I’m a little cranky after a day of reviewing grant proposals, so it’s possible that I’m overreacting. But commenter Neil B has been banging on about quantum measurement for weeks, including not one, not two, but three lengthy comments in Tuesday’s dog post.
For that reason, I am declaring this post’s comments section to be the Official Neil B. Quantum Measurement Thread. Until such time as I declare the subject open again, this is the only thread in which I want to see comments about quantum measurement. Attempts to bring the subject up in comments to other posts– even other posts having to do with quantum mechanics– will be disemvowelled.
So this is not just a public slapping down, I’ll provide some thoughts on the subject below the fold.
There are three different but related things that people mean when they talk about problems of quantum measurement. One problem is, in essence, “If the world obeys quantum rules, why does everything we see look so classical?” We never see interference of macroscopic objects, or superposition states of macroscopic objects. A tennis ball is always either here or there, not here and there at the same time.
This problem is adequately solved by the idea of decoherence, as discussed previously. The basic idea is that unmeasured interactions with the environment make small changes in the wavefunction the prevent us from seeing any sign of interference behavior for macroscopic objects. There is interference, but the pattern that results is always changing, and thus can’t be detected through repeated measurements. This result is indistinguishable from what you would get if the particles you’re looking at obeyed classical rules.
This is not, by the way, restricted to a Many-Worlds Interpretation view of quantum mechanics. Decoherence is a verifiable physical phenomenon that occurs no matter what interpretation you favor. The language you use to talk about it is different for different interpretations, but the physics is the same.
The second problem is, basically, “If objects are described by wavefunctions, how is it that you detect them in single places?” This is the “localization” business that Neil keeps banging on about, and he seems to think that it’s some sort of unbeatable argument against Many-Worlds. The problem is, if it’s an unbeatable argument against Many-Worlds, it’s an unbeatable argument against any interpretation. No interpretation that I’m aware of has an airtight explanation of this aspect of quantum measurement.
The thing is, this part of the problem isn’t that much of a problem. Or, to put it more bluntly, it’s only a problem if, like Neil, you think that the wavefunction is a physical wave like a ripple on a pool of water.
Wavefunctions aren’t water waves, though. They’re probability waves (or the square root of probability waves, to be a tiny bit more precise). They don’t behave like water waves, and they don’t need to behave like water waves.
A colleague likes to use the lottery as an analogy for quantum measurement. Before the measurement is made, you have a distributed probability function– lots of people have tickets, and they each have some probability of holding the winning ticket. At the instant the ping-pong balls pop up, that probability distribution “collapses,” and millions of people are found to be holding worthless scraps of paper, and one person is the winner.
In fact, I would argue that if you really want to harp on this, you have exactly the same problem in classical physics. If you’re being responsible about the job of predicting the result of a classical particle trajectory, you have to talk about it in terms of probability distributions.
If I’ve set up a ball-throwing robot to entertain the dog, the landing place of the ball is uncertain. There will be slight variations in the force with which the robot tosses the ball, and air currents in the room, and so on. All I can really predict is a probability of the ball landing at a given point– I can calculate that it’s most likely to be at one particular position, but there will be some range around that point where I wouldn’t be too surprised to find the ball.
When the ball hits, though, it hits in only one place. So, what happened to the rest of the distribution? It’s not worth worrying about, because it was only ever a probability distribution. If we repeat the experiment over and over, we can expect to trace out the whole distribution, but one shot will only land at one place, because that’s the way the world works.
It’s the same thing with quantum particles. A single electron sent through a double-slit apparatus will appear at one and only one place on a detector screen, because that’s the way the world works. The extended wavefunction that exists before the measurement describes the probability of finding the electron at any given point when you finally make the measurement. That’s all. There’s nothing all that mystical about the disappearance of the rest of the wavefunction, any more than there is about the disappearance of the rest of the probability distribution for the thrown tennis ball.
“Yeah, but in the classical case, you can imagine keeping track of all the various influences on the ball’s flight, all the way along. In the ideal case, you would be able to predict with certainty where it will land, every time.” True enough. That brings us to the third problem, which is, basically, “Why is it that quantum mechanics only describes probabilities, not specific outcomes?”
I don’t have a good answer for that. Nobody does. Quantum measurements are inherently probabilistic in a way that classical measurements are not. You can, in principle, predict the outcome of any given classical process to arbitrary precision– all it takes is a more careful measurement of the initial conditions. It might involve tracking the flapping wings of butterflies in the Amazon, but in principle you can correctly predict the outcome, given enough information.
Quantum physics isn’t like that. There is no way, even in principle, to predict exactly where an electron will hit the screen after passing through a double-slit apparatus. All you can predict is the wavefunction, which gives you a probability distribution. The outcome of an individual measurement is inherently and inescapably random, and nothing you can do will change that.
That’s my take on quantum measurement. If you feel the need to uncork a 1,500-word rant about how wrong I am, go nuts. But only in this comment thread– if it shows up anywhere else, expect lossy compression.