sex with ducks

Thanks to a Nadder, I just discovered the music of Garfunkel and Oates. You really need to listen to the (need I say NSFW) "sex with ducks" track.

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.

Free Will Index

An index to my series on free will:

1. Free will and quantum mechanics
2. The Consequence Argument
3. Some Uninteresting Questions
4. Sphexishness and Other Concerns About Predictability
5. Electrons R Us!
6. Quantum Mechanics Revisited
7. The Problem of Free Will - Solved!
8. A Libertarian's View  
9. Varieties of Libertarianism
10. Caused But Not Determined
11.  Ekstrom's Solution
12. My Gut Says, "Meh..." 
13. Indeterminism Where?
14. Not All Things Considered 
15. Command or Description?  
16. Level With Me
17. Level With Me Again

I make no claim to originality in any of this. My views have been largely shaped by Daniel Dennett's books, but my take on the importance of quantum mechanics for free will is somewhat different from his. A nice collection of articles about free will is linked at this FRDB thread. See especially the articles there from the Stanford Encyclopedia of Philosophy, and this set of articles from the Routledge Encyclopedia of Philosophy.

The Problem of Free Will - Solved!

I decide to pick up my pen - I reach for my pen - and my hand moves in accordance with my will. The connection between my conscious thought and my actions is an empirical fact. If this is free will, there are few who would deny we have free will. And this, I think, is the only sort of free will that really matters.

(Daniel M. Wegner, in The Illusion of Conscious Will, argues that the connection is not nearly so close as our intuition suggests. He points to phenomena such as automatic writing, hypnosis, and multiple personalities that indicate it's possible for there to be action without the feeling of will, and will without a corresponding action. This may well be true, but the "normal" connection of will and action persists nonetheless.)

To summarize what I've been writing about:

• - We need not fear determinism, for the world is not deterministic.
• - We need not fear the fixity of the future; that is the fatalist fallacy.
• - We need not worry that strict microscopic laws of physics allow our every action to be predicted, because chaos and quantum mechanics will not allow such predictability.
• - We need not worry that the electrons are in control, because the electrons are us.

So it seems there's nothing much left to worry about. As Daniel Dennett puts it in Elbow Room (p.169):

When we look closely at the sources of our suspicion and dread, we find again and again that they are not indisputable axioms or overwhelmingly well-supported, empirical discoveries, but unfocused images, hastily glanced at - like the shadows on the bedroom wall that take on an apparent robustness and menace precisely because we do not look at them closely.

There are other varieties of free will discussed by philosophers. Some would prefer an immaterial spirit that somehow affects our material bodies. Others attempt to create free will out of the very quantum jumps that (perhaps) leave our actions unpredictable. 

But the plain ability to decide to reach for my pencil, and then to do so, seems to me a variety of free will "worth wanting," in Dennett's phrase. If I can make my body do what my thoughts choose to do, what more could I want? To defy the laws of physics? Wishing for a supernatural miracle, or a natural, quantum-mechanical miracle, is as pointless as wishing I could leap tall buildings in a single bound.

I do not need such miracles to be content. I can glory in the notion that all of the human race's complex thought is a result of purely physical processes, and that those processes are the result of millions of years of evolution. From simple one-celled organisms whose only need was to find the next organic molecule to devour, through uncountable small changes in the ability to respond to the environment, and hence the ability to survive, came the amazing information-processing creatures we call humans. That's a heritage we can be proud of.

Quantum Mechanics Revisited

Looking back over my free will posts, I see that sometimes I seem to be saying that quantum mechanics is important for free will, and sometimes I seem to be saying the opposite. Let me see if I can clear things up.

I have addressed several different issues regarding the free will debate, and quantum mechanics relates to each issue differently.

Determinism and the Consequence Argument: To the extent to which the Consequence Argument depends on the premise of deterministic laws of nature, quantum mechanics is certainly relevant. Since quantum mechanics is an indeterministic theory, if quantum mechanics is a true description of the world, then the Consequence Argument fails. However, we have seen that the fear behind the Consequence Argument is not really the fear of determinism, but of lack of control: If the electrons are in control, then I am not in control. The problem then is not deterministic laws of nature, but any sort of microscopic laws at all.

