# Magnetic Field is Made of Photons

*Most recent answer: 10/22/2007*

- Douglas (age 35)

Louisiana USA

The electromagnetic interaction is mediated by the constant exchange of photons from one charged object to another. The magnetic field is really just a classical approximation to the photon-exchange picture. In a moving reference frame, a magnetic field appears instead as a combination of a magnetic field and an electric field, so electric and magnetic fields are made of the same "stuff" (photons).

Some electromagnetic interactions involve "real" photons with definite frequencies, energies, and momenta. Electrostatic and magnetic fields involve the exchange of "virtual" photons instead. Very close to an electron is a dense cloud of virtual photons which are constantly being emitted and re-absorbed by the electron. Some of these photons split into electron-positron pairs (or pairs of even heavier stuff), which recombine into photons which are re-absorbed by the original electron. These virtual particle loops screen the charge of the electron so that far away from an electron it appears as if it has less charge than close by.

Normally we wouldn’t call any of these fields "matter", but it is true that the electric and magnetic fields which surround a charged object like an electron do store energy, and therefore have a rest mass, via E=mc^2 (in a reference frame in which the electron has no momentum).

Tom

*(published on 10/22/2007)*

## Follow-Up #1: picturing magnetism

- JS BAIRD (age 67)

Davao City,Philippines

It sounds like what you're asking for is a Feynman diagram to represent electromagnetic interactions. You can get that with a discussion on Wikipedia: https://en.wikipedia.org/wiki/Quantum_electrodynamics.

Meanwhile, I'll take the opportunity to somewhat modify Tom's presentation. We routinely say things like "virtual photons ... are constantly being emitted and re-absorbed by the electron" but that isn't really what we mean. Two particles that are interacting electromagnetically are indeed surrounded by a virtual photon cloud. However, in familiar cases (e.g. a hydrogen atom) that cloud is completely unchanging in time. Nothing at all is going on. The words about things fluctuating around are a rough way to convey one of the peculiar properties of quantum fields. The electric and magnetic fields have not only average values but also ranges of possible values around the average. That's what's so different from classical fields. (It's just like the positions of quantum particles, which have ranges around the average position, unlike classical particles.) You can convey an image of that range by pretending that the fields are jumping around between the different possible values, just like you can pretend that a particle is jumping around among the different positions in its cloud. However, the fields (including their spread of values) no more need to be jumping around than do the particles in space. In a nice stable atomic state, for example, nothing changes in time. The static range of possibilities turns into an actual range of outcomes only when the system interacts in particular ways with the bigger world outside.

Mike W.

*(published on 04/27/2011)*

## Follow-Up #2: back to Maxwell's mechanical fields

- Mark (age 58)

Florida

When Maxwell first came up with his famous equations for electromagnetism, he tried to make a mechanical model with little gears and wheels and things. It was quickly dropped because it added nothing but complication to the field equations.

You have various verbal assertions about what a field "really" is. You say it's not made out of monopoles, but I've never heard of anyone suggesting that it is. You say it has nothing to do with photons, i.e. quantum mechanics. Your picture sounds like it wouldn't fit with special relativity.

The combination of special relativity and quantum mechanics allows calculations of things that can be measured. For example, it gives a prediction for the electron gyromagnetic ratio. Experimentally, the value is 2.00231930462, with a little uncertainty in the last decimal place. "The QED prediction agrees with the experimentally measured value to more than 10 significant figures..."

What value does your model give?

Mike W.

p.s. I can't resist giving the first two lines of a ~ 100 page interview that the Chemical Heritage Foundation conducted with a scientist (my father) who had been working with magnets for ~ 90 years. "As a kid I discovered that I could make the pins in a box stand up, and by moving a magnet around, I could make them march. I had no idea what a magnetic field was and I suspect I have no idea still what a magnetic field is, except for some of the things it does."

*(published on 09/04/2013)*

## Follow-Up #3: electric fields as virtual photon clouds

- JD (age 29)

Louisville, Kentucky, USA

The classical field expression tells you how the virtual photon cloud spreads out. So those virtual photons are no more or less concentrated on the charge than are the classical fields. The shape changes when two charges are present are just those given by adding up the classical vector fields. So yes, there is a particularly strong field between the charges but far away the fields from them tend to cancel.

Mike W.

*(published on 04/11/2015)*

## Follow-Up #4: photons and magnetic fields

- Robert Ponce (age 69)

Port Hueneme

There is one sense in which you're right that you shouldn't think of magnetic fields as being made of photons. If you have any specific numbers of photons of each type, the expected magnetic field is zero. To get anything like a classical well-defined magnetic field you need a big spread of possible photon numbers.* That's a lot different than thinking each photon contributes some field.

On the other hand, maybe you're thinking there's some other ingredient, besides photons. There isn't.

Mike W.

*If you look at, e.g., equation 21 in this paper (https://www.phys.ksu.edu/personal/wysin/notes/quantumEM.pdf) you'll find the expression for the magnetic field in terms of the photon creation and annihilation operators.

*(published on 12/13/2015)*

## Follow-Up #5: photons and magnetism

- James (age 30)

I won't succeed in explaining this, but can clear up a few points.

The photons that contribute to magnet fields are no different than the ones that contribute to electrical fields. The particular pattern of which phases are present for different numbers of photons determines what classical fields are present.

