## GHZ for die-hard local realists

Last time I have discussed the impossibility to locate the particle along the path of an interferometer. However there is an even stronger argument against local realism which was due to Greenberger, Horne, and Zeilinger and was popularized by Sidney Coleman in his famous "Quantum Mechanics on your face" talk.

The setting is as follows: from a central station, three electrons are sent every minute to three very distant laboratories, say on the Moon, Mars, and Neptune, where three experimentalists decide to measure either the spin on the x axis or the spin on the y axis recording +1 or -1 based on the deflection of the electron in a Stern-Gerlach device. Their decision to measure on x or y axis is left at their own free will. The experiment is run for many years collecting a huge amount of data. Then the lab logs are brought back on Earth and compared. The following correlation emerges:

whenever the three experimentalists measure one spin on the x axis and two on the y axis, the product of the answers is +1.

Now is this consistent with quantum mechanics predictions? The initial GHZ state is:

$$|\psi\rangle = \frac{1}{\sqrt{2}}(|+++\rangle - |---\rangle)$$

and for example measuring x-y-y in laboratories 1-2-3 yields

$$\sigma_x^{(1)}\sigma_y^{(2)}\sigma_y^{(3)}|\psi\rangle = |\psi\rangle$$

because $$\sigma_x$$ flips a + into a - and $$\sigma_y$$ does the same thing and adds an $$i$$ factor.

and the same for the other 2 combinations: y-x-y, and y-y-x.

So far so good, but what would happen when all three experimentalists decided to measure all on the x axis? What would a die-hard local realist predict it would happen?

A local realist thinks the value of the measurements exist independent of measurement ("the Moon is there even when I am not looking at it"), and the experiment simply reveals the value. Since the three laboratories are far apart, the decision of what to measure in one laboratory cannot influence what it is measured at the other two laboratories. After all, the measurements are done every minute as the electrons arrive, and it takes more than 1 minute for the speed of light to propagate between any two laboratories.

So if the spin value exists independent of measurement, we have three equations:

$$SpinX_1 SpinY_2 SpinY_3 = +1$$
$$SpinY_1 SpinX_2 SpinY_3 = +1$$
$$SpinY_1 SpinY_2 SpinX_3 = +1$$

and by multiplication we get

$$SpinX_1 SpinX_2 SpinX_3 SpinY_1 SpinY_1 SpinY_2 SpinY_2 SpinY_3 SpinY_3= +1$$

Since the spins are either +1 or -1, the square of any spin is +1 and we simplify the equation to:

$$SpinX_1 SpinX_2 SpinX_3 = +1$$

What does quantum mechanics predict?

Recall that  $$\sigma_x$$ flips a + into a -, and so

$$\sigma_x^{(1)}\sigma_x^{(2)}\sigma_x^{(3)}|\psi\rangle = - |\psi\rangle$$

and the experimental results confirm that indeed

$$SpinX_1 SpinX_2 SpinX_3 = -1$$

in agreement with quantum mechanics and in blatant violation of local realism.

1. Nice. Concerning credit, Coleman used the Mermin presentation of GHZ, i.e. GHZM. Google search for "what's wrong with these elements of reality" and pick the first PDF file. Mermin wrote it for "Reference Frame" in 1990 (Physics Today, not the actual The Reference Frame).

1. Thanks. Sorry did not reply earlier-I am traveling. The argument is short and sweet.

2. Dear Florin,

It is difficult to argue against so many wrong statements at once so let me start clarify first a fundamental misconception regarding local realism.
Let’s start with a simple experiment. Two entangled particles are sent to distant places, say to Alice and Bob. Both make a measurement of momentum. Assume Alice makes the first measurement so she can predict with certainty Bob’s result. Bob’s measurement confirms the prediction.

Obviously, after Alice performs the measurement, Bob’s particle has a well-defined momentum. Did it have a well-defined momentum before? There are two possible options:

1. It didn’t have a well-defined momentum before, something happened to it during Alice’s measurement (this implies non-locality, because there can be an arbitrarily large distance between Alice and Bob)

2. It did have a well-defined momentum before. This is realism.

You can see that locality necessarily implies realism, so the only options you have are local-realism and non-local indeterminism. If you reject realism you reject locality as well.

GHZ does not add anything new to the above conclusion. It is based on a blatant logical fallacy (it assumes what it should prove).

