Quantum Mechanics

Superposition and Shrödinger’s Cat

Below is an excellent description of superposition and the Shrödinger’s Cat thought experiment. An important note is here is that Shrödinger meant for his thought experiment to show how misleading the Copenhagen interpretation of quantum mechanics really is on the macro level or with everyday large things. Though it is often used to communicate the mysteries of quantum mechanics, that popular view in very misleading. Below, Alexandra Hopkins, gives a more precise explanation of what superposition is and makes it clear that that there are numerous interpretations of quantum mechanics and these interpretations ultimately lead to the same reality. Experiments have shown that quantum mechanics accurately describes how things work on the subatomic level, but Shrödinger wanted to make it clear that those same principles do not apply on the large scale, i.e. a cat can’t be both dead and alive at the same time.

Explanation by Alexandra Hopkins

Sometimes, people describe an electron which is in a superposition by saying that it’s in more than one place at the same time. Or it’s spinning both clockwise and counterclockwise at the same time. In the famous Schrodinger Cat Thought Experiment, the cat ends up in a superposition of being both dead and alive at the same time. A superposition can be described in a quick and dirty way as: a state of simultaneously having two or more properties which conflict with each other.

Schrodinger’s cat in a superposition of being dead and alive. [Image source: By Dhatfield – Own work, CC BY-SA 3.0, File:Schrodingers cat.svg]

This video (below) is an animation of an atom that is in a superposition of being in two places at the same time and an atom in a superposition of being at two energy levels at the same time.

So, saying that a quantum particle is in more than one (conflicting) state at the same time is a quick and dirty way to describe a “superposition.” And it gets across the general idea. But it’s not really accurate, and we can’t wrap our minds around it. How can an atom be in more than one place at the same time? How can a cat be both dead and alive? What’s really going on?

Example of a Quantum Superposition

To explain what’s really going on, consider an experiment in which an electron is trapped in a box. The box has magnets lining all its interior surfaces. Electrons act like little magnets, so the electron is repelled by the magnets which surround it on all sides—this is called an “electron trap.” The box also holds an electron detection screen. A pixel in the screen will light up when the electron interacts with it.

Let’s say that a physicist would like to calculate where the electron is. She has data about the trajectory of the electron when it was shot into the box, the strength of the magnets, etc. She calculates using an equation derived from the Schrodinger Wave Equation. This derived equation is called a “wave function.” (A function is a common type of equation, often referred to in algebra.)

If the electron were like a baseball, the wave function would tell us where the electron is at any moment in time. Staying with the baseball analogy, if a batter were to hit the ball with a known amount of force, physicists could calculate its position at any particular moment in time. They would apply the laws of force originally developed by Isaac Newton in the 1600’s. Every moment, the baseball would occupy a different position in spacetime. When it was caught, it would be in spacetime too. It never disappears from spacetime.

This is not the way quantum particles behave.

The wave function derived from Schrodinger’s Equation doesn’t tell us where the electron is. Nor does it tell us that the electron is in many places at the same time. Instead, the wave function tells us a set of probabilities as to where the electron will appear if it is detected. The wave function assigns a probability to each spacetime position in which the electron could possibly be detected.

Graph of a superposition. It graphs the probabilities as to where the electron might be detected in an electron trap. Each wave peak represents a PROBABILITY of an experimental result rather than representing the position of a physical object. According to this graph, the electron is equally likely to be found in six different positions when it is detected (A, B, C, D, E, F).

While the physicist would like to calculate where in the box the electron is at any one moment, the best that she can do is calculate the probabilities of where it will be on the detection screen when it lights up a pixel.

What does this have to do with superpositions?

The electron is in a superposition until detected. When not detected, it isn’t considered to be in position in spacetime. Rather, it’s in a quantum superposition of probabilities. Physicists describe the electron as being in a “probability state” or a “probability wave” or an “electron cloud.” This superposition can be described mathematically. But it cannot be described as an object in a particular position in spacetime or even in more than one position in spacetime.

People do say that the electron is in more than one position at the same time, but this isn’t accurate. This description is like parents talking about the stork when children ask where babies come from—the real answer is daunting.

Quantumland

This explanation of “superposition,” that it is a state which is not in spacetime, comes from the Transactional Interpretation* of quantum mechanics.

In this interpretation, quantum particles are in Quantumland, and Quantumland is a level of reality underlying spacetime. The wave function, not Newton’s Laws, are used to calculate the wavy, apparently insubstantial, possibilities of where the electron will be detected.

Quantumland (on left) and spacetime (on right).Click for an explanation of the phrase “collapse of the wave function.” [Image source: David Chalmers and Kelvin McQueen, “Consciousness and the Collapse of the Wave Function” http://consc.net/slides/collapse… (http://consc.net/slides/collapse…)]

While Quantumland may seem insubstantial, it determines what happens in spacetime. True, Quantumland only sets the probabilities, but the behavior of quantum particles which are detected in spacetime must conform with these probabilities.

This interpretation of the nature of a superposition is only one of about 15 interpretations of quantum mechanics. The various interpretations all provide the same or nearly the same mathematical description of a superposition—the wave function derived from Schrodinger’s Wave Equation. But the interpretations assign different physical meanings to the wave function.

*For more about the Transactional Interpretation, see Dr. Ruth E. Kastner, Understanding Our Unseen Reality, Solving Quantum Riddles.

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