Posts Tagged ‘Bell Inequality’

Entangled Universe: Bell Inequality

May 9, 2016

Abstract: The Bell Inequality shatters the picture of reality civilization previously established. A simple proof is produced.

What is the greatest scientific discovery of the Twentieth Century? Not Jules Henri Poincaré’s Theory of Relativity and his famous equation: E = mcc. Although a spectacular theory, since  Poincaré’s made time local, in order to keep the speed of light constant, it stemmed from Galileo’s Principle of Relativity, extended to Electromagnetism. To save electromagnetism globally, Jules Henri Poincaré made time and length local.

So was the discovery of the Quantum by Planck the greatest discovery? To explain two mysteries of academic physics, Planck posited that energy was emitted in lumps. Philosophically, though, the idea was just to extent to energy the basic philosophical principle of atomism, which was two thousand years old. Energy itself was discovered by Émilie Du Châtelet in the 1730s.

Quantum Entanglement Is NOT AT ALL Classically Predictable

Quantum Entanglement Is NOT AT ALL Classically Predictable

Just as matter went in lumps (strict atomism), so did energy. In light of  Poincaré’s E = mc2, matter and energy are the same, so this is not surprising (by a strange coincidence (?)  Poincaré demonstrated, and published E = mc2, a few month of the same year, 1900, as Max Planck did E = hf; Einstein used both formulas in 1905).

The greatest scientific discovery of Twentieth Century was Entanglement… which is roughly the same as Non-Locality. Non-Locality would have astounded Newton: he was explicitly very much against it, and viewed it, correctly, as the greatest flaw of his theory. My essay “Non-Locality” entangles Newton, Émilie Du Châtelet, and the Quantum, because therefrom the ideas first sprung.

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Bell Inequality Is Obvious:

The head of the Theoretical division of CERN, John Bell, discovered an inequality which is trivial and apparently so basic, so incredibly obvious, that it reflects the most basic common sense that it should always be true. Ian Miller (PhD, Physical Chemistry) provided a very nice perspective on all this. Here it is, cut and pasted (with his agreement):

Ian Miller: A Challenge! How can Entangled Particles violate Bell’s Inequalities?

Posted on May 8, 2016 by ianmillerblog           

  The role of mathematics in physics is interesting. Originally, mathematical relationships were used to summarise a myriad of observations, thus from Newtonian gravity and mechanics, it is possible to know where the moon will be in the sky at any time. But somewhere around the beginning of the twentieth century, an odd thing happened: the mathematics of General Relativity became so complicated that many, if not most physicists could not use it. Then came the state vector formalism for quantum mechanics, a procedure that strictly speaking allowed people to come up with an answer without really understanding why. Then, as the twentieth century proceeded, something further developed: a belief that mathematics was the basis of nature. Theory started with equations, not observations. An equation, of course, is a statement, thus A equals B can be written with an equal sign instead of words. Now we have string theory, where a number of physicists have been working for decades without coming up with anything that can be tested. Nevertheless, most physicists would agree that if observation falsifies a mathematical relationship, then something has gone wrong with the mathematics, and the problem is usually a false premise. With Bell’s Inequalities, however, it seems logic goes out the window.

Bell’s inequalities are applicable only when the following premises are satisfied:

Premise 1: One can devise a test that will give one of two discrete results. For simplicity we label these (+) and (-).

Premise 2: We can carry out such a test under three different sets of conditions, which we label A, B and C. When we do this, the results between tests have to be comparable, and the simplest way of doing this is to represent the probability of a positive result at A as A(+). The reason for this is that if we did 10 tests at A, 10 at B, and 500 at C, we cannot properly compare the results simply by totalling results.

Premise 1 is reasonably easily met. John Bell used as an example, washing socks. The socks would either pass a test (e.g. they are clean) or fail, (i.e. they need rewashing). In quantum mechanics there are good examples of suitable candidates, e.g. a spin can be either clockwise or counterclockwise, but not both. Further, all particles must have the same spin, and as long as they are the same particle, this is imposed by quantum mechanics. Thus an electron has a spin of either +1/2 or -1/2.

Premises 1 and 2 can be combined. By working with probabilities, we can say that each particle must register once, one way or the other (or each sock is tested once), which gives us

A(+) + A(-) = 1; B(+) + B(-) = 1;   C(+) + C(-) = 1

i.e. the probability of one particle tested once and giving one of the two results is 1. At this point we neglect experimental error, such as a particle failing to register.

Now, let us do a little algebra/set theory by combining probabilities from more than one determination. By combining, we might take two pieces of apparatus, and with one determine the (+) result at condition A, and the negative one at (B) If so, we take the product of these, because probabilities are multiplicative. If so, we can write

A(+) B(-) = A(+) B(-) [C(+) + C(-)]

because the bracketed term [C(+) + C(-)] equals 1, the sum of the probabilities of results that occurred under conditions C.

