## Wednesday, April 28, 2010

### How Many Worlds?

The Many-Worlds Interpretation of quantum mechanics (MWI) has become popular in recent years. Among non-physicists, this popularity may be due to the woo factor - imagining a parallel universe in which I won the Nobel Prize, or I didn't eat the last donut, can be lots of fun. However, it has also achieved a certain popularity among physicists - this I find less easy to understand. Let me explain.

In quantum mechanics, we often have to deal with superposition states. These are states in which more than one outcome for some measurement is possible, and we only know the probabilities of each outcome. For example, the state
(|+> + |->)/sqrt(2)
is a superposition state of a spin 1/2 particle in which the "spin-up" state (represented by |+>) and the "spin-down" state (represented by |->) are equally probable. (Here "up" and "down" are defined with respect to some arbitrarily chosen reference direction - not with respect to gravity.)

In the MWI, a superposition state is taken to mean that the world has split into two branches. In one of these branches, the particle really is in the spin-up state, and in the other branch, the particle really is in the spin-down state.

To discuss the MWI it will be helpful to have an alternative interpretation to refer to. My preferred interpretation (at present) is the statistical interpretation (SI). In the SI, any state refers to a collection of identically prepared systems. A superposition state like the one above represents the case where half of the collection is in the up state and the other half is in the down state.

Now, the weird thing about quantum mechanics is that a superposition state is fundamentally different from merely saying there is a 50% probability of spin up and a 50% probability of spin down. That's because a superposition state can exhibit interference, as in the two-slit experiment.

OK, now that we've got some of the basic ideas down I can start to explain what's wrong with the MWI.

Metaphysical excess: In quantum mechanics, superposition states are formed all the time. According to the MWI, that means that the universe is constantly splitting into new branches. So the MWI posits a near-infinity of additional universes, none of which can be detected from whatever branch we happen to land in. This seems to run afoul of Occam's razor.

Compare this to the SI, in which we simply talk about many runs of the experiment. (We need to do many runs in any case, in order to test the probabilities that result from quantum mechanical computations.)

Worlds don't really split in the MWI: We might expect that, once the universe has split into two branches, those branches no longer have anything to do with one another. However, if that were the case, we would never observe quantum interference! In order to retain interference, the MWI must suppose that the different branches of the universe share a ghostly connection that allows interference to occur.

Compare this to the standard interpretation, in which we say that particles sometimes "behave like a wave." For me, it's much easier to imagine a wave moving through real space than a mysterious connection between universes that are separate (but not really).

The basis problem: When do worlds split? If the answer is "whenever there is a superposition", then we have a problem. In quantum mechanics, we can write a state in any basis we like. So in one basis, a given state will have only one term, while in another basis the same state might have two, five, or an infinite number of terms! So how does the universe know how many branches to split into?

The MWI is not so clear on this. The answer is sometimes given as "when a measurement occurs." Then the appropriate basis for branching is taken to be the measurement basis. But how do we decide what sorts of quantum interactions constitute a measurement? Deciding when a measurement has occured is one of the things the MWI was supposed to save us from. But it hasn't.

Even worse is the answer "when decoherence has occurred." Because, if the evolution of the universe is completely quantum mechanical, as the MWI claims, then decoherence is never complete.

Probability problems: If we have a superposition state that has a 50-50 split, then saying the universe branches in two seems to make sense: we have equal probability of ending up in each branch. But what if the probabilities are 2/3 and 1/3? Or 1/sqrt(2) and (1-1/sqrt(2))? The way MWI deals with this is to assume we start with a large number of identically prepared systems, so that the branching can occur according to the usual quantum mechanical probabilities. But this is just the statistical interpretation, sneaking in through the back door!

The bottom line: The MWI doesn't actually solve the problems it is supposed to solve. It doesn't explain interference, it doesn't solve the measurement problem, and it needs to be supplemented with a statistical interpretation in order to reproduce quantum mechanics. So we have paid a huge price in metaphysical multiplication, and have nothing to show for it!

In my opinion, the MWI is an unnecessary and unhelpful load of metaphysical baggage.

1. I think you said you consider Everett's original interpretation to be different to (and more solid) than MWI which you considered a misinterpretation of his theory -- is that correct and if so are you applying the same alleged problems to his theory?

2. In his original relative-state paper, Everett pointed out that a two-particle superposition state can be given an interesting interpretation: from the point of view of one of the particles, the measurement HAS ALREADY TAKEN PLACE. That is, in a superposition like (|+>|+> + |->|->)/sqrt(2), particle #1 can say that particle #2 is "same as me."

This makes a lot of sense to me. If we are to treat the measurement process in a fully quantum manner, then the measuring device (or "observer") should be treated as a quantum system. Then all that matters is how the experimental system (particle #2, in the example) looks RELATIVE TO THE MEASURING SYSTEM.

Everett did not, in my opinion, fully develop this point of view in his paper. But this relative state point of view is a separate issue from whether each branch of the wave function has a separate, real, existence.

A similar approach, but more ambitious, has recently been tried by Carlo Rovelli, see for example

http://arxiv.org/abs/quant-ph/9609002

I hope to address all this more fully in a later post.

3. I see -- in that case it looks to me that your objections are to the imprecise, popularised version of MWI that I encountered first myself. The resource I found useful was this series of posts (it's very long but worth it) http://lesswrong.com/lw/r5/the_quantum_physics_sequence/.

