We assume that objects are more fundamental than the relationships between those objects. However, philosopher George Webster argues that quantum mechanics upends this common-sense picture. In the quantum world, relations like symmetry are more real than the particles themselves. But neither our everyday language, nor the language of logic favored by philosophers, can make sense of this. Webster suggests that we turn to the weird and wonderful language of Gilles Deleuze to truly comprehend the quantum picture of reality.

The everyday picture: a world of objects

We ordinarily think of the world as a collection of things or individual objects: tables, trees, planets, particles, people.

This way of thinking is not only intuitive but also tremendously useful. Whether crossing a busy street or hunting prey, we survive by tracking the motions of objects—judging their distances, anticipating their paths, and timing our actions accordingly. Evolutionarily speaking, this is a worldview to which humanity owes its continued existence.

But it is also a worldview motivated by a very specific practical context. We occupy an extremely limited perspective on the world, and we have little reason to believe that that perspective (i.e., an observational window ranging from millimetres to miles and from milliseconds to a century or so) accurately represents the universe at its grandest quantum and cosmological scales.

Indeed, not only do we have little reason to suppose that our practically motivated model of the world accurately reflects reality, but we also have positive reason to believe that it fails to do so. This is because science—and recent philosophical reflection on the sciences—suggests an alternative account. That is, one according to which not objects but relations are the ultimate constituents of reality.

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What is fundamentally real are not particles as such, but rather the laws and symmetries (such as permutation invariance) that govern their behaviour.

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But this is a strange thought. Relations such as “being in love with” or “standing taller than” or “moving faster than” all seem to presuppose the objects between which they obtain. Relations, in other words, seem to depend upon objects for their existence. So why invert this picture? And how does a figure seemingly irrelevant to contemporary philosophy of science (the twentieth-century “post-modern” French philosopher, Gilles Deleuze) help us to make sense of this inversion?

Quantum theory and why objects are not fundamental

Cause for a relations-based worldview can be found in quantum theory (or, more specifically, quantum statistics).

Two coins flipped simultaneously will produce one of four outcomes—each occurring with equal frequency when the experiment is repeated continuously. Two elementary particles (in this case bosons), on the other hand, fired through an appropriate experimental setup designed to measure analogous properties (e.g., spin-up and spin-down), will produce three outcomes—each occurring with equal frequency.

Classical

Quantum

State

Probability

State

Probability

HH

1/4

↑↑

1/3

TT

1/4

↓↓

1/3

HT

1/4

↓↑ = ↑↓

1/3

TH

1/4

In the case of the coins, the fourfold probability distribution is explained partly by the fact that we can count a mixed result in two distinct ways: one coin displaying heads and the other displaying tails, and vice versa. Even though the coins may be the same denomination (e.g., both fifty-pence pieces), they are distinct objects and so exchanging them counts as a different physical state.