Local realism is more or less the same thing as classical field theories. As I have argued in the commentary section of your previous post this theories do not allow for the existence of independent subsystems (as the three free-willed experimenters should be). A charge cannot be both “free-willed” and follow the equations of electromagnetism. The motion of each charge is strictly determined by the position/momenta of all the other charges no matter how small/distant it is. So, assuming local-realism the conditions required for GHZ cannot be fulfilled. GHZ is simply irrelevant for these theories.

There is also a misunderstanding about what local-realism implies. You write in bold:

“A local realist thinks the value of the measurements exist independent of measurement ("the Moon is there even when I am not looking at it"), and the experiment simply reveals the value.”

This is not necessarily true. A local realist need not believe that an apple which appears red in a white light has the property of “redness” that is revealed by the measurement. There exist however a property of the apple (the electronic structure of the molecules on its surface) that determines its behavior when exposure to light of a certain frequency occurs. So, the issue is a little more subtle.

In conclusion local realism is alive and well, it is the only way to preserve locality given the observed quantum correlations and this status is only confirmed by the weakness of the arguments put against it, all based on such transparent logical fallacies.

Andrei

1. Andrei, nope, you're just wrong. Both options 1+2 in your comments are "realism". You haven't clearly considered the actual non-realist, quantum explanation because your brain is apparently too tiny for that option.

In quantum mechanics, no statement about the observables (about the momentum in your case - but I don't know why you didn't at least try to be on-topic and discuss the spins which are used in this GHZM scenario) before the measurement may be said to be "sharply correct". Before the measurement, only the probabilities of individual outcomes-that-will-be-possible-soon are predicted, calculable, and meaningful from a scientific viewpoint, and one may show that none of these probabilities changes at all due to any remote events or human decisions.

There's no nonlocality and there's no realism in these experiments.

2. Dear Andrei,

Sorry for the delay, I just got back home.

You state: “GHZ does not add anything new to the above conclusion. It is based on a blatant logical fallacy (it assumes what it should prove).”

This is incorrect. If you are right on this one you have a shot of becoming very famous. Let me explain the argument in a different way. Suppose the central station does not issue electrons every minute, but blue/red spheres/cubes. Also suppose that the measurement devices on the “A” setting measures color issuing +1 for red and -1 for blue, and on the “B” setting determines the shape issuing +1 for cube and -1 for spheres. Every minute the central station issues the following combinations to the 3 measuring stations:
Red Cube, Blue Sphere, Blue Sphere OR
Red Sphere, Red Sphere, Red Sphere OR
Blue Cube, Blue Cube, Red Sphere

and their permutations. The three measuring stations measures either the color or the shape and later on confirm the correlations:
color_1 * shape_2 * shape_3 = +1
shape_1 * color_2 * shape_3 = +1
shape_1 * shape_2 * color_3 = +1

What is the result for:
color_1 * color_2 * color_3 ?

Of course, knowing how the central station issues the objects, it is clear that always color_1 * color_2 * color_3 = +1

Now the challenge for you is: can you find a sequence of shapes of appropriate color to be issued by the central station such that:
color_1 * shape_2 * shape_3 = +1
shape_1 * color_2 * shape_3 = +1
shape_1 * shape_2 * color_3 = +1
color_1 * color_2 * color_3 = -1

IT CAN’T BE DONE, but this is what nature achieves. If the values of the shapes and colors exist independent of measurement (local realism) you cannot achieve what nature does. Show how you can do that, and you will prove local realism is alive and well, I will stand corrected, and you will become a very famous person.

Florin

3. Dear Lubos,

The reason I didn’t use the GHZ setup is explained in my post. It makes use of “free-will” which is a meaningless concept in the framework of a classical field theory, rendering it irrelevant for the realism-non-realism debate.

But, fine, I can use a spin-involving experiment.

Two entangled particles are sent to distant places, say to Alice and Bob. Both make a measurement of spin on the X axis. Assume Alice makes the first measurement (she gets +1/2) so she can predict with certainty Bob’s result (-1/2). Bob’s measurement confirms the prediction.

Obviously, after Alice performs the measurement, Bob’s particle has a well-defined spin along X (-1/2). Did it have a well-defined momentum before? There are two possible options:

1. It didn’t have a well-defined spin along X before, something happened to it during Alice’s measurement (this implies non-locality, because there can be an arbitrarily large distance between Alice and Bob)

2. It did have a well-defined spin along X before. This is realism.

I honestly admit that my little brain does not understand your point. The option 1 and 2 are the only logically possible ones (the particle either had a well-defined momentum or it didn’t). So are you saying that the probability 1 (the probability Bob’s particle will give the -1/2 result) does not qualify as well-defined? That would be curious indeed.

