DrChinese said:
1. None of my comments in this post should be taken as disagreement with you. Every time I examine what MWI says about the details, I get squirmy answers (in sources supporting MWI) to the obvious tough questions. So let's examine your 2. and 3. in a very specific MWI example.
I didn't take it as disagreement with my opinions. As I said, I don't understand, what the MWI solves wrt. the observable facts, which for me imply that there's "objective randomness" in Nature, i.e., that we cannot find any causes for the outcome of a measurement of an observable which was not determined by the state preparation before this measurement. For me, from a purely empirical point of view, it also doesn't help that MWI claims that the universe splits into branches, because this also doesn't explain in any way, why the outcome on a specific system was the one that is observed in "my branch".
DrChinese said:
We have a straight Type I PDC setup outputting a pair of entangled photons in the |HH> + |VV> Bell basis. The inputs are single photons oriented diagonal at 45 degrees (which could also be considered an equal superposition of |H> + |V>). Each entangled output pair is sent to linear polarization detector setups far distant from each other, and are measured at the same angle - but at an angle randomly selected mid-flight and outside the light cone of the photons at time of selection. Here are the questions I have:
The input photons are prepared in the pure state
$$\hat{\rho}_{12}=|\Psi \rangle \langle \Psi| \quad \text{with} \quad \frac{1}{\sqrt{2}} (|HH \rangle +|VV \rangle).$$
The single photons' state is then given by the so-called "reduced state", which is the partial trace over the other photon. You get
$$\hat{\rho}_1 = \hat{\rho}_2=\frac{1}{2} \hat{1}.$$
They are not in a pure state but in the maximally uncertain (maximum entropy) state, i.e., perfectly unpolarized photons.
DrChinese said:
i. The output pairs must not yet have a specific definite polarization, correct? Because we need them to match at whatever angle they are to be detected at, and that has not been selected yet. So they must still be in a superposition (due to their "preparation" as you call it).
Indeed they their polarization is maximally uncertain.
DrChinese said:
ii. The selected angle by some RNG is 120 degrees. Alice measures first (say), and gets result V. When exactly does that branching occur? We know in some other MWI branch the outcome was definitely H, right? The polarization detection setup itself consists of 3 components: the polarizing beam splitter (PBS) and the 2 avalanche detectors (one H, and one V). The branching occurs at one or more of these spots: a) the PBS; b) the V detector; and/or c) the H detector (which didn't fire in our branch). And in fact, the relative time of fire of the V and H detectors can be adjusted (by distance of placement after the PBS) so that they are clearly separated. Where/when does the branching occur? a)? Of course, this is a point at which the action is still reversible. b)? Of course, there has certainly been branching by this point in our particular branch, because we measured the V outcome. c)? The H detector did not fire in our branch, but we are certain it did in the other branch. But that outcome presumably came later in that branch, right?
You select to set both polarization filters to be oriented at an angle ##\phi## wrt. the direction you label with H. The states when measuring the linear polarization wrt. to that direction I label with ##|\phi_{\parallel} \rangle## and ##|\phi_{\perp} \rangle##. In terms of the original basis it's
$$|\phi_{\parallel} \rangle=\cos \phi |H \rangle + \sin \phi |V \rangle, \quad |\phi_{\perp} \rangle=-\sin \phi |H \rangle + \cos \phi |V \rangle.$$
The possible outcomes are ##\phi_{\parallel} \phi_{\parallel}##, ##\phi_{\parallel} \phi_{\perp}##, ##\phi_{\perp} \phi{\parallel}##, and ##\phi_{\perp} \phi_{\perp}##. The probabilities are given by
$$\langle \phi_{\parallel} \phi_{\parallel}|\Psi \rangle=\frac{1}{\sqrt{2}} (\cos^2 \phi+\sin^2 \phi)=\frac{1}{\sqrt{2}} \Rightarrow P(\phi_{\parallel},\phi_{\parallel})=1/2,$$
$$\langle \phi_{\parallel} \phi_{\perp}|\Psi \rangle=\langle \phi_{\perp} \phi_{\parallel}|\Psi \rangle =\frac{1}{\sqrt{2}} (-\cos \phi \sin \phi + \cos \phi \sin \phi)=0 \Rightarrow P(\phi_{\parallel},\phi_{\perp})= P(\phi_{\perp},\phi_{\parallel})=0,$$
$$\langle \phi_{\perp} \phi_{\perp}|\Psi \rangle=\frac{1}{\sqrt{2}} (\sin^2 \phi + \cos^2 \phi)=\frac{1}{\sqrt{2}} \; \Rightarrow \; P(\phi_{\perp},\phi_{\perp})=\frac{1}{2},$$
i.e., you get with probability 1/2 either both photons being ##\phi_{\parallel}##-polarized or both photons being ##\phi_{\perp}## polarized, i.e., you have 100% correlation between the outcome of measurements although the single photons' polarization states where maximally uncertain before the measurement.
