Friday, December 3, 2010

Superposition: Not That Strange (1/29/2010)

This was originally posted on a horrible site called Myspace. When Myspace underwent a redesign in Fall 2010, hundreds of insightful reader comments that had been left over the years were lost. I have since deleted my account there.

Quantum mechanics is considered one of the weirdest areas in modern physics, and one of the weirder aspects of quantum mechanics is the idea of superposition. Superposition is the theoretical coexistence or "overlaying" of more than one state of an object, where that object's state is unknown. For example, when a photon of light has not been measured for location, its location is said to be a superposition of all its possible locations. Similarly, a radioactive atom that may or may not have decayed is said to be a superposition of its decayed and undecayed states — that is, until we look to see if the atom has decayed or not, at which time it can be described as being in one state or the other. This is not an intuitive concept on the human scale, as best illustrated by Edwin Schrödinger's famous thought experiment: Imagine a cat in a box along with a radioactive atom, plus a mechanism whereby poisonous gas is released if the atom decays. If the atom has a 50/50 chance of decaying during the hour-long experiment, does that mean the cat is in a state of superposition — i.e., simultaneously both alive and dead — right before the experimenter opens the box? In fact, Schrödinger used this thought experiment to show that it's silly to consider a macroscopic object like an animal being in superposition like this. A cat that's both alive and dead? Yeah, right!

And yet, some interpretations of quantum mechanics — including my favorite, the relational interpretation — suggest that yes, a cat in that situation is, in fact, "both alive and dead." So how can we wrap our brains around this notion?

I have a 16-year-old cat, Pokey. (You may know her as Miss Delilah.) Let's say she has a 50/50 chance of living to age 20. How do I presently describe her state on January 29, 2014? You guessed it: The 2014 cat, as described today, is both alive and dead. As I write this, her future state is a superposition of two states, simply because her future is uncertain to me. Superposition doesn't seem strange at all when viewed this way, because we're used to things in the future being uncertain. It's only strange to think of an object as being in two "overlapping" states at once — but you don't need to think of it so literally. A better description is that from our (present) perspective, the future cat is in a probability state, where there's a 50% chance of 2014 Pokey being alive and and a 50% chance of her being dead.

Similarly,* Schrödinger's cat isn't somehow a ghostly overlap of alive-and-dead cats in that box. From the perspective of the experimenter, the animal simply dwells in a probability state whose final outcome has yet to be discovered. You could say that even though an hour has elapsed and the experiment is over, the state of the cat remains in the experimenter's future, and therefore it's uncertain and/or in superposition.

This view of superposition isn't just my twisting of QM theory to make it more palatable to human intuition; it's fully consistent with the relational interpretation. Consider the three main tenets of RQM:
1. We cannot attribute any absolute states or properties to any object, in and of itself. It would be wrong to say, "The apple has an absolute velocity, spin, color, etc., independent of other objects or observers." Rather, states and properties can only be defined in terms of interactions between things — whether they be microscopic or macroscopic, inanimate or living, observing or not observing. RQM makes no distinctions among these. Our observations of the world consist only of our interactions with objects in the world (e.g., our perception of an apple appearing to be the way it is), not any absolute properties of the objects themselves.
2. Two observers can have different, but equally accurate, descriptions of one object or system, depending on the nature of their respective interactions with that system.
3. Our description of any system depends specifically upon the information transferred or extracted during our interaction with the system.

The key here is that relational quantum mechanics is a theory about information. If we're involved in an interaction where we acquire information about an object's momentum, for example, the property of momentum then becomes defined by us for that object; before that, it remains undefined or uncertain to us. In the case of Schrödinger's cat, at the end of the hour, the cat has received information about the state of the atom, and that is why the cat — from its own perspective — is either alive or dead. Meanwhile, though, the experimenter has no information about what went on inside the box, so from his or her perspective, the cat is in superposition, i.e., its state is uncertain.

