“Metaphorical Worlds Interpretation” (Chad Orzel)

Amazon link

I bought this a couple of weeks ago (Kindle) but it still sits in my stack. Soon!

Peter Woit has this post today, however, where he links to a piece by Chad Orzel.

Orzel thinks there is a better way to think about the "Many Worlds Interpretation":

"The problematic aspect here is that the wavefunction of the universe has everything in complicated superposition states, but when we select out a tiny piece of it as our system of interest, we often see that system only in single states, not a superposition of multiple states. The question that’s too often un-asked, though is: What measurement would you do to demonstrate that your system is really in a superposition?

The answer to this doesn’t need to be a procedure specific enough to actually do the experiment; a general outline would be sufficient. And, in fact, we have a couple of centuries of experience at doing exactly this: When we want to show that something has been in two states at the same time, we do an interference experiment. We put our system of interest in a superposition of two states, arrange for those two states to evolve at slightly different rates for some time, and then bring them back together and measure the final state.

If a superposition exists, there will be some oscillation in the probability of a given final state that depends on the differential evolution in the middle. This takes lots of forms– if the two states of the superposition correspond to passing through spatially separated slits, it’ll show up as an interference fringe pattern in space; if they’re two states of a cesium atom in an atomic clock, it’ll show up as a varying probability of ending up in one of those states as you adjust the frequency of your microwave oscillator.

In every case, though, you’re measuring a probability. And not even a Bayesian can accurately measure a probability from a single experiment. To get a good measurement of a probability of some outcome– let alone the variation in probability that is the signature of a superposition state– you need a large number of repeated measurements. And those measurements have to be made under the same conditions every time.

That’s the key feature that lets you carve out some parts of the giant wavefunction of the universe and choose to treat them as systems in definite states, while others need to be treated as full quantum superpositions. The vast majority of the universe that we’re bracketing off as “the environment” affects the measurement conditions, which changes the probabilities you’re measuring.

If the interaction with the environment is small, though, you can ensure that the conditions are close to identical for enough trials to unambiguously see the changing probabilities that show a superposition exists. That subpart of the universal wavefunction needs to be dealt with as a fully quantum system.

If the interaction with the environment is strong and poorly controlled, though, the conditions of your measurement change enough from one repetition to the next that you’re not really doing the same measurement multiple times. If you could know the full state of the environment for a given trial, you would predict one probability, but knowing the full state of the environment for the next trial would lead you to predict a different probability.

In the absence of that knowledge, adding together repeated results just gets you junk– you won’t see a clear dependence on the different evolution of the different states in the superposition, because it’s swamped by the unknown effect of the environment. If you can’t see the interference effect, that system “looks classical,” and you can treat it as having a definite state.

That process of interaction with the changing state of an unknown environment gets the name “decoherence,” and it’s what enables the bookkeeping trick that lets us split off pieces of the wavefunction and consider them in isolation. If the piece you’re interested in is big enough and interacts with the environment strongly enough, there’s no hope of doing the interference measurement that would show it’s in a superposition state. If you can’t do a measurement that would show the existence of the other piece(s) of the superposition, you can safely treat it as being in a single definite state.

It should be emphasized, though, that this is just bookkeeping, not a real separation between “copies of the universe,” or even copies of the system of interest. There’s only one universe, in an indescribably complex superposition, and we’re choosing to carve out a tiny piece of it, and describe it in a simplified way.

It’s not even true, strictly speaking, that the results of a given experiment for a particular object are unaffected by the presence of the other parts of the superposition for that specific object. If you could do the full probability calculation for the whole wavefunction, including all of “the environment,” the probability you would predict for that experiment would include a contribution from all the various states that are superposed. In the absence of that complete knowledge, though, you can get away with ignoring them, because you’ll never be able to repeat the measurements in the way you would need to see the influence.
...
Rather than “Many-Worlds Interpretation,” I’d go with “Metaphorical Worlds Interpretation,” to reflect the fact that all the different ways of cutting up the wavefunction into sub-parts are fundamentally a matter of convenience, a choice to talk about pieces of the wavefunction as if they were separate, because the whole is too vast to comprehend."

Peter Woit likes this story. What do you think?

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What is decoherence? Read this.