What are Fields? Not Numbers Glued to Space!

[Yes, the featured image for this is not technically a field. It is a Feynman diagram, but it shows the kind of  thing a field actually represents].

If you have studied much physics, then you will have come across the notion of fields.

What is a field?

The Wikipedia article fairly sums up the standard definition of a “field”:

In physics, a field is a physical quantity, represented by a number or tensor, that has a value for each point in space-time.


At first, this might sound an awful lot like a mathematical description of something. Surely it is a mathematical description of the property of something. If so, what is it a mathematical description of?

Does it describe the attributes of stuff in that space? Does it describe relationships between attributes of things in space? Or the actions of something in that region?  These are the questions we need to ask ourselves.

When it is said that a field is a physical quantity, do they attach it to anything? Does it describe the attributes or relationships of matter or anything at all? Or is it just a set of numbers attached to space?

Is it proper to attach numbers to space like this?

Of course not. Space is not a physical thing; it is a concept. It refers to relationships between positions of things. We talk more about space in this article. Space can be said to have some quantities, such as area or volume.

It is perfectly valid to measure aspects of “space” if you keep in mind that what you are measuring is the relationship between entities.

You can even say, that in a sense, space can have measurable quantities such as vacuum permittivity. If you understand that this refers to the properties of or relationships between entities within that space and not the actual space itself.

However, space itself has no physical properties. It is not a kind of matter nor is space-time a special kind of existence. It has none of the sorts of attributes which should be assigned only to matter.

Does this mean that we should throw out the concepts of fields in physics?

No, I don’t think so and I will show why.

The concept of a field is certainly applicable to physical reality. We know that the concept of an electromagnetic field can be used to derive real-world quantities of physical things and to figure out how they should act.

The concept of an electromagnetic field accurately describes something “out there” in reality.

It does not describe numbers floating around magically attached to space. It describes the attributes of things spread within that space, how they act and how they are related. And it is these things which a field tells us about and which a field should help us to understand.

For instance, the electromagnetic field does not describe “space” as such. It tells us about the properties of and relationships between things in that space. It describes attributes of charged particles within a space and how they interact with one another.

Note that the gravitational field does not describe the curvature of space-time. Space is simply a relationship between positions and time is simply a measure of change.

There is no such super-entity of space-time which somehow curves and somehow explains gravity. No. The gravitational field equations describe the properties of things and how they interact.

Sorry Einstein, general relativity does not explain how gravity works.

So, if fields describe the attributes of things and how they interact, what are these things?

This is not a philosophical question as much as it is a physics question. It could be that the answer to “what do fields describe” is that we have not yet noticed the proper way things interact. Perhaps gravity is explainable by some interaction we have not yet observed.

Perhaps to better understand how the various fields in quantum mechanics works, we need to better understand the quantum world. Which would, incidentally, require understanding the quantum world in terms of objective reality and not magic.

Of all the fields, I would say the electromagnetic one is the most understood. But, unless one can explain the electromagnetic field in terms of the properties, actions or interactions of entities, then one does not properly understand what a field is or what it refers to.

Saying “well, space has all of these quantities” is not enough, you need to show how these quantities are the properties, actions or interactions of entities.

Note, that it is fine to admit that we do not yet understand what these fields describe. If we can show that these field equations we have are indeed how this stuff works, then this is an important step. And to be fair, the field equations we have are generally quite successful here.

It is important to acknowledge this. We can make a lot of progress understanding how things behave by studying field equations, making predictions and showing that yes, that is how that stuff works.

However, at some point, we should try to figure out more about what the fields are describing. We should not just stop at the math and say “well, space has these numbers stuck to it”. No, we should try to study the nature of the entities the numbers are describing.

And that is where modern physics fails.

We don’t know what the fields are or what they describe. Certainly not completely, not fully.

This is something like what a field is … not space with numbers glued to it.

Many in physics do see that we should try to figure this out. Many others do not seem to see any need, as though the mathematics is somehow some kind of primary. When it evidently is not.

This is the kind of attitude we need to challenge. Unfortunately, I have no doubt, we will see a lot more of this in our continued exploration of the problems in modern physics.

If you see any physicists or anyone else talking about fields in a rational way, please let us know. We are aware such people exist; however, we would love to collect more such examples. Please message us on Facebook or contact us at contact@metaphysicsofphysics.com.

Leave a comment