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Physik-Institut

Superposition: everything at the same time

The superposition principle states that an object's state need not be confined to a single, specific state; it can exist in multiple possible states simultaneously. Only when a measurement is made does the system "select" one of these states, an idea that we are not familiar with in our everyday lives. In physics, this means that when a measurement is carried out, the wave function "collapses" and the particle immediately assumes a state. In entangled systems, where particles are connected to each other, measuring one particle changes the state of the other particle instantaneously, even if they are far apart. Einstein called this phenomenon "spooky action at a distance." At first, this seems to contradict the theory of relativity's statement that information cannot travel faster than the speed of light. However, it can be shown that no real information is transported by entanglement experiments.

Schrödinger's Cat

Schrödinger's cat is a famous thought experiment that illustrates the principle of superposition.

In quantum mechanics, an atom exists in a superposition — both decayed and not decayed — until it is observed. Similarly, the cat's state is a superposition until it is observed; it is both alive and dead. Only when the box is opened is the cat's state defined — it is either alive or dead.

Fortunately, this thought experiment remains in the realm of imagination — quantum mechanical laws cannot simply be transferred to macroscopic systems.

schroedingers cat
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Illustration of the thought experiment: In a box, from left to right, there is: a Geiger counter, a hammer, a vial of poison gas, and a cat.
When the atom decays, the Geiger counter triggers the hammer to fall. The hammer then breaks the vial of poison gas, which kills the cat. The cat dies. If the atom does not disintegrate, the cat remains alive.
Picture: Ruth Bründler, UZH

 

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More on: Superposition and Entanglement

The simplest way to represent quantum mechanical entanglement is to consider objects characterised by a few quantum mechanical states. For example, an electron's magnetic moment (spin) can point either up (|↑⟩) or down (|↓⟩), as introduced by Paul Dirac. Two spatially separated electrons (i.e. distinguishable electrons) then have four possible states, which we can write as |↑⟩, |↓⟩, |↑⟩, |⟩, , where the first arrow indicates the state of the first electron and the second indicates the state of the second. To explain entanglement, we need to describe two more things:

1) Superposition of states (superposition principle):
Like superposition of multiple waves, quantum mechanics allows a system of two electrons to be in a superposition of multiple states. For example, we can write |↑⟩+|⟩ to signal that the two electrons are in a superposition of the states |⟩ and |⟩. This can be imagined via the polarisation of a light wave, for example, where the superposition of up-down and left-right oscillations results in a diagonally upwards oscillation. However, electron spins do not permit intermediate movements, so we can only speak of the superposition of |↑⟩ and |↓⟩.

2) Measurement in quantum mechanics:
A principle of quantum mechanics states that the measurement of a system can only ever provide one (classical) result. If you measure the spin of an electron, you therefore get the result ↑ or ↓. This is unambiguous if its state is |↑⟩ or |↓⟩. But what if the electron to be measured is in a superimposed state |↑⟩+|↓⟩? Even then, you only get ↑ or ↓ in a measurement, but each result can occur with the same probability. So if you repeat the same experiment 100 times, you will have measured ↑ approximately 50 times and ↓ 50 times. The measurement thus becomes a question of probabilities. This can also be imagined a little more vividly with the polarization of (light) waves. A diagonally polarized wave that falls on a vertical polarizer is only partially transmitted. The reduced intensity corresponds to the reduced probability of finding a particle in one of the two superimposed states and thus the incident polarization can be determined from this intensity.  After the measurement, the system is also in the state that corresponds to the measurement result. So if you measure an electron in the state |↑⟩+|↓⟩ and obtain ↑ as the result, the electron is now definitely in the state |↑⟩. This is also the case with the (light) wave when a polarization measurement is carried out: a diagonally polarized wave is measured with a vertical polarizer and the continuous wave is measured with a vertical polarizer.

 
Let's go back to the two electrons in the state |↑↓⟩+|↓↑⟩. They are entangled in this state. This can be seen in measurements if you first measure electron 1 and then electron 2: If, for example, you measure ↑ for electron 1, the system of the two electrons is certainly in the state |↑↓⟩ after the measurement. If electron 2 is now measured, the measurement result ↓ will therefore be certain. If, on the other hand, electron 2 had been measured without electron 1 having been measured beforehand, the result ↑ or ↓ for electron 2 is 50% likely. The measurement on electron 1 thus influences the possible result for electron 2 - a result of their quantum mechanical entanglement. In principle, this also works if electrons 1 and 2 are infinitely far apart. In practice, it has already been possible to entangle objects over 1000 km apart.

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