Monday, November 9, 2015

Explaining the EPR paradox

A reader asks me to explain my view of the EPR Bohm paradox, since I seem to reject what everyone else says.

Actually, my view is just textbook quantum mechanics. I do not subscribe to hidden variables, superdeterminism, action-at-a-distance, or anything exotic.

I am also a logical positivist, so I stick to what we know, and try not to jump to unsupported conclusions.

Experiments show that electrons and photons have both particle and wave properties. Quantum mechanics teaches that an electron is a mysterious quantum that is not exactly a particle or a wave, but something else. It obeys various physical laws, like conservation of energy and momentum, and Heisenberg uncertainty.

The EPR paper looks at a physical process that emits two equal and opposite electrons. Only I prefer to call them quanta, because they are not really particles with definite position and momentum at the same time.

Mathematically, the two quanta are represented as a single quantum state. A measurement of one collapses the state, according to the rules of quantum mechanics. Quantitative predictions are in excellent agreement with experiment.

In particular, you can measure the momentum of one quantum, and know that the other must be equal and opposite. Physically there is nothing strange about this, as it is a consequence of momentum being conserved.

But it is a little strange if you combine this with Heisenberg uncertainty, which normally prevents us from making a precise statement about momentum until it is measured. Measuring one quantum allows us to say something about a distant quantum.

Bohm pointed out that you get the same paradox when measuring spin, and tried to argue for hidden variables.

One way people have tried to explain this is with action-at-a-distance, with measuring one quantum having an instantaneous physical effect on the other. But that is so contrary to everything else we know about physics, then such an explanation would only be a last resort.

Another is to model the quantum with hidden variables. All such attempts have failed. In particular, if you think of the quantum as having a definite position, momentum, and spin before the measurement, you get contradictions with experiment.

So what is left? There is still the original Bohr logical positivist view. Things are clearer if you avoid trying to answer unanswerable questions. Physics is about observables. Concepts like position, momentum, and spin are not really properties of quanta. They are properties of observations.

We have no true mathematical representation of the quantum. We have a mechanics of observables. We predict observations, and avoid trying to say what is not observed.

When people try to visualize the quantum, they inevitably form some classical (pre-quantum) picture that we know is wrong. So they get paradoxes and say that quantum mechanics is incomprehensible.

Or they try some mathematical model that ends up being a hidden variable model, and it does not work.

So again, here is what happens. A physical process emits two equal and opposite quanta. They seem particle-like and wave-like, but they are physical objects that lack a true mathematical formulation. From the physics, we know that they are equal and opposite, and from quantum mechanics formulas, we can make certain predictions about observables. In particular, observations about the two quanta are correlated. Correlation is not necessarily causation.

Does some physical process like radioactive decay determine the state of an emitted quantum? I have an open mind on that, because I don't see how the question makes any sense. How can any experiment tell us one way or the other? You can believe it or not believe it; it is all the same to me.

Physicists make arguments that EPR-like experiments prove true randomness. I have posted denials of that, and I do not even believe that there is any such thing as true randomness. Randomness is a mathematical formalism that is actually deterministic, or a figure of speech for how certain theories fail to predict certain outcomes. That's all. When physicists talk of true randomness, they are usually talking nonsense.

What about the quanta being separable? Action-at-a-distance seems like hokum to me. It is as implausible as a perpetual motion machine. There is no evidence for it, and a lot of reasons for thinking it impossible.

I say that the physical quanta are separate and cannot influence each other. At the same time, our knowledge of the two quanta are linked, and info about one tells us something about the other.

In the terminology of Bell's theorem, I am rejecting counterfactual definiteness, just as all mainstream physicists have for decades.

Counterfactual definiteness says that the photons in the double-slit experiment must entirely go thru one slit or the other, just as if they were measured as particles at the slits. But mainstream quantum mechanics teaches that this is completely false, and such measurement would destroy the interference pattern. The light goes thru both slits at once.

You cannot do a completely passive observation of a quantum giving it a particular position, momentum, or spin. Any such measurement changes it, because quanta do not have such properties.

