# Should light travel faster between magnets similar to the scharnhorst effect?

Consider two flat infinitely wide and high rectangular magnets located a distance $$L$$ from each other in what is otherwise a vacuum. Visualized below:

If the magnets are aligned properly there will be an attractive force between them. One interpretation of this attractive force is that there is a sea of virtual photons between the magnets and "if the virtual photons have a negative energy, they contribute to the electromagnetic force as an attractive force", so the QED vacuum between the plates has less average energy content than the vacuum external to the plates.

Superficially this sounds similar to the situation with the Casimir effect where the QED Vacuum between the conducting plates ALSO has less average energy than the outside but they are subtly different.

1. The Casimir Effect is strictly because there is a lack of virtual photons between the plates (any photons whose wave length is too big are excluded)

2. The Magnets here could be argued to either:

a. have a surplus of virtual photons with negative energy between them

b. have a lack of virtual photons of positive energy between them.

Nevertheless by carefully tuning the magnet strength, and distance between the magnets we can make two identical setups, one being a casimir conducting plate setup, the other being this magnet setup where both setups have identically shaped plates an identical distance apart, experiencing identically strong attractive forces (assuming they are held in place and not moving and the magnets have less conductivity than the conducting plates).

So how really are their vacuums different?

One way to shed light on exactly what's happening might be to ask how does light behave between the plates? In the Casimir effect it's predicted that very subtly light might travel faster in an effect called the Scharnhorst effect. Between these two magnets we also have vacuum with lower energy density than the surrounding vacuum so its natural to ask the same question: "is the speed of light between the magnets and normal to the magnets different at all compared to the speed of light in the classical vacuum?" intuitively we would expect "is it faster?"

Ideally I would have the technical skillset to repeat Scharnhorst's derivation of computing $$e_0,\mu_0$$ between the plates and then checking for myself but I lack the technical knowledge in QFT to do this at this time.

• This should be answerable using the Euler–Heisenberg Lagrangian. Commented Jan 15 at 5:50
• There is no negative energy between the magnets. A magnetic field has a positive energy density. In a magnetar that field is amazingly dense. I didn't do the math but Wikipedia claims that it can have 10,000 times the density of lead. Commented Jan 17 at 4:36
• single source of magnetic field itself should probably have positive energy density but the space between the two magnets is a little less clear. The conceptual thing I'm not clear about here is that those two magnets are exchanging a large number of virtual photons of negative energy (this is what it means to have an attractive force) and so if you ask about the average energy of all the virtual photons between the magnets you do end up with a large negative number (the stronger the attraction the more negative that number gets) Commented Jan 17 at 18:42
• the logical jump this questions asks is "well okay if the average energy density of the exchanged photons between the magnets is so negative, is it a different kind of negative density than the casimir effect?" that's why i proceed to ask about speed of light between the magnets specifically Commented Jan 17 at 18:43
• For all we know energy is an additive property of spacetime. There is no magnetic energy density and spacetime energy density. There is only total energy density. Dark energy density is roughly equivalent to 1e-31g/cm^3. As soon as there is more baryonic matter (or electromagnetic field) than that anywhere, the overall density is positive. If I trust some of the online calculators a magnetic field of roughly 6e-8T without any additional matter is enough to swamp the current cosmic dark energy density. Such a configuration is not stable. It will dissipate and then dark energy takes over. Commented Jan 20 at 4:21