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Mortimer Adler Rogers Albritton Alexander of Aphrodisias Samuel Alexander William Alston Anaximander G.E.M.Anscombe Anselm Louise Antony Thomas Aquinas Aristotle David Armstrong Harald Atmanspacher Robert Audi Augustine J.L.Austin A.J.Ayer Alexander Bain Mark Balaguer Jeffrey Barrett William Belsham Henri Bergson George Berkeley Isaiah Berlin Richard J. 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Entanglement
Entanglement is a mysterious quantum phenomenon that is widely, but mistakenly, described as capable of transmitting information over vast distances faster than the speed of light. It has proved very popular with science writers, philosophers of science, and many scientists who hope to use the mystery to deny some of the basic concepts underlying quantum physics. Many of them try to deny indeterminism, ontological chance. Entanglement depends on two quantum properties that are simply impossible in "classical" physics. One is called nonlocality. We shall argue that Albert Einstein first caught a glimpse of nonlocality as early as 1905! He made a clear public statement about it at the 1927 Solvay conference, but was misunderstood by Niels Bohr and ignored by most physicists until 1935. The other is nonseparability, which Einstein was first to see, even as he attacked the idea, just as he had reacted to his discovery of indeterminism in 1916. A "weakness in the theory," he called chance. In the EinsteinPodolskyRosen paper, Einstein extended nonlocality beyond the relation between a particle and its wave function. It was now extended from one particle to another with which it had interacted. Erwin Schrödinger called them "entangled." Each of these might be considered a mystery in its own right, but fortunately information physics (and the information interpretation of quantum mechanics) can explain them both, with no equations, in a way that should be understandable to the lay person. This may not be good news for the science writers and publishers who turn out so many titles each year claiming that quantum physics implies that there are multiple parallel universes, that we can travel backwards in time, that things can be in two places at the same time, that we can teleport material from one place to another, and of course that we can can send signals faster than the speed of light. But there are a couple of somewhat weird claims that can be illustrated and explained by measurements of entangled particles, as we shall see. These are that the minds of physicists are manipulating "quantum reality" and that there is nothing "really" there until we look at it.
Einstein's Discovery of Nonlocality and Nonseparability
Albert Einstein was the first to see the nonlocal character of quantum phenomena. He may have seen it as early as 1905, the same year he published his special theory of relativity. But it was perfectly clear to him 22 years later (ten years after his general theory of relativity and his explanation of how quanta of light are emitted and absorbed by atoms), when he described it with a diagram on the blackboard at a conference of physicists from around the world in Belgium in 1927 at the fifth Solvay conference.
In his contribution to the 1949 Schilpp memorial volume on Einstein, Niels Bohr provided a picture of what Einstein drew on the blackboard.
At the general discussion in Como, we all missed the presence of Einstein, but soon after, in October 1927, I had the opportunity to meet him in Brussels at the Fifth Physical Conference of the Solvay Institute, which was devoted to the theme "Electrons and Photons."
Then in 1935, Einstein, Boris Podolsky, and Nathan Rosen proposed a thought experiment (known by their initials as EPR) to exhibit internal contradictions in the new quantum physics. Einstein hoped to show that quantum theory could not describe certain intuitive "elements of reality" and thus was either incomplete or, as he might have hoped, demonstrably incorrect. He and his colleagues Erwin Schrödinger, Max Planck, and others hoped for a return to deterministic physics, and the elimination of mysterious quantum phenomena like superposition of states and "collapse" of the wave function. EPR continues to fascinate determinist philosophers of science who hope to prove that quantum indeterminacy does not exist. Beyond the problem of nonlocality, the EPR thought experiment introduced the problem of "nonseparability." This mysterious phenomenon appears to transfer something physical faster than the speed of light. What happens actually is merely an instantaneous change in the immaterial information about probabilities or possibilities for locating a particle. The 1935 EPR paper was based on a question of Einstein's about two electrons fired in opposite directions from a central source with equal velocities. He imagined them starting at t_{0} some distance apart and approaching one another with high velocities. Then for a short time interval from t_{1} to t_{1} + Δt the particles are in contact with one another.
Note that It was Einstein who discovered in 1924 the identical nature and indistinguishability of quantum particles
After the particles are measured at t_{1}, quantum mechanics describes them with a single twoparticle wave function that is not the product of independent particle wave functions. Because electrons are indistinguishable particles, it is not proper to say electron 1 goes this way and electron 2 that way. (Nevertheless, it is convenient to label the particles, as we do in illustrations below.) Until the next measurement, it is misleading to think that specific particles have distinguishable paths.
