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Entangled electrons' spins aren't oscillating between up-down and down-up

Two days ago, I largely missed a comment by Kashyap Vasavada (although I did read and respond to its followups):

KV: A more exact parallel will be: As soon as someone sees Bertlmann's socks, Bertlmann rushes to the change room and randomly changes or does not change socks. But he leaves the remaining people in doubt whether he has changed socks or not!!
Holy cow. The very purpose of the blog post two days ago was to explain why this parallel is completely wrong, not "more exact" i.e. why the spins and sock colors are demonstrably not blinking in the way imagined by Kashyap and other Bellists. Nothing is "blinking" in the case of the socks, nothing is "blinking" in the case of the spins, and there's absolutely no difference between the two situations when it comes to the absence of blinking. This was really the main point – and, in some sense, the only point – of the blog post I wrote two days ago.

It's just unbelievable what sort of elementary kindergarten explanations are apparently insufficient to make certain people understand some extremely simple points, even after many repetitions and reformulations etc. Kashyap must suffer from some severe brain defect.

It's like when you try to teach addition to a kid who thinks that "2+2=22". After a very long discussion in which you exploit all known and many original ways to shed light on addition and why "2+2=4" in particular, this kid will tell you – with quite some arrogance in its voice and with two exclamation marks at the end of the sentence – that the "more exact value is 2+2=22".

Could you remain calm? I can't. Can't the obnoxiously stupid kid just see that his "improvement" isn't a cosmetic change but something that totally changes the essence of the answer – from right to wrong? Couldn't the obnoxious spoiled brat at least avoid pretending that he is improving things by replacing "2+2=4" with "2+2=22"? You have just spent hours by explaining the kid why two plus two isn't equal to twenty-two and you feel robbed when you see that it was a complete waste of time.

I feel robbed whenever I see that I have completely wasted my time when I tried to explain things like basics of quantum mechanics to people like Kashyap. But I am still apparently unable to learn that lesson. At some moment, I find a pedagogically great new way to present the logic so that even a mule must understand it. But I get proven wrong all the time, again and again. The stupidity of people like Kashyap is so divergent that no finite improvement of one's explanations can do the job.

Cut the legs of Mr Bertlmann and separate them by a light year, just to be sure. Ask two people to make measurements of the two socks at two spacetime points \(P_1,P_2\) with coordinates \(x_1^\mu\) and \(x_2^\mu\), respectively. Regardless of the location and timings, and whether the moments are the same or not, you will get\[

{\rm Color}_1(x_1^\mu) \neq {\rm Color}_2(x_2^\mu)

\] The perfect anticorrelation holds not only when \(t_1=t_2\), at "equal times". It always holds. Just take 5,000 nutty left-wing professors with the different-sock habits, amputate all their legs, and make the measurements of the colors at any moments, with any separation and any delay. You will always get the perfect anticorrelation. It's simply because the individual colors are no longer changing once the legs get separated from each other and from the hands – because Mr Bertlmann's hands in the vicinity of the feet were needed to change the socks.

So Kashyap's assumption that it's enough to guarantee \({\rm Color}_1={\rm Color}_2\) for \(t_1=t_2\) is just wrong. This weaker condition would allow the "simultaneous blinking" of the socks from "red green" to "green red" or vice versa. But the weaker condition is clearly not the whole story. The blinking may easily be ruled out by verifying that the colors are perfectly anticorrelated regardless of the two times when the measurements take place.

It's ultimately special relativity that bans this blinking. If "red green" were changed to "green red" at \(t=0\), there would have to be an instantaneous signal that changes the colors at the "same moment" i.e. simultaneously. But such instantaneous – and all superluminal – signals are prohibited by relativity. A proof – an explanation of the problem – involves a different inertial frame. While \(t_1=t_2\) in the unprimed inertial system, we have \(t'_1\neq t'_2\) in most other systems due to the relativity of simultaneity.

So in other inertial systems, the flip of the left sock's color would occur before or after the flip of the right sock's color, \(t'_1\neq t'_2\). So for some interval of time, we would have either "red red" or "green green". The perfect anticorrelation would be violated from the viewpoint of this primed inertial system. This observer could measure the colors simultaneously – in his frame – and he would get two identical colors, in contradiction with the Bertlmann's predictions and with experiments.

The individual sock colors are simply not blinking or oscillating. They are conserved. They are unknown before they are measured. But "unknown" is something else than "oscillating". A known function of time may be oscillating (non-constant); and an unknown function of time may be constant (not oscillating).

