In field theory the fields are fields on spacetime, not just space.nomadreid said:A field is defined as a distribution throughout all space (or at least a portion of it). But all of (a portion of) space means all of space at a particular moment, no? But that sounds as if it assumes simultaneity. But I thought simultaneity was a meaningless concept, according to relativity. What am I missing here?
The definition of a field is a region of space where a physical quantity, such as temperature, electric charge, or gravitational force, has a measurable value at every point in that space.
Simultaneity refers to the concept that, in a field, all points in that space are affected by the field at the same time.
The definition of a field supposes simultaneity because it is a fundamental property of fields that all points within a field are affected at the same time, regardless of their distance from the source of the field.
While the concept of simultaneity is widely accepted and used in the study of fields, it is not a directly observable or measurable property. It is a theoretical assumption that allows for the mathematical modeling of fields.
Some theories, such as quantum mechanics, suggest that there may be exceptions to the principle of simultaneity in certain extreme situations, such as at the subatomic level. However, for most practical purposes, the principle of simultaneity holds true in the study of fields.