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Nonlocality
Nonlocality is today strongly associated with the idea of entanglement, but nonlocality is a property of a
Nonlocality is an essential element of the dual nature of light as both a wave and a particle. We can
When an electron is freely traveling (as opposed to an electron bound in an atom), or when a photon is emitted from an electron and is traveling though space, there are always many possible locations for an interaction. Therefore we can say that the "possibilities function" (or the more formal quantum wave function) is inherently and intuitively
Since Werner Heisenberg and Paul Dirac first discussed the "collapse" of the wave function (Dirac's
Scattering is better understood as the absorption and rapid
In the case of the photon, it is localized when it has been scattered or absorbed by an electron. In the case of an electron, it might be a collision with another particle, or recombining with an ion to become bound in an atom. The electron is actually never found at a single point in four-dimensional space time, but remains nonlocal inside the minimal phase-space volume re-emission of a photon, as pointed out by Einstein and Paul Ehrenfest in 1933, in response to an article by Wolfgang Pauli h required by the uncertainty principle (for example, a particular electron orbital wave function). Thus some physicists like to say there are no particles, just the ^{3}appearance of a particle.
Albert Einstein was first to have seen single-particle nonlocality, in 1905, when he tried to understand how a spherical wave of light that goes off in many directions can be wholly absorbed at a single location. In his famous paper on the photo-electric effect (for which Einstein was awarded the Nobel Prize), he hypothesized that light must transmitted from one place to another as a discrete quantum of energy.
Einstein did not then use the term nonlocal or "local reality," but we can trace his thoughts backwards from 1935 to see that quantum nonlocality (and later nonseparability) were always major concerns, because neither can be made consistent with a continuous Einstein clearly described wave-particle duality as early as 1909, over a dozen years before the duality was made famous by Louis de Broglie's thesis showed that material particles also have a wavelike property. When Einstein finished his great project of general relativity in 1916, he turned his attention back to light quanta and showed how electrons in atoms emit and absorb radiation. He found the process of emission was probabilistic (statistical). It is impossible to predict the time and the direction of the emission of a quantum of light, he said, just as Rutherford had shown the decay of a radioactive nucleus was statistical. The time and direction of an alpha particle ejected from a nucleus is pure chance.
Einstein said it was a "weakness" that the quantum theory was based on chance (
Let's review Einstein's thinking on nonlocality, starting with his presentation at the fifth Solvay conference. Bohr and Heisenberg tell the story of Einstein at that conference repeatedly attempting to refute the uncertainty principle and perhaps restore deterministic physics. But the fragments that remain of what Einstein said on nonlocality indicate a much deeper criticism of quantum mechanics. Einstein's nonlocality remarks were not a formal presentation and were not reported in the conference proceedings. We know them only from brief notes on the general discussion and from what others said that Einstein said. And here are the notes on Einstein's original remarks from the conference. They contain much of his 1935 EPR paper, except in 1927 only one particle is considered. Entanglement in EPR requires two identical particles.
Bohr's reaction to Einstein's presentation has been preserved. He didn't understand a word! He disingenuously claims he does not know what quantum mechanics is. His response is vague and ends with his vague ideas on complementarity and the inability to describe a causal spacetime reality.
Twenty-two years later, in his contribution to the Schilpp memorial volume on Einstein, Bohr had no better response to Einstein's 1927 concerns. But he does remember and provides a picture of what Einstein drew on the blackboard. Here is Bohr's 1949 recollection:
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." Although Bohr seems to have missed Einstein's point completely, Werner Heisenberg at least came to understand it very well. In his 1930 lectures at the University of Chicago, Heisenberg presented a critique of both particle and wave pictures, including a new example of nonlocality that Einstein had apparently developed since 1927. He wrote: In relation to these considerations, one other idealized experiment (due to Einstein) may be considered. We imagine a photon which is represented by a wave packet built up out of Maxwell waves. It will thus have a certain spatial extension and also a certain range of frequency. By reflection at a semi-transparent mirror, it is possible to decompose it into two parts, a reflected and a transmitted packet. There is then a definite probability for finding the photon either in one part or in the other part of the divided wave packet. After a sufficient time the two parts will be separated by any distance desired; now if an experiment yields the result that the photon is, say, in the reflected part of the packet, then the probability of finding the photon in the other part of the packet immediately becomes zero. The experiment at the position of the reflected packet thus exerts a kind of action (reduction of the wave packet) at the distant point occupied by the transmitted packet, and one sees that this action is propagated with a velocity greater than that of light. However, it is also obvious that this kind of action can never be utilized for the transmission of signals so that it is not in conflict with the postulates of the theory of relativity. Working backwards in time to Einstein's 1905 insight into nonlocality, we now review his amazing arguments about wave-particle duality in 1909.
