tag:blogger.com,1999:blog-8666091.post8817178435127595978..comments2018-11-02T13:26:51.162+01:00Comments on The Reference Frame: Delayed choice quantum eraserLuboš Motlhttp://www.blogger.com/profile/17487263983247488359noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-8666091.post-45523504897504051682011-11-28T18:37:39.706+01:002011-11-28T18:37:39.706+01:00"What puzzles me is that exactly at the momen..."What puzzles me is that exactly at the moment that one electron's sock, triggered by our measurement, becomes green, the other electron's sock becomes instantly red. The wave function or the state vector is not a physical object, so we don't violate relativity. But the probabilistic distribution is something measurable."<br /><br />It's not true that the electron "became" spinning-up or the sock "became" green when we looked. When we looked, we just learned the answer to a question. The question couldn't have any well-defined answer before the measurement, but this also means that you can't say that the sock "wasn't" green before the measurement or the electron "wasn't" spinning up before the measurement. It had some probabilities for any possibility: the measurement, whether it's in classical statistical physics or quantum physics, just showed the answer.<br /><br />Also, the wave function isn't measurable in a single measurement. That's why we say (in physics) that a wave function isn't an observable. This statement is true both "technically" as well as "colloquially". Its predicted distributions may only be "measured" by repeating the same experimental situation many times. But when you do so, you can't talk about "events that happened" during a particular copy of an experiment.<br /><br />According to quantum mechanics, every observable quantity in the world must be encoded in a linear Hermitian operator on the Hilbert space. The wave function isn't one, so it can't be and it isn't an observable.<br /><br />"It abruptly changes at a specific moment in time (unlike Bertelmann's sock) triggered by a measurement event far away."<br /><br />Just a few sentences before this one, you agreed that there wasn't any instantaneous effect and that you would avoid this class of invalid statements. So why did you make this invalid statement, anyway? There isn't any physical change of the other sock or electron occurring when you meausure its first cousin. <br /><br />This fact is true both in the classical sock case as well as the quantum electro case. The only difference is that in classical physics, you may imagine/assume that there exists some "objective answer" to the question about the colors even if you don't look at it. In the quantum case, it's not the case: this very assumption would lead to errors in your predictions. Quantum mechanics implies that there isn't any "certain state" of any objects or degrees of freedom prior to the measurement. Only the probabilities of various observations make a physical sense. But that doesn't mean that something is changing at a distance to "achieve" the correlation. Nothing physical is changing whatsoever. The nonzero probabilities existed for spins "up-down" and "down-up", or "red-green" and "green-red" socks. These options have always been there and they had some probabilities. The observation just means that one of the options was confirmed and became a known fact to the observer. But the observer's learning something doesn't mean that something changed about the socks or the electrons themselves.Luboš Motlhttps://www.blogger.com/profile/17487263983247488359noreply@blogger.comtag:blogger.com,1999:blog-8666091.post-7283865811249045892011-11-28T17:38:09.299+01:002011-11-28T17:38:09.299+01:00Thank you for clarifying the point about the natur...Thank you for clarifying the point about the nature of the singlet. Despite any apparent counter-intuitiveness, I perfectly well understand its quantum-mechanical origin. It's a Hilbert space state vector that would deliver the same probability distribution when expanded on any chosen axis.<br /><br />I will also adopt your wording concerning what happens to probabilistic predictions after a measurement, just to ease your worry that faster-than-light actions are my concern. I am not worried about causality, violations of special relativity or the like.<br /><br />I understand what a correlation is and the difference between a correlation and a cause/effect-dependency.<br /><br />However: the difference, as you yourself point out, between Bertelmann's socks and the electron's spin is that the sock is green or red all the time before and after the "measurement", while the electron's spin is perfectly random and assumes its value at the moment of measurement. Metaphorically speaking, the electrons's sock is yellow, until randomly, exactly at the moment of measurement, it becomes green or red.