Superposition is a quantum principle that refers to a physical system that exists in multiple states simultaneously based on a specific set of solutions. The most commonly used set of solutions is all possible solutions, also known as Hilbert space. In quantum physics, the Hilbert space is the mathematical representation of all the possible states the system can take. If my system is a spinning electron, its Hilbert space is spin up and spin down, since these are the two possible options for the spin direction.

What Is an Example of Superposition?

Superposition may be the most well known quantum physics and quantum mechanics principle. Most people have encountered this principle as Schrödinger’s Cat, a thought experiment that explains the concept and paradox of quantum superposition.

 

How Does Superposition Work?

In the case of Schrödinger’s Cat, the solution space representing all possible cases contains only two states; the cat is either dead or alive. Hence, the superposition of that solution space is that the cat is both dead and alive simultaneously, or in other words, the cat is 50 percent dead and 50 percent alive. As an equation, Schrödinger’s Cat looks like this:

Superposition image illustrating the above-mentioned formula but substituting images of illustrated alive and dead cats.
Illustration of the mathematical principle behind Schrödinger’s Cat. | Image: Sara A. Metwalli

This equation represents the mathematical form of the superposition of two states only. The cat is both dead and alive, with a 50/50 probability of each until we open the box and observe the cat. 

The probability of any state equals the absolute value of the square of the amplitude in the equation. In the cat equation, both states have the same amplitude of 1/√2. If we calculate it, the absolute square will give us one-half, or 50 percent. In the equation, the 2 under the square root represents the size of the Hilbert space.

Superposition is not always uniform or of equal value. In the cat’s case, it’s uniform because the chance is equal that the cat is dead or alive, But that is only sometimes the case. It, of course, depends on your application and the system you are studying.

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Superposition: The 2-Slit Experiment

We see another example of superposition from the world of physics in the behavior of electrons. In this experiment, imagine you have two walls sitting parallel to one another. The wall closest to you has two slits, and the other wall doesn’t. Now assume you shed light on the wall with the slits; what would you think would appear on the wall behind it?

Superposition image illustrating the two-slit experiment detailed below
Illustration of the two-slit experiment. | Image: Sara A. Metwalli

At first, you might say, the light will go through the slits, and you’ll see two slit-shaped light patterns on the far wall. That’s not what happens. Instead, we see three light waves appear on the wall instead. Even though the light particles are electrons, they are also a wave. When the light waves go through the slits, that wave breaks and forms patterns, which is what we see on the back wall.

Light is always a particle . . . and a wave. It remains in such superposition until we observe it in a specific way. For example, if we look at light as rays of light from a lamp, we see light’s particle behavior but in the slit experiment, we observe light’s wave behavior.

Introduction to Superposition. | Video: MIT OpenCourseWare
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More Superposition Applications

Superposition extends beyond just the field of quantum physics into our daily lives. Here are some ways you can observe superposition every day.

  1. Any sound we produce is in superpositions of different wavelengths coming together to make different tones. You can feel that even more when you play any musical instrument.
  2. The sunlight (white light) is a superposition of different light wavelengths and they form a rainbow when they collapse.
  3. In electrical engineering, if you have a circuit with multiple power sources, you can analyze the circuit using one power source at a time to reach the same results. 
  4. Geologists use superposition to determine the relative ages of rock layers. Because the layers of rock are superimposed, the oldest rock layer will be on the bottom and the youngest at the top.
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