The Field
![[url=https://www.flickr.com/photos/brookhavenlab/25156739034/in/album-72157613690851651/]"STAR Detector"[/url] by Brookhaven National Lab is licensed under [url=http://creativecommons.org/licenses/by-nc-nd/2.0]CC BY-NC-ND 2.0[/url]
STAR Detector used at Brookhaven National Laboratory to measure the quark gluon plasma to compare with field theoretic results.](https://www.geogebra.org/resource/n9KVCCmA/lBUt3ChalAdZTLGj/material-n9KVCCmA.png)
We have spoken of fields before. We have drawn pictures of the gravitational field surrounding earth, and did the same with electric and magnetic fields surrounding charges. We used terms like vector field versus scalar field, to distinguish different types of fields. Yet we have not really spent much time clearly defining fields outside of brief mention of mathematical properties.
The notion of a field was first introduced by Michael Faraday in 1845 to explain electric and magnetic fields of which light is made. It was James Clerk Maxwell who built on that concept and came up with equations showing how these electric and magnetic fields propagate through space as waves.
At the end of our studies of electromagnetism we derived light (as Maxwell had done) as waves of these propagating fields. At that point an important transition took place. The fields that may have been previously construed as useful mathematical constructs, suddenly became real entities. The seemingly abstract notion of fields literally keeps us alive by providing energy from our sun in the form of light.
While Isaac Newton was the first to express the gravitational force drawing masses together in the 1600s, he did not speak of the field as a separate entity. It is clear, however, that he was distressed by the notion of objects affecting one another at a distance without any intermediary. He wrote: "That one body may act upon another at a distance, through a vacuum, without the mediation of anything else... 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 [being convinced by] it."
Newton clearly knew something was amiss with action at a distance. Yet it was to be another 250 years before Albert Einstein described gravitation as a field in his famous equations of general relativity and shared them with the world in 1915. While this was a tremendous accomplishment in its own right, Einstein's instinct was that he had only discerned a small part of nature's mystery. He spent the last 25 years of his life searching for something more. He searched for a consistent theory of nature that included only fields.
Fields Defined
While we have spoken of the mathematics of fields, I wish to speak of them differently here. I want to speak of their reality. A field is a property of space. It is therefore not correct to think of them as existing in space or in addition to space. The distinction is important. Waves (fields) propagate on a string of a guitar not in addition to the string, but because of the nature or properties of the string. In the same way, waves (of fields) propagate and exist in space, not in addition to space, but due to the nature and properties of space. You can't have space without waves of fields!
You may have noticed that we've spent a lot of time on waves and even on music. Speaking of his research on quantum field theory, the following quote from Nobel Laureate Frank Wilczek speaks to the usefulness of those prior discussions as applied to the current topic of fields: "Rather than plucking a string, blowing through a reed, banging on a drumhead, or clanging a gong, we play the instrument that is empty space by plunking down different combinations of quarks, gluons, electrons, photons,... and let them settle until they reach equilibrium with the spontaneous activity of Grid... These vibrations represent particles of different mass m... The masses of particles sound the music of the Grid."
He uses the term Grid to describe space because he is speaking of numerical calculations which were forced to discretize (chop into discrete pieces) space to do field calculations just as numerical algorithms used in first semester to calculate interesting dynamics had to chop time into small intervals to do the calculations. The part I don't want you to miss is the part about everything in nature being vibrations of fields, and that includes entities that you likely think of as particles.
Absolutely everything in nature seems to be a vibration or wave of fields played on the instrument or medium of space. All light, all matter and all forces are field vibrations of space. While this sounds crazy, such understanding has led to more precise prediction of experimental values than any other in history. The magnetic dipole moment of the electron, for instance, was calculated to 10 significant digits and matched experiment exactly. Such understanding has also allowed prediction of the members of the "subatomic zoo" of "particles" seen at laboratories the world over with correct corresponding masses. Recent announcement of the detection of gravitational waves only serves to strengthen the case for this view.
You will notice I put the word particles in quotes in the last paragraph. It will certainly be one of our burdens to explain why the notion of particles exists at all in a world full of waves. That leads into our next topic of quantization.