Einstein-Podolsky-RosenLike the Schrödinger's Cat paradox, the 1935 thought experiment proposed by Albert Einstein, Boris Podolsky, and Nathan Rosen (and known by their initials as EPR), was originally proposed 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. Einstein was correct that quantum theory is "incomplete" relative to classical physics, which has twice as many dynamical variables that can be known with arbitrary precision. The indeterminacy principle allows only one of each pair of non-commuting observables (for example momentum or position) to be known accurately. He and his colleagues Erwin Schrödinger, Max Planck, and David Bohm, hoped for a return to deterministic physics, and the elimination of mysterious phenomena like the superposition of states and the "collapse" of the wave function. EPR continues to fascinate determinist philosophers of science who hope to prove that quantum indeterminacy does not exist. Einstein was also correct that indeterminacy makes quantum theory a statistical theory. Its predictions and highly accurate experimental results depend on an ensemble of identical experiments, not on any individual experiment. Einstein wanted physics to be a field theory, in which all physical variables are completely determined by the four-dimensional field of space-time in his theory of relativity. In his autobiography, fifteen years after EPR, Einstein explained his problem in very simple terms "Does a particle have a position in the moments just before it is measured?" If not, the quantum theory is incomplete. Since quantum theory says the particle may have a number of possible positions, with calculable probabilities, it is not only an incomplete theory, it is a theory with alternative possibilities. In the "block universe" of Einstein's field theory, there is only one actual past, with determinate positions for a particle at all past times. Einstein's theory is causal. Quantum theory is acausal. But Einstein was also bothered by what is now known as "nonlocality." This mysterious phenomenon exhibited in EPR experiments is the apparent transfer of something physical faster than the speed of light. What happens actually is merely an instantaneous change in the information about probabilities (actually complex probability amplitudes). 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 - after the measurements - 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 EPR "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.
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.
How Information Physics Helps To "Explain" EPR NonlocalityInformation 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 LawsConservation 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.
Animation of supraluminal information transfer - click to restart
It was simply determined by her measurement.
Why do so few accounts of EPR 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 NonlocalitySchrödinger 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). The only difference in two-particle entanglement and nonlocality is that two particles appear simultaneously (in their original interaction frame) when their wave function collapses.
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.
Animation of a two-particle wave function collapsing - click to restart
"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 distinguishable particles following separate paths to measurement by observer A (and/or observer B).
EPR "Loopholes" and Free WillInvestigators 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". Indeterminism works primarily to block pre-determinism. Without indeterminism, no new information could be created in the universe.