# What IS a field e.g. magnetic field

## Main Question or Discussion Point

My first post. Not sure if it's a silly question ....

I'm curious to know what the best way of actually describing a field such as a magnetic field is. Is it possible to describe it in any way other than it's measurable effect on something else?

e.g. If you have a static magnetic field and you try to analyse what actually exists at a point within the field what do you get??? What is 'going on' at that point in space???

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Every time I've asked this question, the usual answer involves some sort of math statement. I doubt anyone can explain something this basic, yet so elusive and incomprehensible with words.
Let me take it to another level- what is a magnetic field composed of?
It's referred to as a 'force', but from where does the force originate?

Here's a previous discussion on this topic:

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The classical answer is that fields (gravitational, electric, magnetic) are properties of empty space. "Action at a distance" between two objects can occur because something affects the space around it, then another thing responds to the properties of the space that it is in.

Maxwell's mathematical form for summarizing some of Faraday's experiments shows that a changing electric field produces a magnetic field, and a changing magnetic field produces an electric field. One depends on the rate of change of the other.

By the way, when we define what something "is" by really describing what it does or how it works, that's called an operational definition. I'm not sure that a mind is capable of anything else, since all knowledge is just an attempt to generalize about what human senses have observed.

... a changing electric field produces a magnetic field, and a changing magnetic field produces an electric field. One depends on the rate of change of the other...
I find it interesting that a static magnet produces a magnetic field without evidence of any movement or change of its electric field (classical view). And, if the electric field encompassing a magnet is indeed moving- at what speed is it doing so?

If one says 'the speed of light', then it seems to be a valid argument for using the 'virtual photon' theory.

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clem
I find it interesting that a static magnet produces a magnetic field without evidence of any movement or change of its electric field (classical view). And, if the electric field encompassing a magnet is indeed moving- at what speed is it doing so?
The magnetic field of a permanent magnet is predominantly due to aligned spins of bound electrons with nothing moving, as you say. It is a quantum view since electron spin is a purely quantum effect. There is no electric field unless you move the magnet.

The magnetic field of a permanent magnet is predominantly due to aligned spins of bound electrons with nothing moving, as you say. It is a quantum view since electron spin is a purely quantum effect. There is no electric field unless you move the magnet.
I find your explanation a bit confusing.

(1) What constitutes an 'aligned spin'? Are you referring to the crystals within the domain structure of the magnet? If so, how is that 'spin' transferred into a nearby ferrous metal without electromagnetic radiation being present? There are no waves emanating from a magnet (none that I'm aware of, anyway)- that is, unless you are referring to the magnon: http://en.wikipedia.org/wiki/Magnon
which is limited to the confines of the magnet itself.

(2) Furthermore, if something is spinning, isn't it moving?

(3) A magnet resting on a wooden desk does indeed have a magnetic field, even though its electric field isn't moving. From what we have learned, a moving electric field is required to produce a magnetic field, and yet it exists anyway.

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dst
The "spin" is an intrinsic property of certain particles in QM. Think of the angular momentum that an electron orbiting an atom would have - except electrons don't literally orbit. I guess that's the gist of it.

2, you can't define "movement" on the scale we are talking about.

3. I have no idea.

Andy Resnick
Every time I've asked this question, the usual answer involves some sort of math statement. I doubt anyone can explain something this basic, yet so elusive and incomprehensible with words.
Let me take it to another level- what is a magnetic field composed of?
It's referred to as a 'force', but from where does the force originate?

Here's a previous discussion on this topic:

That's because a 'field' is a mathematical object. There's scalar fields, vector fields, tensor fields (some would claim those are all tensor fields)...

A physical quantity like 'temperature' (or energy) can be described mathematically as a scalar field. Thinks like momentum, the electric and magnetic fields (*) are represented by vector fields. Stress is represented by a 2nd rank tensor field.

I prefer to clearly distinguish between a mathematical model of something and the thing itself. As in: Q: 'what is light?' A: 'Nobody knows. Light can be modeled as a wave or as particles.'

