Is there any consistent framework where a future measurement setting can change an earlier observable marginal
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I'm trying to understand the exact boundary between retrocausal interpretations of quantum mechanics and actual backward signaling.
Consider the simplest setup:
- At time T1, an observer records a local result R.
- Later, at time T2, an experimenter freely chooses a setting S, either 0 or 1.
- The observer at T1 has access only to R. They receive no later measurement outcome, post-selection information, or classical communication from T2.
For genuine backward signaling, the statistics available at T1 would have to depend on the later choice.
In other words:
P(R given S=0) would have to differ from P(R given S=1).
Equivalently, there would need to be nonzero mutual information between the later choice S and the earlier record R.
My understanding is that standard quantum mechanics prevents this through the no-signaling structure: an unconditioned operation performed on the other subsystem cannot change the earlier/local reduced state.
That's why delayed-choice experiments, entanglement swapping, weak measurements, post-selection and time-symmetric interpretations can produce unusual correlations without allowing the earlier observer to determine which later setting was chosen.
My question is:
Are there any mathematically consistent post-quantum, generalized probabilistic, retrocausal, or modified-causal frameworks in which a freely selected future setting can alter an earlier observable marginal, without conditioning on a later outcome?
If not, is there a theorem more general than the standard quantum no-signaling theorem that rules out this entire class of models?
I'm particularly interested in which assumptions would have to be relaxed for such an effect to become possible.
I'm not claiming backward signaling exists. I'm trying to determine whether the operational possibility is ruled out in general, or only within particular physical frameworks.