On Wed, Jan 15, 2014 at 7:08 PM, LizR <[email protected]> wrote: > On 16 January 2014 03:51, Jesse Mazer <[email protected]> wrote: > >> >> On Wed, Jan 15, 2014 at 5:10 AM, LizR <[email protected]> wrote: >> >>> On 15 January 2014 22:55, Bruno Marchal <[email protected]> wrote: >>> >>>> >>>> On 14 Jan 2014, at 22:04, LizR wrote: >>>> >>>> Sorry, I realise that last sentence could be misconstrued by someone >>>> who's being very nitpicky and looking for irrelevant loopholes to argue >>>> about, so let's try again. >>>> >>>> Now how about discussing what I've actually claimed, that the time >>>> symmetry of fundamental physics could account for the results obtained in >>>> EPR experiments? >>>> >>>> >>>> Logically, yes. >>>> >>>> But you need "hyper-determinism", that is you need to select very >>>> special boundary conditions, which makes Cramer's transaction theory close >>>> to Bohm's theory. >>>> >>> >>> I'm not sure what you mean by special boundary conditions. The bcs in an >>> Aspect type experiment are the device which creates the photons, and the >>> settings of the measuring apparatuses. These are special but only in that >>> the photons are entangled ... note that this isn't Cramer's or Bohm's >>> theory (the transaction theory requires far more complexity that this). >>> >> >> >> Time symmetry in the laws of physics alone, without any special >> restriction on boundary conditions, can't get you violation of Bell >> inequalities. Ordinary time symmetry doesn't mean you have to take into >> account both future and past to determine what happens in a given region of >> spacetime after all, it just means you can deduce it equally well going in >> *either* direction. So in a deterministic time-symmetric theory (Price's >> speculations about hidden variables are at least compatible with >> determinism) it's still true that what happens in any region of spacetime >> can be determined entirely by events in its past light cone, say the ones >> occurring at some arbitrarily-chosen "initial" tim. This means that in a >> Price-like theory where measurement results are explained in terms of >> hidden variables the particles carry with them from emitter to >> experimenters, it must be true that the original "assignment" of the hidden >> variables to each particle at the emitter is determined by the past light >> cone of the event of each particle leaving the emitter. Meanwhile, the >> event of an experimenter choosing which measurement to perform will have >> its own past light cone, and there are plenty of events in the past light >> cone of the choice that do *not* lie in the past light cone of the >> particles leaving the emitter. >> >> So, without any restriction on boundary conditions, one can choose an >> ensemble of possible initial conditions with the following properties: >> >> 1. The initial states of all points in space that line in the past light >> cone of the particles leaving the emitter are identical for each member of >> the ensemble, so in every possible history generated from these initial >> conditions, the particles have the same hidden variables associated with >> them. >> >> 2. The initial states of points in space that lie in the past light cone >> of the experimenters choosing what spin direction to measure vary in >> different members of the ensemble, in such a way that all combinations of >> measurement choices are represented in different histories chosen from this >> ensemble. >> >> If both these conditions apply, Bell's proofs that various inequalities >> shouldn't be violated works just fine--for example, there's no combination >> of hidden variables you can choose for the particle pair that ensure that >> in all the histories where the experimenters measure along the *same* axis >> they get opposite results (spin-up for one experimenter, spin-down for the >> other) with probability 1, but in all the histories where they measure >> along two *different* axes they have less than a 1/3 chance of getting >> opposite results. Only by having the hidden variables "assigned" during >> emission be statistically correlated to the choices the experimenters later >> make about measurements can Price's argument work, and the argument above >> shows that time-symmetry without special boundary conditions won't suffice >> for this. >> >> If you're right then Price is wrong. However I don't recall him saying > that the only consequence of time symmetry is that events can be, so to > speak, worked backwards equally well. In particular, I read his EPR > explanation as showing that both future and past boundary conditions were > relevant in explaining the violations of B's Inequality. The > "forwards-and-backwards" version would prevent time symmetry having any > detectable effects, as far as I can see. (Also I'd like to see an > explanation of EPR which works backwards from the measurement settings to > the emitter and explains the violation of B's Inequality. That would > definitely be a clincher!) >
