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adam_strandberg comments on Stuff That Makes Stuff Happen - Less Wrong
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You seem to be exaggerating the generality of the causal Markov condition (CMC) when you say it is deeper and more general than the second law of thermodynamics. In a big world, failures of the CMC abound. Let's say the correlation between the psychic cousin's predictions and the top card of the deck is explained by the person performing the test being a stooge, who is giving some non-verbal indication to the purported psychic about the top card. So here we have a causal explanation of the correlation, as the CMC would lead us to expect. But since we are in a big world, there are a massive number of Boltzmann brains out there, outside our light cone, whose brain states correlate with the top card in the same way that the cousin's does. But there is no causal explanation for this correlation, it's just the kind of thing one would expect to happen, even non-causally, in a sufficiently large world. So the CMC isn't a universal truth.
Now, the CMC is a remarkably accurate rule if we restrict it to our local environment. But it's pretty plausible that this is just because our local environment is monotonically entropy-increasing towards the future and entropy-decreasing towards the past. Because of this feature of our environment, local interventions produce correlations that propagate out spatially towards the future, but not towards the past. When you drop a rock into a pond, waves originate at the point the rock hit the water and travel outwards towards the future, eventually producing spatially distant correlations (like fish at either end of the pond being disturbed from their slumber).
Imagine that there is a patch somewhere in the trackless immensity of spacetime that looks exactly like our local environment, but time-reversed. Here we would have a pond with a rock initially lying at its bottom. Spontaneously, the edges of the pond fluctuate so as to produce a coherent inward-directed wave, which closes in on the rock, transferring to it sufficient energy to make it shoot out of the pond. If you don't allow backward causation, then it seems that the initial correlated fluctuation that produced the coherent wave has no causal explanation, a violation of the CMC.
The second law is often read as a claim about the condition of the early universe (or some patch of the universe), specifically that there were no correlations between different degrees of freedom (such as the positions and velocities of particles) except for those imposed by the macroscopic state. There were no sneaky microscopic correlations that could later produce macroscopic consequences (see this paper). Entropy increase follows from that, the story goes, and, plausibly, the success of the CMC follows from that as well. There is a strong case to be made that the second law is prior to the CMC in the order of explanation.
The CMC is not strictly violated in physics as far as we know. If you specify the state of the universe for the entire past light cone of some event, then you uniquely specify the event. The example that you gave of the rock shooting out of the pond indeed does not violate the laws of physics- you simply shoved the causality under the rug by claiming that the edge of the pond fluctuated "spontaneously". This is not true. The edge of the pond fluctuating was completely specified by the past light cone of that event. This is the sense in which the CMC runs deeper than the 2nd law of thermodynamics- because the 2nd "law" is probabilistic, you can find counterexamples to it in an infinite universe. If you actually found a counterexample to the CMC, it would make physics essentially impossible.
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.