The definition of a field supposes simultaneity?

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Discussion Overview

The discussion revolves around the definition of a field in physics, particularly in relation to the concepts of simultaneity and spacetime. Participants explore whether the definition of a field inherently assumes simultaneity, especially in the context of relativity, and how this relates to static versus dynamic fields.

Discussion Character

  • Debate/contested, Conceptual clarification

Main Points Raised

  • One participant questions whether the definition of a field, which is a distribution throughout space, assumes simultaneity, given that simultaneity is considered meaningless in relativity.
  • Another participant suggests that if a field is static, simultaneity becomes irrelevant, but for changing fields, it may be necessary to consider them in four-dimensional spacetime rather than just three-dimensional space.
  • A third participant reiterates the initial concern about simultaneity in the definition of fields, emphasizing that fields in field theory are defined on spacetime.

Areas of Agreement / Disagreement

Participants express differing views on the relevance of simultaneity in the context of fields, with some suggesting it is frame-relative while others question its applicability in defining fields. The discussion remains unresolved regarding the implications of simultaneity for field definitions.

Contextual Notes

There are limitations in the discussion regarding the assumptions about simultaneity and its dependence on the frame of reference, as well as the distinction between static and dynamic fields that are not fully explored.

nomadreid
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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?
 
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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.
 
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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?
In field theory the fields are fields on spacetime, not just space.
 
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Thank you, jbriggs444 and DaleSpam. Your responses were very helpful.
 

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