It stands to reason that electromagnetism is a theory of electric and magnetic fields. But since when is anything in physics so straightforward? Although Maxwell’s equations of electromagnetism in their usual formulation do contain electric and magnetic fields, those equations can be rewritten in terms of a mathematical function called the potential. So what is the true subject matter of the theory? Fields or potential?


Richard Healey, a philosopher of physics at the University of Arizona, discusses this conundrum in an interview I conducted last June at a conference on the philosophy of quantum gravity, organized by Christian Wüthrich at the University of Geneva and Nick Huggett at the University of Illinois in Chicago. And his answer is: neither.



Electric and magnetic fields fail to explain certain electromagnetic phenomena—notably, the so-called Aharonov-Bohm effect. (For more on that weird phenomenon, see my interview with Yakir Aharonov.). The potential, for its part, smacks of mathematical artifact. Its value at any point in space is meaningless. Only the difference between values at two separate locations matters. You can measure the potential difference across two wires—we call it the “voltage”—but your voltmeter won’t tell you the potential of a single wire in isolation.


Healey has pursued an alternative reading of electromagnetism that goes back to Michael Faraday and was developed in the 20th century by physicists such as Paul Dirac, Tai Tsun Wu, and Chen-Ning Yang: that electromagnetic effects are produced by nonlocal objects, ones that do not reside at any specific location and cannot be decomposed into localized parts, but are inherently spread out. You can see this with voltages: They necessarily involve the comparison of two locations. Magnetic effects depend on the value of the potential around closed loops. What we call the electromagnetic field is not a tidy garden but a tangled bank. This breed of nonlocality is quite distinct from the usual example of quantum entanglement.


Healey’s views have shifted somewhat since I talked to him for Chapter 5 of my book. He had hoped that nonlocal objects would fill in the blanks not just of electromagnetism, but also of quantum field theory more broadly. It stands to reason that quantum field theory is a theory of fields. But the word “field” evokes a physical structure with particular values at each location, and a quantum field is nothing like that. Nor, despite the term “particle physics,” can the theory be about particles. The word “particle” connotes a little billiard ball—a localized object with an enduring existence—and quantum field theory permits no such thing. So maybe those nonlocal objects are its true subject matter.


Since then, though, Healey has argued that we should give up the fruitless search for “the” structure that quantum field theory says is out there. He thinks that quantum theory, by its very nature, is incapable of addressing that particular question. If he’s right, we will need to search for a non-quantum theory in order to know what the world is ultimately made of.