What is the true interpretation of the many worlds theory?

[confusedashell]

I've been reading a lot upon the MWI and to my surprise there are more than just 1 interpretation of the "many worlds".
I read a article in the skeptical inquirer where the current was found:

If all these countless billions of parallel universes are taken as no more than abstract mathematical entities-worlds that could have formed but didn't-then the only "real" world is the one we are in. In this interpretation of the MWI the theory becomes little more than a new and whimsical language for talking about QM. It has the same mathematical formalism, makes the same predictions. This is how Hawking and many others who favor the MWI interpret it. They prefer it because they believe it is a language that simplifies QM talk, and also sidesteps many of its paradoxes.

To me this seems more realistic and "sane" than the bizarre version David Deutsch insists on.
This is also what my friend told me 1 year ago when we discussed QM's, but I never understood it, when I think MWI i only think constant splitting, but now I learn splitting is science fiction not reality in this interpretation.

So could anyone explain this "version" in layman terms?
Also why is it still called MWI, when there's only "one world" ? l

Thanks

 

[NateTG]

Instead of thinking of it in terms of a single universe that splits every time a measurement occurs, you could think of it as an infinite number of universes, each of which has a particular result specified for every waveform collapse.

Because the physical rules for each of these individual universes are identical, and they are all strongly deterministic, universes that have common histories are 'parralel'. That is to say, we can't tell which of the universes that corresponds to a particular history we're in.

Now, because there is no interaction between the universes, there is no way to tell whether there are any, except for the one that we're in, so it's possible to think of all of the other universes as purely mathematical constructs.

From a philosophical point of view, this represents a transition from violating Bell reality to invoking strong determinism, since, without these other universes, there's no elegant resolution to the EPR paradox.

 

[confusedashell]

I see, so if MWI turns out to be true the fact of the matter is, me you and everyone is in a 100% predetermined universe, there really is no splitting, because none of us ever "splits" we just follow the predetermined history, right?

 

[muppet]

A question concerning MWI (or not MWI, as the case may be...) is it true to say that Hugh Everett's original relative-state proposal is not well understood?
The book I'm reading at the minute features passages from Everett in the original, and to me it seems relatively clear what he means. But the author repeatedly comments that "this is unclear... it is hard to say what he had in mind..." etc. To me the MWI that each branch of the relative state proposal represents a different world seems to be a corruption of the original, but one that you could argue amounts to a merely semantic distinction with the same underlying structure; albeit one that leads to direct linguistic contradictions between the MWI and relative state variants

For example, in the original Everett explicitly states that there is still only one observer after a measurement has been performed; the MWI says that there is one observer in each of the infinitely many worlds, which are all equally real.

Everett describes the process of measurement as an entanglement between observer and superimposed system. To take the example of an observer O measuring the spin of an electron E in some particular direction:
[tex]\left| ready to take measurement \rangle_{O}\frac{1}{\sqrt{2}}( \left| spin up \rangle_{E} + \left| spin down \rangle_{E})\stackrel{measurement}{\rightarrow}\frac{1}{\sqrt{2}}( \left|sees up\rangle_{O} |spin up \rangle_{E} + \left|sees down\rangle_{O} | spin down \rangle_{E})[/tex]

(apologies for my horrible tex!) His view to me seems to be that our existence is that of an eigenstate in this superposition. There is one observer; he is described by a superposition of eigenstates; his simultaneous measurement of both up and down is real in the exact same sense that the spin is both up and down, or that in the two-slit experiment the electron goes through two slits. Different 'branches' correspond to the subsequent entanglements of each of these eigenstates (which decribe our physicist of having a memory of measuring some determinate property). Of the different interpretions (which I haven't really covered in great detail) the closest to this view seems to me to be the "bare" theory.
Any thoughts??

 

[vanesch]

In MWI, one has to make a distinction between the *physical degrees of freedom* making up "an observer", and the "subjective experience" associated with those degrees of freedom.

The "physical degrees of freedom" are the things that determine the hilbert space of states (for instance, for a single electron, it is the coordinates x,y, and z, together with spin-up and spin-down).

However, with certain STATES of those physical degrees of freedom correspond "subjective observer experiences" (states of mind, if you like). Now, a single physical observer (defined by a certain number of degrees of freedom) can, in MWI, be in a superposition of states that correspond to "states of mind". As such, there is still one single physical observer, but that physical system exists now in "different states of mind". You are supposed to subjectively experience just one of them (the "you" referring to your subjective mind state), and there are "other" you-mind-states which "inhabit the same physical structure" and correspond to the other states of mind in the superposition describing the same physical structure.

In the superposition:

|joe saw electron-up> |electron-up> + |joe saw electron-down> |electron-down>

the two states |joe saw electron-up> and |joe saw electron-down> correspond to the same degrees of freedom (the same "body") and describe the quantum state of that body. However, to each of them corresponds a different "subjective state of mind" and we thus have two "joe-mind states":
one in which "joe experiences an electron-up observation" and
another one in which "joe experiences an electron-down observation".

Moreover, these two different quantum-body states correspond to two different classical body states.

So we can say that the "quantum-body" joe has given rise to two distinct subjective experiences, one in which "joe saw an electron up", and one in which "joe saw an electron down", and these two distinct mind states, both emergent from a single quantum body, will evolve independently one from the other, as if they were "alone in their classically-looking world".

