What is superposition?

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Somebody already asked this question ([here](https://www.reddit.com/r/explainlikeimfive/comments/26uzgu/eli5_quantum_mechanics_superpositions/)), but I did not really understand the explanation, and the post was archived so I can’t ask for a more detailed explanation.

In: Physics

4 Answers

Anonymous 0 Comments

An object in a super position is in all the possible states at once.

The classic analogy is [Schrödinger’s cat](https://en.wikipedia.org/wiki/Schr%C3%B6dinger%27s_cat). One state the cat can be in is alive. The other state it can be in is dead. A super position of the cat is both alive and dead.

A more literal example is can be found in the [double slit experiment](https://www.youtube.com/watch?v=Q1YqgPAtzho). An electron could have passed through one slit or another. When it is in a super position, it travels through both slits, no slits, one slit, and the other, all at the same time. It is in all the possible positions. When observed in such a way that we know what slit it travels through, the super position collapses into one state. It only travels through one slit.

Anonymous 0 Comments

I don’t remember where I saw this explanation but here it goes (it also explains the quantum entanglement).  Let’s say you have a new pair of socks. Before you put them on, both socks can be both left and right at the same time but they are neither until determined (both are in superposition) but as soon as you put one of them on (for example on your right foot), the other one immediately becomes the opposite (left). You cannot know which one is which before you put one of them on and both of them can be right or left with equal probability and as soon as you determine one of them, the other one also gets determined immediately and becomes the opposite of the first one.

Anonymous 0 Comments

Superposition is a common misconception in which things are thought to be in two different states at the same time. The way that an object/particle is indirectly observed can sometimes be written as an equation with two different solutions – or two (or more) possibilities for its state that would show the same result.

Through direct observation, we can sometimes see the actual state. However, direct observation of something like a particle by definition involves interacting with it in some way, which adds bias to the experiment whether we want to or not.

Schrodinger’s cat is a though experiment in which the idea of superposition is explained. We have no way of looking inside the box, and nothing in the box can change anything outside of the box, so to us, the cat could be either dead or alive. Sometimes people think this means that the cat is both dead and alive.

In reality, the cat is not existing in both states. It is either dead, or it is alive. The misconception comes from the fact that to the rest of the universe there is no way to prove if it is dead or alive and thus mathematically it could be either.

Edit: So to clarify, superposition is when something *could* be in *either* state based on indirect observation, not when it is in *both* states simultaneously.

Anonymous 0 Comments

Superposition is an attribute of physical systems described by linear equations.

A linear equation has the property that if x and y are solutions of the equation, and a and b are two arbitrary constants, then a*x+b*y is also a solution to the equation.

If a physical system is described by a linear equation, then physical states correspond to solutions of that equation. For example x and y might be two different electron spins or two different propagating waves. Superposition means that a*x+b*y is also a possible state of the physical system.

Superposition can be found in classical or quantum physics, usually in the context of waves. For example in classical electromagnetism superposition means that some light waveform propagating through space can be described as a sum of a combination of plane waves.

In quantum mechanics superposition is particularly important because states are described by waves functions that are solutions to the Schrodinger equation. A sum of different wavefunctions can be a state of the system.

The principle of superposition it’s important because there is usually some set of solutions that don’t overlap with each other, called an orthogonal basis. For vibrations of a strong tied at two ends they are the normal modes. For a quantum system they are the energy eigenstates. In any case, knowing about an orthogonal basis means operations on a superposition of those states is easy to work with because you can apply the operations to each basis state without affecting the other states.