So, in english:

What is the magnetic field composed of? Nothing. At least nothing measurable. The generation of a magnetic field by matter and the interaction of the magnetic field with matter produces measurable effects (deflection of a current-carrying wire, for example). Magnetic flux lines can be counted in superconductors.

From where does the force originate? The Lorentz force law is a *postulate*, not derivable from anything else.

(*) see the thread elsewhere on PF on the mathematical structure of E, B, H, D and current... they are not quite vectors, but can be under the right circumstances.

That's because a 'field' is a mathematical object. There's scalar fields, vector fields, tensor fields (some would claim those are all tensor fields)...
I'm not a scientist, but I beg to differ with you. Math is used to describe an object, not because the object itself is mathematical to begin with.

So, in english:

What is the magnetic field composed of? Nothing. At least nothing measurable....
Again, I disagree. The field is measurable using many methods. What it consists of and from where it emanates remain a mystery.
Maybe a bright student or researcher will someday reveal its essence, and enlighten us all in a manor mathematics fails to do.

I find it interesting that a static magnet produces a magnetic field without evidence of any movement or change of its electric field (classical view).
Before there was quantum mechanics, using a Rutherford or Bohr "solar system" concept of the atom, the classical answer was this: The electron revolves around the nucleus, and probably spins on its axis as well, so that constitutes a charge moving in a circular path. So lets all use the rule for determining the direction of a magnetic field produced by a loop of wire in which there is a current traveling in a circular path, and now we can visualize every atom as a little electromagnet. Then, if all the atoms are aligned so that these effects from all the atoms add up and do not cancel out, then the whole bulk of material is magnetized.

That is still how it's taught today whenever the teacher and the syllabus and the textbook don't want to "get into" quantum mechanics, e.g., high school level. Frankly, I'm not so sure whether that's a good thing or a bad thing. (I have a New York State teaching certification in high school physics.)

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dst
I'm not a scientist, but I beg to differ with you. Math is used to describe an object, not because the object itself is mathematical to begin with.

Again, I disagree. The field is measurable using many methods. What it consists of and from where it emanates remain a mystery.
Maybe a bright student or researcher will someday reveal its essence, and enlighten us all in a manor mathematics fails to do.
No, not at all. You have to get that kind of conception out of your head. A "field" is a mathematical entity and nothing more. As it turns out, this treatment just works. So it's used (which is more or less the foundation of physics since the empirical method kicked it off).

In real life you can "see" the field using iron filings. That's cheating! You're making measurements, it tells you nothing about "the field". And again you can't avoid the mathematical "field" there either. Your question is phrased wrong - what you're asking for is "What is actually tangible about a magnetic field". Which I'm sure SR is supposed to explain quite well (I'm not that far).

No, not at all. You have to get that kind of conception out of your head. A "field" is a mathematical entity and nothing more. As it turns out, this treatment just works. So it's used (which is more or less the foundation of physics since the empirical method kicked it off).

In real life you can "see" the field using iron filings. That's cheating! You're making measurements, it tells you nothing about "the field". And again you can't avoid the mathematical "field" there either. Your question is phrased wrong - what you're asking for is "What is actually tangible about a magnetic field". Which I'm sure SR is supposed to explain quite well (I'm not that far).
So we have to contend with the fact that a magnetic field is nothing more than a mathematical model and the 'field' does not really exist?

If I place a ferrous plate in close proximity to a strong magnet or electromagnet, what mechanism is responsible for attraction to take place?

Mathematics?

I'm really confused now.

So we have to contend with the fact that a magnetic field is nothing more than a mathematical model and the 'field' does not really exist?

If I place a ferrous plate in close proximity to a strong magnet or electromagnet, what mechanism is responsible for attraction to take place?

Mathematics?

I'm really confused now.
Honestly Pinestone, I'm NOT trying to be sarcastic or insulting. When you ask "what mechanism is responsible for the attraction to take place?", I can only give you the obvious answer. The mechanism is

*magnetism!!!*

If we know the underlying principle more fundamental than that, we would refer to it by the name of that mechanism. Science consists of explaining things in terms of postulates or axioms. An axiom by its very nature cannot be proved, nor resolved into components more fundamental, as it would not be an axiom. At this moment in time, we don't know more than that. Magnetic fields and forces are understood only to a certain level. Trying to go further is futile.

