Decoherence

I finally finished Philip Ball’s Beyond Weird on the nature of quantum mechanics. I feel I haven’t digested it. Maybe that’s because Feynman was right – no one really understands quantum mechanics. I will let some time pass and then take a second stab at it in the near future. Content-wise it overlaps with Manjit Kumar’s Quantum and Amanda Gefter’s Trespassing on Einstein’s Lawn but is stylistically very different. There’s something about Ball’s writing that hits a sweet spot in my brain – maybe it’s his background training in chemistry that employs language that resonates with me.

 

Today I’d like to discuss decoherence. I’m likely not to do so coherently because I don’t understand it. Also, it’s clearly beyond weird. I will have to quote Ball a fair bit since I don’t really know what I’m talking about. And in Ball’s book, quantum mechanics, knowledge is a tripping (or perhaps trippy) factor.

 

Why do we have certain knowledge about larger objects to which the rules of classical mechanics apply? They have well-defined properties. We can say something about both an object’s position and velocity simultaneously; its properties are localized to the object and not “spread out mysteriously through space”. On the other hand, the “quantum world is (until a classical measurement impinges on it) no more than a tapestry of probabilities, with individual measurement outcomes determined by chance.” This wave-like behavior can manifest itself when waves superimpose coherently. We see this in wave interference because there is a “well-defined relationship between the [waves]… when they are in step.”

 

But, “if the quantum wavefunctions of two states are not coherent, they cannot interfere, nor can they maintain a superposition. A loss of coherence (decoherence) therefore destroys these fundamentally quantum properties, and the states behave more like distinct classical systems.” Coherence is what gives us the beyond weird smeary quantum behavior. Decoherence destroys it and provides distinction. What causes decoherence? Somehow making a measurement to extract information from a quantum system does so. How? We don’t know. Making a measurement of two conjugate properties in a different order (because you can’t do so simultaneously) gives different results.

 

Ball latches on to some clues. No system is truly isolated. It has to interact with an environment. Then comes the whopper suggestion. Decoherence is not because quantum states are “fragile” but rather because “they are highly contagious and apt to spread out rapidly.” Here’s how it works. When a quantum particle interacts with another, this “places the two entities in an entangled state. This is, in fact, the only thing that can happen in such an interaction… the quantumness – the coherence – spreads a little further. In theory there is no end to this process… [molecules hit more molecules!] As time passes, the initial quantum system becomes more and more entangled with its environment. In effect, we then no longer have a well-defined quantum system embedded in an environment. Rather, system and environment have merged into a single superposition… [they] infect the environment with their quantumness, turning the whole world into one big quantum state.”

 

Ball continues: “Quantum mechanics is powerless to stop it, because it contains in itself no prescription for shutting down the spread of entanglement… This spreading is the very thing that destroys the manifestation of a superposition in the original quantum system… we can no longer ‘see’ [it] just by looking at the little part of it… What we understand to be decoherence is not actually a loss of superposition but a loss of our ability to detect it in the original system.” This is starting to sound a bit like what we see even in classical thermodynamics. A temperature differential induces heat-flow, essentially a one-way street. Entropy rears its head. You haven’t lost any energy, but you’ve spread it out in such a way that it’s highly improbable you will collect it all back in one ‘place’ so you’ve effectively lost it from the system to the environment.

 

If the nonlocality of quantum mechanics spreads itself everywhere, why do we experience profound locality and distinctiveness in classical objects. The crux has to do with making a measurement. Ball writes: “A measuring device must always have some macroscopic element with which we can interact: a pointer or a display, big enough to see, say.” Decoherence must take place in this interaction and essentially “imprints information about an object onto its environment. A measurement on that object then amounts to harvesting this information from its environment.” It’s what happens when we ‘see’ an object. Our “retinas are responding to the photons of light that have bounced off it.”

 

But beyond weird, decoherence “creates a kind of ‘replica’ of the object… that eventually produces a reading in our classical measuring apparatus”. I sense echoes of Command Copy. Repeated over and over again. Ball writes that “some quantum states are better than others at generating replicas… These are the states we tend to measure, and are the ones that ultimately produce a unique classical signature from the underlying quantum palette. You could say that it’s only the ‘fittest’ states that survive the measurement process, because they are best at replicating copies in the environment that a measuring device can detect. The physicist Wojciech Zurek has dubbed this “quantum Darwinism”. I’m reminded of the notion that perhaps it’s not mathematics all the way down, but biology at every level!

 

It turns out that the position of an object is particularly well suited for this decoherence replica-generating thingamajig. Ball explains: [it’s] because those interactions tend to depend on the distance between the object and elements of its environment, such as other atoms or photons: the closer they are, the stronger the interaction. So interactions ‘record’ position very efficiently. The corollary is that decoherence of position states tends to happen very quickly, because pretty much any scattering of photons from an object carries away positional information into the environment. And so it is really hard to ‘see’ large-ish objects being in ‘two places at once’… The states we can measure are the ones that are most easily found out.”

 

And if all that wasn’t mind-blowing enough: “when we measure a property of a quantum system by probing its ‘replica’ in the environment, we destroy that replica (by entangling it with the measurement apparatus).” This implies that “too much measurement will ultimately make the state seem to vanish.” That’s what makes it hard to make measurements on very, very, very small objects. We perturb it into another state. Ball writes: “Take a peek and you’ve used up all the information that was available about it. Subsequent measurements may then have a different outcome.” This sounds like what we see when we observe beyond weird quantum behavior. Thus we are limited when trying to extract information from a quantum system.

 

There’s more, but I have to stop here. My mind is swimming in decoherence and I’m likely to soon spout nonsense, so I’ll stop before the spread reaches my fingers and my keyboard.