In quantum mechanics, is there an actual difference between 'observation' and interaction? I apologize if this is just me misreading into things.
So in some cases I've read that observation is simply interaction, only given a name that's somewhat misleading to the laymen.
With the observer effect being misinterpreted as a phenomena where retaining information about a system changes that system in itself.
However what really derails this idea for me is the idea of interaction free observations such as with the Elitzur–Vaidman bomb tester thought experiment.
As well as this paper here which apparently is a demonstration of quantum counterfactual communication. That implies an exchange of information mediated without any input of matter or energy.
 A: In short, the answer to the question is no: observations and interactions are one and the same thing. Mathematically they are represented by operators that act on the density matrix of whatever state is observed/interacted with.
As to the Elitzur-Vaidman (EV) thought experiment, you still have a measurement, albeit not in the basis you'd typically think of, namely the energy eigenbasis. Rather you have a measurement in the phase basis. That's why the EV setup requires a Mach-Zehnder interferometer.
To be more exact, the EV experiment is an energy-interaction-free measurement in the sense that there is no information retrieval in the Fock basis. It is however a phase-interaction-full measurement.
PS: To add some subtlety to the semantics, one would typically think of an observation as an operation that extracts information into a classical "format", i.e., the type of information that you and I can read with our macroscopic probes. On the other hand, an interaction is more general and doesn't necessarily require information extraction into the classical realm.
A: There are way too many terms like "observation" and "interaction" floating around. There is, however, an easy way to look at all of this:
There are two different kinds or processes in quantum mechanics: reversible and irreversible.
In a reversible process the quantum system remains undisturbed and the energy in the system stays the same. This is being described by the evolution of the wave function.
In an irreversible process an external system has to interact with the quantum system to either add energy to or to remove energy from the quantum system. The amount of this energy transfer is called "a quantum". We call this "preparation" or "emission" for the process that fixes the initial amount of energy in the system and "absorption" or "measurement" for the process that determines the final amount. This is usually described by the Born rule in standard non-relativistic QM. Once the energy of the system has changed it is not the same system as before.
The difference between a measurement and a simple absorption process is that in a measurement we retain the value of the quantum of energy (together with its momentum and angular momentum) that we are removing from the system. In a simple absorption process we don't care to know. To the quantum system it's all the same. It has lost the exact same amount of energy, whether the "observer" knows that number or doesn't.