Rejection of counterfactual definiteness is essential to XX century physics, and is embodied by these slogans:
Another thing that people have emphasized since quantum mechanics was developed is the idea that we should not speak about those things which we cannot measure. (Actually relativity theory also said this.) [Feynman]

Unperformed experiments have no results. [Peres]
Somehow the 21st century has brought us more and more physicists who would rather believe in spookiness or parallel universes. A serious disease has infected Physics.

You will probably say I am cheating because I am not seeking a complete mathematical description of an electron, or that it is a cop-out to say that the wave function is just a representation of our knowledge.

My answer is that this issue goes to the heart of what science is all about. The job of physics is to use mathematics to predict outcomes for experiments. It is not to provide mathematical representations for things you cannot observe. All of the EPR paradoxes are based on naive expectations for counterfactuals, and not observations. Stick to observables, and the experiments are not so strange.


  1. I don't think you've touched the real issue, which is the demonstrated non-separable aspect of the results of actual measurements. Take, for example, Bohm's version of the EPR experiment, with two entangled electrons emitted in opposite directions. At some distance away are two experimenters with spin measuring devices, each of which can be freely oriented at any desired angle to measure the spin of the respective electron at that chosen angle. If the two experimenters happen to measure the spins at the same angle, they always get opposite results (one UP and one DOWN). Consequently, if the electrons are deterministic and separable (as you say), each individual electron must be prepared to give a particular result for any particular measurement angle. But this implies a certain algebraic inequality on the correlations of the results when measured at UNequal angles. Quantum mechanics predicts that this inequality is violated, and this has been confirmed by experiment. Therefore, the electrons are not deterministic and separable. The only possible escapes from this are things which you reject, e.g., superdeterminism, non-separability, backward causation, etc. (Note that counterfactual definiteness doesn’t mean what you think it means.)

  2. Anonymous,
    When you don't understand something, the answer to your ignorance is not magic or paradox, or the substitution of a calculation for a cause.
    When a magician tricks you, it isn't because of a miracle. It is because you were fooled.

    Study sleight of hand, it's all about fooling people into thinking something happened when in fact nothing did. The palmed item in question never teleports from one hand to the other, it was already there and you just weren't expecting it to be. It's the easiest way to trick someone by convincing them an event occurred when they said it did, and not when it actually happened.

    To understand what is going on, you don't need a duped scientist who thinks he already knows, you need a perceptive con artist who wants to figure it out.

  3. Anonymous, you say: "each individual electron must be prepared to give a particular result for any particular measurement angle. But this implies a certain algebraic inequality on the correlations ..."

    You are skipping one crucial assumption -- that quantum mechanics is wrong and electron spin is explained by local hidden variables. So another possible escape from the experiments is that the local hidden variable theory is wrong.

    The local hidden variable theory is an attempt to impose classical mechanics. It says that the Heisenberg uncertainty is just an illusion about our lack of knowledge of precise values for those hidden variables. A big lesson of XX century physics is that the hidden variable theory is wrong. That was the consensus in 1930, and ought to be the consensus today.

  4. Bell's inequality is not based on the assumption of hidden variables, it's based on the hypothesis that you yourself advocate, that electrons are deterministic and separable. (Some people might argue that the only way of being deterministic and separable is by hidden variables, but that obviously is not your position.) In addition, the derivation of Bell's inequality assumes that quantum mechanics correctly predicts that each electron exhibits quantum spin, yielding either UP or DOWN with equal probability, regardless of the angle of measurement, and that entangled electrons invariably give opposite results when measured at the same angle. From these premises, it follows that the predictions of quantum mechanics for unequal angles are false. Therefore, if quantum mechanics is completely correct, electrons cannot be deterministic and separable. That was the consensus in 1930, and it remains the consensus today, reinforced by the experimental demonstrations of the violations of Bell's inequality.

  5. Anonymous, you are incorrect about Bell's inequality. The Wikipedia article on Bell's theorem states it as "No physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics." So Bell's inequality is very definitely based on the assumption of hidden variables.