I realize that this isn't the answer you were looking for, but I don't have a better answer, and I'm not aware that one exists. Does this help? BR.

dst
So we have to contend with the fact that a magnetic field is nothing more than a mathematical model and the 'field' does not really exist?

If I place a ferrous plate in close proximity to a strong magnet or electromagnet, what mechanism is responsible for attraction to take place?

Mathematics?

I'm really confused now.
I'm sure that someone else can help with regards to that. I mean, for instance, with gravity, we have the sheer curvature of space causing the "attraction". I don't know how it works for magnetism but I can definitely imagine a magnetic field as "curving space" but only for... magnetic elements!

I'm guessing you want a physical mechanism, like the way in which general relativity explains gravity, yes? Well as I said, I think special relativity is supposed to explain that (and magnetic field = electric field in a different reference point which is why I say that), but there are loads of well educated peeps on here who will know.

Mathematics is what you use to describe it, just like you pointing at it and calling it a "field", a person doing it through mathematics would assign a value (of magnetic flux density) at every point in space and time (which is a... field). Just a naming convention, a very precise, elaborate, descriptive one.

most people don't believe fields to be anything physical. it is just a convenient mathematical idea that makes the math easier. for example we say electron sets up an electric field, which means that if you stick a charge into the field, it will be affected by it. but really, it's not affected by the field, it's just affected by that electron. when we talk about the field somewhere we talk about the electric force due to the electron at that place, if we were to stick some other charge in there.

...Magnetic fields and forces are understood only to a certain level. Trying to go further is futile.

I realize that this isn't the answer you were looking for, but I don't have a better answer, and I'm not aware that one exists. Does this help? BR.
Well, your reply is helpful and disappointing at the same time. Looks like I'll have to stick with the equations for now, and try to think in more abstract terms.

I wonder why more research hasn't been done on this simple, primal force that is one of the cornerstones of science? I guess it's something that will remain a mystery...

Thank you.

Andy Resnick
I'm sure that someone else can help with regards to that. I mean, for instance, with gravity, we have the sheer curvature of space causing the "attraction". I don't know how it works for magnetism but I can definitely imagine a magnetic field as "curving space" but only for... magnetic elements!

I'm guessing you want a physical mechanism, like the way in which general relativity explains gravity, yes? Well as I said, I think special relativity is supposed to explain that (and magnetic field = electric field in a different reference point which is why I say that), but there are loads of well educated peeps on here who will know.

Mathematics is what you use to describe it, just like you pointing at it and calling it a "field", a person doing it through mathematics would assign a value (of magnetic flux density) at every point in space and time (which is a... field). Just a naming convention, a very precise, elaborate, descriptive one.
I would be wary of this description- to say GR explains gravity is not exactly true: it provides a mechanism (curvature), but does not say anything about 'causes'.

This is a common misconception- that physics explains 'causes', or that physics explains *why* things happen. Physics (just like any branch of science) can only provide a mechanism, explain *how it is* that something happens, but does not say more than that.

GR is a more satisfying theory of gravity than Newton's for many reasons, and in some cases GR is more accurate than Newton's theory. But GR does not "explain" gravity. Maxwell's laws do not "explain" electromagnetism.

Andy Resnick
Well, your reply is helpful and disappointing at the same time. Looks like I'll have to stick with the equations for now, and try to think in more abstract terms.

I wonder why more research hasn't been done on this simple, primal force that is one of the cornerstones of science? I guess it's something that will remain a mystery...

Thank you.
Because "why" questions are outside of science. "Why" questions are faith-based. Science answers "how" questions. And does it very well.

dst
I would be wary of this description- to say GR explains gravity is not exactly true: it provides a mechanism (curvature), but does not say anything about 'causes'.

This is a common misconception- that physics explains 'causes', or that physics explains *why* things happen. Physics (just like any branch of science) can only provide a mechanism, explain *how it is* that something happens, but does not say more than that.

