On Mon, Jun 18, 2018 at 7:26 PM, Bruce Kellett <[email protected]> wrote:
> From: Jason Resch < <[email protected]>[email protected] > > > > On Mon, Jun 18, 2018 at 7:38 AM, Bruce Kellett < > <[email protected]>[email protected]> wrote: > >> From: Jason Resch <[email protected]> >> >> >> >> In the EPR experiment, a pair of photons is created. Each photon is in a >> super position of every possible polarization, and because it is created as >> a pair, it's dual in the superposed state always has exactly the opposite >> polarization (rotated 180 degrees). >> >> >> OK. >> >> When you perform a measurement of your left-traveling photon on Earth, >> you become entangled (correlated) with it, and all the possible states of >> that photon, when measured, leak into the room, starting with the measuring >> device, then your eyes, then your brain, then your notebook, etc. until now >> everything is in the room, and soon Earth is now in many states which >> contagiously spread from that photon. >> >> >> OK. Your result (and you) become entangled with your environment. >> >> Also, because the photon you measured was entangled (correlated) with its >> pair in the superposition, whatever result you measure for the photon's >> polarization tells you immediately what the polarization of its pair is (in >> your branch at least). So any future communication you get from me on >> Pluto will necessarily align with the result you measured. >> >> >> This is where the mistake creeps in. My measurement tells me the >> polarization of the entangled photon in the branch in which my measurement >> was made. When you come to measure your entangled photon on Pluto, how do >> you know what branch my measurement was made in? You are at a spacelike >> separation from me, and completely independent. So I ask again, how come >> you assume that your measurement will be in the same branch as mine was? >> > > Let's make it more concrete and say there are only 360 possible > polarizations, each having an equal probability. > > > That is not a very good way to look at it. The photon is not in a > superposition of all possible polarization states. You cannot write the > photon wave function as such a superposition: > > |psi> = Sum_i a_i |i> for i running over all 360 possibilities in the > case you outline. > > The most you can ever do is write the state as a superposition of the two > possible polarizations in any particular direction. Thus: > > |psi> = (|+> + |->), ignoring normalization factors. > > This can be written for |+> and |-> being the polarization eigenstates in > any chosen direction. But not all directions at once. > I see. Could you explain the point of error in the following paper? I've excerpted the relevant sections if it helps your search. From: https://arxiv.org/pdf/0902.3827.pdf *According to quantum mechanics, whichever measurement is performed first collapses the entangled twin state superposition to a single polarization state that is identical for both photons.* *[...]* *If we wish to know what the probability is of getting the same measurement for photon 1, we need only figure out what the probability is for a photon with polarization along θ2 to pass through a filter oriented along θ1. This probability is easily calculated according to simple trigonometry. Any arbitrary linear polarization can be thought of as a superposition of polarization along the θ1 direction (which will pass through the filter) and perpendicular to the θ1 direction (which will be absorbed by the filter). For a wave polarized along the θ2 direction, the amplitude component along the θ1 direction is given by cos(θ2 − θ1), and the probability for transmission, given by the wave amplitude squared, is cos2 (θ2 − θ1). That is the prediction of quantum mechanics* *[...]* *The key is to allow more than one possibility for the potential result of a measurement. Orthodox quantum mechanics embraces this notion of multiple possibilities whenever a quantum state is in a superposition. In the absence of measurement (and collapse), there is no single definite potential result. Instead, there are many potential results represented by many components of the superposition.* *[...]* * It is possible to violate Bell’s inequality using either nonlocality or counterfactual indefiniteness alone, and there are examples of each approach. To better understand the role of counterfactual indefiniteness, it is instructive to examine an interpretation of quantum mechanics that relies solely on counterfactual indefiniteness to violate the inequality. One of the most popular of these is the “many worlds” interpretation.* *[...]* *We claim that the many-worlds interpretation passes the Bell test by violating counterfactual definiteness, while still respecting locality. First of all, we argue that after eliminating the nonlocal collapse of orthodox quantum mechanics, the many-worlds interpretation can be formulated as a local theory. In particular, the correlated entangled states used in EPR-Bell experiments can be produced via purely local processes. For instance, two photons with entangled polarizations might be produced from the decay of a parent particle. In this case the entangled state is produced at one location, where the parent decays, and its immediate effects are limited to that one spacetime point. Thereafter, the photons may go their separate ways, and as they separate they carry the correlation to separate locations. It is the original correlation produced at a single location that guarantees measurements will always match in any experiment in any branch where observers compare notes. In this respect the spread of the correlation to distant locations is akin to the delivery of newspapers, where a common story is generated at a central location and disseminated all over the neighborhood. In the many-worlds context, however, different branches (which originally split at a common location) carry different editions of the newspaper.* *[...]* *Measurement induces local branching based on the local measurement result, but it does not cause branching at any distant location. As an example of this thinking, the many-worlds explanation of Bell’s experiment36 argues that when measurements are made on a pair of photons with θ1 = 30◦ for filter 1 and θ2 = −30◦ for filter 2, the result is a superposition of four terms:* *At first glance it would seem that each experimenter has branched into four versions – one branching as a result of the local measurement of his/her own photon and another branching as a result of the distant measurement of the other photon. However, this view is mistaken, for only local branching has really occurred. To illustrate the local nature of that branching, Eq. (4) can be factored into two terms according to:* *After the two experimenters communicate their results to each other, each experimenter is finally split into four distinct branches corresponding to the four two-photon states:* *but this final splitting occurs only following a chain of local communications at sublight speed. In this context we see that entanglement and branching in the many-worlds interpretation are local, point-like operations.