I meant “spontaneous” in the ordinary thermodynamic sense of spontaneity (like when we say systems spontaneously equilibriate, or that spontaneous fluctuations occur in thermodynamic systems), so no violation of microphysical law was intended. Spontaneous here just means there is no discernable macroscopic cause of the event. Now it is true that everything that happened in the scenario I described was microscopically determined by physical law, but this is not enough to satisfy the CMC. What we need is some common cause account of the macroscopic correlation that leads to a coherent inward-directed wave, and simply specifying that the process is law-governed does not provide such an account. I guess you could just say that the common cause is the initial conditions of the universe, or something like that. If that kind of move is allowed, then the CMC is trivially satisfied for every correlation. But when people usually appeal to the CMC they intend something stronger than this. They’re usually talking about a spatially localized cause, not an entire spatial hypersurface.
If you allow entire hypersurfaces as nodes in your graph, you run into trouble. In a deterministic world, any correlation between two properties isn’t just screened off by the contents of past hypersurfaces, it’s also screened off by the contents of future hypersurfaces. But a future hypersurface can’t be a common cause of the correlated properties, so we have a correlation screened off by a node that doesn’t d-separate the correlated variables. This doesn’t violate the CMC per se, but it does violate the Faithfulness Condition, which says that the only conditional independencies in nature are the ones described by the CMC. If the Faithfulness Condition fails, then the CMC becomes pretty useless as a tool for discerning causation from correlation. The lessons of Eliezer’s posts would no longer apply. So to rule out radical failure of the Faithfulness Condition in a deterministic setting, we have to disallow the contents of an entire hypersurface from being treated as a single node in a causal graph. Nodes should correspond to sufficiently locally instantiated properties. But then that re-opens the possibility that the correlation described in my example violates the CMC. There is no locally instantiated common cause.
If there is some past screener-off of the correlation in the time-reversed patch, its counterpart would also be a future screener-off of the correlation in our patch. If we want to say that the Faithfulness Condition holds in our patch (or at least in this example), we have to rule out future screeners-off, but that also implies that the CMC fails in the time-reversed patch.
I meant “spontaneous” in the ordinary thermodynamic sense of spontaneity (like when we say systems spontaneously equilibriate, or that spontaneous fluctuations occur in thermodynamic systems), so no violation of microphysical law was intended. Spontaneous here just means there is no discernable macroscopic cause of the event. Now it is true that everything that happened in the scenario I described was microscopically determined by physical law, but this is not enough to satisfy the CMC. What we need is some common cause account of the macroscopic correlation that leads to a coherent inward-directed wave, and simply specifying that the process is law-governed does not provide such an account. I guess you could just say that the common cause is the initial conditions of the universe, or something like that. If that kind of move is allowed, then the CMC is trivially satisfied for every correlation. But when people usually appeal to the CMC they intend something stronger than this. They’re usually talking about a spatially localized cause, not an entire spatial hypersurface.
If you allow entire hypersurfaces as nodes in your graph, you run into trouble. In a deterministic world, any correlation between two properties isn’t just screened off by the contents of past hypersurfaces, it’s also screened off by the contents of future hypersurfaces. But a future hypersurface can’t be a common cause of the correlated properties, so we have a correlation screened off by a node that doesn’t d-separate the correlated variables. This doesn’t violate the CMC per se, but it does violate the Faithfulness Condition, which says that the only conditional independencies in nature are the ones described by the CMC. If the Faithfulness Condition fails, then the CMC becomes pretty useless as a tool for discerning causation from correlation. The lessons of Eliezer’s posts would no longer apply. So to rule out radical failure of the Faithfulness Condition in a deterministic setting, we have to disallow the contents of an entire hypersurface from being treated as a single node in a causal graph. Nodes should correspond to sufficiently locally instantiated properties. But then that re-opens the possibility that the correlation described in my example violates the CMC. There is no locally instantiated common cause.
If there is some past screener-off of the correlation in the time-reversed patch, its counterpart would also be a future screener-off of the correlation in our patch. If we want to say that the Faithfulness Condition holds in our patch (or at least in this example), we have to rule out future screeners-off, but that also implies that the CMC fails in the time-reversed patch.