Interesting questions at the end, which I can partially answer:

Quadrupole and higher moments: are not possible because of symmetry, specifically rotational symmetry and the fact that the electron has spin 1/2. So the dipole moment does fully characterise the “shape”. The result drops out of considering the impact of the rotational symmetry SO(3) on quantum states – one finds a kind of “triangle rule” that constrains the angular momentum of the states and the operator representing the physical quantity of interest. As the electron has spin 1/2 in its initial and final states, only operators with angular momenta 0 or 1 (i.e. scalar and dipole symmetric properties) have non-zero expectations. Hope that makes some sense! Spin-1/2 particles are indeed strange things.

Magnetic dipole moment: yes, in that sense, and the sense of it having spin, it’s definitely not spherically symmetric. But in terms of its charge distribution it is. Depends on what you mean by “shape” really (see below).

Relativistic transformation: interesting question, and not one I’ve thought about. One point that might be relevant is that the electric dipole moment is time-reversal-symmetry asymmetric, whereas the magnetic-dipole moment is T-symmetric. I don’t think a Lorenz boost can change one to the other, so it must work out some way. But I’m also too lazy to work it out!

Finally, shape: yes, that polarised opinion! A lot of people thought it was just plain wrong, or at least dumbing-down. I don’t agree – perhaps obviously, as it was my idea to describe it that way. Being a resolutely experimental type of chap I would argue for a pragmatic description of shape along the lines of “what an electromagnetic probe feels”. This is essentially the definition people use every day when they pick things up. I prefer not to imagine up some mental construction of how the electron “works” internally, and prefer an operational definition like the above. More importantly though, it does a better job of communicating what we do to non-experts than dipole-moment – and I think those grounds alone justify it

Jony

Said to have acquired chopper when on the rocks (Guardian series) (3,3,5,4)

“One peculiarity about the way the [benefit/cost ratio] is calculated is that it actually takes into account the loss of revenue to the treasury as a result of the reduction of receipts of fuel tax due to people changing mode of travel from car to train. This does seem quite extraordinary. Either fuel tax is a specific tax intended to discourage use of cars (or more accurately oil to power vehicles) or it is a general tax with the sole intention of raising revenue for the chancellor. If it is the former then it is quite absurd that rail projects that reduce oil use are penalised for achieving the objective laid down. If it is the latter then it is madness that the cost benefit analysis of a project depends on the arbitrary way that the chancellor chooses to apportion his revenue streams and not on the project itself. It is the modern equivalent of the 1960′s argument that smoking was a good thing because it provided tax revenue for the government.”

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