What is the relationship between physics field and force?

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Discussion Overview

The discussion revolves around the relationship between fields and forces in physics, exploring concepts from classical physics to general relativity. It addresses whether the presence of a field always results in a force acting on an object within that field, and examines the implications of fields as mathematical constructs versus physical entities.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants propose that whenever there is a field, there will be a force acting on an object placed in that field, questioning if this is always correct.
  • One participant notes that gravity is treated as a field in classical physics that involves a force, but in general relativity, it is described as a result of the geometry of space-time, suggesting a different interpretation of force.
  • Another participant defines a field as a mathematical object with values at every point in space or a manifold, indicating a conceptual distinction between fields and forces.
  • A participant elaborates on the historical development of the concept of fields, emphasizing that understanding fields as physical entities was crucial for advancements in physics, particularly in relation to electromagnetic waves.
  • It is mentioned that while force fields imply a force on appropriate objects, there are various types of fields, and not all fields exert forces on all objects, highlighting the conditional nature of force interactions.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between fields and forces, with no consensus reached on whether the presence of a field always results in a force acting on an object.

Contextual Notes

The discussion includes assumptions about the definitions of fields and forces, and the implications of different physical theories, such as classical physics and general relativity, which remain unresolved.

qorizon
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Whenever there is a field there will be a force whenever the field interacts with an object placed in that field?

Is this always correct?
 
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One thing that occurs to me in this regard is that gravity is a field in classical physics and involves a force, but in GR it's just a result of space-time geometry and no force.
 
Field is a mathematical object which has a value (scalar or vector) at every point in space (or some manifold).
 
qorizon said:
Whenever there is a field there will be a force whenever the field interacts with an object placed in that field?

Is this always correct?

It seems redundant but it was actually a real step forward in understanding when the concept of the field took hold. The story goes that Faraday had the intuition for fields and Maxwell made them mathematical. Prior to fields, forces were thought to "act at a distance," which was another way for saying that we didn't have a clue what was going on, but surely something. Taking the idea of fields seriously, by which I mean thinking of them as actual physical entities rather than mere mathematical abstractions, was a necessary step towards Maxwell's derivation of the self-propagating electromagnetic wave. There is just no way to talk about radiation if you only have the concept of force, and no fields. So while it may seem redundant for certain applications, it was a real step forward for our understanding of physics, the story goes.
 
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qorizon said:
Whenever there is a field there will be a force whenever the field interacts with an object placed in that field?

Is this always correct?
If the field is a force field then, pretty much by definition, if an appropriate object is placed in the field, there will be a force on it- but there are many kinds of fields other than "force" fields. The reason I say "appropriate" object is that there are many different kinds of force fields. Any object with mass will feel a force in a gravitational field but only an object with charge will feel a force in an electric field (and only a moving object, with charge, will feel a force in a magnetic field).
 
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