Talk:Field theory

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Andy, I'm not going to undo something you've written, but a force field and action at a distance are the same thing. Action at a distance means precisely that - one object, affecting another, without touching it. A force field is precisely that - an object generates a field of force around it, which allows it to affect objects without touching them. JacobB 21:22, 15 November 2009 (EST)

Action at a distance certainly is not the same as electromagnetic waves, which do not act instantaneously on a distance object as Newtonian gravity does. Perhaps the meaning of "force field" is ambiguous (it's not defined in my dictionary).--Andy Schlafly 21:24, 15 November 2009 (EST)
You're absolutely right. Newtonian gravity is a theory which implies instant transmission of gravity, and Maxwell's equations set a speed limit. However, both theories constitute "action at a distance," and both constitute "field theories." The term "field theory" is used for theories like Newtonian gravity, Maxwell's electromagnetism, or quantum field theory BECAUSE they describe action at a distance - in opposition to theories like quantum chromodynamics, or general relativity as it is currently incorporated into the standard model, which describe forces as being carried by particles - photons, gravitons, etc. JacobB 21:29, 15 November 2009 (EST)
No, I don't think that's right, Jacob. "Action at a distance" means instantaneous action. Electromagnetic waves don't fit.
"Field theory" used to mean what you say, but I think today it connotes a "field" that takes time to travel ... as in "quantum field theory." I don't think a distinction is made between particles or waves; the key distinction is between instantaneous action versus action at the speed of light.--Andy Schlafly 21:43, 15 November 2009 (EST)
We'll have to agree to disagree. JacobB 21:44, 15 November 2009 (EST)
Could I ask you two to lower the temperature of this a bit? The question of "action at a distance" is one that I was going to work on before all my time got sucked up into the black hole that is the general relativity article. I put out requests to User:KSorenson and User:SaraT requesting their input, because they both have expertise in historical matters like this. They both were kind enough to reply. See their talk pages. It seems that "action at a distance" probably didn't refer to transmission of force faster than the speed of light back in the 1600's, because such issues weren't considered important then. And Newton's theory couldn't have been a "field theory" back then, because "vector fields" hadn't been invented. The "gravitational field" got invented later, and Newton's theory became a "field theory" retroactively. Whether Newton's gravitational field propagated faster than the speed of light isn't important; it's a classical (pre-1900) theory. Some people were concerned with this issue, but it's been replaced by GR. And Sara seems to say that Newton's concern over action at a distance was about other issues, namely, force between things not in physical contact. We can say now that it refers to speed, but that doesn't seem to be what the issue was in the 1600s. PatrickD 21:54, 15 November 2009 (EST)

Excellent points, PatrickD. Jacob, I have an open mind about this. But if you're right, I'm wondering why the term "field theory" is used for "quantum field theory" (which denies action-at-a-distance and relies on the never-found graviton particles), while classical "quantum theory" is not a field theory (it has action-at-a-distance and no gravitons). Can you fit that difference in terminology to your explanation?--Andy Schlafly 21:57, 15 November 2009 (EST)

I agree with Patrick; this isn't worth a big fight. Especially considering we're talking about a totally obsolete concept.
"Action at a distance" is a figure of speech. All it means is an interaction where the mediator hasn't been identified yet. And it has nothing to do with instantaneous anything, so let's not confuse the question.
To say a theory was "based on action at a distance" is not a meaningful collection of words, because "action at a distance" isn't a scientific principle. We might as well say the theory was based on lamb stew. Tasty, but not scientific.
I don't think this concept deserves a detailed article, any more than we'd write a detailed article on the luminiferous aether.
Overall, this article should be erased and replaced with a three-sentence definition and some links:
"A field theory is any theory in physics which describes a fundamental interaction in terms of a field that mediates that interaction. In an abstract field theory, a particle interacts in some way with a field, and then the field in turn interacts with another particle, thereby transferring some quantity (momentum, energy or charge, for instance) from one particle to another. Abstract field theories are considered obsolete in modern physics, and have been replaced with metric theories and gauge-invariant quantum field theories." --KSorenson 22:11, 15 November 2009 (EST)
The term "field theory" is still frequently used, so we can't simply "punt" on this. We should explain it as best we can. Under your proposed definition, which is not the meaning of the original term, Newtonian gravity is not a field theory, correct?--Andy Schlafly 22:17, 15 November 2009 (EST)
The functional would be a very special one, which can be aggregated into a function of a few variables since the underlying field does not have any degrees of freedom, but technically you can create a functional which yields the Newtonian gravity. My definition of Field theory would be equivalent to Ksorenson, but i would formulate differently: A field theory formulates equations describing physical reality (equations of motion, for example) in terms of continuous vector-valued degrees of freedom. Solutions of field theories in which fields do not have own degrees of freedom (in the sense that time derivatives of fields do not appear in Hamiltonian Function(al)s/the Equations of motion) are (AFAIU) equivalent to static theories described by effective forces of the point sources of (infinitely fast propagating) fields (e.g. Newtonian Physics, electrostatics). --Stitch75 13:09, 16 November 2009 (EST)
Still frequently used by whom? I don't hear teenagers on the subway talking about it. It's a technical term and deserves a technical definition.
What do you think the "meaning of the original term" was?
Newtonian gravity was, in Newton's formulation, an acceleration vector field theory, yes. Lagrange rewrote the equations to express it as a scalar field theory and that's what we used until 1916. --KSorenson 22:22, 15 November 2009 (EST)

(Unindent) I really don't want to get bogged down in this just now (I don't think any of us do :-) and I really, really, really should be making the graphs for the GR article (just taking a sanity break). But I think this is roughly the possition we should take on the article: Newton's theory of gravity is a field theory, sort of. It may not satisfy the modern criteria for a field theory (whatever those criteria are; I defer to Kate on that), but we should certainly give it some kind of "honorary" status. Why? Because people learn about the "gravitational field", and that it's a vector field, in high school or whenever. It's probably the first vector field that people learn about. It's the first thing that gets plugged into F=ma. It would be a shame not to call it a field theory. Now Newton had never heard of vector fields. So we should probably give it some kind of status as an "honorary, retroactive field theory". And not worry about whether it really is one under modern standards. OK? PatrickD 22:44, 15 November 2009 (EST)