Schrödinger's Infamous Cat

I need a box, a cat, something radioactive, and a poison vial. It's for science.

The Cat

Quantum Mechanics may be to many a deep mystery, but Schrödinger’s Cat is a fairly well-known legend. It involves, to be clear, an entirely imaginary cat in an entirely imaginary box containing an entirely imaginary fiendish device that — in the space of an hour — will leave it living (and very angry from its confinement) or, as might be poetically said, “legendary” (and forever calm).

Specifically, this (imaginary) cat is inside a fully opaque box with a small lump of some radioactive substance. In addition, there is a nasty mechanism that releases poison gas if it detects a particle from the radioactive sample.¹ Things are arranged to create a 50% probability the device detects a particle given a one-hour timespan.

The cat is meant to be hidden from sight (in fact, utterly isolated from the environment) during that hour. Then the box is opened to discover, with equal probability, either a very angry or a forever calm cat. A key aspect of this being that one invariably does find one or the other. It would be, in our experience, logically impossible — or some sort of magic trick — to find both (or neither).

The Point

More to the point, our experience tells us it is always one or the other even before we open the box and look. At first, the cat is definitely angry at being put in the box. During the hour of its incarceration, it may at some moment become a calm cat, but we suppose it’s always one or the other. In particular, it’s never both. The cat cannot be both angry and calm.

Erwin Schrödinger (1887-1961)² intended to contrast the definitely either angry or calm cat with the quantum world, where quantum “cats” apparently could be angry, calm, or any state between. He intended his cat to illustrate that something was missing from quantum mechanics. Accepting what it seems to say leads to cats that are somehow both alive and dead.

But just as Einstein was wrong about God playing dice, Schrödinger was wrong about quantum cats. Experimental results seem clear that quantum objects can indeed be in multiple states. (Though, as we’ll see, the reality is a bit more nuanced.)

Quantum Cats

In Quantum Mechanics 100 I listed quantum superposition as one of the three key aspects of QM that make it so different from our everyday world of classical mechanics.³ Schrödinger’s Cat is about this aspect — a system in multiple states simultaneously.

If we accept these two poles, classical cats in definite states on the one hand and quantum superposition on the other, then the question is at what point, and how, does quantum become classical?

How does the quantum event of a radioactive atom decaying become the classical event of releasing the (sleeping) gas?

Or does it? The Many-Worlds Interpretation (MWI) of quantum mechanics asserts it does not. The cat “branches” into two worlds, one with a cat asleep⁴ and one with a cat waiting to be let out to express its opinion of the whole affair. Because of its focus on a single quantum event, Schrödinger’s Cat is an emblem for the MWI — it is commonly used as an illustration (for instance, follow that Wiki link).⁵

In the previous post, The Vexing Problem of Wavefunction Collapse, I mentioned the Heisenberg Cut — the putative division between the quantum and classical worlds. Schrödinger’s Cat is also an illustration of this problem of wavefunction collapse. The alternative to branching universes is to find the Heisenberg Cut between the radioactive atom and the cat.

My guess — the short version — is that the detector monitoring the radioactive sample acts like a mousetrap. The tiny disturbance by a quantum “mouse” triggers a large release of energy stored in the trap’s “spring”. This amplifies the quantum event to classical levels.⁶

“Has it been an hour yet?”

Photon Cats

You may be familiar with the idea that light can be polarized. Sunglasses that are polarized block horizontal polarization but pass vertical polarization. This blocks light reflected off horizontal surfaces (like roads and water) because the reflection makes that light horizontally polarized. Normal daylight is both horizontally and vertically polarized, so the vertical part passes through the sunglasses.

There is a bit of quantum stuff to unpack in the previous paragraph, starting with the phrase “normal light is both horizontally and vertically polarized”.

Firstly, light gives us easy access to the mysterious wave-particle duality of the quantum world. Light has obvious wave-like properties — the fuzzy edges of shadows illustrate this — but Einstein won his Nobel Prize for demonstrating the particle-like properties of light in 1905.⁷ We call the quanta of light photons. These are the “pennies” of light — the smallest possible exchange.