Predictability: Suppose someone were to write a computer program that accurately predicts everything I will do and say tomorrow. That would be a huge blow to free will (though perhaps not a fatal one). How can I be anything more than a machine if a mere machine can duplicate my actions? Here, I claim quantum mechanics is relevant. Accurate prediction of a classically chaotic system will run up against the quantum limit in a very short time, forcing us to adopt a quantum description. But a quantum description will never produce perfectly accurate predictions: first, because the computer cannot completely replicate my quantum state (thanks to the no-cloning theorem), and second, because quantum predictions are only probabilistic (even if the exact quantum state were known).

Control: Here it gets a bit tricky. We have seen that for me to be in control of my actions, we need a fair amount of determinism in the world. I have been arguing that quantum mechanics has enough indeterminism to make effective prediction impossible. Does quantum mechanics leave us enough determinism for moral responsibility? I suspect it does, but this point clearly needs more investigation.

For now, let me just say that I think the way to proceed is by distinguishing the lower-level and higher-level laws of nature, as I began to do in the previous post.

Electrons R Us!

An imaginary scenario of NASA headquarters as a new robotic Mars rover begins its mission on the surface of that planet: Evelyn, the software engineer who wrote the code that allows the rover to pick its way across the Martian surface without running into rocks and cliffs, has invited her philosopher friend, Pete, to watch the rover's progress. Evelyn exults as the rover successfully negotiates one obstacle after another, and brags to Pete about how well her control program is working. Pete, however, complains, "It's not your program that controlling the rover; it's just electrons in those electronic circuits following the laws of physics!"

At this point, I can only imagine Evelyn standing there agape, thinking of the years she spent developing that software, unable to come up with any kind of non-insulting reply.

Pete is guilty of level confusion: his objection amounts to the claim that if a physical description of the rover at the level of electrons is correct, then any other description of the rover's behavior must be incorrect. I think the free will deniers are guilty of the same thing.

(Note: I am not making the claim that human brains are like computers in any particular way. I am only proposing the rover story as an analogy to help us understand different levels of description.)

Let's recall Argument #2 from this post:

Argument #2 - Causal Determinism is a Necessary Condition for Moral Responsibility Premise 1: Unless there are extenuating circumstances, persons are (to be) held morally responsible for their actions. Premise 2: Being unable reasonably to have foreseen the consequences of their actions is one such extenuating circumstance. (Recall that young children who cannot reasonably foresee the consequences of their actions are not to be held morally responsible for the consequences.) Premise 3: In order to be able to anticipate or foresee the likely (or even the remotely likely) consequences of one's actions, the world must not be random, i.e. the world must be fairly regular (or causally determined). Thus: Moral responsibility requires that there be causal determinism.

This argument, I think, is sound. In order for there to be moral responsibility, I want my actions to be causally determined. Determined by what? By me, of course! But what am I? I am my thoughts, feelings, desires, beliefs, and so forth. But if we are right in assuming that the mind is a purely physical entity (no magic allowed!), then thoughts, desires, etc., are all the results of some sort of electro-chemical activity in my brain.. ("We are electrons, and electrons are us.") And if my actions are to be determined by my thoughts and desires, then they ought to be determined by those patterns of electrical activity that are the physical counterpart of those thoughts and desires.

So if free-will deniers claim that we can't do other than what we did because "it's all just electrons" following the mindless laws of physics, they are committing the same sort of level confusion as Pete.

There can be a low-level description of an action that consists of electrons following physical laws. And there can be a high-level description of the same action that consists of mental states like thoughts and desires. And there need not be any contradiction between the two descriptions, any more than there is a contradiction between the electron-level description and the program-level description of the rover. At the physical level, all we see is electrons affecting the motion of other electrons. But at the mental level, we have desires affecting thoughts, thoughts influencing desires, and, crucially, a mind capable of reflecting on its own mental state.

Free will is something that exists at the mental level; it is a characteristic of the relationship between thoughts and actions. To try to look for it at the level of electrons is to commit a category error - just as it would be to look for a FOR loop inside the rover. ("All I see is electrons!")

Sphexishness and Other Concerns About Predictability

Philosophers of free will give the issue of predictability short shrift, in my opinion. Typically they are worried about whether, given the past state of the universe and the laws of physics, the future of the universe is completely determined in principle. They aren't particularly worried about whether it is predictable in practice. I think they should be.

