but because of observational bias it just seems like there was a random element to the outcome. As a field physics dislikes having a truly random event because it is essentially unexplainable in physical terms. If we have two samples of a radioactive isotope, we cannot provide a physical reason for why one specific sample decayed and the other did not.
So, if my understanding above is broadly correct, on to my question- and I fully recognize that I am about to veer off here into some uncharted waters.
Again, there are certain events in the universe, like radioactive decay, that we model as stochastic. Early on, it was hypothesized that where QM models contain random processes were really just places where we did not understand some unobserved physical process. That is, there really is some physical process which determines whether a specific isotope decays at some specific time but we just don’t know what the process is. I believe this was largely Einstein’s early argument. Bell’s theorem basically says this is not the case – that there can be no “local hidden variables” which, when incorporated into a physical description of the world will match the predictions which quantum mechanics will make assuming truly stochastic outcomes.
So, if that is true, does not this eliminate the potential for the tiny “compactified dimensions” postulated by string theory and its many variants having any influence on quantum mechanics? (Yeah, I know I just really veered off the deep end here.) When I read about string theory they assert that they are trying to unify QM and general relativity. One way they do this is by postulating more than 3 spatial dimensions, and arguing that, while those extra dimensions are not available in the normal world they are somehow available at very, very small scales (I assume at scales smaller than the Plank length?) But QM already fully describes the universe (except for gravity) in three spatial dimensions with certain things described as stochastic processes, and Bell’s theorem essentially says that those stochastic processes cannot be “local hidden variables” that describe some physical process (or that describe it better than the QM stochastic processes.) So it seems like if these extra dimensions exist they cannot have any effect on QM or the predictions it makes. Because if they did, that would be a “hidden variable”, wouldn’t it? Or am in mis-interpreting either the purpose of the extra dimensions or the meaning of the “hidden variables” (or perhaps extra dimensions are not “local” hidden variables but are universal?)
Again, thanks for indulging me and thanks for reaching out.