Schrodinger's Cat and the Bomb Detector
Whatever you think you know about Schrödinger's famous cat is probably wrong.
by Brian Dunning
January 12, 2016
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The author's cunning, highly-detailed technical diagram of a Mach-Zehnder interferometer in an Elitzur-Vaidman configuration
We've all heard of Erwin Schrödinger's famous thought experiment of the cat in the box, who, when we open the box, turns out to be either alive or dead. Some of us understand the experiment's relevance to quantum mechanics to some degree or another, and many of us don't know much about it other than there's a cat in a box that might be dead. Today we're going to dispel the vagary, and illuminate how the famous cat illustrates one of the most counterintuitive manifestations in all of quantum mechanics: the ability to be in two places, or two states, at once.
This ability is called superposition. The way that Schrödinger's Cat is usually told suggests that the cat inside the box is both alive and dead at the same time, and it's not established which one is true until someone opens the box to look inside. It sounds a lot like the old thought experiment "If a tree falls in the forest and no one is around to hear it, does it make a sound?" But that's a philosophical question, and that's different. For the superposition in the case of the cat experiment is not philosophical, but factual. Let's look closer.
The cat is locked up in a box, which nobody can see into, and which is so solid that nothing happening within can be known from outside. Inside the box with the cat is an atom of unstable radioactive material. Whether and when a radioactive nucleus decays is one of nature's truly random actions. If this one happens to decay, a Geiger counter detects it and releases cyanide gas which kills the cat. Because no outside observation has yet been made, the system remains in a state of superposition — the nucleus has both decayed and not decayed, and the cat has both died and remained alive. Not until someone opens the box and looks inside does the system actually assume one state or the other. And be very clear: it's not just whether the state is known; it actually has both states simultaneously until the observation is made, even if that takes a year.
We call this moment the collapse of the superposition. Nothing is actually collapsing or falling down; think of it as a placeholder term for what happens when a system in superposition assumes one state or the other. When we open the box and see that the cat is dead, that is the moment the superposition collapses. All the ambiguity disappears.
So this is the version of Schrödinger's Cat that you might have heard before. And: it's wrong.
This is what Schrödinger described, but he was using an extreme example to illustrate how incredibly counterintuitive superpositioning is. In fact, nothing as large as a cat could ever be in a state of superposition. A cat (or any other solid object in our classical physics world) consists of many particles, all of which have their own state, and they won't ever all be the same. Any single given particle can easily be in a superposition, however. It is only the decay of this single atom's nucleus that is the only real ambiguous event in this experiment. If and when the emitted particle strikes the Geiger counter, that becomes the observation. The "observation" that causes a superposition to collapse does not mean that a human being sees something. It refers to any interaction with the classical world. The Schrödinger's Cat system is only in an ambiguous state of superposition for a tiny fraction of a second; the period of time between the decay of the nucleus and its interaction with the Geiger counter. For that tiny space of time, the superposition is real. The nucleus did decay, and it did not decay. But the flask of cyanide is a classical world object. It either gets broken or not, and the cat either lives or dies.
So even though the Schrödinger's Cat system may seem a little less incredible than the popularly told version, the superposition of that decaying particle is still just as insane. It is a fact that both of its states — decayed and not — exist at the same time, for that tiny brief period. And here is a real-world experiment that will prove it to you.
Imagine a type of bomb that is triggered by a single photon of light. Let's say we have a whole bunch of these bombs, perhaps stockpiled in preparation for going to war against Lord Xenu of the Galactic Confederacy. All it takes is for a single photon of light to strike the explosive compound inside the bomb, and it will detonate. But the problem is some of the bombs are duds; they don't contain any explosive at all, the photon will pass right through them. Imagine there is no way to test them except to actually hit them with photons and see if they explode or not. How can we test them without destroying them, if the only way to test them will destroy them?
In the classical world, it would be impossible; but not necessarily so in the quantum world. In the quantum world, our bomb can both absorb a photon — which must make it explode — and yet not explode, two different realities, at the same time. And unlike the cat in the box, this bomb test has been conducted in the real world, and been observed to work. It is not merely a thought experiment, and certainly not a mere philosophical construct. It's reality.
All we need to test these bombs is a common lab instrument, a Mach-Zehnder interferometer. It's a simple but useful tool. A light beam enters at one end, where it hits a half-silvered mirror set at 45°. Half the light passes straight through, and half reflects off 90° to one side. These two diverging beams then are bounced back toward each other by fully silvered mirrors. The beams cross each other, and just beyond the intersection, each strikes a detector. These detectors can be anything you want them to be; light meters, particle counters, or even just a white screen. But here's the interesting part. Right where the beams intersect is another half-silvered mirror. Half of the light from each beam passes straight through, and half reflects off to join the light passing straight through from the other beam. Thus, each detector is struck by a 50/50 mix of light from both beams.
