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Nonlocality from Newton to Maxwell

This story is a supplement to the story "Was Einstein Wrong?: A Quantum Threat to Special Relativity"
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The article "A Quantum Threat to Special Relativity" by David Z Albert and Rivka Galchen discusses how the quantum phenomenon of entanglement overturns our intuition that the world is "local". That is, we can directly affect only objects we can touch, and indirect effects must be transmitted by means of a chain of events that each act locally. The great physicists Niels Bohr and Albert Einstein clashed over the implications of apparent nonlocalities in quantum mechanics, but neither imagined the universe could actually be nonlocal. Yet work by theorist John S. Bell in the 1960s and by experimenters beginning in the 1980s has conclusively confirmed the nonlocal quantum nature of the world.

As Galchen and Albert describe here, scientists were haunted by apparent nonlocalities centuries ago, and thought they had successfully banished them from physics.

—The Editors

Nonlocality from Newton to Maxwell

Three hundred years ago, when Isaac Newton produced the first modern scientific description of it, gravity appeared to be a nonlocal force, and thus be ludicrous, and so it earned the doubt-drenched moniker, "action at a distance". Newton himself—after repeated attempts at producing a local account of gravitation, including one in which all of what appears to us to be empty space is in fact filled with tiny invisible jiggling particles—came to regard his own theory as a merely phenomenological account of what happened in gravitating systems, an account that failed to get at the fundamentals. Newton came to regard the apparent nonlocality of his theory (that is) as a symptom of its limitations. And so things stood, for a good, long while.

The study of electromagnetism during the 19th century initially brought with it the same apparent shortcoming, again seemed to show forces acting at a distance, and not through intermediary matter, and not through intermediary anything—a perennially unwelcome magic.

But as the century progressed, what began merely as a notational convenience—the notation of fields—grew fashionable, and field notation allowed physicists, at least formally, to describe electromagnetism in a way that superficially conformed with the requirements of locality. Electrically charged particles (for example) were treated in this notation as giving rise to an electric field, which extended out to infinity, and penetrated into every point in space. And the capacities of such particles to push and pull on one another from a distance was treated in this notation as arising out of a perfectly local interaction between each one of the particles in question and the electric fields associated with the others. Nobody, however, thought of fields, early on, as anything more than a matter of bookkeeping. They were not considered a part of the fundamental ontology of the world, not something you might, say, stub your toe on, not (most certainly) a real thing.

But then, under the influence of Michael Faraday and James Clerk Maxwell, there was a great sea change, precipitated by a number of transformative observations.

First: by the latter part of the 19th century, the laws of conservation of energy and momentum were deeply entrenched in the scientific conception of the world—and it was noticed that the total energies and momenta of isolated collections of material particles were frequently not conserved when electric or magnetic interactions were involved. Maxwell then realized that a very simple formula could assign energy and momentum to fields, and that after doing so, conservation of energy—of particles and fields together—could be restored. (The formula for assigning energy and momentum to fields was remarkably elegant, and therefore compelling.) So there was a kind of invitation: Treat fields as real, and you can hang onto the laws of conservation.

Also: Maxwell discovered that fields have a rich dynamical life of their own. This discovery came about as Maxwell tried to write down generalizable equations, based on the piles of empirical data generated by Faraday, for how fields changed over time. Faraday's data had led Maxwell into a paradox, because depending on how field values were calculated, two different and contradictory answers could be generated.

And here was the beautiful turn. Maxwell tried to look for a minimal modification of his theory that would resolve this paradox, and what he arrived at was the discovery that there can be interestingly evolving electric and magnetic fields even in the complete absence of charged particles—so called charge-free solutions. (This discovery must have felt like discovering, say, that there can be completely disembodied toothaches.) The particleless fields (it turned out) could push one another around, and their subsequent chain of oscillations would propagate through space at a particular velocity, a velocity that just happened to correspond to the then very recently measured speed of light.

This "coincidence" was astonishing. Light was something that physicists had imagined they would get around to sometime in the relatively distant future, it was something understood virtually not at all. But then, suddenly, they not only knew what light was, but the necessity of its existence had been deduced as a matter of logic. A marvel.

And here was the best news: Once Maxwell's equations were modified, you could ask a question about the forces between two charged particles a certain distance apart and you could find out if the attraction between them acted locally. You just had to ask yourself what would happen if you moved one of the particles…at what rate would that lead to the other particle being affected by a different field? It turned out that the spherical shell of readjustments expanded outward at the speed of light.

So electromagnetic (and, for that matter, gravitational) attraction was understood to be a completely local phenomenon. (Physics seemed, suddenly, very nearly over; the euphoric sense was that all that remained to be done was the working out of a few details.) The 300-year thorn of nonlocality simply disappeared, and the cost of all this advancement was just that the fundamental ontology—the furniture of the universe—essentially doubled. There were now material bodies, and fields. And both were real. Maxwell's triumph meant a spectacular validation of our deep intuition of locality.

And it also prefigured locality's falling apart in the work of John S. Bell. It is understandable that a problem with locality was the last thing Niels Bohr or Albert Einstein would have suspected. Since the beginning of physics nonlocality has been the branch tapping at the windowpane, waiting to be acknowledged—a patient but enduring ghost, still waiting to be let in.

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