In the previous post in this series, I said that wave mechanics as represented by the Schrodinger equation was a major advance in our understanding of physics. It adopted the view that all entities had both particle-like and wave-like properties and each of them were manifested by constructing the appropriate experimental set-up. If you set up an experiment that looked for the wave characteristics of (say) an electron, you detected its wave properties. If you set up an experiment that looked for the particle characteristics, you saw that too.

That idea of what has come to be called wave-particle duality worked fine as long as you did not ask the question “But what is an electron really, a wave or a particle?” But the Schrodinger model suffered from two major deficiencies: It could not deal with massless particles like the photons of light and it was not consistent with the theory of relativity.

There were other nagging issues that remained unresolved as a result of entities having this dual nature of particle properties (localized, with boundaries and mass) and wave properties. While this approach seemed adequate in dealing with dynamic situations, such as when an electron is emitted from a source at one location and is detected at another location, it was not so good at enabling the visualization of static or steady state situations. For example, an electron bound in the lowest state of a hydrogen atom has a probability distribution that has a non-zero value everywhere (though it decreases to a very small value as you go further away) that does not change with time. This means that it has some probability of being in an infinite number of places all at the same time. How can a localized particle do this? People try to envision this as the electron whizzing around at high speeds so that its location is a blur and merely gives the illusion of being everywhere at the same time but this does not really work when examined closely.

Another problem was again one that surfaces in the case of that old troublemaker, light. Light particles (photons) had no mass and thus could not be used in Schrodinger’s equation since that required a mass. Light particles were also clearly not things that could be thought of as existing for all time, like electrons, but were being produced and destroyed all the time. The Schrodinger wave equation made no provision for the creation and destruction of any particles, whether they were photons or electrons. The number of particles in a system had to be put in ‘by hand’, so to speak, meaning that you had to know how many you were dealing with at the outset and set up the Schrodinger equation with that number. Any changes in the number did not emerge naturally from the theory.

All these issues suggested, even as wave mechanics as represented by Schrodinger’s equation was accepted as a revolutionary advance, that there needed to be a better, deeper theory to explain the world of elementary particles. And the theory that emerged and is still in use depends on the idea of fields.

So what is a field?

The basic idea is quite simple. A classical field is something that has a value at every point in space. For example, you can talk about the temperature field of the Earth’s atmosphere, since you can associate a temperature with every point in the atmosphere. You can similarly have a pressure field, density field, and so on. But these kinds of fields are not considered fundamental. They are merely descriptive properties of the medium, in this case air. Take the medium away and the fields disappear too.

But there are other fields that even in classical form do not depend upon having a medium and are used to describe how electricity and magnetism and gravity work. These fields are considered more fundamental and overcome the awkward problem of how objects could exert forces on other objects that were not in contact with it. How does (say) the Earth feel the gravitational force of the distant Sun and vice versa?

In the case of gravity, the idea of fields said that any mass created a gravitational field that spread out through all of space. Since it had a value everywhere it can be properly be called a field. Another mass in contact with a gravitational field would feel a force that due to the value of the gravitational field in its immediate vicinity. So a direct mass-to-mass interaction over a long distance became mediated by a field to become a mass-to-field-to-mass interaction, thus overcoming the problem of action at a distance. A similar construct was made for electric and magnetic fields to explain how electric charges exerted forces on each other at a distance or how magnets exerted forces on each other.

Are these fields ‘real’ or just mathematical abstractions to overcome the problem of explaining action at a distance? How would one answer this question? The only tool at our disposal is the measurement of forces between objects, not the fields directly. The fields are inferred, not directly measured. The reality of electric, magnetic, and gravitational fields was an issue that was discussed quite extensively in the days following their introduction but is a question that has faded away as our understanding of the nature of science has developed. In science, if a concept has value and utility and enables us to achieve results that would not be possible otherwise, we treat it as ‘real’. It is this idea that resulted in us now treating quarks (whose inventors initially saw them as purely abstractions) as ‘real’ though we have never been able to isolate them and may never will.

The electric, magnetic, and gravitational fields are more fundamental than those of temperature, pressure, and so on. The Schrodinger wave function, again something that has a value everywhere in space, can also be considered a field.

It was Paul Dirac who introduced an even more fundamental form of fields that overcame many of the problems associated with the fields associated with the Schrodinger equation (the wave functions) and we will look at those fields in the next post.

Next: Relativistic quantum fields.