This is a lovely essay, but I think it goes a little too far in claiming that the electromagnetic field is intangible or immeasurable, in slightly forced analogy with quantum mechanics.
> We now take it for granted that electric and magnetic fields are abstractions not reducible to mechanical models. To see that this is true, we need only look at the units in which the electric and magnetic fields are supposed to be measured. The conventional unit of electric field-strength is the square-root of a joule per cubic meter... This does not mean that an electric field-strength can be measured with the square-root of a calorimeter. It means that an electric field-strength is an abstract quantity, incommensurable with any quantities that we can measure directly.
A more conventional way to think of the dimensions of the electric field is [force]/[charge] (e.g. units of Newtons/Coulomb), and you can observe the electric field by observing the force it exerts on a charged particle through
f=qE
for example by observing the trajectory of an electron in a cloud chamber.
Dyson says that the square of the field is a measurable energy density, but it’s arguably harder to measure an energy density than it is to measure a force.
Dyson’s point is much more true for quantum mechanics, where the only measurable things seem to be quadratic combinations of the wave function, and I do like the analogy he points out with electromagnetism, but I think he oversimplifies a bit to make his point.
> not reducible to mechanical models [...] is much more true for quantum mechanics
Yes, but... a caveat.
How big is an atom? "Unimaginably small" is an oft repeated phrase. What is an atom? "Definitions [...] models [...] skill at switching between models". Electron behavior? Quantum... "unintuitive... the equation is understanding".
So how well is "small" taught? Horribly, even by the lackluster baseline of current science education research. Asking first-tier medical school graduate students how big cells are, is not happy thing. But hey, maybe cells are "unimaginable" too.
So how well are atoms taught? One challenge in teaching high-school stoichiometry, is students not thinking of atoms as real, as physical objects. But hey, maybe that's a failure to "switch models".
So how well is electron behavior taught? Well, when students use the many realistic interactives emphasizing molecular electron density... oh wait. Well, when students view the many molecular dynamics videos showing electron density... oh wait. They do exist... now find them without using google scholar and sending people email. :/ But hey, if students ever do see them some year, maybe no understanding will result, given how unintuitive it all is.
Punchline? Teaching things badly seems associated with failure attribution errors. As with education research that's "we taught atoms really badly... surprisingly that didn't work... so we draw the obvious conclusion... students of this age aren't developmentally able to understand atoms".
And physics side... there often seems a blurred vision of objectives and their properties. There are a great many plausible learning objectives between "atoms are real" and "i∂_{t}ψ=Hψ". And the usefulness of "mechanical" models varies greatly among them. So "the equation is understanding" gets repeated, in contexts where it's inappropriate, and where it distracts from a broad long-term societal failure to improve wretched science education content.
> We now take it for granted that electric and magnetic fields are abstractions not reducible to mechanical models. To see that this is true, we need only look at the units in which the electric and magnetic fields are supposed to be measured. The conventional unit of electric field-strength is the square-root of a joule per cubic meter... This does not mean that an electric field-strength can be measured with the square-root of a calorimeter. It means that an electric field-strength is an abstract quantity, incommensurable with any quantities that we can measure directly.
A more conventional way to think of the dimensions of the electric field is [force]/[charge] (e.g. units of Newtons/Coulomb), and you can observe the electric field by observing the force it exerts on a charged particle through
f=qE
for example by observing the trajectory of an electron in a cloud chamber.
Dyson says that the square of the field is a measurable energy density, but it’s arguably harder to measure an energy density than it is to measure a force.
Dyson’s point is much more true for quantum mechanics, where the only measurable things seem to be quadratic combinations of the wave function, and I do like the analogy he points out with electromagnetism, but I think he oversimplifies a bit to make his point.