How many Higgs fields might be on a head of a pin?

If you have a moment to spare, try a word association game with the word “field”. You might think of words as different as battle, baseball, oil, and strawberries. Now, if a physicist played the game, he (and occasionally she) might come with electrical, gravitational, quantum theory, or some other unusual word.

I was asked whether ‘Higgs field’ is countable (i.e. when a word’s plural and singular forms make sense, and that it is not a mass noun). That question made me realize that it is not always clear what physicists mean when they use the word “field”. Looking for a precise yet non-mathematical explanation, I found in the famous Feynman Lectures on Physics, that a “field” is a “condition” in space. Specifically, Feynman used the concept of a field to explain how positively and negatively charged particles interact:

…the existence of the positive charge, in some sense, distorts, or creates a “condition” in space, so that when we put the negative charge in, it feels a force. This potentiality for producing a force is called an electric field. When we put an electron in an electric field, we say it is “pulled.”

If the explanation seems straightforward, be assured that the notion of field muddles when one approaches the realm of quantum field theories. The electromagnetic field, for example, becomes in some instances a photon. But particles and fields are NOT interchangeable. It required the LHC (the largest particle accelerator in the world) to very briefly generate the Higgs Boson, even though the Higgs field permeates the space. To see a nice illustration of what a field is, and how it is represented, click on a short video published by Scientific American on YouTube.

Back to the question. The particle physics Standard Model has one Higgs field, but there are extensions of the model with more than one Higgs field, so the answer to the question whether ‘Higgs field’ is countable is… inconclusive.

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