I have some issues with your use of the term “meaningless”. It might mean “irrelevant” (it’s meaningless to speak about the color of a fluid when doing a calculation in fluid mechanics, because color does not enter in the equations) or non-existing (it’s meaningless to speak about the color of an object in the dark). In the first case however one can make use of the fluid’s color when dealing with the electronic structure of the fluid’s molecules. You seem to imply that QM’s postulates directly imply the second scenario, but I disagree. I think QM is simply silent about the existence of well-defined properties before measurements and the very existence of theorems like Bell, Free-will, GHZ is a proof for this. Why need those theorems if QM unambiguously implies non-realism?

In conclusion, I do think that the correct use of the term meaningless when dealing with the pre-measurement state is “irrelevant”. We cannot determine those values anyway so the formalism does not take them into account. But they might exist and they might be scientifically useful in the context of a different theory.

So it is true that only probabilities are meaningful as far as QM is concerned but there is no evidence that this holds for science in general.

Coming back to the two options above, you are clearly against the option 2. Please correct my wording for the option 1 so that it suits your position. Did Bob’s particle remain in an undefined state even after Alice’s measurement or what?

Thank you,

Andrei

4. 1. It didn’t have a well-defined spin along X before, something happened to it during Alice’s measurement (this implies non-locality, because there can be an arbitrarily large distance between Alice and Bob)

2. It did have a well-defined spin along X before. This is realism.

3. It didn't have a well defined spin along X before, and nothing happened to it during Alice's measurement. This is the sane option. ;-)

5. Dear Paul Hayes,

"3. It didn't have a well defined spin along X before, and nothing happened to it during Alice's measurement. This is the sane option. ;-)"

If nothing happened to it during Alice's measurement and it didn't have an well defined spin along X before the measurement it follows that its status should be the same after Alice's measurement (no well defined spin) in contradiction with the experimental fact that it has a well-defined spin on X (-1/2).

The "sane" solution has been falsified.

Andrei

6. Dear Andrei,

No, that does not follow. Did you not read the article I linked to? There is no such experimental fact unless Bob measures its X-spin. As Streater says: “The EPR experiment pin-points the need for subjectivity in quantum probability; the same need in classical probability has been known and used since Bayes.”

7. Dear Paul,

This objection is ridiculous. By this definition there can never be a well-defined state of anything. You prepare a particle in an momentum eigenstate. Does it have a well-defined momentum? Nope, because you didn't measure it. You measure it, you get obviously the same result. Does it have a well-defined momentum? Nope, you need to measure it again, and so on...

But forget about experimental facts. Let's change the wording a little bit.

Do you agree that after Alice performs her measurement on X and gets +1/2 Bob's particle is in such a situation that a measurement on it on X will give -1/2 with probability 1? (we may define such a state as "probability 1 undefined state").

If during Alice's measurement nothing happened to the particle it follows that it must have been in the same situation even before the measurement, the situation defined as "probability 1 undefined state". Do you agree with that?

Andrei

8. Andrei, Paul's remarks are exactly right. You just repeated your first incorrect comment almost in verbatim, still offering just options 1 and 2 - both of them are "realism" and both of them are wrong.

It's very hard to understand how someone can have such an incredibly hard time to understand what we're even saying, let alone what it means. It's like one is trying to explain Darwin's theory of the origin of species to someone and the person says that there are two options, 1) species were created by God in one week, that's Genesis, 2) in two weeks – which is the modern, almost heretical, theory the person is willing to consider.

Well, none of them is correct. You just can't fix your theory by changing one week to two weeks. Something much more fundamental is wrong about both answers. And exactly in the same way, none of your statements about Nature in your comments are correct.

Every single one of them is wrong. The only exception is one sentence of yours, the second one below:

"This objection is ridiculous. By this definition there can never be a well-defined state of anything."

The only problem is that your only correct sentence that you have made *anywhere* in your comments was decorated by the assertion (first sentence in the quotes) that it is "ridiculous". Sorry, it may look ridiculous to those who completely misunderstand modern physics but that's exactly how quantum mechanics describes everything in Nature.

Indeed, in principle, there is *never* any well-defined objective statement about anything in Nature. The state of everything is always well-defined only relatively to the perspective of an observer who has gained some knowledge by observations. He must know what were the observations, what weren't, and what were the outcomes of the observations, and that determines the initial state vector. It may be evolved by Schrödinger's equation and at any moment, the probabilities of all outcomes of any new measurements the observer may do - he must still know and "insert as input" what observable he's actually measuring or sensitive to - may be calculated via the formulae including the Born rule.