Einstein greatly expanded his light-quantum hypothesis in a presentation at the Salzburg conference in September, 1909. He argued that the interaction of radiation and matter involved elementary processes that are not Although he could not formulate a mathematical theory that does justice to both the oscillatory and quantum structures - the wave and particle pictures, Einstein argued that they are compatible. This was almost fifteen years before wave mechanics and quantum mechanics. And because gases behave statistically, he knows that the connection between wave and particles may involve probabilistic behavior, which he will prove in 1916. Here he is in 1909:
When light was shown to exhibit interference and diffraction, it seemed almost certain that light should be considered a wave. Now, back to 1905. Einstein's three 1905 papers on relativity, Brownian motion, and the light-quantum hypothesis (mischaracterized by many historians as the photo-electric effect), not only quantize the radiation field (Planck had only quantized matter, the virtual oscillators), but they also show on a careful reading that Einstein was concerned about faster-than-light actions thirty years before his Einstein-Podolsky-Rosen paper popularized the mysteries and paradoxes of quantum nonlocality and entanglement.
Despite his foundational work quantizing radiation, Einstein rarely gets any credit for his contributions. There are a number of important reasons for this, which lead historians of quantum theory to start with Planck's quantum of action, then jump over Einstein's 1905 papers and his 1909 work on wave-particle duality to Niels Bohr's "old quantum theory" of the atom in 1913. Today, Bohr's "quantum jump" of an electron between stationary states is described as emitting or absorbing a "photon" of energy
Besides quantizing energy and seeing the interchangeability of radiation and matter, appearance of) instantaneous action-at-a-distance (1905), wave-particle duality (1909), statistical elementary processes that introduce indeterminism and acausality whenever matter and radiation interact (1916-17), coherence, interference, and the indistinguishability of elementary particles (1925), and the nonseparability and entanglement of interacting particles (1935).
Ironically, and even tragically, Einstein could never accept most of his quantum discoveries, because they conflicted with his basic idea that nature is best described by a continuous field theory using differential equations that are functions of "local" variables, primarily the space-time four-vector of his general relativistic theory. Einstein's idea of a "local" reality is one where "action-at-a-distance" is limited to causal effects that propagate at or below the speed of light, according to his theory of relativity. He also famously disliked indeterminism ("God does not play dice"). Einstein's believed that quantum theory, as good as it is (and he saw nothing better), is "incomplete" because its statistical predictions (phenomenally accurate in the limit of large numbers of identical experiments - "ensembles" Einstein called them), tell us nothing about individual systems. Even worse, he thought that the wave functions of entangled systems predict faster-than-light correlations of properties between events in a space-like separation, violating his theory of relativity. This was the heart of his famous EPR paradox paper in 1935 (which introduced the concept of nonseparability), but we shall now see that Einstein was already concerned about faster-than-light transfer of energy in his very first paper on quantum theory.
The light-quantum hypothesis (1905)
Summary
We have shown that ever since Einstein hypothesized that light consists of small quanta of energy, he was concerned about a conflict with the picture of light as a wave. He saw that in many places distant from the point in space and time where the quantum actually appears as a detected particle, at that instant or a moment before, there existed the possibility (or probability) that the particle might have appeared somewhere else, somewhere separated in space so far as to prohibit signals from the detected quantum to that distant point where the particle did not appear.
How, he asked, or what sort of "action-at-a-distance" suppressed some sort of action happening at one of those other places where the probability of appearance had been non-zero? While Einstein is vague about the action that he has in mind, it is at least the disappearance, the sudden going to zero, of that probability. He cannot be imagining a second appearance of a particle. That would violate conservation of energy. He may be thinking of the interpretation of the wave function as representing some kind of knowledge about where the associated particle is likely to be found. How does that "knowledge" at the distant point or possible points "learn" that the particle will not in fact be appearing there? Why does Einstein think that anything is needed beyond the fact that in this particular experiment, it appeared where it did and nowhere else? something substantial = information For Heisenberg - knowledge Normal | Teacher | Scholar |