We’re Having a Field Day!

by Nicholas Mee on August 12, 2017

Descartes’ Vortices

René Descartes proposed an imaginative explanation for the motion of the planets in the 1630s. He argued in a work known as The World that the existence of a void or vacuum is impossible and therefore space must be filled with some sort of fluid. He suggested that the planets are carried around the sun by vortices in this fluid. Prior to Newton’s theory of gravity this was the leading explanation for the planetary orbits. When Newton published his own theory in the Principia in 1687 he went to great lengths to show that Descartes’ theory could not work.

Newton’s explanation of gravity was a great triumph. It gave an accurate account for the motion of the planets and much else besides. However, the clockwork of the heavens was explained by invoking long range interactions between the sun and planets, and indeed all massive bodies, without any apparent mechanism to transmit the force.

Despite the extraordinary success of Newton’s theories, this action-at-a-distance was heavily criticised by philosophers such as Leibniz.

Isaac Newton at the age of 46 in 1689, painted by Godfrey Kneller.

Newton agreed. He admitted it was difficult to see how there could be a force between two bodies that are not in contact. In a letter to Richard Bentley in 1693 he wrote:

It is inconceivable that inanimate matter should, without the mediation of something else, which is not material, operate upon, and affect other matter without mutual contact…

That gravity should be innate, inherent and essential to matter, so that one body may act upon another at a distance through a vacuum, without the mediation of any thing else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it.

Centuries passed before light was shed on this enigma.

Faraday’s Fields

Michael Faraday unlocked the secrets of electricity and magnetism in his experiments in the first half of the 19th century. One of Faraday’s great innovations was the idea of mapping out electric and magnetic forces at each point in space. These maps plot the electric force experienced by a test charge or the magnetic force experienced by a test magnetic pole, as shown below. They show a representative collection of lines and the strength of the force at each point is indicated by the density of the lines. Faraday referred to them as electric and magnetic fields.

Left: electric field close to two charges. Right: magnetic field close to a bar magnet.

A small positive test charge positioned close to the two charges in the illustration above left would be repelled by the positive charge and attracted to the negative charge. The force on the test charge is the sum of these two forces, so the blue lines indicate the direction of this resultant electric force at each point. Similarly, the red lines in the illustration above right show the sum of the magnetic forces (on a test north pole) due to a repulsion from the north magnetic pole and an attraction to the south magnetic pole.

Although the electric and magnetic fields are depicted separately, a changing electric field generates a magnetic field and a changing magnetic field generates an electric field, so in reality they should be considered as parts of a single electromagnetic field.

James Clerk Maxwell

Faraday agonised over the meaning of the fields and concluded they have a real physical existence, but he was strongly criticised for this. When James Clerk Maxwell formulated a mathematical theory of electromagnetism encapsulating the results of Faraday’s experiments this issue was greatly clarified.

Maxwell’s equations show that waves are produced whenever an electromagnetic field is disturbed and these waves carry energy and momentum, so the field is not just an accounting tool, it really does have an independent existence. The waves are perpendicular oscillations of electric and magnetic forces propagating through space, as shown in the illustration below. (The blue lines indicate the electric field and the red lines indicate the magnetic field.) The changing electric field generates the magnetic field and the changing magnetic field simultaneously generates the electric field, so the oscillating electromagnetic waves are self-perpetuating.

What is most remarkable is that we have always been aware of these waves, they are what we call light. Faraday had suspected that light is an electromagnetic phenomenon following experiments with polarised light. Tragically, when Maxwell visited Faraday to tell him that he was correct, Faraday was close to death and already too ill to understand what Maxwell was saying.

Visible light is rapid, high energy vibrations, with blue light being more rapid and higher energy than red. But Maxwell’s calculations showed that it should be possible to generate electromagnetic vibrations of all frequencies.

Radio Ripples

Maxwell’s theory implies that when an oscillating current passes through a wire, electrons in the wire oscillate and their accelerations generate ripples in the electromagnetic field. In other words, they radiate waves in the electromagnetic field.

Long wavelength vibrations are known as radio waves, a name derived from radius, Latin for the spoke of a wheel. The radio waves are emitted in all directions and move outwards forming a spherical wavefront. (This is analogous to the ripples produced when a stone is dropped into a pond.) When the wavefront impinges on a metal wire or aerial, the radio waves accelerate electrons in the aerial and thereby generate an oscillating current. The spherical wavefront will have spread out so the signal will be much weaker and may need amplification.

This is the basis for an experiment performed by Heinrich Hertz in 1889. Hertz generated radio waves in his laboratory and detected them on the other side of the laboratory. Some of his equipment is shown above.

Quantum Waves

The discovery of quantum mechanics in the 20th century shed further light on the meaning of fields. From a quantum perspective, electromagnetic waves are composed of particles known as photons. They are not particles in the classical billiard ball sense, more like discrete bits of wave. They are sometimes referred to as quanta or even wavicles, as every day concepts such as particles or waves don’t fully capture their properties.

Quantum field theory gives us a remarkable picture of how forces work at the level of particle interactions. For each type of fundamental particle a separate field is presumed to permeate space. Photons are fundamental vibrations of the electromagnetic field, electrons are vibrations of the electron field and so on. Crucially, these fields are not independent. For instance, the particles that are electrically charged, such as electrons, are those whose fields couple to the electromagnetic field. This produces a force between charged particles due to the exchange of pulses in the electromagnetic field. These pulses are photons.

Physicists represent such interactions pictorially in Feynman diagrams. The diagram below shows the exchange of a single photon between two electrons. (Time flows upwards in the diagram.) This is the simplest, but most important diagram representing the interaction between two electrons. Other diagrams would involve more particles.

As the acceleration of charged particles, such as electrons, generates ripples in the electromagnetic field, it is very satisfying to arrive at this quantum description of their interaction. What could be more natural than to describe the change in energy and momentum of two interacting electrons as due to the exchange of pulses of electromagnetic waves between them?

Feynman diagrams provide a bridge between the mathematics of quantum field theory and our conceptual imagination of what is actually going on when particles interact. Niels Bohr, one of the architects of quantum theory, was critical when Feynman introduced them as they appear to hide some of the mystery of what happens at the quantum level. Bohr later apologised when Feynman won the Nobel Prize in Physics.

Richard Feynman with his family in front of the van he decorated with examples of his diagrams.

Einstein Solves Newton’s Puzzle

Einstein’s greatest insight was to solve Newton’s dilemma by banishing action-at-a-distance from gravity using the field concept, as discussed here: Cosmic Ripples. Einstein’s general relativity is a classical theory of gravity, just as Maxwell’s theory is a classical theory of electromagnetism. They deal with continuous waves. The gravitational waves recently detected by LIGO (Laser Interferometer Gravitational-wave Observatory) are classical gravitational waves.

We are still some way from a quantum theory of gravity. Such a theory would describe gravity as due to the exchange of quantum pulses of gravitational waves – hypothetical particles known as gravitons. These would be the gravitational analogues of photons. However, gravity is so weak compared to electromagnetism that the prospects for ever detecting individual gravitons are remote. I have my doubts about whether it is even possible in principle.

Further Information

There is more about the unification of the electromagnetic force by Faraday and Maxwell in my book: Higgs Force: Cosmic Symmetry Shattered. Higgs Force also includes more explanation of Feynman diagrams.

There is a lot more about Einstein’s theory of general relativity in my book: Gravity: Cracking the Cosmic Code.

 

{ 1 comment… read it below or add one }

Julius Mazzarella August 14, 2017 at 10:21 pm

Great article on field theory. I hope you can follow up with more articles on the often overlooked history of Quantum Electrodynamics.

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