Coincidences in quantum physics

Coincidences play a major role in our life. We accidentally make friends, gather experiences or win the lottery. However, random events in our macroscopic world are often not really random yet rather predictable given the full amount of available information. This seems to be different in the quantum world, which as we presently understand it hosts pure coincidences, meaning events with no underlying reason or cause.

Albert Einstein wanted to explain the world as being causal. There should be a cause for every effect, even if we are not always able to recognize it. This is why he was entirely unsatisfied with the occurrence of coincidences in quantum physics, and remained so until the end of his days. His objection to this is often framed by the quote “God doesn’t play dice”; contemporary sources state that he actually phrased this in a much less polite manner. Niels Bohr, his great opponent in quantum physics, basically responded to Einstein by saying that he shouldn’t tell God how to run the world. Today, nearly 90 years after Einstein’s first protests, science is still convinced that randomness governs main areas of quantum physics.

Quantum physics only predicts the results of experiments and/or measurements in a statistical manner. Which of all possible results a single measurement yields is totally coincidental, cannot be traced back to an underlying cause and can therefore not be predicted for a single case. The mathematical tool for the statistical evaluations is the so-called wave function; the square of its absolute value determines the probability of a certain result. So much for background information, now let’s move on to a simple example which is actually of great practical relevance, as we will later see.

Light-Polarization Experiment
Picture 1: Light polarization experiment

In a polarization experiment as shown in picture 1, we send light from a light bulb through two polarizers. We commonly use such polarizers as filters in cameras or in polarized sunglasses, to improve contrast perception under conditions of bad visibility. Light can be polarized or unpolarized; this property determines whether the according light waves oscillate in one direction or in all directions normal to its path of propagation. A polarizer only lets light with one oscillation plane pass, so the light is subsequently polarized.

The light source in picture 1 emits unpolarized light, depicted as four double-headed arrows. The portion of the light whose oscillation plane is normal to the “bars of the grid” passes through the polarizer, the other portion is reflected or absorbed. After the 0° polarizer, the light travels on at half the original intensity and is vertically polarized, as symbolized by the vertical double-headed arrow. This light hits the second polarizer, which is turned by 45°. This light is then polarized by 45°, its intensity again being reduced by 50 %. If this second polarizer were turned by 90°, no light would pass through; if it were aligned with the first polarizer, all the remaining light would pass through, as Malus’ law tells us.

Now where does coincidence come in?

To recognize the random event here, let’s imagine an extremely weak light source that only emits single unpolarized photons. Now half of the photons go through the 0° polarizer; these photons are vertically polarized and hit the 45° polarizer. According to Malus’ law, half of the light that enters the 45° polarizer passes through. However, how can this be explained if we view light as particles? Since, as we know, photons are indivisible, no half-photons can pass through. So on average only every second photon can pass through the 45° polarizer in order to cut the light intensity down by one half. This is where coincidence comes in: Whether a certain photon passes through the polarizer or not is entirely coincidental and cannot be traced back to a certain cause. Averaged across many photons, exactly 50 % pass through.

Every user of polarimeters, which are instruments for determining the optical activity of molecules, conducts the above described experiment – usually without knowing it. Many molecules come in the form of two enantiomers, as shown in picture 2. These molecule variants are like our hands, they mirror each other and can therefore not be superimposed in such a way that their shapes match. Enantiomers typically show the same chemical behavior but can have completely different biological effects. This is why it is extremely important, especially in the case of pharmaceutical ingredients, to be able to differentiate between such molecule variants. This is possible because these variants, brought into solution, rotate the oscillation plane of polarized light in different ways. To analyze this property, you need a polarimeter.

An example of two enantiomers
Picture 2: An example of two enantiomers
Picture source:

The inner setup of a polarimeter matches picture 1, with the sample brought between the two polarizers. The second polarizer is now called an analyzer and can be rotated. By rotating it in such a way that the intensity of the passed light is minimized, we can determine by which angle the sample rotated the light’s oscillation plane. If the concentration of the sample in the solution is known, this measurement tells us whether the sample contains only one of the two enantiomers or a mixture of both. Picture 3 shows the MCP 100 polarimeter from Anton Paar, which conducts this type of measurement fully automatically and is used with great success in the pharmaceutical industry.

Picture 3: MCP 100 polarimeter from Anton Paar

In summary, it is clear to see that quantum physics is still governed by the pure coincidences that gave Albert Einstein such headaches. In any case, the technological basis for state-of-the-art analytical instruments is informed by this kind of coincidence, and these instruments are applied, for example, to make pharmaceutical production safer. In this way, these instruments can help produce the means for getting rid of headaches.

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