The observations that the observer makes are analogous to the evidence in (even) classical probability theory, and the collapse of the wave function is the quantum counterpart of the one step of Bayesian inference when new evidence is collected.

9. The correct option replacing your incorrect options 1,2 is

3) non-realism: there is no well-defined value of any component of the spin (or any observable) prior to its observation, and even the question what it is isn't allowed by physics. The ignorance about "so far not measured" observables isn't just the classical ignorance that may also be observed by probabilities - that obey various rules, such as various rules involving sums of probabilities of intermediate states. Instead, the unknown state of observables before they are measured must be described by the complex probability amplitudes and it's these amplitudes, and not probabilities themselves, that are being added when logical reasoning involves unknown intermediate states.

The "axioms" you are apparently not able to get rid of are axioms of classical physics - that's how physicists call it although you're probably not willing to admit to yourself that classical physics is the maximum in physics you're capable of getting, sort of - and the quantum revolution has indeed proven that they must be abandoned and replaced by things you consider "ludicrous" but that are absolutely needed for the description of Nature at the fundamental level.

These required new principles include the inability to talk about the objective state of *anything* in the absence of an actual observation, i.e. the dependence of all knowledge and "reality" on the observations; the replacement of the probability calculus involving well-defined intermediate states by the probability amplitudes; the unavoidable collapse (projection) of the wave function into an eigenstate of the measured observable induced by any measurement; the linearity of the space of possible states and of the operators associated with all measurable (i.e. physically meaningful) quantities, and a few others.

When one switches to this new framework - which is perhaps less intuitive and more mathematically advanced and abstract and demanding than the framework of classical physics, but it is equally internally consistent - one may see that the correlations following from entangled states have nothing to do with any nonlocal interactions or influences and the influence of a remote experiment on the probabilities of result to be measured here is zero (it's tiny but in principle nonzero in non-relativistic QM theories; it's strictly zero in quantum field theory which respects relativity, but in both cases, it is not the explanation of the correlation).

That doesn't mean that the observations in 2 spacelike separated labs can't be correlated. They are correlated in general. But a correlation isn't a proof of causation. There is no causation between these two measurements. Instead, all these correlations may be explained by the mutual interactions or co-existence of the 2 measured objects in the past (when they were close to each other). This qualitative conclusion is the same as in classical physics (Bertlemann's socks) but the quantitative predictions are different than in any classical theory and they require the quantum formalism to be made (which is why the predictions may deviate from any local realist theory, as Bell's theorem or this GHZM setup shows etc.). All these predictions agree with observations and experiments.

Otherwise the "free will" is a possible phrase that may be used but doesn't have to be used in the GHZM context or other experiments testing the entanglement etc. Totally analogous "free will" exists in the Bell's theorem setup or in the double slit experiment where the experimenter has free will to decide whether he will observe the "which slit" information or wait for the interference pattern to be formed, and measure that pattern (he can't do both with the same particles).

10. Do you really misunderstand what I am trying to tell you, that your comments make it clear that you are confined in an extremely narrow straitjacket, a wrong theory falsified 90 years ago and you are completely incapable so far of even *listening* to the actual correct explanation, just like a creationist who is just incapable of understanding that the species were created by God either in 1 week or 2 weeks and a moderate change of this duration isn't enough for him to get the foundations of the modern biology? It's remarkable because I think one can find many dogs and cats who would be faster in comprehending these things.

3. Dear Florin,

The error in your reasoning is this:

A measurement on the same axis (X or Y) by all three experimenters requires that at the beginning of the experiment the charge distribution is as such that it will necessarily evolve in a state with three detectors aligned on the same axis. Let's call this type of initial state "symmetric state".

A measurement on different axis (X and Y) requires that at the beginning of the experiment the charge distribution is as such that it will necessarely evolve in a state with two detectors aligned on the same axis and a third detector aligned on a different axis. Let's call this type of initial state "non-symmetric state".

Because the production of the entangled electrons depends on the electric and magnetic fields at the sources' location and because those fields are determined by charge distribution and momenta we will have two types of electrons:

1. "symmetric state" electrons
2. "non-symmetric state" electrons

They are different and you cannot infer the spin of "symmetric state" electrons from measurements on "non-symmetric state" electrons. You mix apples with oranges, that's your error.

GHZ adds nothing new to realism - non-realism debate. The same error is involved in Bell's theorem. It is assumed that if measurements on the same axis always give opposite results it means that entangled particles have same spin components when they are measured on different axis as well, which is false in the context of classical field theories as explained above.

