15 April, 2012

Why Many Worlds is Correct

I recently read a four year old article by Eliezer Yudkowsky on why Many Worlds survives Occam's razor. The argument was persuasive enough to cause me to change my mind on a stance I've held for nearly two decades.

The way he explains the issue is a little roundabout, so I thought I'd try my hand at reproducing the basic argument in a more succinct manner. Note that this post assumes some prior knowledge of the Many Worlds Interpretation (MWI) of quantum physics and how it differs from interpretations that involve collapsing wavefunctions. Basically, if you understood the last sentence, you'll be good to go; otherwise the following might be a little jargon heavy. Nevertheless, I'll try to give background where appropriate. (If you're really lost, the best book to pick up is Feynman's QED, but if you're in a hurry, the Everett FAQ can answer basic questions with plain English. It's no substitute for reading Feynman, though.)

Some Background

There are several possible interpretations of quantum theory. MWI explains just as well as any other, but it is often called out as violating Occam's razor. "Stipulating all these extra worlds", proponents of wavefunction collapse theories argue, "certainly counts as extra assumptions." Of course, there's no reason why nature must respect parsimony, just as there's no reason nature must respect induction. Nevertheless, both have proven effective at making correct predictions over time (pun intended), so a good response is needed.

Occam's Razor

The law of parsimony does not refer to complexity in the same way that we use the word in common usage. Most of the time, things are called "complex" if they have a bunch of stuff in them, and "simple" if they have relatively less stuff. But this cannot possibly be what Occam's razor is referring to, since we all gladly admit that Occam's Razor does not imply that the existence of multiple galaxies is less likely to be true than just the existence of the Milky Way alone.

Instead, the complexity referred to in Occam's razor has to do with the number of independent rules in the system. Once Hubble measured the distance to cepheid variables in other galaxies, physicists had to choose between a model where the laws of physics continue as before and a model where they added a new law saying Hubble's cepheid variables measurements don't apply. Obviously, the model with the fewer number of physical laws was preferable, given that both models fit the data.

Just because a theory introduces more objects says nothing about its complexity. All that matters is its ruleset. Occam's razor has two widely accepted formulations, neither of which care about how many objects a model posits.

Solomonoff inductive inference does it by defining a "possible program space" and giving preference to the shortest program that predicts observed data. Minimum message length improves the formalism by including both the data and the code in a message, and preferring the shortest message. Either way, what matters is the number of rules in the system, not the the number of objects those rules imply.

Quantum Mechanics

So when we apply Occam's razor to competing interpretations, we need to be parsimonious with laws, not objects. How then, does MWI stack up?

Theory-wise, MWI is nearly equivalent to other interpretations. MWI will predict what the Copenhagen interpretation will predict, so in terms of accurate predictions, they seem about on par. But while MWI stops there, most other interpretations start tacking on extra assumptions. (Except instrumentalism, of course, but it always wins the parsimony battle, and doesn't really count.)

All theories that posit a wavefunction collapse, for example, are positing something on top of the needed rules that agree with observations (pun intended). Why posit a wavefunction collapse whose only purpose seems to be a method of denying the reality of the wavefunction? Of course, maybe reality is such that the wavefunction does collapse. But Occam's razor would clearly prefer the option asserting fewer assumptions.

"But wait!", say the wavefunction collapsers. "MWI asserts way more stuff than any other theory ever made! Don't you see that the addition of a single simple law of wavefunction collapse does away with having to admit the existence of all the excess crap MWI forces us to believe in?"

Yet they are missing the point. If something is a deductive consequence of the rules of a system, then you get that extra thing for free without having to refer to Occam's razor. As Yudkowski puts it, if P(Y|X) ≈ 1, then P(X∧Y) ≈ P(X). All the "excess crap" that gets posited into existence with MWI is just the deductive consequence of the quantum theory all interpretations agree upon. Even in wavefunction collapse theories, many worlds exist until the collapse occurs. The extra rule positing a collapse is the real "excess crap".

Parable of the Invisible Spaceship

If you're still not convinced, consider Yudkowski's implied invisible spaceship.

