# Magnetic fields, again

I asked a couple of questions about magnetism before and I have to say I was not fully convinced by the answers – so here is another way of stating what puzzles me.

Imagine a static magnet. Now magnetism cannot propagate instantaneous as if it did the magnet would surely immediately cease to be magnetic – even though we know, via Oblers’s Paradox if nothing else, that the universe is finite, we must surely also assume it is very large and contains a very large number of magnetic objects.

So magnetism is propagated at some finite speed. Naturally we will assume that speed is $c$ , the speed of light and the propagation is via photons. But what are these photons?

If they are real, physical particles, then they must carry energy and so the magnet should ‘run down’ – otherwise it would be a perpetual motion machine. But static magnets apparently run down very slowly – so slow I have never been aware of it really happening, though I have no doubt it does.

So what else might they be? Presumably a function of quantum electrodynamics (QED) as formulated by Feynman? In this case then the energy of these “virtual” photons is a function of the uncertainty principle.

This would essentially mean that the strength of these magnetic photons would be limited by $\delta E \delta t \leq h$ where $E$ is the energy of the QED photon, $t$ time and $h$ the familiar Planck constant – a very small number indeed.

Here the particles can come and go in an instance or presumably, live mysteriously for a very long time at very low energies. But no actual energy is expended unless this virtual photon is “observed”.

So, is this right? And if it is, how did anyone explain magnetism before QED? And if it is wrong how do magnetic fields propagate.

## 5 thoughts on “Magnetic fields, again”

1. You have the basic idea I think. Virtual photons, unlike real photons, can have a non-zero mass due to the equivalence of mass and energy. The more energy or mass a virtual photon has, the quicker it disappears. In fact, in QED you can predict the number of virtual photons as a function of distance from the magnetic source and it matches exactly with classical magnetic fields.

Magnets do degrade over time, but that is not because of any problem with virtual photons, that is due to fluctuations in the atomic lattice of the magnet. Magnetic domains in the magnet slowly, due to thermal fluctuations, can rearrange the direction their field points. This process happens extremely slowly in most permanent magnets however because the energy required to knock an atom out of alignment with its neighbors is higher than room temperature thermal energy. If you increased the temperature of a bar magnet to its Curie Temperature, it would lose its magnetic field.

The reason the virtual particles are not the cause of the magnet losing any energy is because of Newton’s third law. As the bar magnet exerts a force on another object by hitting it with virtual photons, that other object is hitting the bar magnet with virtual photons as well causing an equal but opposite force on the magnet. Of course, when you go down to the scale of small numbers of particles, there are measurable fluctuations in the number of exchanged particles, but for everyday items, there are so many particles exchanged that they work out to practically equal every time.

1. Thanks for the reply. I had wondered about the third law aspect after I wrote the post – as I thought of the parallel with gravity.

2. tobi says:

There is nothing wrong with perpetual motion. It exists.

Perpetual _work_ does not exist.

1. Well, Tobi, I actually write of a perpetual motion *machine*, ie., something that does work.

1. tobi says:

You are right.

On the other hand: The concept of a perpetual motion machine is not clearly defined. In a sense the universe in its whole is such a machine.