> But if they are not linked by a stable causal connection, wouldn't they eventually diverge, if we observe long enough?
I'm not sure why you would think so. All that's required is that the process they are following to generate observables is deterministic or law-like random .
Consider a possible universe where everything is deterministic, and at t=0 N=infinity objects created each with some very large number of measurable properties. Some never change, so property p=1,1,1,1,1,1,1, etc. forever. Some change periodicially, p=1,0,1,0,1... etc.
Now I dont really see why there wouldn't be an infinite number of correlated such properties of objects with no casual relationship whatsoever.
Maybe you want to claim that the actual universe is chaotic over long time horizons, with finite objects, finite properties, etc. and as t->inf the probability of finding properties which "repeat together" goes to zero. ... like, Maybe, but that's a radical claim.
I'd say its much more likely that, eg., some electron orbiting some atom somewhere vs. some molecule spinning, etc. will always be correlated. Just because there's so many ways of measuring stuff, and so much stuff, that some measures will by chance always correlate. Maybe, maybe not.
The point is that the world does not conspire to correlate our measures when causation is taking place. We can observe any sort of correlation (including 0) over any sort of time horzion and still there be no causation.
In practice, this is very common. It's quite common to find some measurable aspects of some systems, over horizons we measure them, to "come together in a pattern" and yet have nothing to do with each other. I regard this as the default, rather than vice versa. At least every scientist should regard it as the default.. and yet, much pseudoscience is based on a null hypothesis of no pattern at all.
I'm not sure why you would think so. All that's required is that the process they are following to generate observables is deterministic or law-like random .
Consider a possible universe where everything is deterministic, and at t=0 N=infinity objects created each with some very large number of measurable properties. Some never change, so property p=1,1,1,1,1,1,1, etc. forever. Some change periodicially, p=1,0,1,0,1... etc.
Now I dont really see why there wouldn't be an infinite number of correlated such properties of objects with no casual relationship whatsoever.
Maybe you want to claim that the actual universe is chaotic over long time horizons, with finite objects, finite properties, etc. and as t->inf the probability of finding properties which "repeat together" goes to zero. ... like, Maybe, but that's a radical claim.
I'd say its much more likely that, eg., some electron orbiting some atom somewhere vs. some molecule spinning, etc. will always be correlated. Just because there's so many ways of measuring stuff, and so much stuff, that some measures will by chance always correlate. Maybe, maybe not.
The point is that the world does not conspire to correlate our measures when causation is taking place. We can observe any sort of correlation (including 0) over any sort of time horzion and still there be no causation.
In practice, this is very common. It's quite common to find some measurable aspects of some systems, over horizons we measure them, to "come together in a pattern" and yet have nothing to do with each other. I regard this as the default, rather than vice versa. At least every scientist should regard it as the default.. and yet, much pseudoscience is based on a null hypothesis of no pattern at all.