The Changing Meaning of “Explain”

This is another “explanations are weird” post.

I’ve been reading a biography of James Clerk Maxwell, who formulated the theory of electromagnetism. Nowadays, we think about the theory in terms of fields: we think there is an “electromagnetic field”, filling space and time. At the time, though, this was a very unusual way to think, and not even Maxwell was comfortable with it. He felt that he had to present a “physical model” to justify the theory: a picture of tiny gears and ball bearings, somehow occupying the same space as ordinary matter.

Bang! Bang! Maxwell’s silver bearings…

Maxwell didn’t think space was literally filled with ball bearings. He did, however, believe he needed a picture that was sufficiently “physical”, that wasn’t just “mathematics”. Later, when he wrote down a theory that looked more like modern field theory, he still thought of it as provisional: a way to use Lagrange’s mathematics to ignore the unknown “real physical mechanism” and just describe what was observed. To Maxwell, field theory was a description, but not an explanation.

This attitude surprised me. I would have thought physicists in Maxwell’s day could have accepted fields. After all, they had accepted Newton.

In his time, there was quite a bit of controversy about whether Newton’s theory of gravity was “physical”. When rival models described planets driven around by whirlpools, Newton simply described the mathematics of the force, an “action at a distance”. Newton famously insisted hypotheses non fingo, “I feign no hypotheses”, and insisted that he wasn’t saying anything about why gravity worked, merely how it worked. Over time, as the whirlpool models continued to fail, people gradually accepted that gravity could be explained as action at a distance.

You’d think that this would make them able to accept fields as well. Instead, by Maxwell’s day the options for a “physical explanation” had simply been enlarged by one. Now instead of just explaining something with mechanical parts, you could explain it with action at a distance as well. Indeed, many physicists tried to explain electricity and magnetism with some sort of gravity-like action at a distance. They failed, though. You really do need fields.

The author of the biography is an engineer, not a physicist, so I find his perspective unusual at times. After discussing Maxwell’s discomfort with fields, the author says that today physicists are different: instead of insisting on a physical explanation, they accept that there are some things they just cannot know.

At first, I wanted to object: we do have physical explanations, we explain things with fields! We have electromagnetic fields and electron fields, gluon fields and Higgs fields, even a gravitational field for the shape of space-time. These fields aren’t papering over some hidden mechanism, they are the mechanism!

Are they, though?

Fields aren’t quite like the whirlpools and ball bearings of historical physicists. Sometimes fields that look different are secretly the same: the two “different explanations” will give the same result for any measurement you could ever perform. In my area of physics, we try to avoid this by focusing on the measurements instead, building as much as we can out of observable quantities instead of fields. In effect we’re going back yet another layer, another dose of hypotheses non fingo.

Physicists still ask for “physical explanations”, and still worry that some picture might be “just mathematics”. But what that means has changed, and continues to change. I don’t think we have a common standard right now, at least nothing as specific as “mechanical parts or action at a distance, and nothing else”. Somehow, we still care about whether we’ve given an explanation, or just a description, even though we can’t define what an explanation is.

7 thoughts on “The Changing Meaning of “Explain”

  1. Ander

    I thought an explanation is a mathematical relation which necessarily holds given the physical state of a system. Is this wrong or somehow insufficient?


    1. 4gravitons Post author

      How do you define the physical state, then? 😉

      More broadly, that definition of “explanation” certainly wouldn’t have been enough for Maxwell. He had mathematical relations like that, but he didn’t think of them as relations on their own. I think even now, it wouldn’t satisfy most physicists. There are things I can compute where I can observe that they have some interesting property, for example they’re almost the same up to some factor. That’s a mathematical relationship which necessarily holds, but it doesn’t explain why it holds, especially for a physicist.


  2. Jan Reimers

    Interesting post, Thanks. Nima is emphatic that fields are not fundamental, particles are. Gauge fields are a figment of the theorist imagination, constructed so that we can write down a Hamiltonian (or Lagrangian) with a local interaction. And detectors don’t go “wooow woooow” they go “click click”. On the other hand Sean Carrol is emphatic that fields are more fundamental. As an amplitudologist what’s your position on this?



    1. 4gravitons Post author

      As an amplitudeologist I definitely lean more towards “fields aren’t fundamental”, yeah. I wouldn’t quite say “particles are fundamental” so much as “observables are fundamental”, and everything else is a model meant to fill in the gaps between them, a model that can change if need be. But it’s kind of hard to work without some model. The insight of amplitudes is that there are other options for models than the fields one, at least some of the time.


  3. Guillaume Attuel

    Your entry is nice. IMO, fields are just what Newton disliked mostly : they describe action at a distance mathematically. Let’s think about an electric charge sitting still in its rest frame alone in space, until the field will attract or repel at a distance and instantaneously any added charge any where. (Ok the addition ex nihilo is pretty nonphysical here)
    Fields don’t explain nor describe anything I must agree with you. But the mystery deepens further. Quantum fields are even worse since we have to quantize them even in the absence of any source!



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