Einstein said correctly that at a later time t_{2}, a measurement of one electron's position would instantly establish the position of the other electron  without measuring it explicitly. Schrödinger described the two electrons as "entangled" (verschränkt) at their first measurement, so "nonlocal" phenomena are also known as "quantum entanglement." Note that Einstein used conservation of linear momentum to calculate the position of the second electron. Although conservation laws are rarely cited as the explanation, they are the physical reason that entangled particles always produce correlated results. If the results were not always correlated, the implied violation of a fundamental conservation law would be a much bigger story than entanglement itself, as interesting as that is.
We prefer to describe this phenomenon as "knowledge at a distance." No action has been performed on the distant particle simply because we learn about its position. Note that this assumes the distant particle has not had any interaction with the environment. Einstein had objected to nonlocal phenomena as early as the Solvay Conference of 1927, when he criticized the collapse of the wave function as "instantaneousactionatadistance" that prevents the wave from acting at more than one place on the screen." Einstein's concern was based on the idea that the wave might contain some kind of ponderable energy. At that time Schrödinger thought it might be distributed electricity. In these cases the instantaneous "collapse" of the wave function might violate Einstein's principle of relativity, a concern he first expressed in 1909. When we recognize that the wave function is only pure information about the probability of finding the electron somewhere, we see that there is no matter or energy travelling faster than the speed of light. Einstein's criticism somewhat resembles the criticisms by Descartes and others about Newton's theory of gravitation. Newton's opponents charged that his theory was "action at a distance" and instantaneous. Einstein's own theory of general relativity shows that gravitational influences travel at the speed of light and are mediated by a gravitational field that shows up as curved spacetime. Note that when a probability function collapses to unity in one place and zero elsewhere, nothing physical is moving from one place to the other. When the nose of one horse crosses the finish line, its probability of winning goes to certainty, and the finite probabilities of the other horses, including the one in the rear, instantaneously drop to zero. This happens faster than the speed of light, since the last horse is in a "spacelike" separation. In 1964, John Bell showed how the 1935 "thought experiments" of Einstein, Podolsky, and Rosen (EPR) could be made into real physical experiments. Bell put limits on the "hidden variables" that might restore a deterministic physics in the form of what he called an inequality, the violation of which would confirm standard quantum mechanics. Since Bell's work, many other physicists have defined other "Bell inequalities" and developed increasingly sophisticated experiments to test them. The first practical and workable experiments to test the EPR paradox were suggested by David Bohm. Instead of only linear momentum conservation, Bohm proposed using two electrons that are prepared in an initial state of known total spin. If one electron spin is 1/2 in the up direction and the other is spin down or 1/2, the total spin is zero. The underlying physical law of importance is a second conservation law, in this case the conservation of angular momentum. If electron 1 is prepared with spin down and electron 2 with spin up, the total angular momentum is also zero. This is called the singlet state.
Quantum theory describes the two electrons as in a superposition of spin up ( + ) and
 ψ > = 1/√2)  +  >  1/√2)   + >
The principles of quantum mechanics say that the prepared system is in a linear combination (or superposition) of these two states, and can provide only the probabilities of finding the entangled system in either the +  state or the  + state. Quantum mechanics does not describe the paths or the spins of the individual particles. Note that should measurements result in + + or   state, that would violate the conservation of angular momentum.
EPR tests can be done more easily with polarized photons than with electrons, which require complex magnetic fields. The first of these was done in 1972 by Stuart Freedman and John Clauser at UC Berkeley. They used oppositely polarized photons (one with spin = +1, the other For more on superposition of states and the physics of photons, see the Dirac 3polarizers experiment. John Clauser, Michael Horne, Abner Shimony, and Richard Holt (known collectively as CHSH) and later Alain Aspect did more sophisticated tests. The outputs of the polarization analyzers were fed to a coincidence detector that records the instantaneous measurements, described as + ,  +, + +, and   . The first two ( +  and  + ) conserve the spin angular momentum and are the only types ever observed in these nonlocality/entanglement tests.
