NonlocalityNonlocality is today strongly associated with the idea of entanglement, but nonlocality is a property of a single quantum of light, whereas entanglement is a joint property of two quantum particles, depending on an even more subtle property called nonseparability. Nonlocality is an essential element of the dual nature of light as both a wave and a particle. We can visualize the wave function of quantum mechanics in the following way. The wave function is a probability amplitude ψ whose squared modulus | ψ |2 gives the probability of finding a particle in a particular (sic) location. As this function spreads out in space, we can think of it as a "possibilities function," showing all the locations in space where there is a non-zero probability of finding a particle. The power of quantum mechanics is that we can calculate the probability of finding the particle for each possibility. 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 nonlocal! Since Werner Heisenberg and Paul Dirac first discussed the "collapse" of the wave function (Dirac's projection postulate), it has been appropriate to say that "one of the many possibilities has been made actual." In the language of nonlocality, we can now even more clearly say that one of the nonlocal possibilities has been actualized or localized! 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 h3 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 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 field theory and they may be inconsistent with the principle of relativity. 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 (Zufall in German). His 1916 work on the emission and absorption of light quanta (later called photons) predicted the amazing phenomenon of stimulated emission of radiation, which led to the development of the laser many decades later. As hard as it is to believe, most physicists, and especially Niels Bohr, refused to accept Einstein's theory of light quanta for another decade.
MR ElNSTEIN. - Despite being conscious of the fact that I have not entered deeply enough into the essence of quantum mechanics, nevertheless I want to present here some general remarks. One can take two positions towards the theory with respect to its postulated domain of validity, which I wish to characterise with the aid of a simple example. Let S be a screen provided with a small opening O (Fig. 2), and P a hemispherical photographic film of large radius. Electrons impinge on S in the direction of the arrows. Some of these go through O, and because of the smallness of O and the speed of the particles, are dispersed uniformly over the directions of the hemisphere, and act on the film. Both ways of conceiving the theory now have the following in common. There are de Broglie waves, which impinge approximately normally on S and are diffracted at O. Behind S there are spherical waves, which reach the screen P and whose intensity at P is responsible [massgebend] for what happens at P. We can now characterise the two points of view as follows.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.According to the first, purely statistical, point of view | ψ |2 expresses the probability that there exists at the point considered a particular particle of the cloud, for example at a given point on the screen. 1. Conception I. - The de Broglie-Schrödinger waves do not correspond to a single electron, but to a cloud of electrons extended in space. The theory gives no information about individual processes, but only about the ensemble of an infinity of elementary processes. 2. Conception II. - The theory claims to be a complete theory of individual processes. Each particle directed towards the screen, as far as can be determined by its position and speed, is described by a packet of de Broglie-Schrödinger waves of short wavelength and small angular width. This wave packet is diffracted and, after diffraction, partly reaches the film P in a state of resolution [un etat de resolution]. According to the second, | ψ |2 expresses the probability that at a given instant the same particle is present at a given point (for example on the screen). Here, the theory refers to an individual process and claims to describe everything that is governed by laws. The second conception goes further than the first, in the sense that all the information resulting from I results also from the theory by virtue of II, but the converse is not true. It is only by virtue of II that the theory contains the consequence that the conservation laws are valid for the elementary process; it is only from II that the theory can derive the result of the experiment of Geiger and Bothe, and can explain the fact that in the Wilson [cloud] chamber the droplets stemming from an α-particle are situated very nearly on continuous lines. But on the other hand, I have objections to make to conception II. The scattered wave directed towards P does not show any privileged direction. If | ψ |2 were simply regarded as the probability that at a certain point a given particle is found at a given time, it could happen that the same elementary process produces an action in two or several places on the screen. But the interpretation, according to which | ψ |2 expresses the probability that this particle is found at a given point, assumes an entirely peculiar mechanism of action at a distance, which prevents the wave continuously distributed in space from producing an action in two places on the screen. In my opinion, one can remove this objection only in the following way, that one does not describe the process solely by the Schrödinger wave, but that at the same time one localises the particle during the propagation. I think that Mr de Broglie is right to search in this direction. If one works solely with the Schrödinger waves, interpretation II of
Twenty-two years later, in his contribution to the MR BOHR. I feel myself in a very difficult position because I don't understand what precisely is the point which Einstein wants to [make]. No doubt it is my fault. As regards general problem I feel its difficulties. I would put [the] problem in [an]other way. I do not know what quantum mechanics is. I think we are dealing with some mathematical methods which are adequate for description of our experiments Using a rigorous wave theory we are claiming something which the theory cannot possibly give. [We must realise] that we are away from that state where we could hope of describing things on classical theories. [I] Understand [the] same view is held by Born and Heisenberg. I think that we actually just try to meet, as in all other theories, some requirements of nature, but [the} difficulty is that we must use words which remind [us] of older theories. The whole foundation for causal spacetime description is taken away by quantum theory, for it is based on [the] assumption of observations without interference. ... excluding interference means exclusion of experiment and the whole meaning of space and time observation ... because we [have] interaction [between object and measuring instrument] and thereby we put us on a quite different standpoint than we thought we could take in classical theories. If we speak of observations we play with a statistical problem There are certain features complementary to the wave pictures (existence of individuals). ... The saying that spacetime is an abstraction might seem a philosophical triviality but nature reminds us that we are dealing with something of practical interest. Depends on how I consider theory. I may not have understood, but I think the whole thing lies [therein that the] theory is nothing else [but] a tool for meeting our requirements and I think it does. 