We know that we didn't go from Galilian Invariance to Lorentz Invariance by just adding lenght contraction and time dilation. We also added the speed limit of light as c. So Lorentz Spacetime is a completely new foundation than Galilian Spacetime. And Spacetime foliation as I understood it being a slice of different nows and lengths giving rise to relativity of simultaneity. However, I can't understand what Tim Maudlin was talking about in the article "Non-Local Correlations in Quantum Theory: How the Trick Might Be Done" when he tried to make compatible Bohmian mechanics non-local nature by adding a new "Spacetime Foliation". Maudlin said:(adsbygoogle = window.adsbygoogle || []).push({});

How does it differs to the normal Spacetime foliations in Lorentz Spacetime? Is Mauldin describing about adding Spacetime foliations to Newtonian absolute space and time. Or is it adding additional structure to Lorentz Spacetime? But why did he refer to it as spacetime foliations (which has generic meaning in SR as slicing of spacetime in relativity of simultaneity)? Also wouldn't this end up the same as Lorentz Spacetime? I just can't imagine how the two differs and want to know how their spacetime diagrams differ. If we begin with a non-Relativistic theory that makes essential use of absolute simultaneity, the most obvious (or perhaps crude and flat-footed) way to adapt the theory to a Relativistic space-time is to add a foliation to the space-time, a foliation that divides the space-time into a stack of space-like hyperplanes. One then employs these hyperplanes in place of absolute simultaneity in the original theory. If no attempt is made to produce a further account of the foliation, and it is accepted as intrinsic space-time structure, then such a theory will clearly fail, in the sense described above, to be Relativistic. But the way it fails is worthy of note: no positive part of the Relativistic account of space-time is being rejected: rather, in addition to the Lorentzian metric, a new structure is being added.

The following is prior to the above paragraph to give the context of what Maudlin was describing:

So for the purposes of this paper, we will adhere to two conditions for the physical theories we consider: first, each theory must have some local beables, and second, the physics must predict violations of Bell’s inequality for some possible experimental situations involving experiments performed on the localized objects at space-like separation. Bell’s result proves that this can occur only if the physics is irreducibly non-local, in the sense that the physics governing a beable at a particular space-time point cannot be exhausted by considering only the physical state in the past light-cone of that point. Even once we have conditionalized on the past light-cone, there must be further predictive improvements to be made by conditionalizing on events at space-like separation.

The central physical question, then, is which events at space-like separation must be taken into account and how they must be taken into account.

Until very recently, the only available fully articulated theories took a particular line of the “which?” question, a line that put the theories in tension with Relativity. These theories proceed in the most straightforward way to adapt non-local non-Relativistic theories to the Relativistic space-time, but in doing so, they are forced to add space-time structure, or the equivalent, to the physical picture. So if one interprets Relativity as demanding that the Lorentzian metric be all the space-time structure there is, these theories are not fully Relativistic. The theories need not reject the physical significance of the Lorentzian metric, but they do need to appeal to further space-time structure to formulate their laws. We will examine two examples of such theories first, and then turn to a recently discovered alternative theory, which is completely Relativistic. Our goal will be to assess, as far as we can, the advantages and demerits of these theories.

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# Meaning of Spacetime Foliations

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