The Physics Teacher ◆ Vol. 50, May 2012 DOI: 10.1119/1.3703540 are really two parts of a single black-and-green packet. Even if widely separated in space, they form a single unified field quantum. This is similar to a one-particle wave packet that is separated into two parts (e.g., a photon that has interacted with a half-reflecting mirror and is now a superposition of a wave packet that passed through the mirror and a packet that reflected from the mirror), but now there is a real excitation in each of the two parts. In classes for scientists or engineers, you could follow this qualitative description with an algebraic description.5 One popular entanglement method, used in the experiment described below, is called “spontaneous parametric down-conversion.” When photons pass through a certain kind of nonlinear crystal, a tiny fraction of them split into two photons of equal energy. It’s not understood why this occurs, but Leonard Mandel of the University of Rochester discovered that each pair of daughter photons is entangled. If one of the two entangled particles experiences a macroscopic interaction, for example by striking a viewing screen, that portion of the two-particle wave packet instantly collapses everywhere. According to quantum physics, this instantly affects the other particle, even if the two are light-years apart. Anton Zeilinger’s group has confirmed this effect at distances up to 144 kilometers.6 Alain Aspect’s group has confirmed that the second particle alters its state in response to an interaction of the first particle in a time shorter than is required for light to connect the two particles.7 It’s an irony of physics Teaching Quantum Nonlocality1
The Physics Teacher ◆ Vol. 50, May 2012 DOI: 10.1119/1.3703540 are really two parts of a single black-and-green packet. Even if widely separated in space, they form a single unified field quantum. This is similar to a one-particle wave packet that is separated into two parts (e.g., a photon that has interacted with a half-reflecting mirror and is now a superposition of a wave packet that passed through the mirror and a packet that reflected from the mirror), but now there is a real excitation in each of the two parts. In classes for scientists or engineers, you could follow this qualitative description with an algebraic description.5 One popular entanglement method, used in the experiment described below, is called “spontaneous parametric down-conversion.” When photons pass through a certain kind of nonlinear crystal, a tiny fraction of them split into two photons of equal energy. It’s not understood why this occurs, but Leonard Mandel of the University of Rochester discovered that each pair of daughter photons is entangled. If one of the two entangled particles experiences a macroscopic interaction, for example by striking a viewing screen, that portion of the two-particle wave packet instantly collapses everywhere. According to quantum physics, this instantly affects the other particle, even if the two are light-years apart. Anton Zeilinger’s group has confirmed this effect at distances up to 144 kilometers.6 Alain Aspect’s group has confirmed that the second particle alters its state in response to an interaction of the first particle in a time shorter than is required for light to connect the two particles.7 It’s an irony of physics Teaching Quantum Nonlocality1
Nonlocality arises from the unified “all or nothing” interactions of a spatially extended field quantum such as a photon or an electron.2 In the double-slit experiment with light, for example, each photon comes through both slits and arrives at the viewing screen as an extended but unified energy bundle or “field quantum.” When the photon interacts (randomly2) with the screen, field quantization requires it to alter its state instantaneously rather than gradually. Thus if the photon is absorbed, it must vanish or “collapse” nonlocally and instantaneously across a macroscopic portion of the screen, even across many kilometers in the case of interference patterns of light from a small distant star. The interaction instantly transfers the photons energy to a single atom of the screen. But a quantized field can contain any whole number of “excitations” (particles such as photons or electrons). If a single field quantum contains, say, two excitations, then generally the unified all-or-nothing character of quanta implies that any interaction of one excitation must also instantaneously affect the other excitation, regardless of the distance between them. The particles are then said to be “entangled” (see the “Background” section for a more precise definition of this term). Particles can become entangled by being created together in a single microscopic process, or by interacting with each other. Quantum entanglement is at least as fundamental as quantum uncertainty but is seldom mentioned in physics courses, although it has received broad attention recently in a wonderful book by Louisa Gilder.3 A recent paper in this journal presents entanglement in a manner that is useful for high school and college physics teachers.4 This paper builds on that presentation and looks at a different, more intuitive entanglement experiment that should be accessible to both scientists and nonscientists.