I don't think my argument necessarily conflicts with Price, since I don't remember him clearly saying that the Bell inequality violations could be resolved without time-symmetric boundary conditions alongside time-symmetric physics equations (though it's been a while since I read his book). But I think I should also qualify my statement, because there are different types of conceivable "time-symmetric" theories, and my statement was only dealing with the type of *dynamical* time-symmetric theories that would cover most existing time-symmetric or CPT-symmetric theories, from quantum field theory to Newtonian gravity to the "ADM formalism" of general relativity. In these theories you can divide spacetime into an ordered series of spacelike surfaces--"moments in time"--and if you are given the complete physical conditions on an "initial" moment, that is always in principle sufficient to predict the physical conditions in later moments (or earlier ones, given time-symmetry). In that case, my argument above should apply. However, it's possible to conceive of a type of time-symmetric theory that wouldn't be "dynamical" in this sense of using initial conditions to dynamically generate conditions at other times. For example, the equations of physics might look more like a set of constraint equations that tell you a relation that must hold between physical variables at any given point in spacetime and physical variables at points in the past *and* the future of that point. Then instead of generating histories that conform to these laws in a dynamical way starting with arbitrary initial conditions and evolving forwards/backwards, you would instead imagine a more timeless sort of selection process in which you consider the set of all possible sequences of events in spacetime, then check each one to see if every single point in that spacetime satisfies the constraint relations with points in its past and future, and throw out all those that don't while keeping those that do as histories that are "allowed" by the laws. In its most abstract form, I think general relativity works like this, with the laws just giving constraints between curvature and matter field at each point and the curvature and matter field at infinitesimally nearby points. However, in any spacetime that's "globally hyperbolic" it's possible to "foliate" the 4D spacetime into a stack of 3D spacelike surfaces and re-express the equations in a dynamical form like I described above (this is what the "ADM formalism" is all about). The "realistic" spacetimes that physicists deal with in cosmology work like this. But some possible spacetimes are not globally hyperbolic and can't be foliated in this way, in particular those spacetimes that contain "closed timelike curves" and thus allow an observer to travel back in time to visit his own past (I'm not sure if there are any non-globally-hyperbolic spacetimes that *don't* contain closed timelike curves). And in this case you can't really generate allowed histories dynamically, you instead have to consider entire set of mathematically possible curved spacetimes with matter fields defined on them and see if they satisfy the equations at every point, with those that don't being physically impossible and those that do being physically possible (and the fact that a spacetime satisfies the equations at every point implies that all backwards time travel in such a spacetime will satisfy the Novikov self-consistency principle, outlined at https://en.wikipedia.org/wiki/Novikov_self-consistency_principle ) So, if you had this particular type of time-symmetric theory, one which expressed the laws of physics in terms of constraints on relations between physical facts about one point in spacetime and facts about points in its past and future, and which could *not* be re-expressed as a dynamical theory of the type I described, then you might be able to account for Bell inequality violations without the need to make any additional assumptions about boundary conditions (though the requirement that the entire spacetime satisfies these constraint equations everywhere might still end up constraining the possible boundary conditions as a *consequence*). Perhaps Price's ideas about a hidden-variables theory involving backwards causality as well as forwards are along these lines. Still, the fact remains that if your local realistic time-symmetric theory of physics *is* a dynamical one where later conditions can be derived from initial conditions, then the argument I made in the previous comment you quoted should still apply, and in that case time-symmetry without very specially-chosen initial boundary conditions will be of no help in explaining how Bell's inequality can be violated. So it's not correct to just say that Bell assumed time was asymmetric, and thus that the type of time-symmetry we see in *existing* theories of physics like quantum field theory is enough to discount his proof. In terms of a Venn diagram, there would be an overlap between the circle "time-symmetric (or CPT-symmetric) local realistic theories" and "theories that satisfy the assumptions of Bell's proof", and all existing time-symmetric theories (except for general relativity in non-globally-hyperbolic spacetimes) would fall into that overlap region. Price may be correct that the general *idea* of time-symmetry points to a possible loophole in Bell's proof, but taking advantage of this loophole would require a new and different type of time-symmetric theory from the ones physicists have used in the past to model real-world situations. Jesse -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/everything-list. 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