Similarly

B(+)C(-)   = [A(+) + A(-)] B(+)C(-)

By adding and expanding

A(+) B(-) + B(+)C(-) = A(+) B(-) C(+) + A(+) B(-) C(-) + A(+) B(+)C(-) + A(-)B(+)C(-)

=   A(+)C(-) [(B(+) + B(-)] + A+B C+ + AB(+)C(-)

Since the bracketed term [(B(+) + B(-)] equals 1 and the last two terms are positive numbers, or at least zero, we have

A(+) B(-) + B(+)C(-) ≧ A(+)C(-)

This is the simplest form of a Bell inequality. In Bell’s sock-washing example, he showed how socks washed at three different temperatures had to comply.

An important point is that provided the samples in the tests must give only one result from only two possible results, and provided the tests are applied under three sets of conditions, the mathematics say the results must comply with the inequality. Further, only premise 1 relates to the physics of the samples tested; the second is merely a requirement that the tests are done competently. The problem is, modern physicists say entangled particles violate the inequality. How can this be?

Non-compliance by entangled particles is usually considered a consequence of the entanglement being non-local, but that makes no sense because in the above derivation, locality is not mentioned. All that is required is that premise 1 holds, i.e. measuring the spin of one particle, say, means the other is known without measurement. So, the entangled particles have properties that fulfil premise 1. Thus violation of the inequality means either one of the premises is false, or the associative law of sets, used in the derivation, is false, which would mean all mathematics are invalid.

So my challenge is to produce a mathematical relationship that shows how these violations could conceivably occur? You must come up with a mathematical relationship or a logic statement that falsifies the above inequality, and it must include a term that specifies when the inequality is violated. So, any takers? My answer in my next Monday post.

[Ian Miller.]

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The treatment above shows how ludicrous it should be that reality violate that inequality… BUT IT DOES! This is something which nobody had seen coming. No philosopher ever imagined something as weird. I gave an immediate answer to Ian:

‘Locality is going to come in the following way: A is going to be in the Milky Way, B and C, on Andromeda. A(+) B(-) is going to be 1/2 square [cos(b-a)]. Therefrom the contradiction. There is more to be said. But first of all, I will re-blog your essay, as it makes the situation very clear.’

Patrice Ayme’

QUANTUM NON LOCALITY.

September 1, 2011

ONE & THE SAME, ACROSS THE UNIVERSE.

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Abstract: Why Quantum Physics violates locality. Twentieth-second century primary school version.

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 LOCALITY: What does locality mean? It means that what happens at a point is determined by what is happening in a neighborhood of that point within a small enough distance, as determined by light. Moreover, it means that the universe U is made of points: U = Union points. Points, by definition, are singletons (they have no elements in the sense of set theory), and they have dimension zero: nothing belongs to a point.

 SPACETIME: Generally the universe is called “spacetime”. However, this concept, spacetime, introduces the assumptions of Einstein’s Special Relativity, as boosted by Minkowski, established before Quantum Physics.

 In particular the spacetime hypothesis assumes that the universe is a product of what is called in mathematics the “real line”, which assumes, among other things, what is called a T2, Hausdorff topology. Two different points are separated by different neighborhoods (to use the appropriate concepts from general topology).

 Quantum Physics violates both LOCALITY and SPACETIME.

 How do we know this? When one analyzes the smallest processes, one finds that, in plenty of cases, the SMALLEST PROCESSES, THE INDIVISIBLE PROCESSES, SPREAD IN TIME OVER ARBITRARY BIG REGIONS, ON THEIR OWN (THAT IS WITHOUT ANY INTERACTION WITH THE REST OF THE UNIVERSE). Are they then big, or are they small? Verily, therein a mystery of the Quantum.

 In this innocuous concept I just uttered, they spread as big as they want, although being as small as there is, one finds the entire origin of Quantum non locality. No need for fancy mathematics, or even any equation. The idea is as dramatic as can be.

 Indeed, non locality boils down to a matter of definition. As the indivisible process spreads out, it stays one, well, by definition. It means that touching it anywhere is like touching it everywhere.

 When two particles comes out of such an indivisible process, they are called “ENTANGLED”. The semantics gets in the way. What we do not have is actually two particles, but two possible experimental channels, which can be widely separated, where, if we experiment, two particles will show up, and widely separated, if the channels are so.

 Thus we see that the two channels are entangled, and touching one is also touching the other.

 What are some of these cases where the smallest, indivisible processes spread out macroscopically? Well, they are so common, that they seem to be the rule, not the exception: 

 Diffraction (the 1 slit experiment) is such a case: the slit is small, diffusion gets big. Arbitrarily big.