One-photon sources are important elements in quantum optics. The archetypal example is an atom raised to an excited state at time t = 0, then de-exciting with emission of a single photon. The development of this kind of source depends on progress with experimental techniques, e.g. the possibility of isolating a single atom, molecule or quantum well. In this complement, we present the formalism for describing the corresponding radiation, and use it to discuss some spectacular experiments which bring out properties quite incompatible with a classical description of the electromagnetic field. We begin in Section 5B.2 by describing the anti-correlation between detections on either side of a semi-reflecting mirror, establishing the quantitative difference with a classical field. Section 5B.3 discusses a quantum optical effect that was only demonstrated at the beginning of the twenty-first century, namely the quantum coalescence of two one-photon wave packets on a semi-reflecting mirror, which occurs even when the two photons were emitted by independent atoms. An analogous effect, the Hong–Hou–Mandel effect, is discussed in Chapter 7. These effects exemplify quantum interference involving two photons. Finally, Section 5B.4 is concerned with quantum calculations involving quasi-classical states. As we now know, this leads to results that are identical to the predictions of semi-classical theory.
An earlier paper2 introduces quantum physics by means of four experiments: Youngs double-slit interference experiment using (1) a light beam, (2) a low-intensity light beam with time-lapse photography, (3) an electron beam, and (4) a low-intensity electron beam with time-lapse photography. It's ironic that, although these experiments demonstrate most of the quantum fundamentals, conventional pedagogy stresses their difficult and paradoxical nature. These paradoxes (i.e., logical contradictions) vanish, and understanding becomes simpler, if one takes seriously the fact that quantum mechanics is the nonrelativistic limit of our most accurate physical theory, namely quantum field theory, and treats the Schroedinger wave function, as well as the electromagnetic field, as quantized fields.2 Both the Schroedinger field, or “matter field,” and the EM field are made of “quanta”—spatially extended but energetically discrete chunks or bundles of energy. Each quantum comes nonlocally from the entire space-filling field and interacts with macroscopic systems such as the viewing screen by collapsing into an atom instantaneously and randomly in accordance with the probability amplitude specified by the field. Thus, uncertainty and nonlocality are inherent in quantum physics. This paper is about quantum uncertainty. A planned later paper will take up quantum nonlocality.
The Classic Physics and the Quantum Physics are two branches of the nowadays Science of Physics, which are still incompatible. Einstein's Relativity theories, which are the leading acceptable theories of the nowadays Classic Physics, present the Universe as a "Block Universe", in which Time is not a flow of events, where the past vanishes and does not exist anymore, and the future is not yet created. Instead, the "Block Universe" model presents that the past, present and future are all equally real and coexist tenselessly, and everything, the past, present and future are all predefined and engraved in that "Block Universe" model of the Universe. On the other hand, the Quantum Mechanics presents, that the future is created continuously when particles interact with the environment, and the state of each particle is presented by what the Quantum Mechanics denotes as the "Wave Function" which presents the probabilities to find the particle in various locations, such that, before the particle is measured, or interacts with the environment, it can actually be in all those locations at once, and only after the particle is measured, or interacts with the environment, the "Wave Function Collapses" and the particle "chooses" randomly, to be only in one specific location. Actually, that "Wave Function Collapse" is one of the most mysterious phenomena in Physics. But it seems that Bell's Theorem, and the experiments that followed it, settled that long debate about it, providing the means to establish that the Quantum Mechanics view on this matter is the correct view and the Classic Physics and Einstein's Relativity theories view on this matter is not correct. Bell's Inequality provided the logic and the mathematics behind this decision, and physicists such as Alain Aspect, John Clauser and Anton Zeilinger, who also won the Nobel prize on that, provided the experimental justification. However, although the above debate was settled, there is also still a need, to understand more precisely, what actually happens in experiments relating to Quantum entangled particles, which is what was tested in Alain Aspect, John Clauser and Anton Zeilinger experiments. The author of this paper refers to additional papers, by the author of this paper, which present significant and reasonable arguments, which argue that the nowadays branch of the Classic Physics might be misleading in how it presents the concept of the Space-Time. These additional papers propose to replace the Einstein's "Block Universe" model of the Universe with an alternate model, of a Multi-Space-Times model of the Universe, in which, each Energy might embed its own private Space-Time facet, or attribute, such that each such Space-Time cannot be considered to be a real entity, that really exists in the Universe. And this paper argues, that Bell's Theorem, and the experiments that followed it, might be also used to support the above-mentioned Multi-Space-Times model of the Universe, and this might also fill in the above-mentioned gap, which might be the need, to understand more precisely, what actually happens in experiments relating to Quantum entangled particles, which is what was tested in Alain Aspect, John Clauser and Anton Zeilinger experiments. In addition to the above, the above-mentioned additional papers, also propose additional experiments, based only on the Classic Physics, which if implemented successfully, might provide additional validity to the proposed Multi-Space-Times model of the Universe. The support that might be provided to the proposed model, of a Multi-Space-Times of the Universe, by the Bell's Theorem, and the experiments that followed it, is still based on the Quantum Mechanics. Thus, because these additional experiments, proposed in the above-mentioned additional papers, are based only on the Classic Physics, this might also provide a lead for further narrowing the gap between the Classic Physics and the Quantum Physics. Thus, an implementation of the above-mentioned experiments, or any other experiments that might provide validity to the proposed Multi-Space-Times model of the Universe, as presented in the above-mentioned papers, should be an important and a significant endeavor.
