Register to reply 
Foliation of Space Time Hypersurfaces 
Share this thread: 
#1
Jan1111, 06:46 AM

P: 127

Hello,
Anyone has figure or web site which illustrates how foliation of space time hypersurfaces look like or what they meant in the context of the following statement? "We have presented a means of embedding quantum nonlocality within a background classical spacetime (flat or curved), by introducing an absolute simultaneity associated with a preferred foliation by spacelike hypersurfaces (where the preferred foliation defines a preferred local state of rest)." 


#2
Jan1111, 01:45 PM

P: 2,284

Ummmm... what that paragraph says isn't the case... you know that right? "A preferred rest frame" read" 'New Aether'.
Anyway, I can't imagine how you'd graphically represent spacetimefoliation... although Demystifier or Zenith8 probably do. 


#3
Jan1111, 04:23 PM

Sci Advisor
P: 8,470




#4
Jan1111, 04:56 PM

P: 2,284

Foliation of Space Time Hypersurfaces
I can understand the necessity for spacelike 'slices', of course, it would be rather useless to have a bunch of slices that no longer correspond to the original salami. edit: for worldlines. Also, thanks very much for the link, which has other good links. I have so much to learn, and I love it. 


#5
Jan1111, 05:44 PM

P: 127

I know what spacelike, lightlike, worldlines meant. But how do you model a preferred foliation in spacetime such that you can accomodate quantum nonlocality in Bell's Theorem into spacetime? The idea is this. The original SR metric is lorentz invariant. Now what they do is to add a preferred foliation such that it can connect two spacelike points instantaneously. How do you do that? Illustrations by graphs or words, thanks. 


#6
Jan1111, 06:18 PM

Sci Advisor
P: 8,470




#7
Jan1111, 06:24 PM

P: 2,284

Bohmian, that's 'Schrodinger Trajectories" and trying to keep up with the Bell ansatz leaving QM alone... with deBB... I think. I might be totally off here, but it seems that when your theory is based on interpretation, not unique results... we're no longer talking about meaningful research. Unless the Bohmians are right... then they were unsung heroes. That would be known as, "International CrowEating Day"... may I not see it come to pass. 


#8
Jan1111, 06:38 PM

P: 127

No. That is not talking Bohmian or metaphysics. It is about explaining Bell's Theorem nonlocality in the context of Special Relativity. Bell test Experiment like Aspect's clearly show there was nonlocal correlation that occur instantaneously. How do you explain that in SR? Even though no signal is transmitted. It still violates the spirit of Special Relativity because there is a prefered privileged frame of the nonlocal correlations. So the book is about how to relate Bell's Theorem to Special Relativity. Only Valentin and Maudlin still believe in SR and speculate that the only thing to make SR be compatible with it is to add preferred foliations in SR. While the other authors simply want to go back to absolute space and time. Bell himself stated the following: "I think it’s a deep dilemma, and the resolution of it will not be trivial; it will require a substantial change in the way we look at things. But I would say that the cheapest resolution is something like going back to relativity as it was before Einstein, when people like Lorentz and Poincare ´ thought that there was an aether – a preferred frame of reference – but that our measuring instruments were distorted by motion in such a way that we could not detect motion through the aether. . . . that is certainly the cheapest solution. Behind the apparent Lorentz invariance of the phenomena, there is a deeper level which is not Lorentz invariant. . . . what is not sufficiently emphasized in textbooks, in my opinion, is that the preEinstein position of Lorentz and Poincare´, Larmor and Fitzgerald was perfectly coherent, and is not inconsistent with relativity theory. The idea that there is an aether, and these Fitzgerald contractions and Larmor dilations occur, and that as a result the instruments do not detect motion through the aether – that is a perfectly coherent point of view. . . . The reason I want to go back to the idea of an aether here is because in these EPR experiments there is the suggestion that behind the scenes something is going faster than light. Now if all Lorentz frames are equivalent, that also means that things can go backward in time. . . . [this] introduces great problems, paradoxes of causality, and so on. And so it is precisely to avoid these that I want to say there is a real causal sequence which is defined in the aether. (‘‘John Bell,’’ (1986) interview in Davies and Brown; cf. Bell 1987: 279; see also Bell 1984: 66–76)" *back to me Alfrez* Now since we don't like any Aether or Absolute Space and Time, then the only way to make Bell's Theorem compatible with SR is to add an artifical structure called preferred foliations and many physicists actually do this as you will see in many papers in arvix. I just want to imagine how one do a preferred foliation of spacetime hypersurfaces. Any illustration or pointer or drwaings would be greatly appreciated. 