 The famous 2 slit experiment is another case: the slits are close by, the interference screen is at a large distance. Hey, the 2-slit could be a galactic cluster. A cluster made of galaxies, each 200,000 light years across. 

 Any fundamental process where two particles separate after interacting. (In particular the simple set-up of the Einstein Podolski Rosen thought experiment, such as the Bohm total spin zero variant.)

 It is highly likely that such an effect is used all over biology, to transport energy close to 100% efficiency over macroscopic distances (an allusion to the fact that this is not only about pure science, but the economic fall-out will be considerable, once this is so well understood that we can dominate the processes involved).

 Not all Quantum processes spread all over space. Bohr got the Nobel for his patchy, haphazard atomic theory which worked, because electronic matter waves self interfere coherently onto themselves (these matters waves, the de Broglie waves, are called orbitals, and they make the body of atoms, what we call matter, and sharing orbitals is much of what we call chemistry).

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 Thus we have found the following, from the most basic set-up of Quantum theory:

 A Fundamental Quantum Process, is one, until interacted with, even if it is spread over space. This is what Quantum Non Locality is all about.

 Some crystals can make out of one photon, two photons with opposite polarizations, and they could then be sent in two different channels, a light year apart.

Parallel transporting along the two channels the polarization directions, we would always find them opposite. A more subtle relation between the polarizations holds, and was found to be true even when the polarization angles are moved randomly during the photons flight time (Aspect experiment, for which Alain Aspect got the Wolf Prize in 2010).

 By making all sorts of supplementary hypotheses about local hidden parameters and local measurements of polarizations, though, on finds that should not be the case. This contradiction is called the Bell Inequality (I like Bell very much, and I approve of his quest, which is also my quest. I apologize for his many admirers, by presenting his efforts in an arguably demeaning light).

The preceding, most simple way to look at Non Locality, gives an excellent reason to not do that: the logic of the Quantum is as simple as it gets: as long as I am left alone, says the Quantum, I am one. And indivisible.

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 What does it all mean? First Einstein and company in their “EPR” paper, talked about “elements of reality”. They did NOT talk about ELEMENTS OF SPACE. They did not have the notion. I will argue they should have, but of course, the fact that they did not have it was central to their (erroneous) reasoning. 

 Einstein and company wondered how a particle could communicate with another, even across light years. Wrong amazement. Particles are not “communicating“. Actually, they are not “particles” to start with.

 For decades I have advocated a radical solution, as exposed above, aligning the definition elementarily: the two particles are one and the same, they are in the same place at the time of the Quantum interaction, and stop being so, as a result. The topology used in physics, the same that the dinosaurs used, the T2, separated topology, is not appropriate to the real universe. OK, it was appropriate for pterosaurs. But it’s not appropriate, across the universe. BTW, the pterosaurs, the best fliers, by far, that this planet has known, went extinct, although they were obviously very smart.

 Is this the end all, be all? Quantum Physics a la Bohr reigns, and nothing else can be said? No. If the bare bone theory above is true, the entire theory of spacetime is false: space is not made of points, and it is constructed interactively. The case of time is even more so. Imagine there are no heavens made of points, only the sky you make, etc. Thus more has been said

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Patrice Ayme

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 Note 1: An enlightening analogy: The question of using the Quantum set-up to transmit information superluminally, or what Einstein called “Spooky Interaction At A Distance” has come up. The preceding, as it is, sticking to strict Quantum theory, demolishes both views, with crushing simplicity.

 How? OK, let’s make an experimental metaphor. Suppose we have an infinitely rigid bar between the two entangled particles: each time we experiment with one, we turn the bar, and so it turns at the other end too. Simple. Some will say: ha ha ha, but then I can look at the bar, and I see the bar turn, and so information has been transmitted. Not so fast. We are dealing with as elementary a Quantum process as possible, which means the particle was not observed, before the bar turned. So we see the bar turn, but we do not know if it was, or not, turning before. To tell if a signal was sent, one has first to define a state where one can say no signal was received.  

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 Note 2: I was a rough to the point of inaccuracy with the Bell Inequality above.  There is a subtlety, which can be seen easily say in the case of spin. Spin measurements in various directions are not independent of each other. Thus, if one measures spin in the close channel, a measurement of spin in another, random direction in the distance channel will show that influence, and a local determination of spin in the distant channel by parallel transport will not exhibit this. BTW, introducing the notion of parallel transport in the conversation, which is the whole point of the “local hidden parameter” debate is from yours truly.

 Note 3: And let’s not forget to smile about the naïve who developed frantically supersymmetric superstrings super budgeted super having-nothing-to-do-with reality… While forgetting to think about the fundamentals as described above.

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