With the exception of some of Holt's early results that were found to be erroneous, no evidence has so far been found of any failure of standard quantum mechanics. And as experimental accuracy has improved by orders of magnitude, quantum physics has correspondingly been confirmed to one part in 10^{18}, and the speed of the probability information transfer between particles has a lower limit of 10^{6} times the speed of light. There has been no evidence for local "hidden variables." Nevertheless, experimenters continue to look for possible "loopholes" in the experimental results, such as detector inefficiencies that might be hiding results favorable to Einstein's picture of "local reality." Nicolas Gisin and his colleagues have extended the polarized photon tests of EPR and the Bell inequalities to a separation of 18 kilometers near Geneva. They continue to find 100% correlation and no evidence of the "hidden variables" sought after by Einstein and David Bohm.
An interesting use of the special theory of relativity was proposed by Gisin's colleagues, Antoine Suarez and Valerio Scarani. They use the idea of hyperplanes of simultaneity. Back in the 1960's, C. W. Rietdijk and Hilary Putnam argued that physical determinism could be proved to be true by considering the experiments and observers A and B in the above diagram to be moving at high speed with respect to one another. Roger Penrose developed a similar argument in his book The Emperor's New Mind. He called it the Andromeda Paradox. Suarez and Scarani showed that for some relative speeds between the two observers A and B, observer A could "see" the measurement of observer B to be in his future, and vice versa. Because the two experiments have a "spacelike" separation (neither is inside the causal light cone of the other), each observer thinks he does his own measurement before the other. Gisin tested the limits on this effect by moving mirrors in the path to the birefringent crystals and showed that, like all other Bell experiments, the "beforebefore" suggestion of Suarez and Scarani did nothing to invalidate quantum mechanics. These experiments were able to put a lower limit on the speed with which the information about probabilities collapses, estimating it as at least thousands  perhaps millions  of times the speed of light and showed empirically that probability collapses are essentially instantaneous. Despite all his experimental tests verifying quantum physics, including the "reality" of nonlocality and entanglement, Gisin continues to explore the EPR paradox, considering the possibility that signals are coming to the entangled particles from "outside spacetime."
How Information Physics Explains Nonlocality, Nonseparability, and Entanglement
Information physics starts with the fact that measurements bring new stable information into existence. In EPR the information in the prepared state of the two particles includes the fact that the total linear momentum and the total angular momentum are zero.
New information requires an irreversible process that also increases the entropy more than enough to compensate for the information increase, to satisfy the second law of thermodynamics. It is this moment of irreversibility and the creation of new observable information that is the "cut" or Schnitt" described by Werner Heisenberg and John von Neumann in the famous problem of measurement Note that the new observable information does not require a "conscious observer" as Eugene Wigner and some other scientists thought. The information is ontological (really in the world) and not merely epistemic (in the mind). Without new information, there would be nothing for the observers to observe. Initially Prepared Information Plus Conservation Laws
Conservation laws are the consequence of extremely deep properties of nature that arise from simple considerations of symmetry. We regard these laws as "cosmological principles." Physical laws do not depend on the absolute place and time of experiments, nor their particular direction in space. Conservation of linear momentum depends on the translation invariance of physical systems, conservation of energy the independence of time, and conservation of angular momentum the invariance under rotations. Recall that the EPR experiment starts with two electrons (or photons) prepared in an entangled state that is a mixture of pure twoparticle states, each of which conserves the total angular momentum and, of course, conserves the linear momentum as in Einstein's original EPR example. This information about the linear and angular momenta is established by the initial state preparation (a measurement). Quantum mechanics describes the probability amplitude wave function ψ of the twoparticle system as in a superposition of twoparticle states. It is not a product of singleparticle states, and there is no information about the identical indistinguishable electrons traveling along distinguishable paths.
 ψ > = 1/√2)  +  > + 1/√2)   + > (1)
The probability amplitude wave function ψ travels from the source (at the speed of light or less). Let's assume that at t_{0} observer A finds an electron (e_{1}) with spin up. At the time of the "first" measurement, new information comes into existence telling us that the wave function ψ has "collapsed" into the state  +  >. Just as in the twoslit experiment, probabilities have now become certainties. If the first measurement finds electron 1 is spin up, so the entangled electron 2 must be spin down to conserve angular momentum. And conservation of linear momentum tells us that at t_{0} the second electron is equidistant from the source in the opposite direction.