The basic difference is that the serious version of MWI simply throws away the collapse postulate and takes the Schrodinger equation to be all. (Contrary to popular belief, this is why MWI is preferred by Okham's Razor since it's the collapse postulate that's considered the metaphysical excess.)

When this is followed through, there's no such thing as a discrete world "splitting" off, but rather a continued evolution of superpositions which decohere but do not separate completely and in some circumstances can be brought back together to interact (ie. interference). This is consistent with you pointing out that decoherence is never complete.

Since AFAIK no other interpretation successfully explains the origin of the probabilities, this is a problem common to all current QM interpretations, not just MWI.

I don't know enough to understand the preferred basis objection but just to get it clear: doesn't changing basis measure different aspects of the wave function? For instance if you want to get the positions of some particles do you need to use some specific basis or can you decompose the wave function using any basis?

4. I just had a quick look through the site you linked (thanks!), but my quick responses are:

- This guy is not an expert. (He says so himself,e.g. he doesn't fully understand the no-communication theorem.)

- He confuses decoherence with MWI. I am a big fan of decoherence, but it works in many different QM interpretations (including the statistical interp.) You can have the advantages of decoherence without the metaphysical baggage of MWI.

- He argues for the position basis as the preferred basis, but this solution is known to be flawed.

I admit that I'm not an expert, either, when it comes to MWI. But if I'm going to read up on it, I'll read DeWitt or someone like that, who really knows his stuff.

5. I don't think this addresses the specific points I made. A good paper to look at is Max Tegmarks: http://arxiv.org/abs/quant-ph/9709032. He has the same interpretation as Yudkowsky in that the reasonable interpretation of MW is decoherence and not the magical creation of parallel universes. I don't see how decoherence as the mathematical consequences of the Schrodinger equation has any "metaphysical baggage" since the only baggage it admits to is the equation itself.

Also is there any text you recommend for explaining your statistical interpretation (esp. how it relates to decoherence)?

6. Well, if there are no parallel universes being created, then it doesn't seem accurate to call this a "many worlds" interpretation. If it's just superpositions and decoherence, then it's just the standard interpretation, as far as I can tell. But I'll take a look at the Tegmark article.

7. Oh, and the best textbook for the statistical interpretation is the one by Leslie Ballentine.

8. The Tegmark article was really interesting and informative - thank you! Also the Vaidman article in Tegmark's references. These papers are much more coherent than the Wikipedia version of MWI (big surprise there!).

I suggest we call this version the "No Worlds Interpretation" (NWI). As Vaidman says, "The MWI is not a theory about many objective “worlds”." In the NWI, the only thing that exists is the State of the Universe. Our observable world is only sort of a pale approximation to a tiny segment of this universal wave function.

The NWI avoids the basis problem, since there is no objective splitting of worlds, and the (subjective) perception of a split happens according to decoherence, which itself selects the basis. So I don't have the technical objection to NWI that I had for MWI.

I still think the metaphysics of NWI is problematic, to say the least. The wave function was introduced to help us describe the observable world. Now we turn around and declare that the description is more "real" than the thing being described!

In the NWI, we still need to put in a probability postulate by hand (as in every other version of QM), which means that there is still a statistical interpretation lurking in the background. That means that, in fact, the State of the Universe is NOT the only important quantity in the theory. Rather, there is a whole ensemble of universes out there somewhere.

Finally, I don't see any OPERATIONAL definition of a "state" in any of this. This is a common omission in "postulates of QM" as presented in textbooks. In fact, Ballentine gives the only operational definition of a quantum state that I know of.

It seems to me that we're more likely to make progress with an approach that recognizes our limitations, and that starts from an observable base, rather than by declaring some mathematical construct to be the truth, the whole truth, and nothing but the truth. Rovelli's approach relativises information the way Einstein relativised measurement. I think this could lead to new breakthroughs.

But that's just my own inclination - I guess Tegmark is right that it boils down to whether you are a Platonist or not.

9. I agree with most of these: the popularisation of MWI has had a lot of misnomers. However I don't see any of this as metaphysically problematic. It would be a case of using the world to discover a law or theory (in this case the wave function) and then extrapolating what this theory would say. Isn't this like postulating a relativistic space-time to explain say the Michelson-Morley experiment and then seeing the consequences of the worldview (which in this example would be the various time dilation effects etc). Is the only difference here that the wave function predicts unobservables whereas most theories don't?

PS. I am the same person as Frikle. I just updated my Blogger name as I realised that on blogs like this one where you need a Google account to comment you wouldn't have connected my comments with my blog.

10. I figured that out via the link to your blog on your profile page. (Terrific blog, by the way!)

Certainly there are many examples in physics where theories led to postulating new physical quantities. It seems to me that we take these objects/entities seriously when they have some observable significance, or when they make things mesh together with known physics.

Example 1: General relativity postulates curved spacetime. But GR is not just a way of rewriting Newtonian gravity; its predictions are observably different from Newtonian predictions.

Example 2: The electric field can be considered just a convenient fiction to help us calculate electric forces. But when we learn that electromagnetic waves can carry energy, then we have to treat them as actually existing (or else abandon conservation of energy!).

With the MWI, I don't see any such need, observationally or from the theoretical point of view. It neither solves any theoretical problem nor predicts any new observable phenomena. So why bother, other than because it sounds really cool?