In the future, literally everything is uncertain to us, dwelling in probability states only.** The total lack of information from the future means that everything about it must remain undefined. Even the surest bet we know, that the sun will rise tomorrow, is a probability; there is a
tiny but non-zero chance that the Earth's rotation will be halted by an
asteroid impact before then.***

And this may be a stretch, but you can apply the same principle to the very distant past: How did the first reproducing life form, our earliest ancestor, come about? We have absolutely no direct information about this event, so the best we can do is offer potential scenarios and gauge their respective probabilities. You could say that from our current perspective, the various possible earliest life forms exist in superposition — but "uncertain" feels a lot more natural.

Perhaps that's the most confusing thing about superposition: the word itself. It conjures up an image of overlapping, partially transparent alternate versions of an object. It's no surprise that students and researchers alike have been uneasy about the concept for 80-some years. But superposition is merely uncertainty based on a lack of available information. That's all it is.

* One can well argue that traditional superposition is a mathematically "real" state of affairs for an atom or even a cat, whereas my conception of "future" superposition is a metaphorical extrapolation. While it's definitely an extrapolation, there are fewer differences between these cases than you might expect. Mathematical uncertainty is mathematical uncertainty, such descriptions having no direct bearing on the actual nature of the objects themselves. But that's a topic for another day.

** I floated this idea in an earlier essay, where I argued that time appears to flow in one direction because information only comes from the past, never the future. Even though the "arrow of time" is often explained thermodynamically, where the inevitable increase in disorder (entropy) points in only one direction, that explanation doesn't shed much light on the phenomenon in conscious observers of a definite and unidirectional "flow" of time. Is it a coincidence that both arrows point in the same direction? No — entropy is a key element in quantum information theory.

*** Someone once asked me that if the "realness" of objects depends so strongly on our observations, do the table and chairs in his dining room go away when he goes to bed? It's not that they "go" anywhere; it's just that as soon as information on them stops being collected, they lapse into an increasingly uncertain probability state. There is a small but non-zero chance that his house will be emptied by robbers, a flood will wash out the downstairs, etc., and this goes up the longer he sleeps.


  1. the way this Schrödinger's experiment is usualy taught reminds me of some fables that people began to take for real long ago. you see, some might believe that the cat's fate is only gona be decided when the box is opened. instead, this story is about our own ideas and confusion, not a cat. "fables" that where created to illustrate aspects of nature and time are now religions.

  2. I find this article fascinating, however, if this really is a valid way of understanding superposition, that it's simply a percentage, and not that the cat is literally dead or alive before you open the box (only to you, the scientist doing the opening is it uncertain at that moment) then why isn't it explained this way more often?

    If I go out shopping, and there is a 50/50 chance of my house being gone at the exact time I arrive, due to some complex system based on half life decay, then my house is in a superposition (to me) before I receive information regarding the fate of my house, that doesn't change the fact that it is either gone or still there, I simply can't tell in that moment.

    If superposition is so intuitive, why isn't it taught this way? Or am I misunderstanding something fundamental that still makes it counter-intuitive on a small scale?

    1. Superposition isn't taught this way because relational quantum mechanics is one of the newer interpretations of QM. Despite being slightly less intuitive, the Copenhagen interpretation is so entrenched that it's what most students get exposed to.

      Your take on the relational approach is a little off, though, when you say, "that doesn't change the fact that [my house] is either gone or still there." RQM rejects the notion that there is an objective, absolute state of an object such as your "decaying house" (or a particle), just as we know that an object cannot have an absolute velocity. No such objective state, possessed intrinsically by the object, exists; the state of the object is always relative to the observer of that object, and inextricably a function of the observation event -- even in the case where the "observer" is a single particle. This very elegantly explains the paradoxical result of some quantum experiments where different observers have different (but not contradictory) descriptions of a system. It also accommodates the "observer-centeredness" of quantum mechanics that has troubled physicists since the 1920s. Thanks for the comment!