3rd May 2017

The Paradox of Reality

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Linde Wester, a fourth year DPhil in Computer Science

Reality cannot exist. At least not any reasonable reality. A reasonable reality must satisfy some basic assumptions such as causality: the idea that the past can influence events in the future, but not the other way around.

We’ve known this since 2005, when research groups from The Netherlands and Switzerland conducted the first ‘loophole-free Bell-tests’, named after physicist J.S. Bell. Their experiments demonstrate that there is no objective reality, independent of an observer and a particular setup of an experiment. This phenomenon is called ‘contextuality’ and it lies at the heart of the peculiar behaviour of tiny particles that inspired Nobel Prize winner Niels Bohr to say: ‘If quantum mechanics hasn’t profoundly shocked you, you haven’t understood it yet’.

What we mean by an objective reality, loosely speaking, is a description of the universe in which at each point in time, every particle has a specific place, energy, and other characteristics. Measuring the position or energy of a particle or object means recording their ‘true’ values. The absence of an objective reality is shocking to most scientists, but not to everyone. Nearly all aspects of the human experience are subjective, so why would physics be any different?

Traditionally, physicists seek to understand the world in a way that is independent of our individual perception. This is a somewhat idealised scenario. When we measure the speed of a car, the accuracy of the result may in fact be influenced by the strength of our glasses. However, it should not depend on the colour of our jacket, the time of the day, or the temperature of the North Sea. A good experiment is repeatable and gives the same result every time within a certain margin of error. In general, this works. We understand the laws of physics so accurately, and nature follows them so consistently, that we can get airplanes to fly and televisions to display the news. If the laws of physics are subjective, this can only be very marginally the case.

The same holds for quantum mechanics, but in a subtle way. There are two fundamental differences. Firstly, many aspects of quantum mechanics cannot be predicted with certainty, we can only predict the likelihood of different outcomes with high precision. Secondly, there are certain measurements we can never do simultaneously. As we will see, there is nothing shocking about either of the two differences, but the combination makes very peculiar phenomena possible.

There are many aspects of the world that cannot be predicted with certainty. Take for instance a fair coin toss. We know that when we flip a coin often, roughly half of the time we get heads and half of the time we get tails. This gives us an ‘objective’ way of describing the outcome of a coin toss. It is repeatedly found to be accurate up to a certain, predetermined, margin of error. However, these probabilities are not the only way to describe the process of flipping a coin. If we know the exact speed and angle with which the coin is flipped, as well as its distance to the ground, we could predict which side will land face-up with certainty. It is our lack of knowledge that makes the outcome appear random. This is where uncertainty in quantum mechanics differs. As I will explain shortly, probabilities in quantum mechanics cannot be attributed to our lack of understanding. They must be somehow essential to nature.

The reason why some experiments cannot be performed simultaneously is not surprising either. There are many things in real life that cannot happen at the same time. For instance, we cannot drill a hole and listen to the ticking of a clock, simply because drilling the hole makes too much noise. In a similar way, we cannot do certain measurements at the same time, because they require us to do incompatible actions.

The combination of uncertainty of outcomes and incompatible sets of measurements facilitates a world full of paradoxes: self-contradictory statements that at first seem true. The only reason that we don’t see these contradictions is that we can never observe all aspects of the world at once. To understand how this works, we turn our attention to something totally different: the ‘impossible’ drawings of M.C. Escher.


Imagine that you encounter the building in the picture. It is a very misty day. So misty, that you can only see one of its corners. You would like to understand how it is built, so you walk around it. Wherever you go, you can only see one corner of it at the same time. Depending on how you look at the different parts, the stream seems to be going to the left, or to the right. At any point in your exploration, it looks like a perfectly normal building. Only when you sit down and you try to make a drawing of the entire structure, you realise that you have drawn something impossible: some of the streams are going up and down at the same time. You wonder if you have made a mistake, or if something mysterious is going on. Perhaps the direction of the stream somehow changes at night? Maybe there is some force that we don’t understand, that can explain our seemingly contradictory discovery? No, that cannot be. There is no way to draw each part of the stream of water in a way that all parts can be connected to each other. So even if a mysterious force exists, at no point in time could the total structure make sense.

Similarly, we can do experiments in the lab with sets of incompatible measurements that have no possible joint outcome. The outcomes of the experiments are related to each other in a way that any outcome to the last measurement would contradict the outcomes to all other measurements. There is no complete description of reality that could explain everything we see, which is not as impossible as the drawing of the building. This means that the uncertainty in quantum mechanics cannot be explained by a lack of knowledge of the world. After all, any reasonable explanation would give us a correct drawing of the building.

We are left with two options: either there is no objective reality, or this reality contains contradictions. How can it then be that at a larger scale, the physical world we experience is so well-behaved and predictable? This is exactly the reason why we should be shocked. As Bohr supposedly said, ‘Everything we call real is made of things that cannot be regarded as real’.

Decades later, the reality of quantum mechanics remains puzzling. We still cannot claim to really understand nature, but at least the loophole-free Bell-tests have proven to us that we are right to be puzzled.

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