If you have studied much physics, then you will have come across the notion of fields. What is a field?
What is a field?
The Wikipedia article fairly sums up the standard definition of a “field”:
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.
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