Andrei

1. Andrei, every single sentence of yours is wrong and most of them are absolutely idiotically wrong.

First of all, the GHZM experiment doesn't involve any *charges* or *electric* fields or *magnetic* fields. It is about the measurement of the *spins*. Spins may be nonzero even if all electric charges of all objects and electromagnetic fields in the space are zero (in the ground state). Your repetitive references to "charges" and "electromagnetic fields" indicate that you don't understand this experiment even at a classical level. You completely misunderstand basic words in physics such as the spin, charge, and others. You misunderstand the fact that the experiment is about the principles and the information coming from observations, not some technicalities about how the information is realized via "fields".

Second, it makes no sense to divide the states to "symmetric" and "asymmetric". GHZM involves the state of three spins. The state is symmetric under permutations of any pair of the three electrons. But this symmetry has nothing to do with its being entangled and with the entangled state's ability to produce the prediction (of the relative signs in the correlations of the spins) that is diametrically opposite to the prediction of any local realist theory, as Florin reviewed. So you're focusing on some issues that aren't really relevant for anything in the discussion and overlooking everything that is relevant.

Third, it's just completely wrong to say:

"A measurement on the same axis (X or Y) by all three experimenters requires that at the beginning of the experiment the charge distribution is as such that it will necessarily evolve in a state with three detectors aligned on the same axis."

Whether the experimenters measured the X- or Y-component of the spins was up to their free will. In classical physics, one could have imagined that their decisions are in principle predictable (people may be imagined to be deterministic machines in classical physics) but they were never predictable in practice. An experimenter may basically run a complex pseudorandom generator that decides whether he will press the "X" or "Y" button. Even in feasible classical theories, it's clear that the three spins/electrons can't "reproduce" all the complicated processes in the brain and preemptively predict what the experimenters would press etc.

In quantum mechanics, the random character of the pressed buttons is irreducible and fundamental. Quantum mechanics predicts that the experimenter #3 will press "X" with some probability and "Y" with another probability. What is needed for "XYY" to be possible is that the probability of "XYY" is nonzero. It is simply not true that the probability has to be 100% - and the probability is almost never 100%.

Your statement is absolutely equivalent to the statement that if something has a nonzero probability, it has to have the 100% probability. This statement is simply wrong. It suggests that you don't understand basics of mathematics and probability calculus, even at the classical or basic-school level. It's just embarrassingly silly to make similar statements and you have absolutely no chance to understand quantum mechanics with this hopeless background.

2. Dear Andrei,

Your answer does not address my challenge to you. Let’s ignore for the time the fact that charge distributions are irrelevant to the problem at hand. If I understood the spirit of your answer you basically appeal to superdeterminism (https://en.wikipedia.org/wiki/Superdeterminism). However this position is indefensible because 2 things: (a) the laboratories are spatial separated preventing communication and (b) the number of experiments is unlimited. Together this creates the perfect storm of a conspiracy. However its likelihood can be made arbitrary small by repeating the experiment.

The second point you make: “You mix apples with oranges,” points in a different direction: noncontextuality. Basically here you deny the applicability of Kolmogorov axioms, and in doing so you violate the basic ideas of classical physics. As such your “local realism” is very different from the generally accepted meaning of the term.

I think you also do not properly understand Bell’s theorem. In quantum mechanics there is a surprise: there are correlations which go above Bell limit. When you appeal on contextuality in your argument you basically state two things:
1: there is no surprise in QM because
2: you can go above Bell limit in classical field theories

There is a surprise in QM vs. classical physics, but instead of convincing you of this show me the money and prove you can go above Bell limit in classical field theories. After all it is you who make this very big claim and the burden of proof is on you. Handwavings don’t count. Show how on a classical system you can achieve correlations above Bell limit. If you do that you will become very famous overnight. But it can’t be done the same way you cannot find any classical system able to answer my earlier challenge to you: it is a mathematical impossibility. Even in the classical emulation of a quantum computer where you have an actual Hilbert space you cannot go above Bell limit.

Florin

3. Lubos: “non-realism: there is no well-defined value of any component of the spin (or any observable) prior to its observation, and even the question what it is isn't allowed by physics.”

After Alice performs the measurement (+1/2), QM predicts the spin of Bob’s particle is -1/2 with probability 1. So, QM indeed ascribes a well-defined value to that unmeasured particle, it obviously allows you to ask this question and it gives a perfectly fine answer, -1/2. Bob’s subsequent measurement that is guaranteed to give exactly the already existing value, -1/2 is perfectly useless. It does not make the probability 1 even bigger for obvious reasons so the -1/2 value remains as defined or undefined as before.

