> On 3 Aug 2018, at 13:43, Bruce Kellett <[email protected]> wrote: > > From: Bruno Marchal <[email protected] <mailto:[email protected]>> >> On 2 Aug 2018, at 12:54, Bruce Kellett <[email protected] >> <mailto:[email protected]>> wrote: >>> >>> From: Bruno Marchal <[email protected] <mailto:[email protected]>> >>>>> On 1 Aug 2018, at 21:12, Brent Meeker <[email protected] >>>>> <mailto:[email protected]>> wrote: >>>>> >>>>> >>>>> Indeed. But the common-cause explanation doesn't work for all choices of >>>>> measurement angle. >>>> >>>> It does. Well, it does not if you assume only one Bob and Alice, but the >>>> whole point is that it does if you take into account all Alices and Bobs >>>> in the multiverse. QM explains why in all branches, Alice and Bob will see >>>> the violation of Bell’s inequality, and this without any physical >>>> instantaneous causality on a distance. The MW theory is NOT an hidden >>>> variable theory in the sense of EPR or Bohm. The MW theory is based on the >>>> first person indeterminacy, and illustrate the first person plural aspect >>>> (contagion of duplication). Hidden variable theory in the sense of de >>>> Broglie, Böhm, or Einstein incompleteness are pure 3p theories, not >>>> involving the role of the person in the picture. >>> >>> In that case you have a different theory, which is not quantum mechanics. >>> You can believe anything you like about your own private theories, but you >>> cannot expect others to join in. If we are talking about quantum mechanics, >>> then it would be polite to stick to that theory. >> >> I am talking about Quantum Mechanics without collapse. You are the one >> seeming to interpret ud + du as a superposition of worlds with Alice having >> a particle in state u (and Bob having the corresponding particle in state d) >> with worlds with Alice having a particle in state d (and Bob having the >> corresponding particle in state u). That would contradict the rotational >> symmetry of the singlet state. > > The rotationally symmetric singlet is ud - du. The state you mention, ud+ du, > is the spin zero component of the triplet, which is not rotationally > symmetric.
I meant ud-du, which is the same state as u’d’-d’u’ up to some phase e^i*theta. > > You ask how I interpret the singlet in MWI. That is quite simple -- it is the > same as in a collapse theory. ? > In MWI you just retain all the branches, branches that are discarded in the > single world theory. In both cases, the ud - du state is rotationally > symmetric when prepared, but that rotational symmetry is destroyed as soon as > the spin component of one particle is measured in a particular direction. In the MWI it is never destroyed. It is just entangled with the memory of the observer (or the local environment containing the observer. Alice (ud -du) = Alice ud - Alice du = Alice see up ud - Alice see down ud Bob(ud -du) = Bob ud - Bob du = Bob see down ud - Bob see up ud Alice and Bob get their opposite spin, without transmission of action faster than light, still less instantaneous. If they measure in arbitrary direction, or the one to verify Bell’s inequality violation, the reasoning is more long, but see Price (below) for a good approximation. If in some branches there has been a FTL action, you might need to explain to me how that is possible, and why to postulate this. It does not follow from EPR which assumes definite results for a measurement, where we get only definite result in the memory of the observer(s). > The external magnet is not rotationally symmetric, so as soon as it interacts > with the singlet, the overall rotational symmetry is lost. That is surely > obvious. The overall rotational symmetry is lost for the individual particles, but not for the state Alice + two particles (even if far apart). I mean the state (Alice see up ud - Alice see down ud) is still rotationally in variant. > That is why I don't understand why you go on about infinities of Alice's and > Bob's who can measure in any direction continuing after the first measurement > interaction. It only needs to the entanglement of the observers with the particles. No rotational symmetry is lost, except for the first person pop of the observer, but that is only because of their ignorance or abstraction from the real quantum state. You persist talking like if some collapse did occur after the measurement, but that never happens. So when we get (Alice see up ud - Alice see down ud), that is still equal to (Alice see up u’d' - Alice see down u’d’), as no collapse