#9
Jan1111, 06:53 PM

Sci Advisor
P: 8,470




#10
Jan1111, 07:19 PM

P: 127

Are you saying that only Bohmian models use the concept of adding preferred foliations in spacetime hypersurfaces? Let's say we don't add any foliations. But the fact is that nonlocal correlations really happen in Bell's experiments. You explained that Many World Intepretation can explain them. But what if MWI is not correct? Then how do you make sense SR and Bell's Theorem? Let's assume the Copenhagen is right that there are no position properties before measurement, in other words, the particle doesn't exist in position B before it is measured. This means no signal is being exchanged and realism doesn't hold. But the fact that there are correlations in the wave function means the wave function itself has instantaneous capability. This would still violate the spirit of Relativity. Also maybe you are saying the correlations is just random. No signal is being interchanged. So since causality is not violated, SR remains. But the fact is that the wave function itself can correlate itself faster than light outside of spacetime. That still violate SR, no?? About the papers at arvix, you may be right that only Bohmians use preferred foliations, but I'll search more. 


#11
Jan1111, 07:26 PM

P: 1,781

I dont know why this upsets people. There may be nothing in relativity that calls out a special frame. But if there was a special frame for a particular physical phenomenon that is outside of relativity theory that doesn't mean relativity is broken.
Personally I think it's an elegant solution to the problem. You can always find a frame in which two widely separated events are simultaneous. It seems like the perfect frame to use with correlated observations. The paradoxes go away in that frame. Is this that much different than the relativistic limo that fits into the short garage in one frame but not another? Relativity may not prefer the short car over the short garage but maybe QM requires they be the same length to have an expiation that doesn't seem paradoxical. 


#12
Jan1111, 07:32 PM

P: 2,284




#13
Jan1111, 07:39 PM

P: 127

point.23 The point is that such correlations furnish the means of establishing relations of absolute simultaneity and a fundamental frame.24 As Maudlin points out In Minkowski spacetime this theory of wave collapse no longer makes sense. The collapse can be instantaneous in at most one reference frame, leading to two possibilities: either some feature of the situation picks out a preferred reference frame, with respect to which the collapse is instantaneous, or the collapse is not instantaneous at all. (Maudlin 1994: 196; cf. pp. 137–38, 144) The problem posed by instantaneous collapse of the wave function for relativity theory can be clarified by realizing that since, according to SR, simultaneity is relative to reference frames, the collapse of the wave function for spatially separated photons will itself become relative to a reference frame. The problem is that properties like polarization and spin are not relational, but intrinsic properties of photons (Ryff 1992: 249). If the universe contained a single photon, it would have a definite polarization. Therefore the possession of such properties should not be made hyperplane dependent. After surveying various attempts to integrate Bell’s Inequalities with relativity theory, Maudlin concludes that these attempts ‘‘entail such severe dislocations of our physical view that one must seriously consider whether our grounds for adhering to Relativity are really strong enough to justify such extreme measures’’ (Maudlin 1994: 239; cf. Eberhard 1978: 392–419). ‘‘Indeed, the cost exacted by those theories which retain Lorentz invariance is so high that one might rationally prefer to reject Relativity as the ultimate account of spacetime structure’’ (Maudlin 1994: 220). 


#14
Jan1111, 07:43 PM

P: 2,284

You still believe that collapse is REAL? 


#15
Jan1111, 08:12 PM

Sci Advisor
P: 8,470




#16
Jan1111, 08:21 PM

Sci Advisor
P: 8,470

In any case, whatever you believe about what is "really happening" behind the scenes, do you dispute my basic point that in orthodox QM and relativity, regardless of which interpretation you choose, there is no experimental method that will pick out any physically preferred definition of simultaneity? 


#17
Jan1111, 08:32 PM

P: 127

Bottom line is, there are correlations. How can you explain them using local realism?? 


#18
Jan1111, 08:47 PM

Sci Advisor
P: 8,470




Register to reply 
Related Discussions  
Explanation of word foliation in quantum gravity?  Beyond the Standard Model  3  
Foliation, fibration, fiber bundle?  Differential Geometry  1  
Hypersurfaces and induced connections.  Differential Geometry  0  
A bit introduction to foliation in GR and some question.  Special & General Relativity  1 