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." 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.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 reversible, a deep insight into the irreversibility of natural processes. While incoming spherical waves of radiation are mathematically possible, they are not practically achievable. Nature appears to be asymmetric in time. He speculates that the continuous electromagnetic field might be made up of large numbers of light quanta - singular points in the field that superimpose to create the wavelike behavior. 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. The greatest advance in theoretical optics since the introduction of the oscillation theory was Maxwell's brilliant discovery that light can be understood as an electromagnetic process...One became used to treating electric and magnetic fields as fundamental concepts that did not require a mechanical interpretation. This path leads to the so-called relativity theory. I only wish to bring in one of its consequences, for it brings with it certain modifications of the fundamental ideas of physics. It turns out that the inertial mass of an object decreases by L / c2 when that object emits radiation of energy L...the inertial mass of an object is diminished by the emission of light.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 The energy given up was part of the mass of the object. One can further conclude that every absorption or release of energy brings with it an increase or decrease in the mass of the object under consideration. Energy and mass seem to be just as equivalent as heat and mechanical energy. Relativity theory has changed our views on light. Light is conceived not as a manifestation of the state of some hypothetical medium, but rather as an independent entity like matter. Moreover, this theory shares with the corpuscular theory of light the unusual property that light carries inertial mass from the emitting to the absorbing object. Relativity theory does not alter our conception of radiation's structure; in particular, it does not affect the distribution of energy in radiation-filled space. Nevertheless, with respect to this question, I believe that we stand at the beginning of a development of the greatest importance that cannot yet be surveyed. The statements that follow are largely my personal opinion, or the results of considerations that have not yet been checked enough by others. If I present them here in spite of their uncertainty, the reason is not an excessive faith in my own views, but rather the hope to induce one or another of you to deal with the questions considered. In the kinetic theory of molecules, for every process in which only a few elementary particles participate (e.g., molecular collisions), the inverse process also exists. But that is not the case for the elementary processes of radiation. According to our prevailing theory, an oscillating ion generates a spherical wave that propagates outwards. The inverse process does not exist as an elementary process. A converging spherical wave is mathematically possible, to be sure; but to approach its realization requires a vast number of emitting entities. The elementary process of emission is not invertible. In this, I believe, our oscillation theory does not hit the mark. Newton's emission theory of light seems to contain more truth with respect to this point than the oscillation theory since, first of all, the energy given to a light particle is not scattered over infinite space, but remains available for an elementary process of absorption. Consider the laws governing the production of secondary cathode radiation by X-rays. If primary cathode rays impinge on a metal plate P1, they produce X-rays. If these X-rays impinge on a second metal plate P2, cathode rays are again produced whose speed is of the same order as that of the primary cathode rays. 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 hν. In actuality, Bohr fought against Einstein's light-quantum hypothesis until the mid-1920's. Besides quantizing energy and seeing the interchangeability of radiation and matter, E = mc2, Einstein was the first scientist to see many of the most fundamental aspects of quantum physics, e.g., nonlocality and 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)
The energy of a ponderable body cannot be subdivided into arbitrarily many or arbitrarily small parts, while the energy of a beam of light from a point source (according to the Maxwellian theory of light or, more generally, according to any wave theory) is continuously spread over an ever increasing volume. The wave theory of light, which operates with continuous spatial functions, has worked well in the representation of purely optical phenomena and will probably never be replaced by another theory. It should be kept in mind, however, that the optical observations refer to time averages rather than instantaneous values. In spite of the complete experimental confirmation of the theory as applied to diffraction, reflection, refraction, dispersion, etc., it is still conceivable that the theory of light which operates with continuous spatial functions may lead to contradictions with experience when it is applied to the phenomena of emission and transformation of light. It seems to me that the observations associated with blackbody radiation, fluorescence, the production of cathode rays by ultraviolet light, and other related phenomena connected with the emission or transformation of light are more readily understood if one assumes that the energy of light is discontinuously distributed in space. In accordance with the assumption to be considered here, the energy of a light ray spreading out from a point source is not continuously distributed over an increasing space but consists of a finite number of energy quanta which are localized at points in space, which move without dividing, and which can only be produced and absorbed as complete units. We therefore arrive at the conclusion: the greater the energy density and the wavelength of a radiation, the more useful do the theoretical principles we have employed turn out to be; for small wavelengths and small radiation densities, however, these principles fail us completely. [W]e further conclude that: Monochromatic radiation of low density (within the range of validity of Wien's radiation formula) behaves thermodynamically as though it consisted of a number of independent energy quanta. The usual conception, that the energy of light is continuously distributed over the space through which it propagates, encounters very serious difficulties when one attempts to explain the photoelectric phenomena, According to the concept that the incident light consists of energy quanta..., however, one can conceive of the ejection of electrons by light in the following way. Energy quanta penetrate into the surface layer of the body, and their energy is transformed, at least in part, into kinetic energy of electrons. The simplest way to imagine this is that a light quantum delivers its entire energy to a single electron; we shall assume that this is what happens.
SummaryWe 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