* *[...]* *One may not like the many-worlds interpretation for several reasons (and this author might agree), but it does provide an example in which locality can survive. The many-worlds interpretation is thus realist (in the sense that superpositions can be regarded as real entities and that every possible measurement result exists in some branch), deterministic (the superpositions evolve according to a deterministic wave equation), and local (involving only point-like interactions), but counterfactually indefinite. In this case the multiple possibilities described by the superposition preclude a single definite possibility, and thus provide the means for violating counterfactual definiteness. The many-worlds interpretation is not only counterfactually indefinite, it is factually indefinite as well. Even when measurements are actually performed, many different results can exist in a multitude of different branches. A single definite result is not guaranteed.* > > > The photon pair is then in a superposition of 360 possible states. The > photon pair must be considered as a single object, because if your photon > is 240 degrees, mine is -240 (120 degrees), and so on. There are only 360 > possible values that could be obtained from measurement, not (360 * 360). > > > There are only ever two possible polarization states, although these can > be defined in any of an infinity of possible directions. But once a basis > is chosen, that defines the total superposition. > > When I measure my photon on Pluto, I am self-locating myself to a branch > (one of 360 possible branches of the wave function corresponding to each of > the 360 possible polarization of the photon on Pluto). Once I have located > myself to this branch, I may not know which measurement angle you will set > your filter at, I remain in a super position of all possible measurement > angles you might choose (let's say there are 3 possible measurement angles). > > After your measurement, you first transmit, not your result, but your > measurement angle. Once the photons from this radio signal reach me, I > have located myself to one of the 3 possibilities for the measurement > angle. At this moment, I have all the information I need to be able to > completely predict the statistics of your measurement result, based on my > measurement result and angle which I knew since the time of measurement, > and now with your measurement angle information having reached me. When > you transmit your measurement result to me, I find it in agreement with my > expectations for having located myself to a branch that had (360 * 3) > possibilities that were unknown to me at the time prior to performing the > experiment. > > > We can make it simpler than this. Even though the two measurements are > supposed to be independent -- at independent angles -- we can relax this > for the purposes of illustration and say that the two experimenters agree > to both measure at some particular angle. If you on Pluto make a > measurement at this angle, there are only two possible outcomes, the |+> or > |-> states in the notation I have used above. So you are in a superposition > of two possible worlds, one for each result. Because of conservation of > angular momentum, you know that if you got the |+> result, then the other > photon of the entangled pair would, if measured at the same angle, give > |->, and similarly if you are in the branch that got a |-> result. > > When I make my measurement at the same agreed angle, I also have two > possible results, |+> or |->. But I have no control over which result I > get. A long sequence of measurements will show that I get each result with > approximately 50% probability. In order for my result to be determined by > the result that you obtained on Pluto, somehow it must be arranged that I > get only the part of the entangled pair corresponding to your result. In > other words, I must already be in the branch corresponding to your result. > If I were not in that branch, then I would get |+> or |-> with equal > probability. Unless there is some non-local effect which sets me on the > branch corresponding the your result (be it |+> or |->), then there is > nothing to stop me getting |+> when you get |+>, or |-> when you get |->, > results that are in conflict with the conservation of angular momentum and > the definition of the entangled singlet state. > Is this comment addressed by the second-to-last paragraph I quoted (I didn't attempt to paste the equations because the symbols did not carry through) but they are in the paper. I would appreciate if you could highlight the error in the equation of that paper. (equations 4, 5, and 6 on page 15). Is your argument is that MWI works but is non-local due to the immediacy of branch selection/determination? What is wrong with the idea that the necessary information is generated at the point the pair is created, and then travels at the speed of light to each measurement location? Are you assuming that there are no "hidden multi variables" (for lack of a better term) in the MWI? My understanding, (which may be in error), is that hidden variables can work to explain Bell's inequality if one gives up contra-factual definiteness. > > You have confused your account by introducing branches for each possible > measurement angle, but this is never the case -- there are no such branches > in Everettian quantum mechanics. There are only ever two branches > corresponding to the two possible outcomes for your polarization > measurement. > I agree there are only two possible outcomes of the measurement (absorbed or transmitted) but how does this related to your statement that the polarization might be along any possible angle? Does the math prevent us from viewing this as a superposition of the every possible polarization angle? > So given two independent experimenters making independent polarization > measurements, there are only ever 4 possible branches -- the '++', '+-', > '-+', and '--' branches. If the measurements are made on the same singlet > state, the '++' and '--' branches cannot exist. You have not explained why > these are possibilities are ruled out. By assuming that they are, you have > introduced an unrecognized non-locality into your account > They are ruled out for the same reason that we get consistent measurements. When we measure the same property twice in a row we always observe the same outcome. Measuring my Pluto photon, and measuring your radio signal is an example of this measurement consistency. Asking why "++" and "--" are ruled out is, in my view, equivalent to asking why we observe either "spin down" and "spin down" or "spin up" and "spin up" when we measure the spin of the same electron twice in a row, and never measure "spin down" and "spin up" or "spin up" and "spin down" when measuring the same electron's spin twice in a row. Jason -- 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 https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