Consider the curious habits of the Sphex wasp. She lays her eggs underground, then flies off to get a cricket, which she paralyzes and places in the burrow for the hatchlings to eat when they emerge. In doing so, she follows a strict routine: after dragging her prey to the burrow, she goes inside to check on the eggs, then comes back out and finishes the task of dragging the cricket inside. Now, if some devious human moves the cricket away from the entrance to the burrow while she is inside checking on the eggs, she comes out, drags the cricket to the entrance again, and once again goes inside the burrow to check on the eggs.

If again the cricket is removed a few inches while the wasp is inside, once again she will move the cricket up to the threshold and re-enter the burrow for a final check. The wasp never thinks of pulling the cricket straight in. On one occasion this procedure was repeated forty times, always with the same result.

(Wooldridge, quoted in Dennett,  Elbow Room, p. 11.)

The first thing to note about the strange behavior of Sphex is that this is not a case of an agent doing the exact same thing under the exact same microscopic conditions. It doesn't matter if the experimenter moves the cricket three inches or four, the "same behavior" is repeated. And by "same behavior", we don't mean the microscopically exact same behavior, rather we mean the same general class of behavior. This is, I think, a much more interesting question than the question of whether we would do the exact same thing under the exact same conditions. Is there some general class of conditions under which I, as a human, would necessarily produce the same general response? If so, this is a more serious threat to free will than the possibility that I would do the exact same thing under the exact same conditions.

What is so striking about Sphex is the mindless predictability of her behavior. She apparently never stops to think, "Hey, didn't I just do this? Do I really need to do it again?" She is apparently pre-programmed to execute a series of steps. If those steps are interrupted, the series must be re-started at the point of interruption.

Are humans at all sphexish? Are there circumstances under which we will mindlessly repeat a certain behavior? We seem to be exempt from such behavior because of our ability to reflect on our own actions. Yet, if we behave according to (reasonably) deterministic laws of nature, there ought to be some (perhaps very small, yet not microscopically exact) set of conditions under which we would produce nearly the same behavior.

We can imagine someone, a burglar, say, who somehow gets hold of a complete physical description of  someone - down the quantum state of her very molecules. The burglar uses this information to predict when the victim will be out of her house, and then goes in and robs her.

This seems a reasonable concern, if the universe runs according to strict physical laws. But the laws of physics have been invoked to conjure up the spectre of sphexishness, and now the laws of physics rush in to the rescue. In a sufficiently complex, deterministic system, something called "chaos" comes into play. In a chaotic system, the set of conditions needed to produce with certainty a particular outcome is exponentially small. If we stipulate that humans are sufficiently complex, then the set of conditions needed to guarantee a particular human behavior will be smaller than the quantum limit allows, even for very short times. In other words, it will be impossible, without violating the laws of quantum mechanics, to predict the future behavior of a human from physical principles for more than some very short time.

If we move to a quantum mechanical description of our human (supposing such a thing to be possible, which is doubtful), one thing improves: quantum systems are never chaotic, as long as the Hamiltonian (the function that describes how the system changes with time) is completely known. So at first glance we seem to be better off with a quantum description, in terms of being able to predict outcomes. However, there are several problems with the quantum approach.

First problem: the Hamiltonian is never completely known as long as the system interacts with its environment. So, we could apply quantum mechanics to a person who was completely isolated from everything (including air, water, food, etc.)  - an unattractive prospect - or we could try to include the entire environment in our quantum description, greatly magnifying the difficulty of the task.

Second problem: Even with an exact quantum description (of, say, the person plus her environment) we will only get probabilistic results. That is, we can say she will have eggs for breakfast with 38% probability, jam and toast with 12% probability, etc. This is no more useful - and no more a violation of free will - than taking a survey of her eating habits.

Finally, I should point out that the problem I glossed over, of obtaining an exact quantum description of someone (to say nothing of her environment) is not just difficult, it is physically impossible. This is because of the no-cloning theorem I mentioned last time: it's impossible to take an unknown quantum system and make an exact copy of it.

So it seems that, from the point of view of predictability, free will has nothing to fear from the fundamental laws of physics. That is not to say that there couldn't be some higher-level laws that provide more predictability. After all, the same quantum considerations apply to Sphex, who remains quite predictable. (Not to mention a rock - also, presumably, a quantum system - whose behavior is extremely predictable.) So there is no way at this point to rule out the possibility of a nefarious burglar who exploits some as-yet-undiscovered psychological principles to generate useful predictions. But from what we have seen, there is no reason to think that the existence of such laws follows necessarily from the physical description of humans.

Next time: Electrons R Us.