"Suppose you're going to launch a spaceship, at nearly the speed of light, toward a faraway supercluster.  By the time the spaceship gets there and sets up a colony, the universe's expansion will have accelerated too much for them to ever send a message back." They will be unable to interact with us even in principle, as they can never intercept our world-line. "Do you deem it worth the purely altruistic effort to set up this colony, for the sake of all the people who will live there and be happy?  Or do you think the spaceship blips out of existence before it gets there?"

If you're like me, you'll find it intuitive to believe the spaceship and its colonists continue existing, even after they reach the point of no return, because claiming they cease to exist requires extra laws that wink them out of existence when they get too far away. Parsimony demands that we accept implied invisibles.

A Personal Note

Although I only just recently was convinced of this stance by Yudkowsky, the basic argument is quite old, and I really should have run into it before now.  I guess the main reason I never did is because quantum physics was something I spent a lot of time on while I was still young, and I just haven't kept up with the field since I was a teenager. Since I didn't encounter Bayesian probabilities until studying philosophy of science at Spring Hill College, I just never put two and two together. Let this be a lesson to myself to never stop learning, and always update old beliefs with newly acquired information. (c:

Oh, and by the way, if you're wondering why I called this write-up succinct, you should see how much Yudkowsky writes on the topic.


  1. Just as a point of clarification from questions I've received on facebook: this article is meant to show that Occam's Razor is not a good reason to dismiss MWI, but is instead a reason in favor of MWI. However, that doesn't mean MWI is necessarily correct -- only that it is more likely to be correct than I had before considered. There's still other issues with MWI that prevent it from being strictly better than other interpretations, such as the the Born rule. But my new stance puts it on equal footing with any other interpretation I've looked at.

  2. MWI has a lot of implicit assumptions which makes it almost identical to other interpretations in terms of parcimony: what is an observer inside a "world" and how probabilities are assigned to it.

    Moreover, relational interpretations survive much more to Occam's Razor. They don't posit the existence of an absolute objective reality: that's one less assumption.

    1. You give two examples of implicit assumptions: what constitutes an observer, and how probability is assigned. While the latter is a real problem (the Born rule does seem a bit ad hoc), the former is just not factually true. The measurements MWI talks about are just interactions that correlate values between otherwise distinct systems. They do not require the concept of an observer. Admittedly, Everett didn't bother defining his terms well in his paper, but I think current MWI supporters would never claim a requirement of observers.

      However, your relational interpretation comment is indeed strictly true. MWI does assume objective reality whereas Relational QM does not.

    2. Ok you are right that observers are not a necessary feature in MWI, only measurements are. Yet the question of phenomenology is not adressed.
      As long as other possible worlds are assumed to be as real as our own world, then our past and future, and even every possible pasts futures, can be considered "real" as well (especially if we introduce general relativity: there is no absolute simultaneity, thus no time frame that could be considered the only "real" one).
      In a sense, it is like saying: ok, we don't want to constraint our view, Occam's razzor you know, but then, just everything we can imagine exists on the same level. Then does the verb "exist" mean anything at all? How to account for simple phenomenology (and the associated probabilities -- the problem is actually related)?

      One could argue these questions are beyond the sole scope of physics: they involve philosophy of science and maybe philosophy of mind. But precisely, Quantum Physics challenges those fields, which MWI (but collapse theories as well) seems to neglect. For example, the fact that the formalisation of QM is akin to a generalisation of probability theory...

      I think we shouldn't forget that scientific theories are produced by our thinking abilities and are supposed to account for our experience. As Bohr sais, physics concerns "what we can say about nature". It is not supposed to reveal some transcendant metaphysical reality...

    3. While at one level I feel compelled to agree with the sentiment behind what you are saying, I nevertheless find myself disagreeing with your specifics.

      Consider Yudkowski's implied invisible spaceship. Once it travels a specific distance, nothing about this ship can ever reach us, even in principle. They are no longer causally connected to us in any way. Yet we still are willing to grant that the ship exists. In a way, this is a form of revealed transcendental metaphysical reality.

      If it stopped existing, that would imply that several other laws stopped working for no good reason. Conservation of energy, second law of thermodynamics, etc. So we assume it continues existing even though we will no longer have any access to it whatsoever.

