The Four Forces

Einstein’s General Relativity reproduces special relativity when gravity is absent, and it makes almost the same predictions as Newton’s theory of gravity in the weak-gravity environment of our solar system—but not quite.

In fact, if general relativity were not taken into account in GPS satellite navigation systems, errors in global positions would accumulate at a rate of about ten kilometers each day!

However, the real importance of general relativity is not its application in devices that guide you to new restaurants, but rather that it is a very different model of the universe, which predicts new effects such as gravitational waves and black holes.

And so general relativity has transformed physics into geometry. Modern technology is sensitive enough to allow us to perform many sensitive tests of general relativity, and it has passed every one.

Though they both revolutionized physics, Maxwell’s theory of electromagnetism and Einstein’s theory of gravity—general relativity—are both, like Newton’s own physics, classical theories. That is, they are models in which the universe has a single history. As we saw in the last chapter, at the atomic and subatomic levels these models do not agree with observations.

Instead, we have to use quantum theories in which the universe can have any possible history, each with its own intensity or probability amplitude. For practical calculations involving the everyday world, we can continue to use classical theories, but if we wish to understand the behavior of atoms and molecules, we need a quantum version of Maxwell’s theory of electromagnetism.

If we want to understand the early universe, when all the matter and energy in the universe were squeezed into a small volume, we must have a quantum version of the theory of general relativity.

We also need such theories because if we are seeking a fundamental understanding of nature, it would not be consistent if some of the laws were quantum while others were classical. We therefore have to find quantum versions of all the laws of nature. Such theories are called quantum field theories.

The known forces of nature can be divided into 4 classes:

1. Gravity.

This is the weakest of the four. But it is a long-range force and acts on everything in the universe as an attraction. For large bodies, the gravitational forces all add up and can dominate over all other forces.

2. Electromagnetism.

This is also long-range and is much stronger than gravity. But it acts only on particles with an electric charge. It is:

• repulsive between charges of the same sign
• attractive between charges of the opposite sign.

This means the electric forces between large bodies cancel each other out. But on the scales of atoms and molecules they dominate. Electromagnetic forces are responsible for all of chemistry and biology.

3. Weak nuclear force.

This causes radioactivity. It plays a vital role in the formation of the elements in stars and the early universe. We do not, however, come into contact with this force in our everyday lives.

4. Strong nuclear force.

This holds together the protons and neutrons inside the nucleus of an atom. It also holds together the protons and neutrons themselves, which is necessary because they are made of still tinier quarks.

The strong force is the energy source for the sun and nuclear power. But, as with the weak force, we do not have direct contact with it.

Quantum Electrodynamics, Bosons, Fermions

The first force for which a quantum version was created was electromagnetism.

The quantum theory of the electromagnetic field, called quantum electrodynamics, or QED, was developed in the 1940s by Richard Feynman and others.

It has become a model for all quantum field theories.

According to classical theories, forces are transmitted by fields.

But in quantum field theories, the force fields are made of various elementary particles called bosons.

• These are force-carrying particles that fly back and forth between matter particles, transmitting the forces.

The matter particles are called fermions.

• Electrons and quarks are examples of fermions.

The photon is the particle of light.

• It is an example of a boson.
• It is the boson that transmits the electromagnetic force.

A matter particle, such as an electron, emits a boson or force particle.

The matter particle recoils from it, like a cannon recoiling after firing a cannonball.

The force particle then collides with another matter particle and is absorbed, changing the motion of that particle.

Charged particles are those that feel the electromagnetic force.

According to QED, all the interactions between charged particles are described as the exchange of photons.

The predictions of QED have been tested and found to match experimental results precisely.

There is a quantum requirement to include all the histories by which an interaction can occur, such as all the ways the force particles can be exchanged.

This makes the mathematics of QED complicated.

To solve this the following were invented:

• the notion of alternative histories
  • It is a way of thinking about quantum theories described in the last chapter
• a neat graphical method, called Feynman diagrams, to account for the different histories and visualize each term in the sum over histories.
  • This method is today applied not just to QED but to all quantum field theories.

In QED, the sum over all possible histories can be represented as a sum over Feynman diagrams like those below, which represent some of the ways it is possible for two electrons to scatter off each other through the electromagnetic force.

In these diagrams the solid lines represent the electrons and the wavy lines represent photons.

Time is understood as progressing from bottom to top, and places where lines join correspond to photons being emitted or absorbed by an electron.

Diagram (A) represents the two electrons approaching each other, exchanging a photon, and then continuing on their way.

That is the simplest way in which two electrons can interact electromagnetically, but we must consider all possible histories. Hence we must also include diagrams like (B).

That diagram also pictures two lines coming in—the approaching electrons—and two lines going out—the scattered ones—but in this diagram the electrons exchange 2 photons before flying off.

The diagrams pictured are only a few of the possibilities. In fact, there are an infinite number of diagrams, which must be mathematically accounted for.

Feynman diagrams come with rules that allow you to read off, from the lines and vertices in each diagram, a mathematical expression.

The probability that the incoming electrons, with some given initial momentum, will end up flying off with some particular final momentum is then obtained by summing the contributions from each Feynman diagram.

That can take some work because there are an infinite number of them.

Although the incoming and outgoing electrons are assigned a definite energy and momentum, the particles in the closed loops in the interior of the diagram can have any energy and momentum.

That is important because in forming the Feynman sum one must sum not only over all diagrams but also over all those values of energy and momentum.