13
1.3. Particle interactions in the Standard Model
a competent faculty of thinking can ever fall into it. (Letter from
Newton to Bentley)
Newton could find no satisfactory mechanism or physical model, for the transmission of the gravitational force between two distant bodies; but his dynamical equations provided a powerful predictive framework, given the (unexplained) gravitational force law; and this eventually satisfied most people.
The 19th century saw the precise formulation of the more intricate force
laws of electromagnetism. Here too the distaste for action-at-a-distance theories led to numerous mechanical or fluid mechanical models of the way electromagnetic forces (and light) are transmitted. Maxwell made brilliant use
of such models as he struggled to give physical and mathematical substance
to Faraday’s empirical ideas about lines of force. Maxwell’s equations were
indeed widely regarded as describing the mechanical motion of the ether – an
amazing medium, composed of vortices, gear wheels, idler wheels and so on.
But in his 1864 paper, the third and final one of the series on lines of force
and the electromagnetic field, Maxwell himself appeared ready to throw away
the mechanical scaffolding and let the finished structure of the field equations
stand on its own. Later these field equations were derived from a Lagrangian
(see chapter 7), and many physicists came to agree with Poincar´ e that this
‘generalized mechanics’ was more satisfactory than a multitude of different
ether models; after all, the same mathematical equations can describe, when
suitably interpreted, systems of masses, springs and dampers, or of inductors, capacitors and resistors. With this step, the concepts of mechanics were
enlarged to include a new fundamental entity, the electromagnetic field.
The action-at-a-distance dilemma was solved, since the electromagnetic
field permeates all of space surrounding charged or magnetic bodies, responds
locally to them, and itself acts on other distant bodies, propagating the action
to them at the speed of light: for Maxwell’s theory, besides unifying electricity
and magnetism, also predicted the existence of electromagnetic waves which
should travel with the speed of light, as was confirmed by Hertz in 1888.
Indeed, light was a form of electromagnetic wave.
Maxwell published his equations for the dynamics of the electromagnetic
field (Maxwell 1864) some forty years before Einstein’s 1905 paper introducing
special relativity. But Maxwell’s equations are fully consistent with relativity as they stand (see chapter 2), and thus constitute the first relativistic
(classical) field theory. The Maxwell Lagrangian lives on, as part of QED.
It seems almost to be implied by the local field concept, and the desire to
avoid action at a distance, that the fundamental carriers of electricity should
themselves be point-like, so that the field does not, for example, have to
interact with different parts of an electron simultaneously. Thus the pointlike nature of elementary matter units seems intuitively to be tied to the local
nature of the force field via which they interact.
Very soon after the successes of classical field physics, however, another
world began to make its appearance – the quantum one. First the photoelectric effect and then – much later – the Compton effect showed unmistakeably
1.3. Particle interactions in the Standard Model
a competent faculty of thinking can ever fall into it. (Letter from
Newton to Bentley)
Newton could find no satisfactory mechanism or physical model, for the transmission of the gravitational force between two distant bodies; but his dynamical equations provided a powerful predictive framework, given the (unexplained) gravitational force law; and this eventually satisfied most people.
The 19th century saw the precise formulation of the more intricate force
laws of electromagnetism. Here too the distaste for action-at-a-distance theories led to numerous mechanical or fluid mechanical models of the way electromagnetic forces (and light) are transmitted. Maxwell made brilliant use
of such models as he struggled to give physical and mathematical substance
to Faraday’s empirical ideas about lines of force. Maxwell’s equations were
indeed widely regarded as describing the mechanical motion of the ether – an
amazing medium, composed of vortices, gear wheels, idler wheels and so on.
But in his 1864 paper, the third and final one of the series on lines of force
and the electromagnetic field, Maxwell himself appeared ready to throw away
the mechanical scaffolding and let the finished structure of the field equations
stand on its own. Later these field equations were derived from a Lagrangian
(see chapter 7), and many physicists came to agree with Poincar´ e that this
‘generalized mechanics’ was more satisfactory than a multitude of different
ether models; after all, the same mathematical equations can describe, when
suitably interpreted, systems of masses, springs and dampers, or of inductors, capacitors and resistors. With this step, the concepts of mechanics were
enlarged to include a new fundamental entity, the electromagnetic field.
The action-at-a-distance dilemma was solved, since the electromagnetic
field permeates all of space surrounding charged or magnetic bodies, responds
locally to them, and itself acts on other distant bodies, propagating the action
to them at the speed of light: for Maxwell’s theory, besides unifying electricity
and magnetism, also predicted the existence of electromagnetic waves which
should travel with the speed of light, as was confirmed by Hertz in 1888.
Indeed, light was a form of electromagnetic wave.
Maxwell published his equations for the dynamics of the electromagnetic
field (Maxwell 1864) some forty years before Einstein’s 1905 paper introducing
special relativity. But Maxwell’s equations are fully consistent with relativity as they stand (see chapter 2), and thus constitute the first relativistic
(classical) field theory. The Maxwell Lagrangian lives on, as part of QED.
It seems almost to be implied by the local field concept, and the desire to
avoid action at a distance, that the fundamental carriers of electricity should
themselves be point-like, so that the field does not, for example, have to
interact with different parts of an electron simultaneously. Thus the pointlike nature of elementary matter units seems intuitively to be tied to the local
nature of the force field via which they interact.
Very soon after the successes of classical field physics, however, another
world began to make its appearance – the quantum one. First the photoelectric effect and then – much later – the Compton effect showed unmistakeably