have occurred. We keep an infinity of worlds where Alice found always up, but with different spin direction. If the choice of direction was decided or not change nothing to this: because (Alice see up ud - Alice see down ud) = e^i.theta (Alice see up u’d' - Alice see down u’d’), and the phase factor would not change the measurement that anyone could do in principle on the overall state (which would be technically difficult to here, but that is not relevant for our attempt to agree (or not) on the interpretation of the MW theory. > The symmetry is lost, so there can only ever be four worlds: the uu, ud, du, > dd, worlds that I have been mentioning all along. These are the worlds that > survive from one measured singlet pair in MWI. Each branch of this can be > considered a single world, and since the branches are disjoint, the relevant > statistics must be separately satisfied in each such branch. That survive in the mind of Alice and Bob, when they have decided the direction in advance, I can agree with this, but no worlds has ever disappeared, and indeed, Alice could have measure u’/d’ instead of u/d, and that plays a role to explain the violation of Bell’s inequality in the local MW way, like the one by Price (which we have discussed, and eventually you did agree that there is no FTL, just inseparability). > > It is not actually very difficult to understand once you have broken the > initial symmetry. A series of trials on such singlets will just lead to a > branching tree of 2^N copies of matched Alices and Bobs. It is the fact that > they always interact with the components of the same singlet state in each > trial that keeps the worlds in order. But the measurements that each make are > made non-locally. Well indeed, and that leads to Price “psi-3”. The measurement are local, but the splitting of the “universe” propagate locally in all circumstances. > And the relative probabilities of their separate results (probabilities of > the 'worlds' or 'branches') depend on the non-locally set relative > orientation of their measurements. Bell's theorem is then just the > observation that the observed correlations cannot be reproduced by a local > hidden variables, such as would represent a 'common cause' that is carried > along from the point of creation of the singlet In one world. But in The MW the common cause is made in all words, and propagate locally to the correlated state in each branches. See the Q32 in Price's FAQ. We can discuss it again step by step. Bell’s theorem discard local hidden variable which would determine the state in each branch, or in the unique reality. That does not happen, as Alice and Bob have a trans-world identity: as long as they have not measured their spin, or got the spin result communicated, they exists on different world/branches simultaneously. May be this is what you are missing. > . Bell's theorem applies to each branch in the many-worlds superposition and > cannot be deflected by appeals to counterfactuals or any such irrelevance. I guess you mean that in each branch the violation of Bell’s inequality occur. I agree. But the reason why that occurs without any FTL is typically due to the trans world identity of Alice and Bob. Bruno I copy the Q32 below, and you might recall me where you think he get things wrong: ====================== Q32 Does the EPR experiment prohibit locality? What about Bell's Inequality? The EPR experiment is widely regarded as the definitive gedanken experiment for demonstrating that quantum mechanics is non-local (requires faster-than-light communication) or incomplete. We shall see that it implies neither. The EPR experiment was devised, in 1935, by Einstein, Podolsky and Rosen to demonstrate that quantum mechanics was incomplete [E]. Bell, in 1964, demonstrated that any hidden variables theory, to replicate the predictions of QM, must be non-local [B]. QM predicts strong correlations between separated systems, stronger than any local hidden variables theory can offer. Bell encoded this statistical prediction in the form of some famous inequalities that apply to any type of EPR experiment. Eberhard, in the late 1970s, extended Bell's inequalities to cover any local theory, with or without hidden variables. Thus the EPR experiment plays a central role in sorting and testing variants of QM. All the experiments attempting to test EPR/Bell's inequality to date (including Aspect's in the 1980s [As]) are in line with the predictions of standard QM - hidden variables are ruled out. Here is the