Relationship between atomic electric and magnetic dipole moments So in quantum theory, typically the interaction between a photon and an atom is described by the following interaction term in the Hamiltonian:
\begin{equation}
H_{\text{int}} = e \mathbf{E}\cdot \mathbf{d}_e
\end{equation}
where $\mathbf{d}_e$ is the electric dipole moment of the atom and $\mathbf{E}$ is the incident photon electric field.  Would it be possible to instead write this in terms of a magnetic field and magnetic dipole moment $\mathbf{d}_m$?  Such as:
\begin{equation}
H_{\text{int}}\propto \mathbf{B}\cdot \mathbf{d}_{m}
\end{equation}
My reasoning behind this is, $\mathbf{B}$ and $\mathbf{E}$ are describing the same physical object, and are related by simple operations.  I would also guess that $\mathbf{d}_e$ and $\mathbf{d}_m$ are directly related, as an atoms magnetic dipole moment originates from the "current" caused by the moving electrons.
So would this work / does this make sense?  I would love to hear the insight of people more knowledgeable than I.
 A: No, this is provably impossible. The electric and magnetic fields are different object, and they interact with different aspects of atomic and molecular systems, and you cannot transform them into each other.
If you want specific counter-examples, try the following:


*

*It is possible to arrange a field configuration with an oscillating electric field but no magnetic field (such as e.g. an electric field antinode in a standing wave). You can then put in a system with no electric dipole moment and a nonzero magnetic dipole moment, and it will be completely untouched by the field.

*It is possible to arrange a field configuration with an oscillating magnetic field but no electric field (such as e.g. an electric field node in a standing wave). You can then put in a system with no magnetic dipole moment and a nonzero electric dipole moment, and it will be completely untouched by the field.


The electric and magnetic fields are not "the same physical object": they describe different aspects of the same physical object (i.e. electromagnetic radiation), with the emphasis on different.