When it comes to the existence or absence of blinking, the case of the two electrons' spins is absolutely identical and this very point – aggressively disputed by Kashyap, including excessive exclamation marks – was indeed the main point of my previous blog post (and many others). The two individual electrons' spins are conserved; they can't remotely communicate; their simultaneous flip at one moment of time would be ill-defined because "one moment of time" depends on the inertial system while the laws of physics don't depend on the inertial system.

Once a particle decays to two spin-1/2 fermions, the fermions' spins are associated with operators \(\vec J_1(t)\) and \(\vec J_2(t)\). When the particles are freely moving through the space, their spins are conserved. So the Heisenberg equations of motion may simply be integrated to\[

\vec J_1(t_1) = \vec J_1(t_1+\epsilon)

\] and similarly for \(\vec J_2\). This simply implies that the individual spin polarizations such as \(J_{1z}\) and \(J_{2z}\) aren't changing or blinking at any moment. It doesn't matter when you measure either of them. You may verify this claim experimentally. The experimental verification is absolutely identical to the verification in the case of the socks – and it has the same results. That's why our certainty that there's no blinking is exactly as strong in the case of the two spins as it is in the case of the two socks.

The only way to make \(J_{1z}(t_1)\) different from \(J_{1z}(t_1+\epsilon)\) is to make the spin interact – touch – some other object in between, e.g. at the moment \(t_1+\epsilon/2\). For example, we may measure \(J_{1x}(t_1+\epsilon/2)\). By this measurement, we bring the spin to an eigenstate of \(J_{1x}\). And because \(J_{1x}\) doesn't commute with \(J_{1z}\), we change the predictions for future measurements of \(J_{1z}\) (to 50%-50% for up-down).

From the viewpoint of the observer who makes this measurement of \(J_{1x}(t_1+\epsilon/2)\), the state of the spin changes because measurements change the spin. From the viewpoint of a third party, this measurement is some process involving other physical systems. The Hamiltonian \(H(t)\) is more complicated and contains the "interaction Hamiltonian" between the spin and the measurement apparatus. And because of this interaction Hamiltonian, it is no longer true that \[

[H(t'), J_{1z}(t')]=0.

\] for times \(t'\) between \(t_1\) and \(t_1+\epsilon\). So the individual spin vector isn't conserved during the measurement – either because measurements induce a collapse (the viewpoint of the immediate observer); or because measurements require the interactions with other objects (the viewpoint of another external observer).

But as long as there is no measurement of the individual spins, \(\vec J_1(t)\) and \(\vec J_2(t)\) remain independent of time \(t\). The specification of the time \(t\) is irrelevant – as long as we understand that we mean some moment after the entangled pair is created. We can therefore omit the characters \((t)\) if we know that each individual spin will only be measured once.

When we measure \(J_{1z}\) and \(J_{2z}\), we will get perfectly anticorrelated results. But as proven by direct experiments or by relativity, there couldn't have been any blinking values of the two spins, jumping between the discrete choices "up down" and "down up". Instead, when we measure these two \(z\)-components of the spin and get some results, we should interpret the results as some truth that already existed before the measurements – from the very moment when the entangled pair was created.

The entangled pair was created and the values of \(J_{1z}\) and \(J_{2z}\) were immediately known to be anticorrelated but their individual values weren't known. Once we measure these values, we may say that these values, while unknown, were true for the whole time. For example, we may assume that the state \(\ket{\uparrow\downarrow}\) was there already before the measurement, since the birth of the entangled pair.

This assumption about the state would lead to wrong predictions for the coordinated measurements of \(J_{1x}\) and \(J_{2x}\): all four arrangements would have the probability of 25%. So indeed, we are not allowed to think that the system was in the eigenstate of \(J_{1z}\) and \(J_{2z}\) if still have the freedom to measure something else that doesn't commute with these \(z\)-components, e.g. \(J_{1x}\) and \(J_{2x}\). But once we know what we measured (or once we are decided and guaranteed what we will measure), it is OK to assume that the physical system is in an unknown eigenstate of the measured observables, even before the observation.

If we change our mind in the last moment and measure \(J_{1x}\) and \(J_{2x}\) instead, we may then reinterpret the past differently and say that the particle pair was in this eigenstate of these two operators, e.g. \(\ket{\leftarrow\rightarrow}\), even before the observation. This is clearly a different reconstruction of the pre-measurement past than any reconstruction we can get in the world in which we measure \(J_{1z}\) and \(J_{2z}\). But this inequivalence of the reconstructions isn't a contradiction of any sort.

It's simply an example of Bohr's principle of complementarity. The physical system – two particles with spins, in this case – may be probed in many different ways and a universal description of the "state of the system" and a "classical reconstruction" that would be ready for all kinds of measurements that can be made doesn't exist. And it doesn't need to exist because it isn't possible to live in a Universe where both \(J_{1x}\) and \(J_{1z}\) are the first measured quantity. And when one measures one of them, the predictions for the second measurement get changed.