Unlike the twoslit experiment, where the collapse goes to a specific point in 3dimensional configuration space, the "collapse" here is a "jump" or "projection" into one of the two possible 6dimensional twoparticle quantum states  +  > or   + >. This makes "visualization" (Schrödinger's Anschaulichkeit) difficult or impossible, but the parallel with the collapse in the twoslit case provides an intuitive insight of sorts. If the measurement finds an electron (call it electron 1) as spinup, then at that moment of new information creation, the twoparticle wave function collapses to the state  +  > and electron 2 "jumps" into a spindown state with probability unity (certainty). The results of observer B's measurement at a later time t_{1} is therefore determined to be spin down. Notice that Einstein's intuition that the result seems already "determined" or "fixed" before the second measurement is in fact correct. The result is determined by the law of conservation of momentum.
But as with the distinction between determinism and predeterminism in the freewill debates, the measurement by observer B was not predetermined before observer A's measurement.
Why do so few accounts of entanglement mention conservation laws?
Although Einstein mentioned conservation in the original EPR paper, it is noticeably absent from later work. A prominent exception is Eugene Wigner, writing on the problem of measurement in 1963:
If a measurement of the momentum of one of the particles is carried out — the possibility of this is never questioned — and gives the result p, the state vector of the other particle suddenly becomes a (slightly damped) plane wave with the momentum p. This statement is synonymous with the statement that a measurement of the momentum of the second particle would give the result p, as follows from the conservation law for linear momentum. The same conclusion can be arrived at also by a formal calculation of the possible results of a joint measurement of the momenta of the two particles.
Visualizing Entanglement and Nonlocality
Schrödinger said that his "Wave Mechanics" provided more "visualizability" (Anschaulichkeit) than the Copenhagen school and its "damned quantum jumps" as he called them. He was right.
But we must focus on the probability amplitude wave function of the prepared twoparticle state, and not attempt to describe the paths or locations of independent particles  at least until after some measurement has been made. We must also keep in mind the conservation laws that Einstein used to discover nonlocal behavior in the first place. Then we can see that the "mystery" of nonlocality is primarily the same mystery as the singleparticle collapse of the wave function. As Richard Feynman said, there is only one mystery in quantum mechanics (the collapse of probability and the consequent statistical outcomes). We choose to examine a phenomenon which is impossible, absolutely impossible, to explain in any classical way, and which has in it the heart of quantum mechanics. In reality, it contains the only mystery. We cannot make the mystery go away by "explaining" how it works. We will just tell you how it works. In telling you how it works we will have told you about the basic peculiarities of all quantum mechanics. In his 1935 paper, Schrödinger described the two particles in EPR as "entangled" in English, and verschränkt in German, which means something like crosslinked. It describes someone standing with arms crossed. In the time evolution of an entangled twoparticle state according to the Schrödinger equation, we can visualize it  as we visualize the singleparticle wave function  as collapsing when a measurement is made. The discontinuous "jump" is also described as the "reduction of the wave packet." This is apt in the twoparticle case, where the superposition of  +  > and   + > states is "projected" or "reduced: to one of these states, and then further reduced to the product of independent oneparticle states  + > and   >. In the twoparticle case (instead of just one particle making an appearance), when either particle is measured we know instantly those properties of the other particle that satisfy the conservation laws, including its location equidistant from, but on the opposite side of, the source, and its other properties such as spin.
Compare the collapse of the twoparticle probability amplitude above to the singleparticle collapse here. We can enhance our visualization of what might be happening between the time two entangled electrons are emitted with opposite spins and the time one or both electrons are detected. Quantum mechanics describes the state of the two electrons as in a linear combination of  +  > and   + > states. We can visualize the electron moving left to be both spin up  + > and spin down   >. And the electron moving right would be both spin down   > and spin up  + >. We could require that when the left electron is spin up  + >, the right electron must be spin down   >, so that total spin is always conserved. Consider this possible animation of the experiment, which illustrates the assumption that each electron is in a linear combination of up and down spin. It imitates the superposition (or linear combination) with up and down arrows on each electron oscillating quickly. Notice that if you move the animation frame by frame by dragging the dot in the timeline, you will see that total spin = 0 is conserved. When one electron is spin up the other is always spin down.
