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Concepts behind Field


Ashish
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“Action at a distance” whenever this comes to play, in physics we tend to think of this in terms of fields whether it may be due to Electric, Magnetic and Gravitational (Well I know these only). Oh yes there’s one more and its Einstein’s Fields equation well I don’t know much about it.

So whats the real concepts behind field. Because from my intuition In order to make any change, movement or disturb something you need to touch it, for example if I want to move some object then I need to touch it and give it some force and that seems to be really in sense.

But on the other hand there are few physical phenomenon like Electric, Magnetic and Gravitational forces in which there in no need of actual physical contact as they have action at a distance.

In dictionary the formal meaning of “Field” is some sort of region. So in concerned with field in physics what really constitute field in each case as there is what that makes it possible to have such action at a distance.

Edited by Ashish
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For example a scalar field associates with every point [math]x[/math] (usual abuse here using same notation for coordinate and point) a number [math]\phi(x)[/math]. This we can think of as a section of a line bundle.

 

A more physical example is that of the magnetic field. At all points the electromagnetic field is given by a magnitude and a direction. It is thus a vector field. Vector fields are sections of the tangent bundle.

 

There are many other kinds of bundles and their sections that are of interest in physics.

 

You should not worry too much if fields are "real or not". They are mathematical constructs that allow us to describe the natural world.


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Just noticed I said something not quite correct. You can think of the "magnetic force field" as a vector field.

 

Depending of the formulation, the electromagnetic field is a connection. To see this as a section we need affine bundles.

Edited by ajb
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I agree with Ashish's interrogation.

Field is a widely used concept. But if you think very (very) deeply about the concept, it is pure mystery.

A field is like an aura of knowledge around an object. The object "feels" something when it is in the range of "feeling" of another object, and is attracted through action at distance. But physics is not about "feelings" so it calls that a field. And action at distance has been accepted without any trouble, although without tangible explanation. IMHO it's all still unexplained stuff.

 

IMHO, and under all reservations, if you want my point of vue about what a field is, I have come to the conclusion that a field is nothing else but the object itself, i.e. that the Earth is not the globe only , but the globe + its field (gravitational) extended all around (until infinite).

The "what is it made of" is another question. Not the right question actually.

The right question is "what was it made of", because a field is extending in space & in time, and is always in the past of an object.

This must be a clue.

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But in my view i think field as an intrinsic property of charge, mass, magnet for electric, gravitational and magnetic interaction respectively.

 

Whenever there is a object having mass then there will be gravitational field of its own and similarly for charge and magnet.

 

and one more thing is that field has more something physical than only mathematical construct as swansont says; and we've not really understood it.


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I agree with Ashish's interrogation.

IMHO it's all still unexplained stuff.

.

 

Well I dont know anything about IMHO but I really like your point......

Edited by Ashish
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  • 2 weeks later...

From what I understand a "field" is a condition in space created by the parent particle. Each particle like the electron gives off "virtual particles" that exist for the most briefest of moments then the virtual particle snaps back to the parent then the VP again extends out from the parent particle in a different direction.

 

Imagine yourself as an electron and you have one arm to push in a random direction. Your hand would effect other electrons by pushing on their hands and keeping their distance. Mind you, you would have to extend your arm and snap it back to yourself at a super incredible rate.

 

Let me know if this sounds right. :)

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From what I understand a "field" is a condition in space created by the parent particle.

 

Classically you mean that certain particles can act as sources of certain fields.

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A field is nothing else but a force standing in the equation of motion of a probe particle. It cannot be explained differently. As soon as we can put our particle anywhere in the space, we may assign to the space points certain fields (forces). When our particle goes from x1 to x2, the force changes from F(x1) to F(x2). The concept of field is quite similar to the concept of space - of all possible particle positions. But is is always a certain "number" in the particle equation of motion.

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Hi Vlad (i have a friend called Vladimir we all call Vlad, I hope that doesn't bother you), i thought you went away. Glad to see you again.

A field is nothing else but a force standing in the equation of motion of a probe particle. It cannot be explained differently.

 

I am also glad that you seem to understand something.

From your explanation, I understand nothing. Could you please develop?

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From your explanation, I understand nothing. Could you please develop?

 

Yes, I can. One particle acts on another. We may say that one particle is a source of a field that exists everywhere. But the true sense of this field is the force term appearing in the second particle equation as an external force. Similarly we may say about the second particle in respect to the first one. In both equations we have the same force depending on the distance between particles. Working with such forces does not cause any physical and mathematical problems. However working with proper fields, for example, calculating their energy, gives infinities and some conceptual problems. I want to say that when we assign an independent meaning to the field, it becomes overly complicated mathematically and physically. Another example is a self-action - when we insert the proper field into the first particle equations of motion.

