We ordinarily begin by assuming that things exist independently and that relationships arise between them. A tree exists, a bird exists, and the relationship between them might be that the bird nests in the tree. The relationship depends upon the things involved, but the things do not necessarily depend upon that particular relationship.
This seems an entirely reasonable way of understanding the world. Yet quantum entanglement invites us to reconsider whether it is always adequate.
In the previous instalments, we encountered two particles whose shared quantum state could not be adequately described by assigning each particle an independent state. We also discovered that the correlations between them could persist even when the particles were spatially separated.
We can now ask a rather different question.
What if the relationship between two things is not simply something that exists between them, but something that participates in determining what the system comprising them is?
To understand why this question arises, we need to return briefly to the mathematics of quantum entanglement.
When physicists describe a composite quantum system, they can assign a quantum state to the whole and, where appropriate, describe its constituent subsystems separately. In an ordinary unentangled state, the joint state can be expressed as a combination of the independent states of its parts.
An entangled state cannot be expressed in this way.
The distinction has an important consequence. Knowing the quantum state of the whole does not necessarily allow us to reconstruct it simply by knowing the individual states of its constituent parts.
Indeed, an entangled system can have a perfectly well-defined joint quantum state while the individual subsystems, considered separately, have mixed states. The whole can therefore possess a definite quantum description that is not recoverable from the descriptions of its parts considered independently.
This is not a limitation imposed by our inadequate knowledge of the particles. It is a feature of the mathematical structure of the quantum state.
Consider again a pair of spin-entangled particles. If we measure the spin of either particle along a particular direction, the individual result is unpredictable. Yet the results obtained from measurements of both particles along that direction are perfectly correlated or anticorrelated, depending on the state.
The relationship between the outcomes is specified by the joint quantum state, even though neither individual outcome is determined in advance in the ordinary classical sense.
The information needed to describe the system is therefore not contained entirely within the separate descriptions of its parts.
This is sometimes called quantum holism or quantum nonseparability. The terminology reflects a departure from the assumption that the state of a whole physical system can always be understood in terms of the independently specified states of its constituent subsystems.
But we should be careful about what follows.
Entanglement does not mean that the individual particles cease to exist. Nor does it mean that every property of either particle is determined by its relationship with the other. The particles remain distinguishable subsystems, and we can still investigate them separately.
What changes is the adequacy of describing the complete system as though its parts possessed all the information required to characterise the whole.
The relationship, in this sense, is not merely an additional feature of an otherwise independently specified system.
It is part of the system's physical description.
There is a philosophical distinction here that deserves our attention.
We can distinguish between two broad ways of understanding relationships.
In the first, entities possess their properties independently, and relationships are established between them. The entities are primary; their relationships are secondary.
In the second, the relationships between entities participate in constituting the nature of the system to which they belong. The entities cannot be fully understood without taking those relationships into account.
Quantum entanglement provides a striking example of the second situation, at least at the level of the quantum state.
It does not, by itself, settle the philosophical question of whether relations are more fundamental than the entities they relate. Physicists and philosophers continue to disagree about how the mathematical structure of quantum mechanics should be interpreted ontologically. Some approaches emphasise the whole system; others give greater importance to relations between its constituent systems.
But the question itself is no longer merely abstract.
Quantum mechanics has provided us with a physical situation in which the assumption of independently complete parts fails.
There is another qualification worth making. Entanglement is defined relative to a particular division of a quantum system into subsystems. The same physical system can sometimes be described using different choices of subsystems, with different consequences for whether its state is entangled. This reminds us that even the identification of the parts involved in a relationship requires care.
We should therefore resist turning entanglement into a universal philosophical principle. It does not establish that everything in nature is constituted by relationships in the same way.
Nevertheless, it gives us a reason to question a deeply familiar assumption: that relationships must always be secondary to the things related.
Perhaps the more interesting possibility is that the relationship between entities can sometimes be part of what makes them the particular entities they are within a larger system.
This takes us beyond quantum physics, although we should not confuse the different kinds of relationships involved.
A biological organism, for example, cannot be adequately understood simply by listing its constituent cells. The organisation and interactions of those cells are essential to the functioning of the organism. Similarly, a social community cannot be understood simply by listing its members. The relationships between them participate in constituting the community itself.
These are not instances of quantum entanglement. They involve different physical and organisational processes. But they illustrate a broader conceptual possibility: the nature of a whole may depend upon relationships that cannot be understood merely by examining its parts separately.
And this brings us to a question that will accompany our wider exploration.
Perhaps we have too readily assumed that things must first exist independently before they can enter into relationships.
What if, in some circumstances, the relationships are already part of what makes the things what they are?
Quantum entanglement does not provide a universal answer. But it makes the question considerably more interesting.
We have moved from two particles sharing a quantum state to the possibility that relationships can be constitutive of the systems in which they occur.
Our next question concerns another relationship: the one between a quantum system and the process through which we observe it.
For if the state of a quantum system cannot always be understood independently of the other systems with which it is entangled, what happens when one of those systems is the measuring apparatus?
And does the presence of an observer change anything fundamental?
That is where we shall turn next.
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