The Classic Physics and the Quantum Physics are two branches of the nowadays Science of Physics, which are still incompatible. Einstein's Relativity theories, which are the leading acceptable theories of the nowadays Classic Physics, present the Universe as a "Block Universe", in which Time is not a flow of events, where the past vanishes and does not exist anymore, and the future is not yet created. Instead, the "Block Universe" model presents that the past, present and future are all equally real and coexist tenselessly, and everything, the past, present and future are all predefined and engraved in that "Block Universe" model of the Universe. On the other hand, the Quantum Mechanics presents, that the future is created continuously when particles interact with the environment, and the state of each particle is presented by what the Quantum Mechanics denotes as the "Wave Function" which presents the probabilities to find the particle in various locations, such that, before the particle is measured, or interacts with the environment, it can actually be in all those locations at once, and only after the particle is measured, or interacts with the environment, the "Wave Function Collapses" and the particle "chooses" randomly, to be only in one specific location. Actually, that "Wave Function Collapse" is one of the most mysterious phenomena in Physics. But it seems that Bell's Theorem, and the experiments that followed it, settled that long debate about it, providing the means to establish that the Quantum Mechanics view on this matter is the correct view and the Classic Physics and Einstein's Relativity theories view on this matter is not correct. Bell's Inequality provided the logic and the mathematics behind this decision, and physicists such as Alain Aspect, John Clauser and Anton Zeilinger, who also won the Nobel prize on that, provided the experimental justification. However, although the above debate was settled, there is also still a need, to understand more precisely, what actually happens in experiments relating to Quantum entangled particles, which is what was tested in Alain Aspect, John Clauser and Anton Zeilinger experiments. The author of this paper refers to additional papers, by the author of this paper, which present significant and reasonable arguments, which argue that the nowadays branch of the Classic Physics might be misleading in how it presents the concept of the Space-Time. These additional papers propose to replace the Einstein's "Block Universe" model of the Universe with an alternate model, of a Multi-Space-Times model of the Universe, in which, each Energy might embed its own private Space-Time facet, or attribute, such that each such Space-Time cannot be considered to be a real entity, that really exists in the Universe. And this paper argues, that Bell's Theorem, and the experiments that followed it, might be also used to support the above-mentioned Multi-Space-Times model of the Universe, and this might also fill in the above-mentioned gap, which might be the need, to understand more precisely, what actually happens in experiments relating to Quantum entangled particles, which is what was tested in Alain Aspect, John Clauser and Anton Zeilinger experiments. In addition to the above, the above-mentioned additional papers, also propose additional experiments, based only on the Classic Physics, which if implemented successfully, might provide additional validity to the proposed Multi-Space-Times model of the Universe. The support that might be provided to the proposed model, of a Multi-Space-Times of the Universe, by the Bell's Theorem, and the experiments that followed it, is still based on the Quantum Mechanics. Thus, because these additional experiments, proposed in the above-mentioned additional papers, are based only on the Classic Physics, this might also provide a lead for further narrowing the gap between the Classic Physics and the Quantum Physics. Thus, an implementation of the above-mentioned experiments, or any other experiments that might provide validity to the proposed Multi-Space-Times model of the Universe, as presented in the above-mentioned papers, should be an important and a significant endeavor.
Abstract The Mach–Zehnder interferometer experiment described earlier shows why and how quantum mechanics is different from classical mechanics. A photon sent through a beam splitter behaves like a particle when it is observed by only one of the two detectors. When two beam splitters are used, the photon “interferes with itself” and behaves like a wave. This is the so-called wave-particle duality of quantum mechanics which leads to quantum entanglement. This chapter discusses quantum superpositions when two or more particles are present. Understanding and analysing entanglement is one of the most interesting directions in the field of quantum information. First, a historical background of quantum entanglement is given, followed by a discussion on Bell's inequalities, separable states that do not violate Bell's inequalities, pure states that violate Bell's inequalities, mixed states that do not violate Bell's inequalities, and entanglement in second quantisation.