paradox of the EPR experiment. It seems to imply that any physical theory must involve faster-than-light "things" https://www.hedweb.com/manworld.htm#do Page 26 of 43 The Everett Interpretation 03/08/2018, 16*13 going on to maintain these "spooky" action-at-a-distance correlations and yet still be compatible with relativity, which seems to forbid FTL. Let's examine the EPR experiment in more detail. So what did EPR propose? The original proposal was formulated in terms of correlations between the positions and momenta of two once-coupled particles. Here I shall describe it in terms of the spin (a type of angular momentum intrinsic to the particle) of two electrons. [In this treatment I shall ignore the fact that electrons always form antisymmetric combinations. This does not alter the results but does simplify the maths.] Two initially coupled electrons, with opposed spins that sum to zero, move apart from each other across a distance of perhaps many light years, before being separately detected, say, by me on Earth and you on Alpha Centauri with our respective measuring apparatuses. The EPR paradox results from noting that if we choose the same (parallel) spin axes to measure along then we will observe the two electrons' spins to be anti-parallel (i.e. when we communicate we find that the spin on our electrons are correlated and opposed). However if we choose measurement spin axes that are perpendicular to each other then there is no correlation between electron spins. Last minute alterations in a detector's alignment can create or destroy correlations across great distances. This implies, according to some theorists, that faster-than-light influences maintain correlations between separated systems in some circumstances and not others. Now let's see how many-worlds escapes from this dilemma. The initial state of the wavefunction of you, me and the electrons and the rest of the universe may be written: |psi> = |me> |electrons> |you> |rest of universe> on in on Earth deep Alpha space Centauri or more compactly, ignoring the rest of the universe, as: |psi> = |me, electrons, you> And |me> represents me on Earth with my detection apparatus. |electrons> = (|+,-> - |-,+>)/sqrt(2) represents a pair electrons, with the first electron travelling towards Earth and the second electron travelling towards Alpha Centauri. |+> represents an electron with spin in the +z direction |-> represents an electron with spin in the -z direction It is an empirically established fact, which we just have to accept, that we can relate spin states in one direction to spin states in other directions like so (where "i" is the sqrt(-1)): |left> = (|+> - |->)/sqrt(2) |right> = (|+> + |->)/sqrt(2) |up> = (|+> + |->i)/sqrt(2) |down> = (|+> - |->i)/sqrt(2) (electron with spin in -y direction) and inverting: (electron with spin in -x direction) (electron with spin in +x direction) (electron with spin in +y direction) https://www.hedweb.com/manworld.htm#do Page 27 of 43 The Everett Interpretation 03/08/2018, 16*13 |+> = (|right> + |left>)/sqrt(2) = (|up> + |down>)/sqrt(2) |-> = (|right> - |left>)/sqrt(2) = (|down> - |up>)i/sqrt(2) (In fancy jargon we say that the spin operators in different directions form non- commuting observables. I shall eschew such obfuscations.) Working through the algebra we find that for pairs of electrons: |+,-> - |-,+> = |left,right> - |right,left> = |up,down>i - |down,up> I shall assume that we are capable of either measuring spin in the x or y direction, which are both perpendicular the line of flight of the electrons. After having measured the state of the electron my state is described as one of either: |me[l]> represents me + apparatus + records having measured and recorded the x-axis spin as "left" |me[r]> ditto with the x-axis spin as "right" |me[u]> ditto with the y-axis spin as "up" |me[d]> ditto with the y-axis spin as "down" Similarly for |you> on Alpha Centauri. Notice that it is irrelevant how we have measured the electron's spin. The details of the measurement process are irrelevant. (See "What is a measurement?" if you're not convinced.) To model the process it is sufficient to assume that there is a way, which we have further assumed does not disturb the electron. (The latter assumption may be relaxed without altering the results.) To establish familiarity with the notation let's take the state of the initial wavefunction as: |psi>_1 = |me,left,up,you> /\ first electron in left state heading towards me on Earth /\ second electron in up state heading