Quantum Mechanics and Philosophy I: The Superposition of Paths

Author: Thomas Metcalf
Category: Philosophy of Science
Word Count: 1000

Editor’s Note: This essay is the first in a series authored by Tom on the topic of quantum mechanics and philosophy. Read the second essay here and the third essay here.

I. Introduction: A Story

I’m going to tell a complicated and counter-intuitive story.1 The real-world situations the story is describing (by analogy)—measurements of microscopic particles and systems—are complicated and counter-intuitive, so the story must be as well.

Suppose you’re having a party at your house. There are two doors: a front door and a side door. You asked 60% of the guests to bring food and 40% to bring drinks.

1. Paths

Here is the first strange thing that happens. It has to do with the paths the guests take to get into your house.

You are in the kitchen when guests begin arriving. You ask the first guest which door she came through, and she reports that she went 70% through the front door, but 30% through the side door. Does she mean that most of her body went through the front door, and the rest through the side? No; the way she entered the house was a combination comprising 70%-front-door-way, and 30%-side-door-way. That is, 100% of her went 70% through the front, and 100% of her went 30% through the side.

2. Watching

That’s weird, so you start watching the front door. Then you notice the second strange thing. It has to do with what happens when you watch for (measure the position of) the guests.

You observe several guests arrive. About 70% of the guests overall are coming in through the front door. And they look perfectly normal; when you ask them, they have no idea what the other guests were talking about. ‘I’m 100% coming in through the front door,’ they say. Your friend has been monitoring the side door, and she reports the same thing: 30% of the guests come in that way, but they are all 100% using that entrance and 0% using the other one.

3. The Effect of Observation

The third strange thing you observe has to do with the effect of watching the guests enter on the item (food or drink) they bring.

When no one is monitoring the entrances, then 60% of the guests arrive in the kitchen having brought food, and 40% brought drinks, as you requested. But when you start watching the front door, you notice that 50% of the guests walking through that entrance bring food, and 50% bring drinks, and the items arriving in the kitchen are indeed split 50-50 that way. Yet when you stop monitoring the entrance, the ratio goes back to 60-40. You conclude that somehow, going 100% through a particular entrance changes which item a guest brought, sometimes.

(Suppose you see a guest parking her car across the street, carrying food. If you don’t monitor which door she uses, then she’ll reach the kitchen with food at 100% certainty. But if you watch which door she uses, she’ll be 50% likely to turn out to be bringing drinks instead.)

4. Knowledge

The fourth strange thing you observe is as follows. It has to do with whether the guests use 100% one door and 0% the other, or instead use 70% one and 30% the other. It seems to show that it’s your knowledge itself that determines which item the guests bring, and that guests are affected by regions of space that they don’t have any causal contact with.

Suppose you try another experiment. You lock the front door, but then go back to the kitchen and don’t watch either door. And now only about 30% of the guests are arriving. And 50% are bringing food and 50%, drinks. Why would this be? Well, you know which door they’re using, now, since you know they’re not using the (locked) front door. And remember, having 100% used one door “resets” which item they brought. (These guests are all using the side door and not going anywhere near the front door, but somehow, having the front door locked changes which item the side-door guests bring. It seems to do so instantly, even, as if the information about the front door being locked was transmitted to the side-door guests at faster than the speed of light.) A bunch of guests who are not passing through the front door are still affected by whether it was locked. When you unlock the side door, the ratio of items brought goes back to 60-40 food-drinks. (Why do side-door guests “care” or even know whether the front door is locked?)

(Notably, when you watch the entrances—and the food and drink ratio is “reset” to 50-50—the guests have absolutely no explanation for why they happened to bring food, or drinks. Nothing about them (including whether they left their houses with food or drink) can predict which one they’ll bring.)

6. Conclusion: Superposition

So when you’re not monitoring the entrances, how, overall, are the guests getting into your kitchen?

They’re not entering 100% through the front door, nor 100% through the side door. If they were, they’d be 50-50 bringing food or drinks.

They’re not entering through both at once. When you look for them, you always see them enter either through the front or through the side.

They’re not using neither. When you lock both doors, no one gets in.

The guests enter in what physicists call a “superposition” comprising 70%-front-door and 30%-side-door. When someone actually looks, the guests don’t seem to be in superpositions anymore. Why does looking matter? (What counts as “looking”?)

II. The Math versus the Physics

The “party” story corresponds to real experiments about microscopic systems.2 Everyone agrees about the measurement results. Quantum theory allows us to predict results of experiments with a higher certainty than anything else we’ve ever developed.3 Where people disagree is about what’s going on in the real world. Indeed, everyone agrees that the Schrödinger equation4 is extremely accurate when it comes to predicting how systems will evolve over time. But no one is sure what these particles are actually doing, before and after when we measure them.5

The answer is, in some ways, a philosophical choice, with philosophical implications. We’ll talk more about those in the next article in this series.6

Notes

1This example is a version of the metaphor in Albert (1992: ch. 1).

2Usually photons and electrons, and most commonly, spin-properties; cf. Albert 1992: 1, n. 1.

3Ismael 2014; Polkinghorne 2002: 39-40; Greene 2011: 201.

4Here’s the equation, if you’re curious (Polkinghorne 2002: 104-05):

It’s a way of taking the state of a system at one time and predicting its state at a future time.

5We don’t have empirical instruments that can tell us, either. Indeed, we may never have adequate instruments to empirically discover this. See Albert 1992: 84-92.

6It’s non-empirical, at least. Partisans sometimes appeal, for example, to the value of simplicity or intuition, or to positivistic considerations; cf. Greene 2011: 209 and Polkinghorne 2002: 46-56.

References

Albert, David Z. (1992). Quantum Mechanics and Experience. Cambridge, MA: Harvard University Press.

Greene, Brian. (2011). The Hidden Reality: Parallel Universes and the Deep Laws of the Cosmos. New York: Random House.

Ismael, Jenann. (2014). “Quantum Mechanics.” In Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy (Spring 2014 edition), URL = <http://plato.stanford.edu/archives/spr2014/entries/qm>

Polkinghorne, John. (2002). Quantum Theory: A Very Short Introduction. New York: Oxford University Press.

Tom is a visiting assistant professor at Spring Hill College in Mobile, AL. He received his PhD in philosophy from the University of Colorado, Boulder. He specializes in ethics, metaethics, epistemology, and the philosophy of religion. Tom has two cats whose names are Hesperus and Phosphorus. Website: http://colorado.academia.edu/ThomasMetcalf