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Section 4: Early Unification for Electromagnetism

The electromagnetic force dominates human experience. Apart from the Earth's gravitational pull, nearly every physical interaction we encounter involves electric and/or magnetic fields. The electric forces we constantly experience have to do with the nature of the atoms we're made of. Particles can carry electric charge, either positive or negative. Particles with the same electric charge repel one another, and particles with opposite electric charges attract each other. An atom consists of negatively charged electrons in the electric field of a nucleus, which is a collection of neutrons and positively charged protons. The negatively charged electrons are bound to the positively charged nucleus.

The electromagnetic force and the constituents of matter.

Figure 10: The electromagnetic force and the constituents of matter.

Source: © David Kaplan. More info

Although atoms are electrically neutral, they can attract each other and bind together, partly because atoms do have oppositely charged component parts and partly due to the quantum nature of the states in which the electrons find themselves (see Unit 6). Thus, molecules exist owing to the electric force. The residual electric force from electrons and protons in molecules allows the molecules to join up in macroscopic numbers and create solid objects. The same force holds molecules together more weakly in liquids. Similarly, electric forces allow waves to travel through gases. Thus, sound is a consequence of electric force, and so are many other common phenomena, including electricity, friction, and car accidents.

We experience magnetic force from materials such as iron and nickel. At the fundamental level, however, magnetic fields are produced by moving electric charges, such as electric currents in wires, and spinning particles, such as electrons in magnetic materials. So, we can understand both electric and magnetic forces as the effects of classical electric and magnetic fields produced by charged particles acting on other charged particles.

The close connection between electricity and magnetism emerged in the 19th century. In the 1830s, English scientist Michael Faraday discovered that changing magnetic fields produced electric fields. In 1861, Scottish physicist James Clerk Maxwell postulated that the opposite should be true: A changing electric field would produce a magnetic field. Maxwell developed equations that seemed to describe all electric and magnetic phenomena. His solutions to the equations described waves of electric and magnetic fields propagating through space—at speeds that matched the experimental value of the speed of light. Those equations provided a unified theory of electricity, magnetism, and light, as well as all other types of electromagnetic radiation, including infrared and ultraviolet light, radio waves, microwaves, x-rays, and gamma rays.

Michael Faraday (left) and James Clerk Maxwell (right) unified electricity and magnetism in classical field theory.

Figure 11: Michael Faraday (left) and James Clerk Maxwell (right) unified electricity and magnetism in classical field theory.

Source: © Wikimedia Commons, Public Domain. More info

Maxwell's description of electromagnetic interactions is an example of a classical field theory. His theory involves fields that extend everywhere in space, and the fields determine how matter will interact; however, quantum effects are not included.

The photon field

In the quantum description of the electromagnetic force, there is a particle which plays the role of the force carrier. That particle is called the photon. When the photon is a virtual particle, it mediates the force between charged particles. Real photons, though, are the particle version of the electromagnetic wave, meaning that a photon is a particle of light. It was Albert Einstein who realized particle-wave duality—his study of the photoelectric effect showed the particle nature of the electromagnetic field and won him the Nobel Prize.

When light shines on a metal, electrons pop out.

Figure 12: When light shines on a metal, electrons pop out.

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Here, we should make a distinction between what we mean by the electromagnetic field and the fields that fill the vacuum from the last section. The photon field is the one that characterizes the photon particle, and photons are vibrations in the photon field. However, charged particles—for instance, those in the nucleus of an atom—are surrounded by an electromagnetic field, which is in fact the photon field "turned on". An analogy can be made with the string of a violin. An untouched string would be the dormant photon field. If one pulls the middle of the string without letting go, tension (and energy) is added to the string and the shape is distorted—this is what happens to the photon field around a stationary nucleus. And in that circumstance for historical reasons it is called the "electromagnetic field." If the string is plucked, vibrations move up and down the string. If we jiggle the nucleus, an electromagnetic wave leaves the nucleus and travels the speed of light. That wave, a vibration of the photon field, can be called a "photon."

