  Are the electromagnetic scalar and vector potentials dispensable? Lev Vaidman
has suggested that local interactions of gauge-invariant quantities, e.g.
magnetic torques, suffice for the description of all quantum electromagnetic
phenomena. We analyze six thought experiments that challenge this suggestion.
All of them have explanations in terms of $local$ interactions of
gauge-dependent quantities, in addition, some have explanations in terms of
nonlocal interactions of gauge-invariant quantities. We claim, however, that
two of our examples have no gauge-invariant formal description and that, in
general, no local description can dispense with electromagnetic potentials.