  6. They say that because they (along with most other people) equate hidden variables with being deterministic and separable. I do too. But you don't, because you claim that the electrons are deterministic and separable while at the same time you reject hidden variables. You say the electrons must be separable because "action at a distance seems like hokum to you", but that's a misunderstanding, because lack of separability does not imply action at a distance. Everyone agrees that quantum mechanics does not entail any action at a distance, because no information or energy propagates faster than light. Nevertheless, the entangled parts of a quantum system are not separable, and this is precisely what the violations of Bell's inequality demonstrate. Classically the only way things could not be separable would be by action at a distance, but the weirdness of quantum mechanics is that things can be non-separable without implying any action at a distance. The non-separability is subtle, but it represents a profoundly non-classical aspect of the world.

  7. No, I say that local hidden variables are required for Bell's Theorem because that is an explicit mathematical requirement. That Wikipedia page quotes Bell himself, and says: "Bell concluded: 'In a theory in which parameters are added to quantum mechanics ...'" Those parameters are the hidden variables.

    You say: "Everyone agrees that quantum mechanics does not entail any action at a distance ..."

    That used to be true, but as I quoted from the book review: "In his book, George lays out how the attitude of scientists towards nonlocality has gone from acceptance to rejection and makes a case that now the pendulum is swinging back to acceptance again. I think he is right that this is the current trend (thus the workshop)."

    Even Krauss says: "the second electron is affected by the measurement of the first electron with no time delay".

    So yes, mainstream physicists have gone soft on this issue.

  8. Let me try to say clearly what I mean. Bell's inequality can be (and is) derived from the assumptions of determinism and separability. You claimed that electrons are deterministic and separable. Therefore, so I say that the demonstrated violations of Bell's inequality prove that your claim is wrong. To counter this, you say "No, Bell's inequality is based on hidden variables, which I reject", so your belief in determinism and separability is unscathed by the violations of Bell's inequality. But I see this as a non-sequitur and self-contradictory evasion, because "hidden variables theory" is really just a historical term for theories that satisfy determinism and separability. I challenge your claim that electrons are deterministic and separable. I say these are precisely the attributes of a hidden variable theory that are used in the derivation of Bell's inequality.

    I also said everyone agrees that no energy or information propagates faster than light according to quantum mechanics, and you say I'm wrong, i.e.,you think some scientists believe that information and/or energy propagates faster than light. I think you misunderstand what they are saying, precisely because you haven't gotten the distinction between action at a distance and the non-separable aspects of quantum mechanics. Have you actually worked through Bell's inequality yourself, to be sure you understand it? It's a subtle effect. When Krauss says the second electron is affected by the measurement of the first, he is talking about this subtle effect of non-separability, not about action at a distance. I'm quite sure if you asked him, he would deny that any energy or information travels faster than light. Even Bell himself, who was sort of a crank on this topic, admitted that instantaneous action at a distance is inconsistent with the well established Lorentz invariance.

  9. Part of the confusion here is over terminology. Bell and his followers were believers in spooky nonlocality, so they keep changing their definition of locality in order to argue that it has been disproved. See this 2014 Nature article about how physicists are divided into localist and non-localist camps. I am in the localist camp.

  10. I agree that the terminology in this subject is a big problem. No two people agree on the meanings of words like locality, realism, causation, influence, determinism, etc., whereas there is actually broad agreement on many of the concepts. For example, everyone agrees that no information or energy propagates faster than light, but not everyone agrees to call this "localism". Everyone would have agreed to call this "localism" prior to quantum mechanics, but with the recognition of the non-classical correlations of quantum mechanics, as exemplified by violations of Bell's inequality, came a perceived need for a more sophisticated concept of non-locality, recognizing that the responses of entangled entities to (presumed) freely-chosen interactions at spacelike-separated events exhibit correlations that defy explanation under traditional notions of causation. When you say you are in the localist camp, you might just mean that you believe no energy or information propagates faster than light, in which case everyone agrees with you, or you might mean that you deny the existence of correlations that defy explanation under traditional notions of causation, in which case no one agrees with you. It all depends on what you mean, so it's essential to be clear and explicit. Simply saying "I'm in the localist camp" doesn't make your meaning clear, and saying that electrons are deterministic and separable tends to suggest a lack of recognition of the violations of Bell's inequality. (By the way, the 2014 Nature article was abysmal.)