As for the relation of photon numbers to classical fields, I can suggest an analogy that you could study that might be easier to picture. Look at the wave functions that represent states of a simple harmonic oscillator (mass on a spring). (https://en.wikipedia.org/wiki/Quantum_harmonic_oscillator) Ones with definite energy are just like photon states with definite numbers and hence definite energies. The SHO single-energy states are always equally distributed about the midpoint, with no average displacement and no average velocity. By exact analogy, the definite-number photon states have no average magnetic field or electric field. To get an SHO to swing around classically, you need to make states where interference between parts with different energies causes cancelations in some parts and enhancements in others. As the wave changes in time, the positions of those low and high density points swing back and forth, meaning changing positions and velocities. The analog for photons is changing fields.

Mike W.

*(published on 01/16/2017)*

## Follow-Up #6: ingredients of magnetism?

- Mike Collins (age 71)

Gwynedd, Wales

You're right that in general we don't know all the ingredients of the world. We probably don't even know the basic form of the theory, how spacetime emerges from some deeper forms, etc. Nevertheless, within the context of what we do know, there is no special mystery to magnetism. In fact, magnetism is part of the electroweak theory, which is the best-known theory we have of anything. It predicts, for example, the magnetism of an electron to better than one part in one hundred billion.

The waves you mention are all describable as a type of behavior of underlying media- water, air, etc. At a deeper level, however, the ingredients of the universe (photons, quarks, neutrinos, gluons,...) are currently only describable as pure quantum waves in and of themselves. Photons are as basic as any of the other ingredients we have.

Maybe someday some deeper ingredients will be found and all of our currently fundamental particle fields will be seen as emerging from the behavior of that deeper theory. Will the deeper theory then turn out to emerge from a still deeper one? Will that pattern go on forever or reach a deepest level? We don't know. So long as there are dangling ends (inconsistency between general relativity and quantum field theory, dark energy and dark matter,...) we know we aren't at the bottom of the stack. If some point is reached with no basic dangling ends, then maybe we will be at the deepest level.

Mike W.

*(published on 06/15/2017)*

## Follow-Up #7: are magnetic fields necessary?

- Andrew (age 67)

Shropshire, England

You're right that the forces between classical currents with fairly static arrangements can be expressed directly in terms of the currents and the displacements between them. It's not as simple as electrostatics because the direction of the displacement and the directions of the currents enter in a slightly more complicated. way. But still, for that case the use of magnetic field descriptions is just an optional mathematical convenience. Once you start talking about *accelerating* classical charges, however, the full electromagnetic field equations become involved. It would be extremely inconvenient to describe electromagnetic waves (e.g. radio waves and light) in a notation based on charges and currents, because those waves propagate freely far from any charges and currents.

Once you wish to include quantum spins, descriptions that leave out magnetic fields or even more abstract entities (vector potentials,..) become useless. Practical magnetic materials all involve such spins.

Mike W.

*(published on 07/26/2017)*

## Follow-Up #8: quantum fluctuations

- Rhodri Orders (age 33)

Douglas, Isle of Man, British Isles

A physical interaction doesn't necessarily mean that something is going on, at least in the usual sense of the words. For example, think of a box sitting on the floor. The box and the floor are certainly interacting. But not much is going on. Nothing is changing.

"Even in a pure vacuum, there is a lot going on i.e. there exists the fluctuations of zero-point energy. " That is true in the following sense: the values of various fields are not fixed exactly at zero, but have a spread around that, just like the position of a wave is spread out. Nevertheless, the field spread isn't changing in time.

I think the sloppy language is used because we instinctively try to squeeze quantum reality into classical pictures.

Mike W.

*(published on 09/30/2017)*

## Follow-Up #9: electromagnetic field speculations

- Astral (age 33)

Poland

There's a flaw in your reasoning here: ""normal" photons are not affected in any visible way by electrostatic and magnetic fields - so by logic they can't carry them, as separate forces." So long as the equations for a field are linear, as the classical EM equations are, then any component of the field has no effect on the behavior of any other component. So the lack of interaction between static fields and propagating ones just says the equations are linear, not whether the same fundamental types of fields can show these different behaviors.

Your argument that virtual photons cannot give rise to the long-range (1/distance-squared) static interactions is not correct. Exactly that behavior is expected for the virtual photon picture.

Mike W.

*(published on 11/01/2017)*

## Follow-Up #10: polarized light and bird compasses

- Astral (age 33)

Poland

That's a very cool result, strongly supporting the theory of my late colleague Klaus Schulten on one way birds sense magnetic fields. The mechanism involves some non-equilibrium chemical reaction rates that depend on magnetic fields to an unusual extent. The polarization of the light only serves to get the right chemistry going in the birds' eyes. The information about the field isn't present at all in the light wave.

Mike W.

*(published on 11/10/2017)*

## Follow-Up #11: magneto-optics

- Astral (age 33)

Poland

Many materials show Faraday effects and Kerr effects- ways in which the propagation or reflection of polarized light depends on the magnetic field on the material. Saying that a magnetic field changes optical properties of materials is very different from saying that the light waves themselves already carry information about those static fields, even in a vacuum.

Mike W.

*(published on 11/16/2017)*