This use of the Mach-Zehnder interferometer to test bombs is called an Elitzur-Vaidman bomb tester, named for the two physicists who came up with the idea in 1993. The following year, other physicists built, tested, and proved its function. Here's what they did. As we know, light travels with a frequency, which determines its color. The interferometer's arrangement is adjustable, allowing us to tune the device so that when the two beams are added together by the final half-silvered mirror, each beam can consist of two waveforms that are out of phase with one another. The peaks and valleys of each waveform might be just slightly offset; or they might be exactly in-phase so that the peaks and valleys are doubled in height (called constructive interference); or they might be exactly out-of-phase so that they cancel each other out to zero (called destructive interference). This interference of the waveforms with one another is what gives the interferometer its name. By studying the patterns of these waves on the detector screens, experimenters can learn (among many other applications) what effect a sample object has when you place it in the path of one of the beams.
So that's what we're going to do with one of our bombs: we're going to place it in the path of one of the beams. And for each bomb that we test, we're going to fire exactly one single photon through the interferometer. Logically, to our classically thinking brains, this arrangement suggests that we have a 50% chance of triggering any live bomb that we place into the beam, depending on whether that photon bounces off the first mirror or passes straight through and hits the bomb.
But that 50/50 interaction with the half-silvered mirror is a quantum effect. That photon is now in a state of superposition; until it interacts with something and its superposition collapses, it is following both paths. Again, this is not a philosophical thought experiment, it's observable.
We have arranged this interferometer so that light striking Detector 1 undergoes constructive interference, and light striking Detector 2 undergoes destructive interference. If the bomb is a dud and has no explosive in it, both possible beam pathways are open, and the interference will proceed normally. Destructive interference guarantees nothing can ever be detected in Detector 2, and constructive interference guarantees the photon will always be detected in Detector 1. Thus, all dud bombs will always produce a result only in Detector 1.
But if it's a live bomb, one pathway is blocked by the explosive, so neither constructive nor destructive interference will take place, thus the photon would have an equal chance of being seen at Detector 1 or at Detector 2. Unfortunately, the photon also has an equal chance of traveling either the unobstructed path or of striking the explosive and detonating the bomb.
If the photon's interaction is to strike the explosive, then the superposition collapses from the interaction, and boom, the bomb will go off, and that photon will obviously never get as far as Detector 1. But half the time you'll be lucky and it will hit Detector 2, and you'll know you had a good bomb. Congratulations, you just detected the presence of explosive whose existence could only be detected by blowing it up, but you did it without blowing it up. What you did would be impossible, if not for the reality of quantum mechanics.
Since a result at Detector 1 could happen in either scenario, you have to retest those, and if you retest every bomb until you have a definitive answer for each, you'll eventually have one third of the live bombs left, all proven to be good. But this setup is the simplest example; physicists have designed more complicated systems with more beam splitters that can detect almost 100% of the live bombs without detonating any of them.
No matter how hard it is for our classical brains to comprehend, things at the quantum level of single particles can actually do two things at once. We can test it, we can observe it, and we can prove it every time. For real. So give your cat a snuggle, and please don't lock it in any boxes with radioisotopes and cyanide canisters.
By Brian Dunning
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Cite this article:
Dunning, B. "Schrodinger's Cat and the Bomb Detector." Skeptoid Podcast. Skeptoid Media,
12 Jan 2016. Web.
10 Dec 2016. <http://skeptoid.com/episodes/4501>
References & Further Reading
Editors. "Schrödinger's Cat." Experiments. Information Philosopher, 7 May 2009. Web. 4 Jan. 2016. <http://www.informationphilosopher.com/solutions/experiments/schrodingerscat/>
Elitzur, A., Vaidman, L. "Quantum mechanical interaction-free measurements." Foundations of Physics. 1 Jul. 1993, Volume 23, Issue 7: 987-997.
Kwiat, P. "Interaction Free Measurements." Physics Illinois. University of Illinois, 7 Aug. 2009. Web. 4 Jan. 2016. <http://physics.illinois.edu/people/kwiat/interaction-free-measurements.asp>
Schrödinger, E. "Die gegenwärtige Situation in der Quantenmechanik." Die Naturwissenschaften. 1 Nov. 1935, Volume 23: 807-812; 823-828; 844-849.
Wolfson, R. Essential University Physics. Boston: Addison-Wesley, 2012.
Zetie, K., Adams, S., Tocknell, R. "How Does a Mach-Zehnder Interferometer Work?" Physics Education. 1 Jan. 2000, Volume 35, Number 1: 46-48.
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