I’m not sure that the “arrows” are more real in all cases.
Well, first, as far as bijective deterministic thing, I’m going to say that there is no prefered direction, no “true” internal causality direction, given that the rule in all candidate directions is equally simple in either direction and equally local. In that case, claiming any arrows would seem to be epiphenomenal. I mean, it looks like the only thing it could mean there is if something external to the system violated its fundamental rules, reaching in and altering the system somewhere. Then the direction in which the change would propagate would be the causality direction. But then, that just brings in a larger external system and one can ask about the total causality of that...
Perhaps from there we ought take the idea that a simple discrete unique direction of causality is simply a fundamentally wrong model?
Now, if you have some deterministic system which is not bijective, then it does seem pretty clear that the direction in which it’s deterministic would perhaps the the most objectively valid direction for “objective causality”
A refinement: Bijective and local, but if we consider a step in some direction, A → B, such that to determine the state of a neighborhood in B of size x, you need a neighborhood in A of size y, but if going in the B → A direction, to determine state of neighborhood of size x in A you need neighborhood of size z > y in B, then I think I’d say A → B is the “natural” direction of causality.
Frankly, I’m semi suspecting that perhaps the concepts of locality and causality are deeply tied to one another.
Anyways, let’s consider Barbour’s universe for a moment… What would we consider ultimate cause and effect? The basic rule for the amplitude field + boundry conditions = ultimate cause of everything going on, right?
Perhaps we mean “given that, and given some other thing, but changing some other thing, what happens?”
It looks like perhaps some notion of “relative causality” or “conditional causality” may be in order, rather than simply being tied to a single absolute causality.
Sorry some of this is vague, I’m still thinking it through.
Oh… With Barbour’s Platonia, there actually would be something that fits with some of the above: The whole thing about neighborhood size. I THINK the direction away from the origin may be the prefered direction based on that criteria, at least if one starts with a neighborhood as “wide” as it needs to be to hit the boundries.
On the other hand, what if someone started midPlatonia with a hyperspherical shell shaped neighborhood of known values? Then away from the origin of that would be the locally prefered direction… until one hit the boundries. Then stuff would start getting odd.
As I said, I’m still thinking it through, but it does look like some form of notion of relative of conditional causality is really needed.
Consider our brain states… Given that and the physics, there’s presumably a natural “forward” direction, or group of prefered directions. (There can’t be a single prefered direction in Platonia anyways… I mean, you’ve got effective branching into the decoherent worlds and all that...)
Now, given some locally prefered direction, we might ask if we held fixed the “tag”/dimensions representing us, but varied some other factors/dimensions that we’re curios about, then peek ahead in whatever the “obvious relative to us” prefered directions are for each of the states we’re testing, what would be different in each? That would tell us something about what the changing thing causally affects, relative to us.
Sorry this is a bit rambling. I’m confused on this issue too, I’m just here poking and prodding at it and hoping I get out some useful insight.
I’m not sure that the “arrows” are more real in all cases.
Well, first, as far as bijective deterministic thing, I’m going to say that there is no prefered direction, no “true” internal causality direction, given that the rule in all candidate directions is equally simple in either direction and equally local. In that case, claiming any arrows would seem to be epiphenomenal. I mean, it looks like the only thing it could mean there is if something external to the system violated its fundamental rules, reaching in and altering the system somewhere. Then the direction in which the change would propagate would be the causality direction. But then, that just brings in a larger external system and one can ask about the total causality of that...
Perhaps from there we ought take the idea that a simple discrete unique direction of causality is simply a fundamentally wrong model?
Now, if you have some deterministic system which is not bijective, then it does seem pretty clear that the direction in which it’s deterministic would perhaps the the most objectively valid direction for “objective causality”
A refinement: Bijective and local, but if we consider a step in some direction, A → B, such that to determine the state of a neighborhood in B of size x, you need a neighborhood in A of size y, but if going in the B → A direction, to determine state of neighborhood of size x in A you need neighborhood of size z > y in B, then I think I’d say A → B is the “natural” direction of causality.
Frankly, I’m semi suspecting that perhaps the concepts of locality and causality are deeply tied to one another.
Anyways, let’s consider Barbour’s universe for a moment… What would we consider ultimate cause and effect? The basic rule for the amplitude field + boundry conditions = ultimate cause of everything going on, right?
Perhaps we mean “given that, and given some other thing, but changing some other thing, what happens?”
It looks like perhaps some notion of “relative causality” or “conditional causality” may be in order, rather than simply being tied to a single absolute causality.
Sorry some of this is vague, I’m still thinking it through.
Oh… With Barbour’s Platonia, there actually would be something that fits with some of the above: The whole thing about neighborhood size. I THINK the direction away from the origin may be the prefered direction based on that criteria, at least if one starts with a neighborhood as “wide” as it needs to be to hit the boundries.
On the other hand, what if someone started midPlatonia with a hyperspherical shell shaped neighborhood of known values? Then away from the origin of that would be the locally prefered direction… until one hit the boundries. Then stuff would start getting odd.
As I said, I’m still thinking it through, but it does look like some form of notion of relative of conditional causality is really needed.
Consider our brain states… Given that and the physics, there’s presumably a natural “forward” direction, or group of prefered directions. (There can’t be a single prefered direction in Platonia anyways… I mean, you’ve got effective branching into the decoherent worlds and all that...)
Now, given some locally prefered direction, we might ask if we held fixed the “tag”/dimensions representing us, but varied some other factors/dimensions that we’re curios about, then peek ahead in whatever the “obvious relative to us” prefered directions are for each of the states we’re testing, what would be different in each? That would tell us something about what the changing thing causally affects, relative to us.
Sorry this is a bit rambling. I’m confused on this issue too, I’m just here poking and prodding at it and hoping I get out some useful insight.