towards you on Alpha Centauri After the electrons arrive at their detectors, I measure the spin along the x-axis and you along the y-axis. The wavefunction evolves into |psi>_2: local |psi>_1 ============> |psi>_2 = |me[l],left,up,you[u]> observation which represents me having recorded my electron on Earth with spin left and you having recorded your electron on Alpha Centauri with spin up. The index in []s indicates the value of the record. This may be held in the observer's memory, notebooks or elsewhere in the local environment (not necessarily in a readable form). If we communicate our readings to each other the wavefunctions evolves into |psi>_3: https://www.hedweb.com/manworld.htm#do Page 28 of 43 The Everett Interpretation 03/08/2018, 16*13 remote |psi>_2 ============> |psi>_3 = |me[l,u],left,up,you[u,l]> communication where the second index in []s represents the remote reading communicated to the other observer and being recorded locally. Notice that the results both agree with each other, in the sense that my record of your result agrees with your record of your result. And vice versa. Our records are consistent. That's the notation established. Now let's see what happens in the more general case where, again,: |electrons> = (|+,-> - |-,+>)/sqrt(2). First we'll consider the case where you and I have previously arranged to measure the our respective electron spins along the same x-axis. Initially the wavefunction of the system of electrons and two experimenters is: |psi>_1 = |me,electrons,you> = |me>(|left,right> - |right,left>)|you> /sqrt(2) = |me,left,right,you> /sqrt(2) - |me,right,left,you> /sqrt(2) Neither you or I are yet unambiguously split. Suppose I perform my measurement first (in some time frame). We get |psi>_2 = (|me[l],left,right> - |me[r],right,left>)|you> /sqrt(2) = |me[l],left,right,you> /sqrt(2) - |me[r],right,left,you> /sqrt(2) My measurement has split me, although you, having made no measurement, remain unsplit. In the full expansion the terms that correspond to you are identical. After the we each have performed our measurements we get: |psi>_3 = |me[l],left,right,you[r]> /sqrt(2) - |me[r],right,left,you[l]> /sqrt(2) The observers (you and me) have been split (on Earth and Alpha Centauri) into relative states (or local worlds) which correlate with the state of the electron. If we now communicate over interstellar modem (this will take a few years since you and I are separated by light years, but no matter). We get: https://www.hedweb.com/manworld.htm#do Page 29 of 43 The Everett Interpretation 03/08/2018, 16*13 |psi>_4 = |me[l,r],left,right,you[r,l]> /sqrt(2) - |me[r,l],right,left,you[l,r]> /sqrt(2) The world corresponding to the 2nd term in the above expansion, for example, contains me having seen my electron with spin right and knowing that you have seen your electron with spin left. So we jointly agree, in both worlds, that spin has been conserved. Now suppose that we had prearranged to measure the spins along different axes. Suppose I measure the x-direction spin and you the y-direction spin. Things get a bit more complex. To analyse what happens we need to decompose the two electrons along their respective spin axes. |psi>_1 = |me,electrons,you> = |me>(|+,-> - |-,+>)|you>/sqrt(2) = |me> ( (|right>+|left>)i(|down>-|up>) - (|right>-|left>)(|down>+|up>) ) |you> /2*sqrt(2) = |me> ( |right>(|down>-|up>)i + |left> (|down>-|up>)i - |right>(|down>+|up>) + |left> (|down>+|up>) ) |you> /2*sqrt(2) = |me> ( |right,down> (i-1) - |right,up> (1+i) + |left,up> (1-i) + |left,down> (1+i) ) |you> /2*sqrt(2) =( + |me,right,down,you> (i-1) - |me,right,up,you> (i+1) + |me,left,up,you> (1-i) + |me,left,down,you> (1+i) ) /2*sqrt(2) So after you and I make our local observations we get: |psi>_2 = ( + |me[r],right,down,you[d]> (i-1) - |me[r],right,up,you[u]> (i+1) + |me[l],left,up,you[u]> (1-i) + |me[l],left,down,you[d]> (1+i) ) /2*sqrt(2) Each term realises a possible outcome of the joint measurements. The interesting thing is that whilst we can decompose it into four terms there are only two states for each observer. Looking at myself, for instance, we can rewrite this in terms of states relative to *my* records/memories. |psi>_2 = https://www.hedweb.com/manworld.htm#do Page 30 of 43 The Everett Interpretation 03/08/2018, 16*13 ( |me[r],right> ( |down,you[d]> (i-1) - |up,you[u]> (i+1) ) + |me[l],left> ( |up,you[u]> (1-i) + |down,you[d]> (1+i) ) ) /2*sqrt(2) And we see that there are only two copies of me. Equally we can rewrite the expression