Is this decoherence? I have a very basic understanting of decoherence (i.e. I,ve read the Wikipedia page), but I was recently reading Heisenberg's The Physical Principles of the Quantum Theory and I came across a thought experiment which, I think, is decoherence, as it shows loss of interference and seems analogous to optical decoherence. According to Wikipedia decoherence was first developed in 1952 and this book is from 1930, so I don't know.
This is, not exactly but paraphrased, the experiment.
To begin with, imagine a beam of atoms of width $d$ is sent through a field $F$ which is inhomogeneous in the $x$-direction, and which can separate atoms into states $n$ and $m$ with energies $E_n$ and $E_m$ respectively (Like the Stern-Gerlach experiment). The energy of state $m$ depends on the field so the force in the $x$-direction experienced by an atom in that state will be
$$-\frac{\partial E_m}{\partial x} \, .$$
Thus the beam will be deflected by an angle 
$$\frac{\partial E_m}{\partial x}\frac{T}{p}$$
where $T$ is the amount of time the atom spends in the field and $p$ is the atom's momentum. The angular separation of the beams in state $m$ and state $n$ is therefore
$$\alpha=\left(\frac{\partial E_m}{\partial x}-\frac{\partial E_n}{\partial x}\right)\frac{T}{p} \, .$$
For the beam to be split into separate beams the angular separation must be larger than the natural scattering of the beam by diffraction, so
$$\alpha\ge\frac{\lambda}{d}=\frac{h}{pd}$$
where $d$ is the beam width and $\lambda$ is the wavelength of the particles.
Since $E_m$ depends on field strength, there will be a change in the phase of the the atom's state $|m\rangle$ associated with the atoms passing through the field, with $\varphi_m$ being the phase change and $\varphi=\varphi_m-\varphi_n$. However, since the beam has a width and the Field is not uniform, the phase change will vary depending on the atom 'passing' through different parts of the field. This will introduce an uncertainty $\Delta\varphi$ in the phase change difference. Since the phase change is
$$\varphi_m=\frac{2\pi}{h}E_m T$$ 
And the uncertainty in position is the width of the beam $d$ the uncertainty in the energy will be
$$\frac{\partial E_m}{\partial x}d$$
So we have
$$\Delta\varphi=2\pi\left(\frac{\partial E_m}{\partial x}-\frac{\partial E_n}{\partial x}\right)\frac{Td}{h}=2\pi \frac{pd}{h}\alpha$$
So $\Delta\varphi\ge 2\pi$, so the phase is entirely undetermined and random.
Now imagine a beam of atoms in state $n$ is sent to a detector which detects if an atom is in a state $l$. The probability of measuring an atom in the state $l$ when it is in the state $n$ is
$$|\langle l | n \rangle|^2=|\sum_m\langle l | m \rangle\langle m | n \rangle|^2=\sum_{m'm''}\langle l | m' \rangle\langle m' | n \rangle\langle m'' | l \rangle\langle n | m'' \rangle$$
Now imagine before the atoms get to the detector, we introduce the field seen previously which separates the atoms in their states $m$ now to the probability we must necessarily introduce the phase factor, averaged out over all the possible phase changes introduced by the field
$$\sum_{m'm''}\langle l | m' \rangle\langle m' | n \rangle\langle m'' | l \rangle\langle n | m'' \rangle\langle e^{\varphi_{m'}-\varphi_{m''}}\rangle$$
And (assuming the phase difference has the same probability for all possible values, reasonable given its large uncertainty)
$$\langle e^{\varphi_{m'}-\varphi_{m''}}\rangle=\delta_{m'm''}$$
And so the probability becomes
$$\sum_m|\langle l | m \rangle|^2|\langle m | n \rangle|^2$$
The interference is lost, and the classical probability is obtained.
 A: Formally this is decoherence - loss of coherence that results in the density matrix of the atom becoming mixed.
But assume that the field is static and all its fluctuations are only spatial in its nature. Let's replace the detector with some sort of mirror (that also changes the state of the atom in such a way that the field has the opposite effect) and put detector near the beam emitter. Then on the way back the state of the atom will evolve as if time was reversed. As result the original state of the atom will be restored to the initial one without loss of information.
The decoherence in the general sense can happen due to very different processes and sometimes the distinction is made. What is often called "true decoherence" happens due to the entanglement of the system under consideration with the uncontrollable environmental degrees of freedom. What you describe however is what is called "fake decoherence" which is much more classical in its nature - it is the loss of coherence that happens because of our lack of knowledge of the fundamentally unitary evolution of the system.
Both happen because of certain lack of knowledge however the latter is constrained to the system itself whereas the former involves the whole macroscopic environment. In the "fake decoherence" the information about the initial state is recoverable if only in principle from the knowledge just about the system itself. In contrast in the "true decoherence" the information about the initial state is lost in a much more severe way as to recover it even in principle you need to know the state of the whole macroscopic environment.
A: Wikipedia is mistaken if it says that decoherence was only developed in 1952. Decoherence is simply part of quantum theory, and it is there in many early discussions of the interactions of small systems with measuring apparatuses, such as the one you describe from Heisenberg. Heisenberg judged that these sorts of physical descriptions were valuable in understanding what is going on, but they do not resolve all the issues concerning measurement and observation. He was right about that.