So in general, there are dormant fields that carry all the information about the particles. Then, there are static fields, which are the dormant fields turned on but stationary. Finally, there are the vibrating fields (like the waves in the lake), which (by their quantum nature) can be described as particles.

The power of QED

The full quantum field theory describing charged particles and electromagnetic interactions is called quantum electrodynamics, or QED. In QED, charged particles, such as electrons, are fermions with half-integer spin that interact by exchanging photons, which are bosons with one unit of spin. Photons can be radiated from charged particles when they are accelerated, or excited atoms where the spin of the atom changes when the photon is emitted. Photons, with integer spin, are easily absorbed by or created from the photon field.

Arthur Holly Compton (left) discovered that the frequency of light can change as it scatters off of matter.

Figure 13: Arthur Holly Compton (left) discovered that the frequency of light can change as it scatters off of matter.

Source: © Left: NASA, Right: David Kaplan. More info

QED describes the hydrogen atom beautifully. It also describes the high-energy scattering of charged particles. Physicists can accurately compute the familiar Rutherford scattering (see Unit 1) of a beam of electrons off the nuclei of gold atoms by using a single Feynman diagram to calculate the exchange of a virtual photon between the incoming electron and the nucleus. QED also gives, to good precision, the cross section for photons scattered off electrons. This Compton scattering has value in astrophysics as well as particle physics. It is important, for example, in computing the cosmic microwave background of the universe that we will meet in Unit 4. QED also correctly predicts that gamma rays, which are high-energy photons, can annihilate and produce an electron-positron pair when their total energy is greater than the mass energy of the electron and positron, as well as the reverse process in which an electron and positron annihilate into a pair of photons.

Physicists have tested QED to unprecedented accuracy, beyond any other theory of nature. The most impressive result to date is the calculation of the anomalous magnetic moment, , a parameter related to the magnetic field around a charged particle. Physicists have compared theoretical calculations and experimental tests that have taken several years to perform. Currently, the experimental and theoretical numbers for the muon are:

These numbers reveal two remarkable facts: The sheer number of decimal places, and the remarkably close but not quite perfect match between them. The accuracy (compared to the uncorrected value of the magnetic moment) is akin to knowing the distance from New York to Los Angeles to within the width of a dime. While the mismatch is not significant enough to proclaim evidence that nature deviates from QED and the Standard Model, it gives at least a hint. More important, it reveals an avenue for exploring physics beyond the Standard Model. If a currently undiscovered heavy particle interacts with the muon, it could affect its anomalous magnetic moment and would thus contribute to the experimental value. However, the unknown particle would not be included in the calculated number, possibly explaining the discrepancy. If this discrepancy between the experimental measurement and QED calculation becomes more significant in the future, as more precise experiments are performed and more Feynman diagrams are included in the calculation, undiscovered heavy particles could make up the difference. The discrepancy would thus provide the starting point of speculation for new phenomena that physicists can seek in high-energy colliders.

Changing force in the virtual soup

The strength of the electromagnetic field around an electron depends on the charge of the electron—a bigger charge means a stronger field. The charge is often called the coupling because it represents the strength of the interaction that couples the electron and the photon (or more generally, the matter particle and the force carrier). Due to the quantum nature of the fields, the coupling actually changes with distance. This is because virtual pairs of electrons and positrons are effectively popping in and out of the vacuum at a rapid rate, thus changing the perceived charge of that single electron depending on how close you are when measuring it. This effect can be precisely computed using Feynman diagrams. Doing so reveals that the charge or the electron-photon coupling grows (gets stronger) the closer you get to the electron. This fact, as we will see in the following section, has much more important implications about the theory of the strong force. In addition, it suggests how forces of different strength could have the same strength at very short distances, as we will see in the section on the unification of forces.

QED at high energies and short distances.

Figure 14: QED at high energies and short distances.

Source: © David Kaplan. More info


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