Since quantum mechanics says we cannot know the spin until it is measured, our best estimate is a 50/50 probability between up and down. This is the same as assuming Schrödinger's Cat is 50/50 alive and dead. But what this means of course is simply that if we do a large number of identical experiments, the statistics for live and dead cats will be approximately 50/50%. We never observe/measure a cat that is both dead and alive! As Einstein noted, QM tells us nothing about individual cats. Quantum mechanics is incomplete in this respect. He is correct, although Bohr and Heisenberg insisted QM is complete, because we cannot know more before we measure, and reality is created (they say) when we do measure. Despite accepting that a particular value of an "observable" can only be known by a measurement (knowledge is an epistemological problem, Einstein asked whether the particle actually (really, ontologically) has a path and position before we measure it? His answer was yes. Here is an animation that illustrates the assumption that the two electrons are randomly produced in a spinup and a spindown state, and that they remain in those states no matter how far they separate, provided neither interacts until the measurement. Any interaction does what is described as decohering the two states.
How Mysterious Is Entanglement?
Some commentators say that nonlocality and entanglement are a "second revolution" in quantum mechanics, "the greatest mystery in physics," or "science's strangest phenomenon," and that quantum physics has been "reborn." They usually quote Erwin Schrödinger as saying
"I consider [entanglement] not as one, but as the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought."Schrödinger knew that his twoparticle wave function could not have the same simple interpretation as the single particle, which can be visualized in ordinary 3dimensional configuration space. And he is right that entanglement exhibits a richer form of the "actionatadistance" and nonlocality that Einstein had already identified in the "collapse" of the single particle wave function. But the main difference is that two particles acquire new properties instead of one, and they do it instantaneously (at faster than light speeds), just as in the case of a singleparticle measurement. Nonlocality and entanglement are thus another manifestation of Richard Feynman's "only" mystery. In both singleparticle and twoparticle cases paradoxes appear only when we attempt to describe independent particles following a path to measurement by observer A (and/or observer B).
How Information Philosophy Explains Entanglement
Here we must explain the asymmetry that Einstein and Schrödinger have mistakenly introduced into a perfectly symmetric situation, making entanglement such a mystery. Every follower of their early thinking introduces this false asymmetry.
The classic EPR idea is completely symmetric about the origin of the state preparation. Einstein introduced the mistaken idea of measuring one particle "first" and then asking how it influences subsequent measurements of the "second" particle. Schrödinger's twoparticle wave function "collapses" at all positions in an instant of time. Both particles then appear in a disentangled spacelike separation. Is it remotely possible that Einstein deliberately added an asymmetry to a problem that he surely knew is symmetric, in order to get physicists thinking more seriously about the questions he had been raising for decades, with no one ever taking them, or him, seriously? The perfectly symmetric picture shows that neither Alice nor Bob can in any way influence the other's experiment, as can be seen best in what we can call a special frame. There is a special frame in which the collapse of the twoparticle wave function is best visualized. It is not a preferred frame in the special relativistic sense. But observers in all other inertial frames in relative motion along the experiment axis will see one of the measurements before the other. Relativity contributes confusion to what is going on. Almost every presentation of the EPR paradox begins with something like "Alice observes one particle..." and concludes with the question "How does the second particle get the information needed so that Bob's measurements correlate perfectly with Alice?" There is a fundamental asymmetry in this framing of the EPR experiment. It is a surprise that Einstein, who was so good at seeing deep symmetries, did not consider how to remove the asymmetry. Even more puzzling, why did he introduce it? Why do most all subsequent scientists accept it without question? Consider this reframing: Alice's measurement collapses the twoparticle wave function. The two indistinguishable particles simultaneously appear at locations in a spacelike separation. The frame of reference in which the source of the two entangled particles and the two experimenters are at rest is a special frame in the following sense. As Einstein knew very well, there are frames of reference moving with respect to the laboratory frame of the two observers in which the time order of the events can be reversed. In some moving frames Alice measures first, but in others Bob measures first. If there is a special frame of reference (not a preferred frame in the relativistic sense), surely it is the one in which the origin of the two entangled particles is at rest. Assuming that Alice and Bob are also at rest in this special frame and equidistant from the origin, we arrive at the simple picture in which any measurement that causes the twoparticle wave function to collapse makes both particles appear simultaneously at determinate places with fully correlated properties (just those that are needed to conserve energy, momentum, angular momentum, and spin).
In the twoparticle case (instead of just one particle making an appearance), when either particle is measured, we know instantly those properties of the other particle that satisfy the conservation laws, including its location equidistant from, but on the opposite side of, the source, and its other properties such as spin. It's just "knowledgeatadistance."
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