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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.

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."
Note that they wanted Einstein's reaction to their work, but actually took little interest in Einstein's concern about the nonlocal implications of quantum mechanics.
At the Solvay meetings, Einstein had from their beginning been a most prominent figure, and several of us came to the conference with great anticipations to learn his reaction to the latest stage of the development which, to our view, went far in clarifying the problems which he had himself from the outset elicited so ingeniously. During the discussions, where the whole subject was reviewed by contributions from many sides and where also the arguments mentioned in the preceding pages were again presented, Einstein expressed, however, a deep concern over the extent to which a causal account in space and time was abandoned in quantum mechanics.

To illustrate his attitude, Einstein referred at one of the sessions to the simple example, illustrated by Fig. 1, of a particle (electron or photon) penetrating through a hole or a narrow slit in a diaphragm placed at some distance before a photographic plate.

photon passes through a slit

On account of the diffraction of the wave connected with the motion of the particle and indicated in the figure by the thin lines, it is under such conditions not possible to predict with certainty at what point the electron will arrive at the photographic plate, but only to calculate the probability that, in an experiment, the electron will be found within any given region of the plate.

The "nonlocal" effects at point B are just the probability of an electron being found at point B going to zero instantly (as if an action at a distance) the moment an electron is localized at point A
The apparent difficulty, in this description, which Einstein felt so acutely, is the fact that, if in the experiment the electron is recorded at one point A of the plate, then it is out of the question of ever observing an effect of this electron at another point (B), although the laws of ordinary wave propagation offer no room for a correlation between two such events.

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 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 t0 some distance apart and approaching one another with high velocities. Then for a short time interval from t1 to t1 + Δt the particles are in contact with one another.

After the particles are measured at t1, quantum mechanics describes them with a single two-particle 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 t2, 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 "nonlocality" 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.

This idea of something measured in one place "influencing" measurements far away challenged what Einstein thought of as "local reality." It came to be known as "nonlocality." Einstein called it "spukhaft Fernwirkung" or "spooky action at a distance."

Einstein had objected to nonlocal phenomena as early as the Solvay Conference of 1927, when he criticized the collapse of the wave function as "instantaneous-action-at-a-distance" that prevents the wave from acting at more than one place on the screen."

Einstein's criticism 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 space-time.

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 "space-like" 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
spin down ( - ),

| 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
spin = -1) coming from a central source. Again, the total photon spin of zero is conserved. Their data, in agreement with quantum mechanics, violated the Bell's inequalities to high statistical accuracy, thus providing strong evidence against local hidden-variable theories.

For more on superposition of states and the physics of photons, see the Dirac 3-polarizers 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 1018, and the speed of the probability information transfer between particles has a lower limit of 106 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 "before-before" 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 space-time."

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 two-particle 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 two-particle system as in a superposition of two-particle states. It is not a product of single-particle 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 t0 observer A finds an electron (e1) 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 two-slit 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 t0 the second electron is equidistant from the source in the opposite direction.

As with any wave-function collapse, the probability amplitude information travels instantly.

Unlike the two-slit experiment, where the collapse goes to a specific point in 3-dimensional configuration space, the "collapse" here is a "jump" or "projection" into one of the two possible 6-dimensional two-particle quantum states | + - > or | - + >. This makes "visualization" (Schrödinger's Anschaulichkeit) difficult or impossible, but the parallel with the collapse in the two-slit case provides an intuitive insight of sorts.

If the measurement finds an electron (call it electron 1) as spin-up, then at that moment of new information creation, the two-particle wave function collapses to the state | + - > and electron 2 "jumps" into a spin-down state with probability unity (certainty). The results of observer B's measurement at a later time t1 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 pre-determinism in the free-will debates, the measurement by observer B was not pre-determined before observer A's measurement.
It was simply determined by her 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.

One can go even further: instead of measuring the linear momentum of one particle, one can measure its angular momentum about a fixed axis. If this measurement yields the value mℏ, the state vector of the other particle suddenly becomes a cylindrical wave for which the same component of the angular momentum is -mℏ. This statement is again synonymous with the statement that a measurement of the said component of the angular momentum of the second particle certainly would give the value -mℏ. This can be inferred again from the conservation law of the angular momentum (which is zero for the two particles together) or by means of a formal analysis. Hence, a "contraction of the wave packet" took place again.

It is also clear that it would be wrong, in the preceding example, to say that even before any measurement, the state was a mixture of plane waves of the two particles, traveling in opposite directions. For no such pair of plane waves would one expect the angular momenta to show the correlation just described. This is natural since plane waves are not cylindrical waves, or since [the state vector has] properties different from those of any mixture. The statistical correlations which are clearly postulated by quantum mechanics (and which can be shown also experimentally, for instance in the Bothe-Geiger experiment) demand in certain cases a "reduction of the state vector." The only possible question which can yet be asked is whether such a reduction must be postulated also when a measurement with a macroscopic apparatus is carried out. [Considerations] show that even this is true if the validity of quantum mechanics is admitted for all systems.

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 two-particle 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 single-particle 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 cross-linked. It describes someone standing with arms crossed.

In the time evolution of an entangled two-particle state according to the Schrödinger equation, we can visualize it - as we visualize the single-particle 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 two-particle 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 one-particle states.

In the two-particle 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 two-particle probability amplitude above to the single-particle collapse here.

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 two-particle wave function could not have the same simple interpretation as the single particle, which can be visualized in ordinary 3-dimensional configuration space. And he is right that entanglement exhibits a richer form of the "action-at-a-distance" 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 single-particle measurement.

Nonlocality and entanglement are thus just another manifestation of Feynman's "only" mystery. In both single-particle and two-particle 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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