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inflector
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I've been exploring an idea for reconciling the possibility of local realism with the various experimental proofs of violations of Bell's Inequalities. Since it seems like an idea that must have been explored and considered elsewhere, I am looking for relevant papers which have considered the idea before. I haven't found any yet, but I feel like there must be some as it seems like a rather obvious idea so there must be some error in the logic of it or I would have seen it before.
Consider a 2D slice of an object that exists in 3-space, an elastic tube where the 2D slice shows only two closed curves, C1 and C2 which are not connected in any way, the change in size and shape in a continuous fashion over time, i.e. For the sake of the example, consider that the tube vibrates according to wave equations that are well known. An observer in 3-space could determine the relationship between the shapes of a particular slice according to this set of equations.
If you only had access to the 2D slice, you would not easily see any connection between the two closed curves C1 and C2, yet one exists. There is in fact a causal connection to changes in the curves. If you changed one of the curves, say C1, by applying a force to the edge of one of them there would be a corresponding vibratory change in C2 at some later point. The delay in the change would appear to be random if you only had access to the time-evolving curves in 2-space since there would be no way of knowing how far apart the two curves were in 3-space. Some might even say that the curves were "entangled" in some way.
If the 2D slice were itself curved, it would be possible to have C1 and C2 located much closer in 3-space than they would be in the 2D slice. You can see how this would work if you took a 3-ring hole-punched paper and curved it back so that two holes are penetrated by a single pencil, they holes might be 10mm distant in 3-space (i.e. nearly adjacent on the pencil) but 300mm apart in the curved 2D slice represented by the piece of paper. In this instance, a change in one of the curves might cause an affect in the other curve that appeared to be super-luminal since the distance traveled by the cause in 3-space was much shorter than the distance traveled in the 2D slice. It might even be fast enough to seem to be "spooky action at a distance".
I am trying to find threads here or papers on the subject of an analogous 3D slicing of a structure that existed in 4-space where the causal connections exist in 4-space but might not be visible or apparent in the 3D slice, and the idea that entanglement might involve causal connections that appear to be superluminal in the 3D-slice, i.e. nonlocal in 3-space but that are in fact, local and sub-luminal in 4-space.
Any pointers to relevant papers would be greatly appreciated.
Consider a 2D slice of an object that exists in 3-space, an elastic tube where the 2D slice shows only two closed curves, C1 and C2 which are not connected in any way, the change in size and shape in a continuous fashion over time, i.e. For the sake of the example, consider that the tube vibrates according to wave equations that are well known. An observer in 3-space could determine the relationship between the shapes of a particular slice according to this set of equations.
If you only had access to the 2D slice, you would not easily see any connection between the two closed curves C1 and C2, yet one exists. There is in fact a causal connection to changes in the curves. If you changed one of the curves, say C1, by applying a force to the edge of one of them there would be a corresponding vibratory change in C2 at some later point. The delay in the change would appear to be random if you only had access to the time-evolving curves in 2-space since there would be no way of knowing how far apart the two curves were in 3-space. Some might even say that the curves were "entangled" in some way.
If the 2D slice were itself curved, it would be possible to have C1 and C2 located much closer in 3-space than they would be in the 2D slice. You can see how this would work if you took a 3-ring hole-punched paper and curved it back so that two holes are penetrated by a single pencil, they holes might be 10mm distant in 3-space (i.e. nearly adjacent on the pencil) but 300mm apart in the curved 2D slice represented by the piece of paper. In this instance, a change in one of the curves might cause an affect in the other curve that appeared to be super-luminal since the distance traveled by the cause in 3-space was much shorter than the distance traveled in the 2D slice. It might even be fast enough to seem to be "spooky action at a distance".
I am trying to find threads here or papers on the subject of an analogous 3D slicing of a structure that existed in 4-space where the causal connections exist in 4-space but might not be visible or apparent in the 3D slice, and the idea that entanglement might involve causal connections that appear to be superluminal in the 3D-slice, i.e. nonlocal in 3-space but that are in fact, local and sub-luminal in 4-space.
Any pointers to relevant papers would be greatly appreciated.