  11. I accept this Wikipedia definition: "In physics, the principle of locality states that an object is only directly influenced by its immediate surroundings."

    I say that an event can only influence what is in its forward light cone. This implies that no information or energy propagates faster than light. Measuring an entangled particle might give us info about the paired particle, but cannot have a physical effect on it.

    I used the word "influence", and you say not everyone agrees to what that means.

    Perhaps it is clearer if I say I agree with most of what Krauss says, until he says "the second electron is affected by the measurement of the first electron with no time delay". I could agree with saying that our prediction for a measurement of the second electron is affected by the outcome of a measurement of the first electron, with no time delay". We know that the measurement affects our knowledge of the electron. But affecting the electron?! Where's the proof for that? Why hasn't a Nobel Prize been given to whoever proved that?

  12. Basic quantum mechanics already contains the weird non-classical correlations that are highlighted by the violation of Bell’s inequality, and several people got Nobel prizes for this, including Bohr, Heisenberg, Schrodinger, Dirac, and Born. Understanding why the quantum correlations are so difficult to fit into any prior conceptual framework requires some careful thought. Let me try to explain.

    Consider two entangled electrons, heading toward two experimenters at distant locations. Each experimenter has a spin measuring device, which he can orient at will to measure the incoming electron’s spin (Up or Down) along any axis he chooses. For simplicity, let’s agree that they will measure only along one of three directions, 0, 120, or 240 degrees. Each experimenter finds that, whichever direction he measures, half the electrons are spin UP and half are spin DOWN. Each experimenter keeps a record of his measurements, noting the angle he selected and the result (UP or DOWN) that he got for each incoming electron. When the experimenters get together later to compare their results, they make an astounding discovery: Every time the two experimenters happened to measure a pair of entangled electrons along the same direction, they ALWAYS got opposite results (one UP and one DOWN), and whenever they measured in different directions they got the same result (both UP or both DOWN) 3/4 of the time. Barring super-determinism, backward causation, or some other non-classical premise, these results are impossible to reconcile with the assumption that the electrons are deterministic and separable. Do you see why?

  13. No, those results are impossible to reconcile with the idea that electron spin is controlled by some hidden variable to a definite value, even if no measurement has taken place. But we know from quantum mechanics that there is an uncertainty principle for spin, and no such hidden variable theory is compatible with quantum mechanics.

    Go ahead and go thru the Bell proof. You will find that you always have to make a hidden variable assumption to get the inequality. To relate spin at one angle to spin at another angle, you have to assume either quantum mechanics or hidden variables.

  14. Again, determinism and separability imply hidden variables (although the converse is not true). To understand this, note that the two experimenters can be arbitrarily far apart, and they can each freely choose which direction to measure, and yet if they happen to measure in the same direction they invariably get opposite results. In other words, if experimenter A finds UP for one electron at his detector at a given angle, then experimenter B MUST find DOWN for the corresponding electron at his detector at that same angle. Now, if we believe the electrons are separable, it follows that B must find DOWN for that electron at that angle, whether A measures at that angle or not. This is a key point. The only way to avoid hidden variables is to give up separability, which you are not willing to do. So, you must conclude that each electron must be prepared to give a definite result for any selected measurement angle. From this, Bell's inequality follows. And we know Bell's inequality is violated, so the premise of separability is wrong (barring some even more "bizarre" assumption).

  15. So after arguing that "Bell's inequality is not based on the assumption of hidden variables", you now admit that it assumes hidden variables. Namely, it assumes determinism and separability, but gives contrived definitions that imply hidden variables.

    I will post another essay to address this point in detail.