      All I'm saying is that we should apply the same kind of thinking to QM. QM implies things interfere with themselves, hence the default position should be that there are several things in existence doing the interfering. Maybe MWI is wrong, but it seems like it should be the default view from which other interpretations must do better in order to make up for their extra rules that claim these things do not exist.

      I'm not saying the phenomenology of MWI isn't an issue for philosophers. It definitely is. But it doesn't count when it comes to considering Bayesian probability. All that Occam cares about is the rules of the system, not the implied invisibles it creates.

    4. Just a few remarks:
      - the things that interfere together (superposed states) cannot be measured separatly. Only the consequence of their interfering can be measured. This is a subtle difference with the spaceship: the nature of superposed state is primarily representational (their genuine existence is a metaphysical speculation), while the spaceship is very concrete.
      - We can never be sure that the spaceship did not explose for some unknown reason just after it left us. In that sense, we cannot really state that the spaceship still exist once it left our horizon. Any assumption of existence is subordinated to a possible measurement, and I can't think of any reason why this rule should not be applied to QM.
      - A prior measurement is required before you can build a wave-function "of something" and this wave-function is relative to what is measurable. Then how could there be a "wave-function of the universe"? In relation to what? It sounds a bit absurd.

      Having said that I understand the appeal of MWI: it is the best interpretation (as you said the "default view") as far as one consider that a "God-view" representation of the world is possible. In my view, MWI highlights the failure of such representations.

  3. I'm on a mobile device, but I think the author over complicates other theories like how she or he asserts others over complicate MWI. Also, I would like to know why I should favor or consider MWI over instrumentalism or any interpretation that has no additional baggage.

    1. Instrumentalism is not an interpretation; it is the lack of one. So it is unclear if it even really counts when it comes to applying Occam's razor.

      I've heard proponents of the ensemble interpretation claim their view requires no assertions, but that's just wrong. They refuse to take the math of QM seriously when it comes to single particles, which counts as an extra rule that Occam would disapprove of. Ignoring math's description of reality when only one particle is described is not more parsimonious, but less.

      As for other interpretations, they all seem to have baggage, too -- MWI included. MWI asserts the Born rule; Copenhagen interpretation asserts wavefunction collapse; relational QM asserts no objective reality; etc. No interpretation is assertion free, except possibly instrumentalism, and that's just equivalent to not even trying.

      The point of the article is to show that Occam's razor does not discriminate on the multitude of entities MWI implies, and so MWI is "in the game" as it were when it comes to quantum interpretations. Furthermore, some popular theories do seem to assert even more than MWI does. Asserting wavefunction collapse at a certain threshold size is a *much* bigger assumption than assuming Born probabilities are chosen in a particular way, for example.

    2. So your article is just to point out that metaphysical parsimony and Ockham's Razor are not equivalent? I thought that was obvious?

      More to the more, MWI has to do, I think, quite a bit of extra work to be taken as a serious interpretation. In particular it needs to explain how the world has "branch", explain what the ontological consequences of this are, etc. I think these rules will end up being far more complex than rules of wave collapse, etc.

    3. "So your article is just to point out that metaphysical parsimony and Ockham's Razor are not equivalent? I thought that was obvious?"

      As embarrassing as this may sound, yes. I learned physics well before I started learning philosophy, and by the time I learned philosophy, I had long abandoned physics. I only just now put two and two together when I stumbled upon an article on Less Wrong.

      To your second point, I'm not sure that it takes additional explanations to explain branching. The math seems to indicate branching occurs; when other interpretations include their assertions, the effect is to claim the math "doesn't count" when it describes such branching.

      Of course, I'm not saying MWI is definitely correct. I'm only saying that it seems like Occam's razor is more in its favor than I ever previously thought. Maybe you considered MWI on par with other interpretations all along, but it is a new idea for me to realize that Occam's razor would favor MWI over the Copenhagen interpretation, for example.

    4. "Instrumentalism is not an interpretation; it is the lack of one. So it is unclear if it even really counts when it comes to applying Occam's razor."

