Philosophers
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. Bernstein Bernard Berofsky Robert Bishop Max Black Susanne Bobzien Emil du BoisReymond Hilary Bok Laurence BonJour George Boole Émile Boutroux F.H.Bradley C.D.Broad Michael Burke C.A.Campbell Joseph Keim Campbell Rudolf Carnap Carneades Ernst Cassirer David Chalmers Roderick Chisholm Chrysippus Cicero Randolph Clarke Samuel Clarke Anthony Collins Antonella Corradini Diodorus Cronus Jonathan Dancy Donald Davidson Mario De Caro Democritus Daniel Dennett Jacques Derrida René Descartes Richard Double Fred Dretske John Dupré John Earman Laura Waddell Ekstrom Epictetus Epicurus Herbert Feigl John Martin Fischer Owen Flanagan Luciano Floridi Philippa Foot Alfred Fouilleé Harry Frankfurt Richard L. Franklin Michael Frede Gottlob Frege Peter Geach Edmund Gettier Carl Ginet Alvin Goldman Gorgias Nicholas St. John Green H.Paul Grice Ian Hacking Ishtiyaque Haji Stuart Hampshire W.F.R.Hardie Sam Harris William Hasker R.M.Hare Georg W.F. 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Willard Gibbs Nicolas Gisin Paul Glimcher Thomas Gold A.O.Gomes Brian Goodwin Joshua Greene Jacques Hadamard Patrick Haggard Stuart Hameroff Augustin Hamon Sam Harris Hyman Hartman JohnDylan Haynes Donald Hebb Martin Heisenberg Werner Heisenberg John Herschel Art Hobson Jesper Hoffmeyer E. T. Jaynes William Stanley Jevons Roman Jakobson Pascual Jordan Ruth E. Kastner Stuart Kauffman Martin J. 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Dieter Zeh Ernst Zermelo Wojciech Zurek Fritz Zwicky Presentations Biosemiotics Free Will Mental Causation James Symposium 
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. Entanglement depends on two quantum properties that are simply impossible in "classical" physics. One is called nonlocality. The other is nonseparability. 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 the minds of physicists are manipulating "quantum reality," that there is nothing "really" there until we look at it, 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.
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. After 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 just 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).
EPR "Loopholes" and Free Will
Investigators who try to recover the "elements of local reality" that Einstein wanted, and who hope to eliminate the irreducible randomness of quantum mechanics that follows from wave functions as probability amplitudes, often cite "loopholes" in EPR experiments. For example, the "detection loophole" claims that the efficiency of detectors is so low that they are missing many events that might prove Einstein was right.
Most all the loopholes have now been closed, but there is one loophole that can never be closed because of its metaphysical/philosophical nature. That is the "(pre)determinism loophole." If every event occurs for reasons that were established at the beginning of the universe, then all the careful experimental results are meaningless. John Conway and Simon Kochen have formalized this loophole in what they call the Free Will Theorem. Although Conway and Kochen do not claim to have proven free will in humans, they assert that should such a freedom exist, then the same freedom must apply to the elementary particles. What Conway and Kochen are really describing is the indeterminism that quantum mechanics has introduced into the world. Although indeterminism is a requirement for human freedom, it is insufficient by itself to provide both "free" and "will". Philosophers and scientists (Roger Penrose, for example) have speculated that nonlocality might be involved in consciousness.
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