Murray Gell-Mann and others like to explain this "freedom to reconstruct the past differently, depending on what we measured" as the "decoupling of different branches of the history". It's "cute" when these would-be Everettian ideas are presented as some insights showing limitations of Niels Bohr's understanding of quantum mechanics. Why? Because when formulated carefully and correctly, these ideas attributed to Hugh Everett are actually nothing else than what the founders of quantum mechanics have always called the Bohr's principle of complementarity.

The very fact that this term – Bohr's complementarity – has largely disappeared from textbooks and courses shows the influence of the anti-quantum religious sect. At the end, this principle is necessary for a correct understanding of quantum mechanics, anyway. Bohr has simply realized that physical systems may be probed in various ways and there's no way to reconcile the description of the physical system resulting from these different ways into one "master description". It's not necessary because these different ways can't exist simultaneously in one history of the Universe. This is what Bohr's principle of complementarity means. So in the best case, people have to reinvent it and reword it, in terms of "Everettian branches" and similar constructions. Everything that makes sense about these constructions was invented by Niels Bohr and pals; everything that is new is unphysical gibberish.

I think that I have made a more general observation about the psychology of these deluded people. One self-fooling trick that makes people like Kashyap stick to their absolute misunderstandings of quantum mechanics – and many other issues – is that they believe or want to believe that once their ideas are proven wrong, they may just change the names of several concepts in these ideas and this resuscitates the ideas.

So you see it all the time. It already looks like they have understood what they were doing absolutely incorrectly. But they change some word to a synonym and think that "now they have the right new theory and explanation how it works". It's exactly the same wrong rubbish they were saying previously, just with slightly changed words, but they believe that the slight modification of the terminology is enough to resuscitate wrong ideas and make them correct.

The wrong nonlocal "explanation" of the correlation between the two spins' polarizations has always clearly involved some "forced change of the other spin" once the first spin is measured. Kashyap uses the words "rushes... and randomly changes" and he believes that now it's great and this is his "more exact parallel". But it's still exactly the same wrong claim about the nonlocal influence behind the correlations. Can't he see it? Can't he see that it is still exactly the same mistake for which I have considered him an idiot before?

And these "subtle rewordings" that obviously don't change anything about the essence seem to be omnipresent.

Another widespread example in these discussions is the totally bogus "discrimination" of the words "signalling" and "influence". For example, Lawrence Crowell wrote:
I have not understood Lubos Motl's claims against nonlocality. He seems to equate nonlocality with signalling or some superluminal influence. Of course we know that no information or qubits travel on spacelike intervals...
I seem to equate nonlocality with nonlocal signalling and superluminal influence because I do equate nonlocality with nonlocal signalling and superluminal influence. And I do equate them because they're the very same thing.

How could they be different? Special relativity obviously prohibits superluminal influences and signals and everything else of this sort. If a signal is sent from the spacetime point P to the point Q, then something at the point P has influenced something at the point Q. Information influences things. So a signal is obviously a special kind of an influence.

On the other hand, if we have an influence that is not used to send signals, we may always use it to send signals. For example, we may find a black box that is influenced by another black box through some electromagnetic influences. We may realize that this could be useful. Once we start to use these black boxes, someone may tell us that we found two Wi-Fi routers on the sidewalk. Every damn influence may be exploited to send signals. It's just about our subjective practical evaluation of the phenomena – but the essence is the same.

Special relativity obviously prohibits this superluminal action whether we call it "signals", "influence", or anything else.

People like Crowell tell us that "they obviously know that no information travels superluminally but...". They say such things because they sort of realize that whoever fails to understand that signals can't be sent superluminally is a hopeless crank. But they add a "but" and if you read the sentence following this "but", it really says: "But the superluminal influences are possible and omnipresent, anyway."

Well, they're not. They're as strictly forbidden as superluminal signals because they're exactly the same thing. Whenever some information is sent somewhere, it is sent through influences. So Crowell and Kashyap are like the obnoxiously arrogant yet stupid kid who tries to impress others so it says something like "Everyone knows that 2+2 isn't twenty-two but the evil tutor doesn't seem to distinguish 22 and twenty-two and he completely fails to see that 2+2=22." Well, no, crackpots, 2+2 is neither 22 nor twenty-two. And both superluminal influences and superluminal signals are prohibited by relativity and this ban is exactly as strong in quantum mechanics as it was in classical physics.

People participating in these discussions often like to suggest that they believe that they're discussing the deepest things in the Universe and they're very smart. But when I look at most of these discussions, they look like attempts to tutor totally retarded kids. Kids who are arrogant spoiled brats at the same moment.

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