I've been wondering about microcausality for some time now (a recent question of mine regarding the topic) and i'm wondering if its possible to devise an experiment to detect potential violations
I thought something like this: the hypothesis to test is that if two atoms A and B are close enough, and by close enough i mean that the cross-section of atom B and photons emitted in all/random directions from A is roughly of the order $\frac{4 \pi}{100}$, so statistically, and assuming no dipolar couplings affecting the orientation, if A is excited and B is on the base state, 1% of photons emitted from A will be absorbed by B if microcausality holds, and any deviations from this average will suggest a causality violation (i.e: that the atom B at time $t + \tau_0$ absorbs an advanced photon that "causes" A at time $t$ to emit it, where $\tau_0 = \frac{d}{c}$)
In order to detect when photons are emitted from each atom, actually we'll arrange so atom A favours a two-photon decay $\omega_0$ and $\omega_A$ from the excited state, and B, when in its base state, will accept $\omega_0$ but quickly decay to a metastable level sending a photon of $\omega_B$. We will use timings of $\omega_A$ and $\omega_B$ photons to roughly time the emission and absortion times of each atom
But there is still a problem with the above setup: is entirely time-symmetric, so there is no good reason to expect that the atom B at the future, even if emitting advanced photons, will be more likely to interact with the past A atom (because both atoms will see each-other cross sections to be symmetrical). So in order to fix this, we actually arrange not one, but many atoms like A surrounding the atom B, so there is a probability $p_R$ of all the atoms A emitting a photon that is absorbed by B in the future (if only retarded causes are allowed), but there is a higher probability $p_A$, say, very close to 1, that the atom B will absorb an advanced photon from some of the A atoms. Any experimental outcome between $p_R \le p \le p_A $ would imply a mixture between retarded and advanced causation.
Does this sounds like something that makes sense, and if it does, sounds like something that is doable? I've think about this from time to time, but never actually found a reason why it would not work.
Obviously, sayings stuff like "this is nonsense because microcausality holds and i know it because etc." its useful but not the point of the question, and with that i mean, if there are theory arguments against a positive result (beyond assuming causality holds ad hoc) it would be great to know them. But my question is regarding the experiment itself. For instance if you can sketch and argument about, say, $\Delta E \Delta t \ge \hbar $ implies that any correlations will be swamped by quantum noise, that is completely relevant to the question and you should write about that
thanks!!!
