A field can be anything, from a field of corn, to the water in a lake to the air that surrounds us to electromagnetic fields (commonly known as light). Wave equations are used to describe what happens in a field, like the familiar waves that ripple across a pound or sound waves in the air. What is being described is the movement of energy from one point in space to another over a certain period of time. The wave equations (which I won’t write down in this study) for all of these fields are the same. I say the plural equations because there are classes of equations that apply to certain kinds of fields under specific conditions. (For a detailed description of fields, waves and particles with the math included, see www.profmattstrassler.com)
In many cases as you can see from the examples above, a field can be a tangible thing or as they say in physics, the field has a medium associated with it whether it be water or air or any physical entity that can convey energy in space and time. However, one of the examples is an important exception and has no medium associated with it. Can you guess which one? I am sure some of you may have already guessed that it is the electromagnetic field or light. It was once believed that light did have a medium associated with it. It was called the aether. You can think of it as a kind of invisible substance that the energy associated with light rippled through. But Einstein and others proved that this was not the case. The equations that Einstein developed to explain the photoelectric effect (the effect that allows solar panels to create electricity from sunlight), showed that no medium was necessary and hence light is what physicists like to call a fundamental entity of existence. In other words it is not dependent on anything else for its existence. This is not the case with a wave of water that is dependent on the water, or a sound wave that needs the air. Light does not need anything.
THIS IS A GREAT MYSTERY. It is baffling to even scientists who must accept the indisputable evidence that the energy that is transferred from one point in space to another over a period of time needs no medium in which to travel. Now some of you may be thinking naively, so what? What’s the big deal about that? Well here’s the big deal, the layman and the scientist both experience everything on a day to day basis via the transfer of energy through some type of medium. Our physical senses depend on waves of air to vibrate our eardrums so that we can hear. We taste, smell and feel because of the molecules that travel through the air and interact with our physical bodies. Ah, but think about light for a moment. There is no physical medium associated with it. You may say no big deal because you are tricked into believing that light is passing through the air as a wave or through space from the sun, but this is NOT true.
Though we know that light is made up of discreet particles (or more accurately individual quanta) and that these quanta can manifest themselves as particles or waves, they exist independent of anything else; and the wave equations that describe them are the same wave equations that describe sound waves, water waves, etc.
The deep question then, becomes, what is light and where did it come from? How does it exist and its energy move through the vacuum of space if there is no medium in which it moves. An analogy would be, how can you swim if there is no water in which to swim. If you go even deeper and ask about the nature of the field itself the best you can do is describe the energy associated with it through the wave equations, but you will know nothing about its make up. In other words, if you asked what is it? There is no answer to that question. Does that mean we have reached the limits of our ability to understand reality? Are there some things that we will never know? Does this become cause for us to immediately invoke, God.
I always caution my friends and colleagues not to fall into the trap of using the “God in the gap” argument, which is if something can’t be explained then it must be God. To the contrary, God is revealed through knowledge and understanding; and within the exposure to reality. What we should take from this mystery about fields is how great and marvelous are the ways of God and an increased desire to discover more. Each time we uncover the reality behind a mystery, the more clearly will we see the face of God. One day we will know even more about the nature of light and perhaps come face to face with God in all of His Glory.
To God Be The Glory