<br /><br />This is not puzzling me. What puzzles me is that exactly at the moment that one electron's sock, triggered by our measurement, becomes green, the other electron's sock becomes instantly red. The wave function or the state vector is not a physical object, so we don't violate relativity. But the probabilistic distribution is something measurable. It abruptly changes at a specific moment in time (unlike Bertelmann's sock) triggered by a measurement event far away. How does nature achieve this? I am aware of he fact that it doesn't violate any fundamental principles by doing so, and I do not want to disprove or challenge quantum mechanics, since it's predictions are undisputably in accordance with experiment, but how the hell does nature go about to abruptly change the probability distribution of a quantum system everywhere in the universe instantly, when a measurement occurs somewhere in it? How does the second sock become red exactly at the moment we measure the first sock to be green, not a moment earlier and not am moment later? What mechanism does nature employ to achieve this?<br /><br />This question certainly doesn't affect the predictive or explanatory power of quantum mechanics and is furthermore irrelevant for the practioner. But it does puzzle me. <br /><br />Regards, Dimitrisbmkhttps://www.blogger.com/profile/10175899495086792778noreply@blogger.comtag:blogger.com,1999:blog-8666091.post-4962832422170093932011-11-24T10:26:15.133+01:002011-11-24T10:26:15.133+01:00Dear bmk,
let me first correct you in one of your...Dear bmk,<br /><br />let me first correct you in one of your misconception implicitly written in your comment. When two electrons' spins are in the singlet state, they're in the singlet state relatively to *any* axis. This is a trivial consequence of the singlet's being SO(3) invariant as a quantum state. <br /><br />Such a correlation of a bit "with respect to any direction" may be counterintuitive if we think in terms of classical physics, but this is the first insight of EPR about the entanglement.<br /><br />"The wavefunction of the system collapses accordingly as a result of this measurement."<br /><br />The wave functions never "collapse" as they're not "material objects" or "observables". You wanted to say that "After the first measurement, we switch from the overall probabilistic predictions for the second electron to the conditional ones."<br /><br />"swallow... that ... directly affects the measurable probability distribution"<br /><br />No, nothing is directly affecting anything else faster than light. The two electrons are just entangled - they're correlated with each other. They're correlated because these two electrons were in contact in the past when they were produces at a single place of space. There's nothing mysterious about finding a perfect correlation between two particles that were created in a perfectly correlated state, namely the singlet state.<br /><br />The right analogy is Bertelmann's socks: he always takes different colors of 2 socks in the morning so if you see one of them as red, you may be sure that the other won't be read. The only difference in QM is that it allows far richer correlations in many quantities, something that can't be represented by classical correlations assuming that the electrons have some well-defined properties at each point. But once you accept they don't have such properties before the measurement, the correlation of their final properties is fully analogous to correlations in classical physics and may be predicted probabilistically in QM just like in statistical classical physics.<br /><br />"wavefunction manages to instantly collapse everywhere"<br /><br />Again, the wave function never collapses. The wave function isn't an actual observable wave. It's a (template for) a probability distribution.<br /><br />Cheers<br />LMLuboš Motlhttps://www.blogger.com/profile/17487263983247488359noreply@blogger.comtag:blogger.com,1999:blog-8666091.post-42812121727600414702011-11-23T20:12:02.762+01:002011-11-23T20:12:02.762+01:00Hello Lubos,
consider Lab A and Lab B at a distan...Hello Lubos,<br /><br />consider Lab A and Lab B at a distance of 10 lightminutes from each other. Consider furthermore an entangled pair of electrons in the singlet state of their z-axis spin. Assume measurement 1 measures the z-axis spin of electron 1 in Lab A and finds it to be +1/2. The wavefunction of the system collapses accordingly as a result of this measurement. Measurement 2 of the z-axis spin of electron 2 occurs 5 seconds later in Lab B and of course respects the collapsed wavefunction to measure -1/2. All this naturally doesn't violate any physical principles, but isn't it hard to "swallow" how an action 5 seconds ago and 10 lightminutes away (measurement 1) directly affects the measurable probability distribution here and now at lab B?<br /><br />Regards, Dimitris<br /><br />PS. I by no way mean to defend any hidden-variables theory or the like - I am perfectly quantum-mechanically minded - but I find it intriguing how the wavefunction manages to instantly collapse everywhere in the universe. (And entanglement is obviously not a precondition for instant collapse, it just makes this effect experimentally measurable ...)bmkhttps://www.blogger.com/profile/10175899495086792778noreply@blogger.com