I have no issue regarding the formalism of QM, but it proves nothing. If you think you can prove that this formalism is unique I invite you to present that proof. The existence of a statistical theory does not necessarily imply the non-existence of an exact theory. ‘t Hooft for example has published an article:

https://arxiv.org/pdf/1405.1548

claiming that QM on a complex vector space is equivalent, from a mathematically point of view with a discrete cellular automaton. I am not qualified to evaluate it but the man got the Nobel prize in this field so, I’ll credit him with my trust.

Lubos: “The state of everything is always well-defined only relatively to the perspective of an observer who has gained some knowledge by observations.”

OK, so let’s only discuss the experiment from the subjective point of view of Alice. She measures her particle, she gets +1/2, she knows Bob’s particle must be -1/2. Do you agree that the spin of Bob’s particle, from the subjective point of view of Alice is well defined (-1/2)? Does she need to wait for Bob to perform his measurement and confirm it to her before calling the -1/2 value well-defined?

Lubos: “First of all, the GHZM experiment doesn't involve any *charges* or *electric* fields or *magnetic* fields. It is about the measurement of the *spins*. Spins may be nonzero even if all electric charges of all objects and electromagnetic fields in the space are zero (in the ground state). Your repetitive references to "charges" and "electromagnetic fields" indicate that you don't understand this experiment even at a classical level. You completely misunderstand basic words in physics such as the spin, charge, and others. You misunderstand the fact that the experiment is about the principles and the information coming from observations, not some technicalities about how the information is realized via "fields".”

I think you misunderstood my point. By charges I do not mean macroscopically charged objects, currents in copper coils or something like that. I am just stating the obvious fact that matter consists of atoms which have negatively charged electrons and positively charged nuclei. Everything that happens in GHZ, Bell, double-slit, delayed-choice or not, can be reduced to a great number of charges moving around.

If we ignore for now gravity and nuclear reactions everything that takes place during the experiment is a manifestation of EM.
Now, classical electromagnetism is a deterministic field theory. The “field” part is important because it ensures the contextuality needed to explain the quantum correlations. The force acting on each particle is a function of the electric and magnetic fields at that location and those fields are a function of the position/momenta of all field sources (particles).

When the entangled particles are produced (either photons or electrons or atoms created by splitting a diatomic molecule) the electric and magnetic fields acting on that location matter. The particle produced under the influence of the field produced by three detectors on X are different than those produced under the influence of the field associated with two detectors on Y and one on X. In other words, the hidden variable depends on the detector settings.

4. Lubos: “Whether the experimenters measured the X- or Y-component of the spins was up to their free will. In classical physics, one could have imagined that their decisions are in principle predictable (people may be imagined to be deterministic machines in classical physics) but they were never predictable in practice. An experimenter may basically run a complex pseudorandom generator that decides whether he will press the "X" or "Y" button. Even in feasible classical theories, it's clear that the three spins/electrons can't "reproduce" all the complicated processes in the brain and preemptively predict what the experimenters would press etc.”

Predicting in practice the evolution of a brain is impossible but this is irrelevant. The electrons need not “reproduce” anything. They are correlated with the detector settings by means of the electric/magnetic fields of the particles in the detectors. The fact that the experiment is complicated is also irrelevant. Nature does not have any problem evolving a system of any number of bodies even if the calculations humans can do are limited to a very small number. You cannot make an electron not to obey the equations of electromagnetism by adding more and more charges around, even if those groups of charges appear to you as a free-willed human or a computer running a random number generator. This is like saying that gravity should stop working if enough stars are added to a galaxy.

Lubos: “In quantum mechanics, the random character of the pressed buttons is irreducible and fundamental.”
This is indeed what you need to prove. Asserting it does not make it so.

A local-realistic account for the single-particle interference in a double slit setup about which Feynman said:

“"a phenomenon which is impossible […] to explain in any classical way, and which has in it the heart of quantum mechanics. In reality, it contains the only mystery [of quantum mechanics]."

Has been realized be Yves Couder:
https://arxiv.org/pdf/1401.4356

And guess what? There was no need for probabilities (irreducible or not), subjectivity of the observer, anything like that. Only a vibrating plate, some silicon oil and the good-old local-realism.

Andrei

1. Andrei, your writing about these matters is not only wrong in every individual statement but it is also self-contradictory. On one hand, you want to defend "local realism". On the other hand, you say things like

"They are correlated with the detector settings by means of the electric/magnetic fields of the particles in the detectors."

