The definition of a field supposes simultaneity?

[nomadreid]

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?

 

[jbriggs444]

If a field is static then simultaneity is irrelevant. If a field is changing then one may need to describe it as a field over four dimensional space-time rather than just three-dimensional space.

Simultaneity is not meaningless in special relativity. It is just that it is frame-relative rather than a universal invariant.

 

[Dale]

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?

In field theory the fields are fields on spacetime, not just space.

 

[nomadreid]

Thank you, jbriggs444 and DaleSpam. Your responses were very helpful.