I don't think most MWIers would agree with this. Normally they consider worlds to have split only once (irreversible, or approximately irreversible) decoherence has set in. An electron in the coherent state |z+> + |z-> = |x+> wouldn't qualify.
In fact, this seems to be one of the biggest difficulties of the interpretation. Nobody knows whether there even is such a thing as in-principle irreversible decoherence, and if there's not, then the point at which it is "approximately irreversible" is arbitrary.
Edit: Add the state change in the measurement
(|z+> + |z->)|obs> => |z+,obs+> + |z-,obs->
First there is an electron in one of two states, and the observer is uncorrelated. After the measurement, the observer becomes correlated with the electron.
For your unentangled state on the left, Sean Carroll explicitly describes it as a state that doesn't have two worlds yet. I can find the post if you like, or maybe we already agree and I'm misunderstanding.
In what I am describing, the two "worlds" don't really separate. It is possible that they can interact, theoretically. However, you can't construct an experiment to detect the different parts of the wavefunction interacting because of decoherence. You just can not make a coherent quantum system that invovles real people (to my knowledge). So in practice you can not do the experiment.In anything we observe, the two resulting observers (in a measurement with two choices) are effectively isolated.
In other words, decoherence is automatic. Also, it is inherently irreversible.
But, I am sure he (or whoever wrote that post) is saying something sensible so I would be interested in seeing it.
"We wouldn’t think of our pre-measurement state (1) as describing two different worlds; it’s just one world, in which the particle is in a superposition. But (2) has two worlds in it. The difference is that we can imagine undoing the superposition in (1) by carefully manipulating the particle, but in (2) the difference between the two branches has diffused into the environment and is lost there forever."
(State 1 is when the particle is in a superposition by itself and state 2 is when it's entangled with a macroscopic apparatus.)
My issue is that he uses words like "forever" and "impossible." These convey a sense of finality, but the decision of where to draw the boundary is subjective. The worlds can in principle (and under certain cosmological models, must) recohere.
See, for example: https://arxiv.org/abs/1105.3796
"Decoherence - the modern version of wave-function collapse - is subjective in that it depends on the choice of a set of unmonitored degrees of freedom, the "environment"."
See in particular Section 3.2 (Failure to irreversibly decohere: A limitation of finite systems)
(Edit: I should mention that I am not a physicist, by a long shot. Just a curious amateur.)
And the MWI postulates a magical branching into different "worlds", doesn't it?
If the universe is an isolated quantum system evolving unitarily, how does the MWI help to understand the laws of physics that we observe?
It definitively answers the question of when wave collapse occurs and what causes it.
The answer given by the Everett Interpretation is simply that there is no wave collapse, and what we observe is the result of our brains being in a superposition of multiple states.
1) we have a one-particle system that has been prepared into a pure state by measuring the spin along the x-axis
2) we are going to measure the spin along the z-axis
3) the quantum state before is a superposition of the |up> and |down> states (in the basis corresponding to the Sz operator)
4) the theory predicts that we are going to find either |up> or |down> with equal probability
5) immediately after the measurement the quantum state will be either |up> or |down>, depending on the outcome
What is the answer given by the Everett Interpretation? What is the description of the initial conditions? What is the prediction of theory? What is description of the end state?
I hope the answer is not just handwaving and mumbling about "superposition".
I don't understand why this would be difficult to understand.
Are you saying they are "now" in a superposition, meaning they were not before the observation?
If so then how can the act of us observing the thing cause us, our brains to go into super-position? And is it just our brain that goes into super-position? Why not the rest of my body too? And what if I'm holding the hand of another person, does she too go into super-position?
If you cannot say that the particle is in a well defined up or down state after the measurement then you cannot say either that it remains in a superposition of up and down states. Because that original state was the result of a previous measurement. You cannot even say that the particle (or you, for that matter) does actually exist. The universe is a superposition of states where it does and states where it doesn't. (Does the universe exist at all?)
The standard interpretation of QM:
- we want to explain the physical world that we experience
- we come up with a theory based on a mathematical description of physical states and the equation describing its evolution
- the theory allows for superpositions of states, incompatible with the physical world where we observe only definite states
- why do we observe only definite states?
- we postulate that when we measure the wave function changes becomes and becomes consistent with the observation
- we also postulate the Born rule to compute the probability of observing each potential outcome
- everything is experimentally verified, there are open questions (what is a "measurement"?) but the theory works fine in practice
- we know that this is not a complete description of the world (gravity!)
The Everett interpretation:
- let's assume that the physical world that we experience is just one aspect of a larger, out-of-reach thing
- what is real is the mathematical description (nevermind that it's incomplete), evolving according to the Schroedinger equation
- why do we observe only definite states?
- because this is the way our brains experience the physical world! (see how easily we solved the issue with measurement?)
- what is the probability of observing each outcome?
- ... (but, hey, did you notice how elegantly did we skipped, I mean, solved the measurement problem?)
- we have a collapse-free interpretation of QM! (but remember that if you want to study the physical world that we experience you have to use the projection postulate, because this is the way our brains experience the physical world)
I find interesting that the MWI is so popular among cosmologist, given that QM doesn't handle cosmological issues well. But of course this interpretation "solves" the problem of why the observed universe is precisely the one that we observe.
Everett's theory is interesting, but not a panacea. Maybe decoherence is the key to explaining "collapse", maybe gravity is the key, maybe the answer is somewhere else...
If you take away any sensient beings, or whatever it is that is required to make one of these "measurements", then copoenhagen is the same as the many world interpretation. Wave functions go on evolving and there is no collapse. For example, an electron can be in spin up or spin down. It is not in both states. In one "world" it is spin up. In another "world" it is spin down. That is strange enough for all of us. But for some reason people have trouble extending this idea to people, so that a person can be in mulitiple states at the same time (in the different "worlds", in the same sense as the electron being in different "worlds".)
What made this strike home to me was when I was in graduate school and my advisor told me "There are no magic external observers. The observer is subject to quantum mechanics too. He is part of the experiment."
To describe the correspondance between copenhagen and "many worlds", suppose an observer measures if an electron is spin up or spin down. In "many worlds" case his memory of the outcome is correlated with the measured state of the electron. So in the "world" where the electron is spin up (that portion of the wave function) the observer also thinks the electron was measured as spin up. And in the "world" where the electron is spin down, the observer thinks the electron was measured as spin down.
In this "many worlds" case, The observer who measures the electron as spin up will not interact with the observer that measured it as spin down. For all intents in purposes, it is as if that other observer never existed. In the copenhagen case, that other observer does _not_ exist. In this interpretation, the wave function collapsed to only include the part with a single observer.
In effect the observed outcome of the two interpretations is the same. The difference being one of them, the copenhagen interpretation, postulates a magical change in the wave function of the universe.
(Aside - The fact that those observers will not interact is just in a practical sense, to my knowledge. I don't know if it is impossible for them to interact in theory. I don't think it is. Maybe someone else knows the answer to that.)