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The physics fields are, for every point in space (or spacetime if you prefer), there is a vector. A vector is usually represented by a little arrow; it has a length and a direction. It can also be represented by curved directional lines where the tangent to the line gives the direction and the density of the lines gives the strength (this is the usual representation for magnetic fields). The vector tells you the strength and direction of the field at that point. What I'm describing is, of course, a mathematical construct rather than a physical object or thingamajig. Telling what the field is really "made of" is meaningless to science unless there are corresponding predictions made by said understanding. Classical physics just says the field is there, don't worry about it. Quantum physics says it is made of virtual particles.

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As some minor remarks:

 

The physics fields are, for every point in space (or spacetime if you prefer), there is a vector. A vector is usually represented by a little arrow; it has a length and a direction.

A field does not need to be an assignment of a vector to each point in space. It can also be other stuff, e.g. a rank-2 tensor, a scalar, a spinor. The issue is even a bit more complicated than it might seem now because the common meaning of the term "vector" is not consistent over all physics. Ajb said "value" (including the "") on purpose.

 

Classical physics just says the field is there, don't worry about it. Quantum physics says it is made of virtual particles.

I don't think this statement is correct or even sensible.

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A field does not need to be an assignment of a vector to each point in space. It can also be other stuff, e.g. a rank-2 tensor, a scalar, a spinor. The issue is even a bit more complicated than it might seem now because the common meaning of the term "vector" is not consistent over all physics.

 

In the context here, section of a vector bundle which includes vector fields (section of the tangent bundle) would be a wide meaning here. However, it would not be enough to encompass all the fields we find in physics.

 

 

Ajb said "value" (including the "") on purpose.

 

Indeed, all I mean is that at each and every point on space-time (or just space depending on what we are doing) a mathematical object is assigned, a "value" as such. Doing this in a nice smooth way means that the fields are sections of fibre bundles. These need not be vector bundles. Typically, matter is understood as sections of a vector bundle and forces are connections so that is sections of affine bundles. But we could for sure think about more general things than these.

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(...)What I'm describing is, of course, a mathematical construct rather than a physical object or thingamajig. Telling what the field is really "made of" is meaningless to science unless there are corresponding predictions made by said understanding. Classical physics just says the field is there, don't worry about it. Quantum physics says it is made of virtual particles.

 

I worry seriously about it.

I cannot accept action at distance without any logical explanation, and the entire field concept is based upon action at a distance.

 

As mentionned before, I have the conviction that fields have to be connected with the concept of Time (because distance & space are time-related) and with the concept of scale factor (because it is also space & time related). All 3 together can make some sense.

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There is no magical mystical action-at-a-distance. Even Newton knew that over three hundred years ago. In a letter to Richard Bentley on 25 February 1692, he said:

 

“That gravity should be innate, inherent, and essential to matter, so that one body may act upon another at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it”.

 

Once you remove action-at-a-distance, what you're left with is this: a field is a region of space where the properties of space vary, and the interaction of a particle with this space results in altered motion. You might prefer to say it some other way, and you might want to discuss the causative body or particle. But once you drop that magical mysterious action-at-a-distance, I think it always comes back to the same in the end: a field is a region of inhomogeneous space.

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thanks everybody but till now also I'm not satisfied. I think there is something more than what we've learn yet.

 

Well I used to think of functions and fields two be two different entity; for example:

 

Consider an area of circle, A(a) = pi*a2 ----------------- (1)

 

magnitude of electric field of a charge q, E(a) = kq/a2 ----------------- (2)

 

electric field of a charge q, E(a) = kq*a/a3----------- (3)

 

 

So equation (1) and (2) are simple scalar function and equation (3) is a vector function.

 

but do check the below image too which I've uploaded from the book

"Advanced Calculus, Robert C Wrede, Murray Spiegel, 2e" page no. 156

 

 

untitled.JPG

 

after this i thought that the entity (field) too which I used to think is different isn't but its too function that too vector function.

 

now the question comes in mind from direct intuition that the electric, magnetic and gravitational field we're learning is not the field but its only a function (vector function); but from this we didn't get the some real perspective of the physical field we've in our mind.

 

If I'm wrong then please do intimate me about this

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Well, although we are not in speculations, I will make public my own salad:

"a field is a particle's past".

 

For a force between two bodies to exist, it is not necessary to have a field everywhere. For example, two bodies connected with a spring. Or two not-completely-separated pieces of a chewing gum. They interact because they are pieces (parts) of something complex? They cannot be ever separated, as a matter of fact. Thus there is no problem with the action-at-a-distance (there is no true separation) and there is no field in each point of space. Only where our probe body is.

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For a force between two bodies to exist, it is not necessary to have a field everywhere. For example, two bodies connected with a spring. Or two not-completely-separated pieces of a chewing gum. They interact because they are pieces (parts) of something complex? They cannot be ever separated, as a matter of fact. Thus there is no problem with the action-at-a-distance (there is no true separation) and there is no field in each point of space. Only where our probe body is.

 

Are you suggesting there is no field inside a body?

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