Sorry, detectors can't be correlated with the particles they are going to measure *before* they have interacted. Such a correlation would surely, by definition, contradict locality, right?

5. Dear Florin,

Let me propose you the following "proof" that relativity is wrong:

Relativity is wrong because you can use a warp drive to exceed the speed of light.

You would probably agree that the argument is correct. The problem is with the assumption that a warp-drive can be built. All details regarding the design of the experiment in which the warp-drive can be used are irrelevant. So your well-justified answer will be:

"proove me that an warp drive can be built and I would concede the point"

All those no-go theorems (GHZ included) that are supposed to rule out local realism are based on the assumption that it is possible to prepare an experiment in which more or less distant entities (detectors, PDC crystals, whatever) evolve independently of one another. My point is that such an experimental arrangement is impossible to prepare in practice. The only difference between the warp drive and the existence of independently evolving entities is that the warp drive is trivial to test. It is impossible to experimentally observe if between a brain and a PDC 1Km away a correlation between the motion of their subatomic particles exists. The only way to test that possibility is to carefully evaluate the mathematical structure of a classical field theory. So my question for you is this:

Is it possible to have a distribution of charged particles satisfying the two propositions bellow?

1. Some charges/groups of charges evolve independently of other charges/groups of charges.

2. all charges move in agreement with Maxwell's theory.

If you think this is possible please exemplify. You can place the charges at any distance you want, in any configuration you want.

Andrei

1. The actual correct formulation of the implication argument is "warp drives cannot exist because they contradict relativity".

2. Warp drives are a solution to Einstein field equations. You might eliminate them by demanding T^{00} >= 0, but then one might question whether there can be squeezed states of the quantum gravity vacuum that violate this weak energy condition of Hawking and Penrose.

In the end the issue of warp drives leads to very subtle questions on the relationship between global and local principles. We might have some principle that tells us that quantum gravity is "mod local symmetries," or some local symmetries. In this way we might understand questions of cosmic censorship better.

I tend to think that warp drives do not physically exist, or if they do they are completely unstable under any perturbation, even quantum fluctuations, so they do not FAPP exist. As yet we have no hard proof of this. Much the same goes for wormholes, or at least the boosted wormholes that would form time machines.

LC

6. Lubos: "Sorry, detectors can't be correlated with the particles they are going to measure *before* they have interacted. Such a correlation would surely, by definition, contradict locality, right?"

No, Lubos, two distant clocks can be correlated before they come close to each other because they were syncronized sometimes in the past.

You can also think about the motion of the stars in a galaxy. The motion of two stars 100000 light years away can be correlated even if they never met. If it happens that they collide at a certain time it is incorrect to assume that their relative motion was random prior to collision.

The case of charged particles is similar. Those particles existed in one form or another since the Big bang so their relative motion must be correlated as well.

It is my opinion that even in the case of subatomic particles the experimenter should adopt the view of the astronomer. Those particles cannot be created out of nothing at the time the experiment starts. the experiment is just a glimpse into their evolution just like a picture of a galaxy is a glimpse in the evolution of that galaxy. It would be absurd for the astronomer to assume that the stars move randomly before he looks at them and they only start to correlate their motion when he starts observing them.

Andrei

7. Lubos: "The actual correct formulation of the implication argument is "warp drives cannot exist because they contradict relativity"."

Well, you cannot convince someone who denies relativity in this way because you assume what you have to prove. If someone claims relativity is wrong because he can build a warp drive it is his burden of proof to provide evidence for that. If he cannot provide that evidence his argument fails.

Andrei

8. Dear Andrei,

You said:

"Let me propose you the following "proof" that relativity is wrong:

Relativity is wrong because you can use a warp drive to exceed the speed of light.

You would probably agree that the argument is correct."

Huh? This is word salad and I don't get your point. Do I agree that the warp drives exceed the speed of light? No, they don't exist. Do I agree that relativity is wrong? Only on April first day :)

Now I think you are back on superdeterminism. However to take this approach you need a foundation. 't Hooft is basing his approach on cellular automata. Then one can discuss in a scientific way the merits of such a model. What is the basis of your superdeterminism claim?

"all charges move in agreement with Maxwell's theory." is just simply incorrect handwaving.

As I type this message my fingers press the keys due to tiny electric signals between neurons in my body. Each key on the keyboard has a huge number of electrons but they do not interfere with my thought process via Maxwell's equations.

Without a model the idea that all is connected in the great circle of life works for Lion King or for New Age but not in science.

