# The non-locality mess

## Demystifying quantum mechanics VII

The title comes from a section heading in a paper a recently saw. Due to a serious issue with some confusion that exists in the literature, the author advocates that the physics community abandon the notion of non-locality in favor of correlations that can be observed experimentally.

The problem with the community is that it consist of a very diverse collection of people with diverse perspectives. So, the chances are small that they’ll abandon the notion of non-locality. However, it is not unreasonable that one may be able to clarify the confusion so that the community will al least know what they are talking about.

The problem comes in because people mean different things when they use the term “non-local.” The traditional meaning is associated with “spooky action at a distance.” In other words, it refers to a non-local interaction. This meaning is best understood in the context of special relativity.

Consider two separate events, which one can think of as points in space at certain moments in time. These events are separated in different ways. Let’s call them A and B. If we start from A and can reach B by traveling at a speed smaller than the speed of light, then we say that these events have a time-like separation. In such a case, B could be caused by A. The effect caused by A would then have travelled to B where a local interaction has caused it. If we need to travel at the speed of light to reach B, starting from A, the separation is called light-like and then B could only be caused by A as a result of something traveling at the speed of light. If the separation is such that we cannot reach B from A even if we travel at the speed of light, then we call the separation space-like. In such a case B could not have been caused by A unless there are some non-local interactions possible. There is a general consensus that non-local interactions are not possible. One of the problems that such interactions would have is that one cannot say which event happened first when they have a space-like separation. Simply by changing the reference frame, one can chance the order in which they happen.

As a result of this understanding, the notion of non-local interactions is not considered to be part of the physical universe we live in. That is why some people feel that we should not even mention “non-locality” in polite conversation.

However, there is a different meaning that is sometimes attached to the term “non-locality.” To understand this, we need three events: A, B and C. In this case, A happens first. Furthermore, A and B have a time-like separation and A and C also have a time-like separation, but B and C have a space-like separation. As a result, A can cause both B and C, but B and C cannot be caused by each other.

Imagine now that B and C represent measurements. It would correspond to what one may call “simultaneous” measurements, keeping in mind that such a description depends on the reference frame. Imagine now that we observe a correlation in these measurements. Without thinking about this carefully, a person may erroneously conclude that one event must have caused the other event, which would imply a non-local interaction. However, based on the existence of event A, we know that the cause for the correlation is not due to a non-local interaction, but rather because they have a common cause. In this context, the term “non-local” simply refers to the fact that the observations correspond to events with a space-like separation. It does not have anything to do with an interaction.

When it comes to an understanding of entanglement, which we’ll address later in more detail, it is important to understand the difference between these two notions of non-locality. Under no circumstances are the correlations that one would observe between measurements at space-like separated events B and C to be interpreted as an indication of non-local interactions. The preparation of an entangled state always require local interactions at A so that the correlated observations of such a state at B and C have A as their common cause. The nature of the correlations would tell us whether these correlations are associated with a classical state or a quantum state.

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