in terms of states relative to your records/memory. |psi>_2 = ( ( |me[l],left> (1-i) - |me[r],right> (i+1) ) |up,you[u]> + ( |me[r],right> (i-1) + |me[l],left> (1+i) ) |down,you[d]> ) /2*sqrt(2) And see that there are only two copies of you. We have each been split into two copies, each perceiving a different outcome for our electron's spin, but we have not been split by the measurement of the remote electron's spin. After you and I communicate our readings to each other, more than four years later, we get: |psi>_3 = ( + |me[r,d],right,down,you[d,r]> (i-1) - |me[r,u],right,up,you[u,r]> (i+1) + |me[l,u],left,up,you[u,l]> (1-i) + |me[l,d],left,down,you[d,l]> (1+i) ) /2*sqrt(2) The decomposition into four worlds is forced and unambiguous after communication with the remote system. Until the two observers communicated their results to each other they were each unsplit by each others' measurements, although their own local measurements had split themselves. The splitting is a local process that is causally transmitted from system to system at light or sub- light speeds. (This is a point that Everett stressed about Einstein's remark about the observations of a mouse, in the Copenhagen interpretation, collapsing the wavefunction of the universe. Everett observed that it is the mouse that's split by its observation of the rest of the universe. The rest of the universe is unaffected and unsplit.) When all communication is complete the worlds have finally decomposed or decohered from each other. Each world contains a consistent set of observers, records and electrons, in perfect agreement with the predictions of standard QM. Further observations of the electrons will agree with the earlier ones and so each observer, in each world, can henceforth regard the electron's wavefunction as having collapsed to match the historically recorded, locally observed values. This justifies our operational adoption of the collapse of the wavefunction upon measurement, without having to strain our credibility by believing that it actually happens. To recap. Many-worlds is local and deterministic. Local measurements split local systems (including observers) in a subjectively random fashion; distant systems are only split when the causally transmitted effects of the local interactions reach https://www.hedweb.com/manworld.htm#do Page 31 of 43 The Everett Interpretation 03/08/2018, 16*13 them. We have not assumed any non-local FTL effects, yet we have reproduced the standard predictions of QM. So where did Bell and Eberhard go wrong? They thought that all theories that reproduced the standard predictions must be non-local. It has been pointed out by both Albert [A] and Cramer [C] (who both support different interpretations of QM) that Bell and Eberhard had implicity assumed that every possible measurement - even if not performed - would have yielded a single definite result. This assumption is called contra-factual definiteness or CFD [S]. What Bell and Eberhard really proved was that every quantum theory must either violate locality or CFD. Many-worlds with its multiplicity of results in different worlds violates CFD, of course, and thus can be local. Thus many-worlds is the only local quantum theory in accord with the standard predictions of QM and, so far, with experiment. [A] David Z Albert, Bohm's Alternative to Quantum Mechanics Scientific American (May 1994) [As] Alain Aspect, J Dalibard, G Roger Experimental test of Bell's inequalities using time-varying analyzers Physical Review Letters Vol 49 #25 1804 (1982). [C] John G Cramer The transactional interpretation of quantum mechanics Reviews of Modern Physics Vol 58 #3 647-687 (1986) [B] John S Bell: On the Einstein Podolsky Rosen paradox Physics 1 #3 195-200 (1964). [E] Albert Einstein, Boris Podolsky, Nathan Rosen: Can quantum-mechanical description of physical reality be considered complete? Physical Review Vol 41 777-780 (15 May 1935). [S] Henry P Stapp S-matrix interpretation of quantum-theory Physical Review D Vol 3 #6 1303 (1971) ====================== > > Bruce > > -- > 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] > <mailto:[email protected]>. > To post to this group, send email to [email protected] > <mailto:[email protected]>. > Visit this group at https://groups.google.com/group/everything-list > <https://groups.google.com/group/everything-list>. > For more options, visit https://groups.google.com/d/optout > <https://groups.google.com/d/optout>. -- 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.