1. Florin: ""all charges move in agreement with Maxwell's theory." is just simply incorrect handwaving.

As I type this message my fingers press the keys due to tiny electric signals between neurons in my body. Each key on the keyboard has a huge number of electrons but they do not interfere with my thought process via Maxwell's equations."

So, do you deny from the start that charged particles interact according to classical electromagnetism? If it is so, you just assume what you need to prove and GHZ is redundant. The point of GHZ is to assume first that local-realism is correct and only then reach a contradiction. If you do not follow that procedure there is no argument to speak about, you are just asserting your unsupported beliefs.

PS

I have noticed that Lubos posted a very gentlemanish text on his blog. I only hope that, after a thorough evaluation of my IQ he would take the time to answer to the simple question I have asked:

"OK, so let’s only discuss the experiment from the subjective point of view of Alice. She measures her particle, she gets +1/2, she knows Bob’s particle must be -1/2. Do you agree that the spin of Bob’s particle, from the subjective point of view of Alice is well defined (-1/2)? Does she need to wait for Bob to perform his measurement and confirm it to her before calling the -1/2 value well-defined?"

Andrei

2. Hi Andrei,

"do you deny from the start that charged particles interact according to classical electromagnetism?"

Not at all, but basically here I am talking about a limit. As I put it before, a rover on Mars is not affected in any way by how an ant walks on Earth.

On Alice-Bob question for Lubos, you are basically repeating EPR's argument and this was well refuted. Still, one question remains: how can we explain quantum correlations? Here the positions are split. The ontic camp (the Bohmians) demand an explanation while my take on this is that no explanation is needed: correlations are simply there as a result of quantum formalism and interaction in the past. Don't like it? Tough luck, find yourself another universe of lower correlations.

On the IQ thing, there are no grounds to complain in a superdeterministic world where free will does not exist.

Florin

9. Just a superpeaceful innocent comment. You have wrong spacings in the kets +++ and –––. It's because the operators plus and minus try to divide things around and put bigger spaces around the "main" plus or minus.

A fix: write {+}{+}{+} and {-}{-}{-} to the kets, a way to make TeX know that they're not binary operators.

1. Thanks. By the way, I am glad I got upgraded to "confused" LOL :) Let me reciprocate, you were helpful with the comment above.

2. Thanks, Florin. It would be even better if such upgrades were guaranteed to be irreversible.

Concerning your sinful past life, I ran into your short review of the Bricmont book - which I found because it was the only "followup" of Alford's "nonlocality in EPR" paper. It's a long misleading pro-Bohmian nonlocal tirade. I can't understand how you can both "get" GHZM etc., which you apparently do, and simultaneously defend naive things such as Bohm's theory.

3. LOL. Read my next post. I am still reading Bricmont book and this is why I only gave a short review. I am thinking to host here a dialog between him and an opposing point of view (mine or someone else). I am working to disprove the Bohmian approach in a clean mathematical way using cohomology arguments, but this does not mean I do not respect a well argumented opposing point of view. You win an argument when the opposing side agrees with you, not when you destroy them. For this to happen both sides needs to be honest in their intentions and I believe this is the case here.

4. There is nothing well argumented about Bricmont book. It's just a constant irrational denial of quantum mechanics and attack on its founders. Bohr is correctly quoted as saying that there's no quantum world, just an abstract description - physics is about making statements about Nature, not about creating a model, and Bricmont follows it with several pages of dissatisfied whining.

I don't believe that Bricmont has a chance to understand quantum mechanics - i.e. 'agree with me". All university professors have been unable to teach QM to him and he's been unable to learn it for several other decades. Now he has written a whole book boasting his stupidity. Why should I believe it's feasible that he will suddenly agree with me? Give me a break.

10. Dear Florin,

You speak about a limit. Please justify that limit from the point of view of classical electromagnetism.

Hint: there is no limit. In the approximation that charges do not move much you would expect the "limit" to be the same as in gravity (Coulomb's law is mathematically similar with Newton's law of gravitation, except for the constant which does not help you much).

The only limit comes from your intuition. You focus on very complex systems (rover, ant, planet) with 10^30 or so particles. It's better to thing about just two charges, say 1 light year apart. Do they move independently or not? Then add more charges at each point and try to find out what happens.

In regards to my question to Lubos you are invited to answer. It's not the same argument as EPR (too many irrelevant assumptions there). If you think that it has already been refuted, please do it again here. I'm not asking you to write a book, just answer a very simple question.

Till now, only crickets can be heard from Lubos' microphone. I'm still looking forward to see his explanation of how the stars need to bump into each other in order for the gravity to start working and correlate their motion in a nice spiral galaxy.

Andrei