GR is a more satisfying theory of gravity than Newton's for many reasons, and in some cases GR is more accurate than Newton's theory. But GR does not "explain" gravity. Maxwell's laws do not "explain" electromagnetism.
I thought that's what he/she was asking though? What mechanism causes something to be "magnetized" at a point in space. What about gravitational lensing though? Doesn't that show that GR's mechanism is actually correct (for all intents and purposes)? And "WHAT" questions are hardly outside of physics, I mean we have answers for something like "What causes a light bulb to emit light?", and a vague answer for "What is light?", so if that can be done, why not for magnetic fields?

Andy Resnick
I thought that's what he/she was asking though? What mechanism causes something to be "magnetized" at a point in space. What about gravitational lensing though? Doesn't that show that GR's mechanism is actually correct (for all intents and purposes)? And "WHAT" questions are hardly outside of physics, I mean we have answers for something like "What causes a light bulb to emit light?", and a vague answer for "What is light?", so if that can be done, why not for magnetic fields?
Well, the OP was asking something slightly different, but the underlying question is close to yours. And I absolutely did not say that *what* questions are outside of physics, I said *why* questions are outside of physics.

Even so, you need to be careful- in order to answer "what causes a light bulb to emit light", you need to first decribe a physical model. For example:

Q: What causes something to be magnetized?
A: We model atoms as having a dipole moment, this is a consequence from how we model atoms. Alternatively, materials can be modeled as possessing a dipole density. The magnetic dipole moment interacts with the magnetic field, giving an interaction energy which can then be minimized if the atoms are free to move.

Do you see how I answered that? I explicitly referred to a physical model- unlike reality, models can be changed and adjusted as we learn new things. Models come from us, they are not dictated to us. That answer above contains a wealth of invented constructs and concepts that took centuries to develop and years to learn today.

So, although you may be taught that GR is a 'correct mechanism', and experimental results not obtainable from Newton's theory are duly trotted out to support this claim, you should keep in mind that GR is also a model created by humans, and subject to revision as new experimental results are obtained. That is, GR is not a 'correct' anything, it's a more accurate description of reality. More cumbersome, as well.

We have mature quantitative models for many things- that's one of the great triumphs of physics. But having a well-verified descriptive model for reality is different for claiming that we have some underlying knowledge of the nature of reality.

movement of fields

I find it interesting that a static magnet produces a magnetic field without evidence of any movement or change of its electric field (classical view). And, if the electric field encompassing a magnet is indeed moving- at what speed is it doing so?

If one says 'the speed of light', then it seems to be a valid argument for using the 'virtual photon' theory.
neither the field nor the electrons in the magnet are moving. just as an electric field is simply a property of charges so the magnetic field is simply a property of the magnet.

nevertheless fields themselves do move. the best way to understand this is to picture the energy stored in the field as a fluid that flows from place to place. it is the relative motion of a charged particle and a magnetic field that produces an emf.

vector fields arent normally thought of as having the property of motion but electric and magnetic fields are particular kinds of vector fields that obey certain conservation laws. i suppose that is why it is possible to speak of motion of electric and magnetic fields.

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neither the field nor the electrons in the magnet are moving. ...

...nevertheless fields themselves do move. the best way to understand this is to picture the energy stored in the field as a fluid that flows from place to place...
OK, which is it? You seem to have a little conflict going here. If the energy is 'stored' it's obviously not in motion, and can not 'flow' from place to place, as you indicate.

OK, which is it? You seem to have a little conflict going here. If the energy is 'stored' it's obviously not in motion, and can not 'flow' from place to place, as you indicate.
fields in general are capable of moving.

Is it possible fields originate from certain properties being somehow imbued into the space-time manifold creating some kind of differential? I suppose that's a crude of way putting it. There's a fair chance it could be an entirely illogical idea, too. lol.

Is it possible fields originate from certain properties being somehow imbued into the space-time manifold creating some kind of differential? I suppose that's a crude of way putting it. There's a fair chance it could be an entirely illogical idea, too. lol.
differential?

not sure what you are saying but the equations describing fields are identical to those that describe stress and strain in a solid.