Secondly, to say a photon is “both horizontally and vertically polarized” to some extent overleverages the word “both”. What we really mean is that the polarization of an individual photon is some combination of horizontal and vertical polarization. We describe this mathematically like this:

\(\Psi=\alpha\,|\text{Horizontal}\rangle+\beta\,|\text{Vertical}\rangle\)

Where Psi (Ψ) stands for the wavefunction representing the photon, and the |Horizontal⟩ and |Vertical⟩ represent horizontal and vertical polarization respectively (we’ll denote the angles as 0° and 90° respectively). The funny brackets around them are significant, but for now see them as just saying “quantum state”. The beauty is the latitude we have with regard to what we put in the brackets. We might, for instance, represent our cat as |😺⟩ and |😿⟩.

The alpha (α) and beta (β) are coefficients⁸ — numbers that determine the percentage of respective states (and those percentages must add up to 100%). This is what we mean by a superposition — a blend of specific states, ones we might measure.

If the photon happened to be exactly horizontally polarized, we describe it as:

\(\Psi={1.0}\,|\text{Horizontal}\rangle+{0.0}\,|\text{Vertical}\rangle\)

And note that this is still a superposition, but it’s entirely one-sided.

This seems straightforward, but here’s a wrinkle. We can also describe the same photon in the same state as:

\(\Psi=\alpha\,|\text{Diagonal}\rangle+\beta\,|\text{Anti-Diagonal}\rangle\)

That is, as some combination of diagonally polarized light (a 45° angle) and anti-diagonally polarized light (at a 135° angle). Note that, as with horizontal and vertical polarization, we pick two polarization states at 90° from each other.

Orthogonality

That’s because we want the two defining states to be orthogonal to each other. A common expression of orthogonality is lines at a 90° angle to each other, but the term more generally means ‘completely independent of each other’. In the case of the lines, one can go up and down on a vertical line without moving on the horizontal one (and vice versa). So, horizontal and vertical movement are independent of each other.

Likewise, any two lines at a 90° angle, so we can describe light polarization as a combination of any two orthogonal directions. This gives us an infinite number of linear polarization types. When it comes to light, there also are a rather different pair of orthogonal directions, left-circular and right-circular polarization.

The point is that we can describe the state of a quantum system as a combination of two orthogonal basis states. That is, two (or more) states that between them define all possible states the system could be in.

This is not restricted to photons. Quantum superposition is a distinctive — if mysterious — property of the quantum world. Nor is it restricted to polarization. Many quantum properties can be in superposition. One example is location. When we say a quantum particle “could be anywhere” we mean that it is in a superposition of all possible locations with a probability coefficient for each. In this formulation, each possible location is a state the system could be in.

An awake cat, |😺⟩, and a sleeping cat, |😿⟩, can, at least in principle, form a basis for superposition as Schrödinger’s Cat suggests. Except we know cats are classical and superposition doesn’t apply to them.⁹ Cats are not — in our experience — quantum objects, so they don’t have quantum properties (that we can detect).

Further, because quantum mechanics doesn’t include gravity, we know QM must be, at best, incomplete.¹⁰ Likewise, our theory of gravity, which doesn’t include QM. Unifying these two well-tested theories is one of the key goals in physics today.

“Let me out. I dare you!”

Further Reading: See Jim Baggott’s excellent essay about Schrödinger’s Cat:

Schrödinger’s Cat and Heisenberg’s Cut

Until next time…

1. In a kinder, gentler version of this thought (meaning imaginary) experiment, we can imagine the cat is gently sent to dreamland with a non-toxic, easily metabolized sleeping gas. Which gives the same experimental result: a very angry cat or a very calm one (who may be angry upon waking).

2. Who loved animals and often used them in his entirely imaginary thought experiments.

3. The other two are quantum interference and quantum entanglement.

4. Since the radioactive decay can happen at any time during the hour, we actually have a series of sleeping cats plus one awake cat. For every possible moment decay could happen, there is in the MWI a cat who got gassed that moment.

5. For the record, I file the MWI under “fairy tale physics”.

6. For details, find the long version of my guess in Measurement Specifics (Apr 2022).

7. My guess is that light and all matter — per QFT — is quintessentially wave-like. What we call “particles” are only point-like interactions between two quantum wavicles.

8. Why do physicists use Greek letters? Because it looks cool!

9. Lewis Carroll aside.

10. At worst, somehow very wrong.