DrChinese said:
iii. Here's the hard part: how does the branching from ii. above affect the photon Bob is getting ready to detect? That photon is far away. How does the branching action over by Alice affect Bob? Because we presumably determined Bob's photon was still in superposition as a result of i. above, right? Some of us here suspect that something "nonlocal" might be occurring. Even Vaidman seems to acknowledge something along this line. To quote, and note that there were no answers to any of my questions in his
paper (and certainly no answers in his "next" section):
"
But there are connections between different parts of the Universe, the wave function of the Universe is entangled. Entanglement is the essence of the nonlocality of the Universe. “Worlds” correspond to sets of well localized objects all over in space, so, in this sense, worlds are nonlocal entities. Quantum measurements performed on entangled particles lead to splitting of worlds with different local descriptions. Frequently such measurements lead to quantum paradoxes which will be discussed in the next section."
I'd say the branching occurs as soon as the outcome of the first measurement occuring. I.e., in your assumption when A's detector fixes the polarization state of her photon. Then, because of the preparation in the original entangled state, according to our above analysis, the other photon's polarization, i.e., what Bob will measure later, is also determined to be the same, because you have ##\phi_{\parallel} \phi_{\parallel}## or ##\phi_{\perp} \phi_{\perp}##, and thus the split is in these two possible branches.
DrChinese said:
But in his parlance, whatever "nonlocal" occurs cannot quality as "action at a distance". I don't have a particular objection to this characterization, but I would not call it "spot on" either.
According to relativistic QFT there's no action at a distance. What's non-local is the correlation due to the preparation in the entangled state, i.e., a correlation between the outcomes of measurements at far distant polarization-measurement places, not the interaction between the measurement devices and the single photons. They are local at the place where the equipment is built up to measure the polarization.
The above analysis in fact is based on the assumption that A's measurement doesn't influence in any way B's photon, before B measures its polarization.
DrChinese said:
iv. And finally, this little gem of a question which is often overlooked with Type I PDC. We may say MWI is deterministic, but this leads to something of a paradox. Type I PDC consists of 2 thin orthogonal crystals placed face to face. One has an input of H and produces |VV>, while the other takes an input of V and produces output of |HH>. Neither of those are entangled outputs! So how does the entanglement occur? The answer is that the diagonal input to the pair of crystals takes an indistinguishable path, and the particular spot where down conversion occurs is indeterminate. So for the MWI explanation to make sense, we need to assert that NO branching occurs as the input photon splits into 2 entangled photons. What? So branching occurs everywhere else BUT the very spot where/when there's a choice of paths through the PDC setup. Huh?
As you say, the entanglement occurs, because you can't say whether you get ##|VV \rangle## or ##HH \rangle## when choosing precisely those photon pairs, where this "which-way information" is not known, i.e., that they come out precisely in the said state ##\hat{\rho}_{12}##.
Concerning the PDC process you have of course a lot of splittings, according to all possible outcomes of sending a coherent laser-light state into the crystal. The two-photon down-conversion probabilities are usually in the order of magnitude of ##10^{-6}## only!
DrChinese said:
We must have the entangled pair exit in a superposition for the rest of the MWI magic to occur. And yet, we need there to be branching by the time Alice and Bob read and record their respective results. But aren't we capable of establishing a consistent rule as to when branching occurs that doesn't appear ad hoc? Because I say that according to the MWI concept of definite deterministic outcomes: the diagonal input photon split at either the H PDC crystal (in our branch) or the V PDC crystal (in the other branch, or vice versa) - and would NOT have led to an entangled state if either of those things occurred. They would instead exit as VV or HH, and there would not be perfect correlations when later measured at 120 degrees (as selected by the RNG).
But I thought according to MWI the splitting always occurs according to the possible outcomes of measurements given the state, i.e., the branchings can only be into 100% correlated ##120_{\parallel} 120_{\parallel}## or ##120_{\perp} 120_{\perp}## branches.
DrChinese said:
Making sense of this kind of setup causes me all kinds of confusion, and yet this is precisely the kind of experiment that a viable interpretation should explain today. I am *not* trying to support or reject MWI by any of my comments, I am just trying to understand the rules MWI plays by. Every interpretation seems to have some consistency issues at some level, and I believe MWI does too.
I think, all that can be observed are what's really measured, and the outcome is random, i.e., there's no cause for a specific outcome. What "additional explanation" MWI gives, to solve this quibble of the measurement problem, i.e., to find a cause for the specific outcome, I never understood since in which branch of the world my equipment will be and determining to what I as the experimenter read off as a measurement result is simply random with probabilities given by Born's rule.
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