  16. The full quote was: "Bell's inequality is not based on the assumption of hidden variables, it's based on the hypothesis that you yourself advocate, that electrons are deterministic and separable. (Some people might argue that the only way of being deterministic and separable is by hidden variables, but that obviously is not your position.)" I've continued to make this point in all subsequent messages. Let me try to be even more explicit: We begin with the assumption that the electrons are deterministic and separable. Combining this with the perfect anti-correlation predicted by quantum mechanics for pairs of entangled electrons when measured along the same angle, it follows that the electrons must be prepared to respond in a definite way to a spin measurement at each angle. Thus from these premises we must conclude local hidden variables. But then the quantum mechanical correlations at unequal angles prove that no local hidden variables can work. So, although Bell's theorem does indeed rule out local hidden variables, it is not based on the assumption of local hidden variables, it is based on the assumption of deterministic and separable electrons.

    I honestly tried in my previous message to explain, as clearly as I could, why the perfect anti-correlation at equal measurement angles, together with the assumption of determinism and separability, unavoidably implies definite prepared responses for each electron and measuring angle (i.e. hidden variables), which then leads to Bell's inequality. I don't understand what you mean by "contrived definitions". I believe I'm using the same definitions of the words deterministic and separable that everyone else (except perhaps you) uses. Could you tell me what you mean by "deterministic and separable", and in particular could you tell me how your concept of "deterministic and separable" can account for the perfect anti-correlation without hidden variables?

  17. Thanks for your comments. I will post a response.

  18. "Another is to model the quantum with hidden variables. All such attempts have failed."

    That is not true. Joy Christian has presented an EPR-Bohm classical local-realistic model since 2007 that gives the same prediction as quantum theory. The hidden variable is simple and very common sense and not contrary to the quantum theory prediction. It doesn't really model the quantum with a hidden variable but models the system of the pair of quanta with a hidden variable. The pair can either be left hand oriented or right hand oriented upon creation. A 50-50 chance in Nature. Pretty common sense, isn't it?

  19. Joy Christian's work is wrong, as shown by Motl, Gill, Aaronson, and Aaronson again.

    1. All those references are old. A lot of progress was made since then. Especially since now there is numerical validation of Christian's analytical results via a computer program, GAViewer. The math tells the truth.

      If anyone needs help to understand it, please ask.

  20. No. He cannot disprove a theorem. If he were right, a reputable journal would publish his papers. He is wrong.

  21. Bell's theorem is not a true mathematical theorem so it can be dis-proven. It is just a statement about a faulty interpretation of the inequalities. The self-brainwashing is so widespread about Bell's argument, that it is not easy to get it published. But one paper did get published so you are wrong about that or just not up-to-date.

    For another thing, it is mathematically quite impossible for anything to violate the Bell type inequalities. QM does not violate them. Easy to prove.

  22. No. The Bell inequalities are violated by QM theory, and by experiment. See Bell test experiments for details.

  23. I am very familiar with all the Bell test experiments. All they really do is confirm that the QM theory prediction is correct for the EPR scenario. And... we fully accept that. However to date, no experiment has ever violated the Bell inequalities. What happens is they shift to a different inequality upon analysis. Easy to demonstrate. We will use the Bell-CHSH inequality as it is most common for experiments. Here are the expectation terms,

    E(a, b) - E(a, b') + E(a', b) + E(a', b')

    Each expectation term in the inequality can range from -1 to +1 so we could have for independent terms,

    (+1) - (-1) + (+1) + (+1) = 4

    4 is the actual absolute bound for the CHSH inequality with independent terms, not 2. IOW, the CHSH inequality is "rigged" for local hidden variable theories because the terms are made dependent on each other. But QM theory and the experiments don't adhere to that dependency that is restricting LHV models for their apparent "violations". IOW, they shift to an inequality where the actual bound is 4 not 2.

    You will never see this in a wikipedia article as the Bell fans immediately edit out the truth about this as soon as anyone tries to tell the truth. This demonstration by simple inspection can be done for all the Bell type inequalities. Even Bell's original inequality which can be arranged as follows,

    E(a, c) - E(b, a) - E(b, c) =< 1

    Again, each expectation term can be between -1 and +1 so we could have by simple inspection with independent terms,

    (+1) - (-1) - (-1) = 3 not 1

    The question for you is why are LHV models subject to the dependency and QM theory and the experiments aren't? The easy answer is that Bell was wrong in his argument.