      That is a good point. It seems like a similar rule could be applied, but I am not sure if Occam's Razor applies either.

      I'm not so sure about your second paragraph. What interpretations ignore single particle cases?

      "No interpretation is assertion free, except possibly instrumentalism, and that's just equivalent to not even trying."

      I take issue with that. Why should we try to interpret QM? At this point in our understanding it seems like we are all blind people guessing the color of the wallpaper.

      There are worse interpretations of QM, I'll agree to that. I need to reexamine other interperatations first before agreeing it is comparitavly good however.

    5. "As embarrassing as this may sound, yes. I learned physics well before I started learning philosophy, and by the time I learned philosophy, I had long abandoned physics. I only just now put two and two together when I stumbled upon an article on Less Wrong."

      Fair enough haha. Shock was more at the article you summarised, than you learning that, or at least that's what I should have conveyed more clearly.

      Personally, I'm suspicious of how strictly we should interpret mathematics, particularly in cases such as the world branching. While the mathematics says that there's a branch, that's not a physical explanation for how there's a branch. I'm off the opinion that any mathematics that cannot be given a physical interpretation and explanation is either i) incomplete; or ii) surplus structure, mathematics that we require to achieve a physical statement later down the mathematical chain.

      So saying that the mathematics "shows" that the world branches is insufficient for me. I need some physical account of what happens when a photon in a superposition state is measured and we result in a world where it's spin up and one where it's spin down; what's the physical process that splits the world thus? There's nothing in the QM formalism to answer that question.

  4. Occam's razor is just a general guideline, a tool that can help you save time by determining the most likely avenues to pursue. Nothing has to survive it.

    1. That's a great use of Occams razor, but it isn't the only use.

      Consider the questions of what statements we are justified in believing. I don't know about you, but I think Occam's razor is a great tool to distinguish between which statements are more deserving of belief.

      It is in this way that Occam's razor is useful in choosing between quantum interpretations. If two interpretations both equally fit the available data, it just makes more sense to prefer the interpretation that introduces fewer extra assertions. Not as a tool to figure out what to test next, but as a method to determine which interpretation is more likely to be true.

    2. sure, but the truth is often stranger than fiction, and nature is stuffed full of highly improbable phenomina that could (incorrectly) be explained by far simpler stories.

    3. Agreed. But surely when you decide on which stuff you put your faith in, it just makes more sense to bet on the stuff that isn't improbable.

      After all, I'm not talking about believing in stuff that disagrees with evidence. I'm talking solely about differentiating between two possibilities that equally explain data. (Technically the length of the data also counts, but please ignore this overly specific distinction for clarity.)

      If science finds evidence that X causes Y, then Occam's razor prefers the idea that reality is such that X causes Y. Maybe this is wrong, and X does not in fact cause Y, but all the available evidence indicates that X causes Y. To the extent that evidence exists, we should prefer putting our faith in what Bayesian probability dictates. Period. You're correct in saying we might be wrong, but to prefer belief in something Occam's razor disagrees with is simply not rational.

      (I do not mean any of this as an insult, and I hope you'll take what I'm saying in the manner it is intended.)

    4. "To the extent that evidence exists, we should prefer putting our faith in what Bayesian probability dictates. Period. You're correct in saying we might be wrong, but to prefer belief in something Occam's razor disagrees with is simply not rational."

      I suppose. but this assumes that we can know all of the relevant data needed to correctly calculate the probabilities in the first place. which we cannot be certain of. and even if we do this, improbable things happen all the time.

  5. I've seen strong argument that Occam shouldn't weight data the same as it weights code. I've not seen strong argument that the weight of data should be zero.

  6. it is always fun to contemplate the MWI!

    Beyond physical phenom like 'observers altering outcomes' and thought experiments like the dead/live cat, MWI gets a boost from the famous "multiple dimensions" explanation for the Gravity problem.

    So, the problems solved by MWI are: behavior of light, observers perverting outcomes, and explaining gravity.

    Perhaps Occam's Razor would rather lead us to accept we are not-yet-complete with our models of (light/observer/gravity), than allow MWI to explain what "happened"?