EDIT:
to illustrate this, and to show where it comes from, consider first a single electron. "position" is a degree of freedom associated with an electron, that is, with each different position in space corresponds an orthogonal state in hilbert space. It corresponds to the classical position states of electrons.
The superposition principle of quantum mechanics allows us to have electrons in superpositions of position states: |P1> + |P2> where P1 and P2 are two different points in Euclidean 3-dim space.

Now, assuming for sake of illustration that electrons have subjective experiences, it might be that an electron in position P1 is a "sad" electron, and an electron in position P2 is a "happy" electron.
Well, an electron in the state |P1> + |P2> is then not a "sad electron" or a "happy" electron, or a half-sad electron, but rather, it is a single quantum electron whose quantum state makes emerge two different "electron-states-of-mind": one of a happy electron, and one of a sad electron.

Now, of course, we don't really think that single electrons have states of mind: we need systems with many more degrees of freedom before we usually assume that they can have a subjective experience. Usually, we assume that they need at least the complexity of a cat's brain. The quantum cat is then inhabited by two or more "cat-experiences": a happy-cat-experience and a sad-cat-experience.

The conceptual difficulty some people have with this view is related, not so much to quantum theory per se, but because it puts the finger on a difficult philosophical problem: the mind-brain problem: how does a physical entity give rise to a subjective experience ? How does subjective experience emerge from physics ?
Traditionally, one assumes a 1-1 link between *physical degrees of freedom* (physical objects, say) and an eventual subjective experience. In MWI, one assumes not a 1-1 link with the physical degrees of freedom, but rather with *states* of those degrees of freedom. Through the quantum superposition principle, a single degree of freedom can correspond to several states, and this leads then to several subjective experiences related to one and the same physical degree of freedom.

This 1-1 link assumed implicitly between physical degrees of freedom and subjective experiences is so strong, that we don't have linguistic tools to separate both! It is what confuses many MWI explanations. When we talk about "the observer", do we talk about the physical degrees of freedom (the body) or do we talk about his mind "the subjective experience" ? In a 1-1 relationship, this confusion/identification doesn't matter, but if it is a 1-many relationship, this makes the wording of it difficult.

 

[muppet]

That's a brilliantly clear explanation of how I understood Everett in the original- thank you. This all then sounds quite different from the "actual splitting worlds" interpretation of MWI. Bizarrely, I found out that Wheeler (one of the original proponents of this interpretation) supervised Everett's doctorate, and presented the "actual splitting" version as a reading of Everett!
Can anyone tell me about the criticisms that MWI doesn't yeild the same statistical predictions as the orthodox formulation? I would have expected the maths to be the one unambiguous thing about the interpretation... How does Everett justify the squaring of the probability amplitudes of the standard formulation, and what problem do people have with this?

 

[vanesch]

That's a brilliantly clear explanation of how I understood Everett in the original- thank you. This all then sounds quite different from the "actual splitting worlds" interpretation of MWI. Bizarrely, I found out that Wheeler (one of the original proponents of this interpretation) supervised Everett's doctorate, and presented the "actual splitting" version as a reading of Everett!

The splitting comes from the following consideration:
once a term containing ONE "mind state" of a body is sufficiently entangled with its environment, it will most probably be "irreversible", that it, this mind-state (and the states of the things it is entangled with) will never "de-entangle" (that's the kind of irreversibility one also finds in classical statistical mechanics: it is simply too improbable that the exact right dynamical evolution will take place that disentangles the bits and pieces).

As such, this stuff will then evolve as if it were a whole wavefunction by itself (although it is just a piece of the bigger wavefunction). Handwavingly, we can then say that this "world" did just "split off from the rest" (and that rest consists of just OTHER wavefunctions of a similar kind, which can be seen then also as "split off worlds"). Hence, the single big quantum world can be looked upon as a superposition of almost entirely independent "classical worlds".

Can anyone tell me about the criticisms that MWI doesn't yeild the same statistical predictions as the orthodox formulation? I would have expected the maths to be the one unambiguous thing about the interpretation... How does Everett justify the squaring of the probability amplitudes of the standard formulation, and what problem do people have with this?

I'm a heretic here, I warn you. One of the ambitions of Everett was to DEDUCE the Born probability rule (the squaring of the amplitudes) from the unitary part of quantum theory. There are different arguments that go in that direction:
- there is first of all Gleason's theorem
- then there is Dewitt's argument which shows that all branches of the wavefunction in which an observer notices a deviation of the Born rule will have an infinitesimal Hilbert norm which will go to 0 in the limit of infinite observations
- Deutsch has a "rational decider's" argument in which he shows, by setting up some decision theory, that a rational decider must use the Born rule for his estimations of probability.

Personally, I think all of these arguments are wrong, in that they all introduce a hidden assumption, which is equivalent to assuming the Born rule ; I wrote a paper on that which has however been refused by Foundations of Physics and by the Proceedings of the Royal Society, but not because it was wrong, but because it was apparently trivial. (you can find it on the arxiv by looking for my name (Van Esch) on the quant-phys archive).

However, there is no need to deduce the Born rule ; you can keep it as a postulate that assigns probabilities to the different worlds to be experienced by "you" - in other words, that the mindset that you happen to experience, is generated by this or that state.

Most people would like to assign "equal probabilities" to all worlds as "all of them are realized", but also this uniform distribution is an axiomatic given. So why not take the right one (the hilbert norm) from the start ?

In any case, as I pointed out, you hit the mind-brain problem somewhere with these considerations.

 

[muppet]

Heresy is fine with me... I'm just writing an essay on this stuff atm so criticism is good!