How do Force Fields Occupy Space?
 

An electron has a Force Field around it which acts to repel other electrons and attract positively charged protons.

A moving electron generates a Magnetic Force Field which acts to attract or repel other magnetic objects.

There are also force fields created by strong and weak nuclear forces.

There is also the Gravitational Force Field which extends through space by actually deforming the space-time continuum. But how do the electic, magnetic, strong, and weak force fields extend through space and occupy it? They don't bend space like gravity. They aren't physical objects in the sense of having mass of their own. Yet somehow they reach out through space to attract or repel other objects with similiar force fields of their own. What are these things called force fields exactly?

PairTheBoard

Re: How do Force Fields Occupy Space?
 

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What are these things called force fields exactly?

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x-men

Re: How do Force Fields Occupy Space?
 

There's no such thing as a force field , it's just a name we use to make the concept intuitive.

All we know is that when two objects are placed near each other, they start moving toward each other. The rest is still a mystery I believe, but I've been out of the loop a long time.

Re: How do Force Fields Occupy Space?
 

This is what I want to understand most about physics, but I don't understand it. I've heard it has something to do with photon emission (from electrons) - photons "carry" the "message" to the protons.

I don't think anyone knows about gravity, but I think the "graviton" has been postulated to "carry" the field.

Re: How do Force Fields Occupy Space?
 

A quote from Rovelli's "Quantum Gravity":

"In newtonian and special-relativistic physics, if we take away the dynamical entities -- particles and fields -- what remains is space and time. In general-relativistic physics, if we take way the dynamical entities, nothing remains. The space and time of Newton and Minkowski are re-interpreted as a configuration of one of the fields, the gravitational field. This implies that physical entities -- particles and fields -- are not immersed in space, and moving in time. The do not live on spacetime. They live, so to say, on one another.

It is as if we had observed in the ocean many animals living on an island: animals on the island. Then we discover that the island itself is in fact a great whale. So the animals are no longer on the island, just animals on animals. Similarly, the Universe is not made up of fields on spacetime; it is made up of fields on fields."

Re: How do Force Fields Occupy Space?
 

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This is what I want to understand most about physics, but I don't understand it. I've heard it has something to do with photon emission (from electrons) - photons "carry" the "message" to the protons.

I don't think anyone knows about gravity, but I think the "graviton" has been postulated to "carry" the field.

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The problem with thinking like this is it assumes that particles (and thus all physical entities) are distinct "things" that need some media to communicate their presence with each other. I believe that more and more we are learning that this view is flawed and that "things" don't exist distinctly. I think each particle (and thus each physical entity) is a "field" in itself and can't be separated out completely to a point in space-time that we observe. We're all fields, man. Hey stop tickling me.

Re: How do Force Fields Occupy Space?
 

Since you are a math guy, start here:

wiki

Basically, the presence of particles, or virtually anything, changes the metric of whatever manifold you are looking at. (Or it changes the Hamiltonian, whatever.) The effect is that the Levi-Civita connection (or whatever structure you are considering on your manifold) is changed, which means that geodesics (or your Lagrangian submanifold) get changed. This is the fundamental paradigm of general relativity.

So when a charged particle is present, the geodesics of nearby charged particles get changed.

Finally, in physics lingo, particles choose paths that are critical points for the "action." In other words, they try to minimize the "work" that they have to do, or at least try to find a path that is a local minimum (the mathematics is essentially the same as 1st semester calculus where one finds local minima via the derivative, etc. Look up the calculus of variations.)

Anyway, this is not really my area of expertise, so there may be technical difficulties in my exposition. But the general idea is that "fields" are simply attributes of the manifold (usually some sort of configuration space) that one must take into consideration in any physical problem. Strictly speaking, they are smooth functions from M to E, where M is your manifold, and E is some sort of bundle over your manifold.

Re: How do Force Fields Occupy Space?
 

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There's no such thing as a force field , it's just a name we use to make the concept intuitive.

All we know is that when two objects are placed near each other, they start moving toward each other. The rest is still a mystery I believe, but I've been out of the loop a long time.

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Oh that's so 18th Century. You really have been out of the loop.

Re: How do Force Fields Occupy Space?
 

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But the general idea is that "fields" are simply attributes of the manifold (usually some sort of configuration space) that one must take into consideration in any physical problem. Strictly speaking, they are smooth functions from M to E, where M is your manifold, and E is some sort of bundle over your manifold.


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ok. But is this mathematical machinery much different in principle than the old high school physics explanation that the Force Field is a collection of vectors defining the direction and magnitude of force that the field would apply at various locations? Where do these vectors come from? How do they get there? What are they made of? So now instead of just vectors we have the mathematical structures of manifolds, connections, bundles, submanifolds, smooth functions, etc. Yes these concepts model well and provide good calculations. But do they give us any better sense of answers to the above questions?

PairTheBoard

Re: How do Force Fields Occupy Space?
 

[ QUOTE ]
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There's no such thing as a force field , it's just a name we use to make the concept intuitive.

All we know is that when two objects are placed near each other, they start moving toward each other. The rest is still a mystery I believe, but I've been out of the loop a long time.

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Oh that's so 18th Century. You really have been out of the loop.

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And how exactly have we come beyond this point? Unless something has changed in the 8 or so years, I never saw any insight into the nature of the fundamental forces, merely mathematical descriptions of their effects