Momentum from static E and H fields? (So this video claims)

[vanhees71]

Sure, a changing $\vec{E} \times \vec{B}$ means there's change in energy flow/momentum density with time and this means some net force is acting on the system. For a closed system the total momentum doesn't change due to spatial translation invariance which is a fundamental symmetry of Minkowski space and thus this must hold true for any properly defined special-relativistic theory.

 

[Swamp Thing]

So when the E x B changes, the system becomes temporarily "open" to that extent -- it that the EM radiating away as a wave or EM pulse?

 

[vanhees71]

If you take into account all charges and fields, it's a closed system.

That's the deeper reason why we need the electromagnetic field to describe nature! Given the well-established fact that space and time have to be described relativistically (special relativity is sufficient for the argument of course) and that this still implies that for any inertial observer space is a Euclidean affine manifold which is homogeneous and isotropic, also the momentum-conservation law must hold (because of homogeneity of space due to Noether's theorems).

On the other hand there cannot be causal instantaneous interactions, i.e., in a closed system of interacting charges the acceleration of one charge, i.e., the change of its momentum due to the forces from the other charges, cannot instantaneously be compensated by a change of the other charges momentum. So you need some local entity that takes up the momentum to keep momentum conservation right at all times, and that's the electromagnetic field.

 

[Swamp Thing]

Sure, a changing $\vec{E} \times \vec{B}$ means there's change in energy flow/momentum density with time and this means some net force is acting on the system.

Re. my post #28 with the coaxial capacitor and axial magnetic field, and considering that changes in hidden momentum should result in mechanical impulses...

Let the magnetic field be provided by a pair of solenoids in series, one at each end of the coaxial capacitor.

Let's excite the capacitor and coil with frequencies in the MHz range, such that the reactive power is a couple of hundred watts. But let the E and H frequencies differ by, say 1 KHz. Then the hidden angular momentum will have a 1 KHz oscillation from clockwise to anticlockwise around the capacitor's axis as per the phase variation between the E and the H. Can the resultant torque on the capacitor and/or coil be detected with a suitable acoustic transducer (maybe fiber optic based to avoid EMI) ?

Better still, we can use a toroidal coil to make sure that there is no energy radiating away, and that E and H don't overlap anywhere except in the capacitor.

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[vanhees71]

Of course you also have to take into account the "mechanical (Poincare) stresses" to keep the entire system in balance. Doing so you have a closed system, where the center-momentum theorem (aka center-of-energy theorem) is fulfilled.

For more simple examples of this kind, look for "Trouton-Noble experiment" and "Tolman's paradox".