The blind ghost

[Rivendale]

I can try to give a version of my "entanglement for dummies" lecture. It's an illustration of one specific case of an entangled state, known as the Greenberger-Horne-Zeilinger ("GHZ") state. The state itself is a bit more complicated than the more commonly cited Bell states, but it shows the weirdness of quantum entanglement much more clearly. I

Quite complex apparatus is needed to magnify those tiny things by amplifying tiny signals. When you realize that, the wonder isn't that measuring submicroscopic things is so weird, but that it is possible at all. A reasonable expectation would be that training a massive amplification device onto a single electron would produce all kinds of weird unstable signals, among which the effects of the target electron were just a drop in the ocean. The astonishing miracle of quantum mechanics is that it introduces a kind of digitalisation which makes possible the massive amplification of extremely faint signals, so that gigantic creatures like us actually can see the effects of single electrons.



There are a number of ways in which the simple rules of quantum mechanics are different from the simple rules that human intuition expects. There can be probabilities and minimum values and stuff. Entanglement is one of the more complicated kinds of divergence between quantum mechanics and human intuition, and it can be an especially dramatic divergence, as it is in the GHZ case. The entanglement is the feature that we have a superposition of conditions of multiple objects, which does not factorise into a simple product of states of the individual objects.

Entanglement is to superposition what correlation is to probability. This time, finally, that's not just an analogy, but an exact definition.

Thank you for this. I haven't had a course on quantum mechanics and I have never read any examples of how qm defy probability models like you explained. Let me try and summarize to see if I am following. Entanglement using qm models provide a robust predictable model more readily than logical/statistical analysis. I think it is the most accurate human model ever created when one views how well it predicts outcomes. Using qm involves simple arithmetic operations that involve multiplying combinations of "measurements" of binary states, in this case with three entities instead of two. If I remember right the actual experiments are done with polarizers. Humans as of this point evolved to survive on the savannah and apparently do not have the mental construct to understand what is happening on this ultra microscopic level. Partly because of the mental construct and partly because the act of making a measurement creates paradoxes. These weird effects get "washed" out when we apply them to things like people and rocks. Things like hidden variables have been ruled out with Bell's theorem. Apologists, (to connect this with a religious world view) like to use qm or the woo of qm to justify a belief in metaphysical realm. Supported by the fact we have not found a mechanism that explains these spooky action at a distance phenomenon. Our sheer human reason is essentially flawed (at least for the micro world) from the outset thereby justifying belief in unfalsifiable perspectives.

[Physics Guy]

Entanglement using qm models provide a robust predictable model more readily than logical/statistical analysis. I think it is the most accurate human model ever created when one views how well it predicts outcomes. Using qm involves simple arithmetic operations that involve multiplying combinations of "measurements" of binary states, in this case with three entities instead of two. If I remember right the actual experiments are done with polarizers.

It's not really that quantum mechanics provides predictions more readily. It provides certain quite specific predictions; when experiments can be controlled well enough, as in fact they often can be, the quantum mechanical predictions are usually unique and unambiguous with no wiggle room, and yet they are found to agree precisely with experimental results.

Moreover, no specific alternative models exist besides quantum mechanics. The alternative notion of "hidden variables" is just the vague, general concept that maybe some kind of definite properties exist, and follow the usual rules of logic, and it's just that we can't see these properties directly. The remarkable feature of entangled quantum states is that actually no possible set of hidden properties that obey logic could ever reproduce their behavior. This is what Bell's Theorem shows, in a case of two entangled systems, and it's what the GHZ state of three entangled systems shows dramatically. It's quite surprising that one can demonstrate such a conflict between the specific predictions of quantum mechanics and the very general predictions of "some kind of hidden variables". One might think that "some kind of hidden variables" would be compatible with anything. It actually isn't, though. Experiments have been done which are really very difficult to explain with any kind of hidden variable model, but which perfectly fit the predictions of quantum mechanics.

Quantum mechanics is not always about binary properties. That's just a simple case. It's good for conceptual illustration, but it's also experimentally convenient, because binary quantum properties really do exist and are relatively easy to access. Polarisation states of photons are one example, which can be measured and controlled with polaroid filters. Spin states of electrons and atoms are also examples of two-state quantum systems; they can be measured and controlled with magnetic fields.

Quantum mechanics is always mathematically simple in one sense: it's all linear algebra. It can all be expressed in terms of vectors and matrices. The tough part is that in general the vectors are in abstract spaces with large numbers of dimensions. Even a single atom requires an abstract space with a literally infinite number of dimensions. One can only get down to just two by carefully isolating a single feature of a tiny system. This is looking under the lamppost with a vengeance.

Humans as of this point evolved to survive on the savannah and apparently do not have the mental construct to understand what is happening on this ultra microscopic level. Partly because of the mental construct and partly because the act of making a measurement creates paradoxes. These weird effects get "washed" out when we apply them to things like people and rocks. Things like hidden variables have been ruled out with Bell's theorem. Apologists, (to connect this with a religious world view) like to use qm or the woo of qm to justify a belief in metaphysical realm. Supported by the fact we have not found a mechanism that explains these spooky action at a distance phenomenon. Our sheer human reason is essentially flawed (at least for the micro world) from the outset thereby justifying belief in unfalsifiable perspectives.

Whether humans can understand this stuff might depend on what we mean by "understand". I don't think anybody finds it intuitive, but if you study it for a few years you can get to know how the rules work. In that sense it's like any technical trade.

It's true that the quantum effects that we find weird don't generally manifest on large scales. We even understand quite a bit about why they don't. Presumably this is why we don't find quantum effects intuitive. Our brains have evolved to handle situations in which they never appear.

The only argument from quantum mechanics in favour of religion or woo that I can buy is just to use it as a cautionary tale, to show that reality might be weirder than you expect. Quantum mechanics is anything but permissive. It's obnoxiously narrow-minded; it's like the brash engineer whom you try to perplex with subtle philosophical questions, who never even pauses to consider your deep questions respectfully but just fires back a pragmatic answer immediately, every time. Quantum mechanics is Philistine. It has its own detailed agenda with specific answers for everything, and that agenda has nothing whatever to do, as far as I can see, with any human ideologies.