270 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 experi- ment 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 discov- ered that each pair of daughter photons is entangled. If one of the two entangled particles experiences a macro- scopic interaction, for example by striking a viewing screen, that portion of the two-particle wave packet instantly collaps- es 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 inter- action 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 Nonlocality 1 Art Hobson, University of Arkansas, Fayetteville, AR N onlocality arises from the unified “all or nothing” in- teractions of a spatially extended field quantum such as a photon or an electron. 2 In the double-slit experi- ment 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 (randomly 2 ) with the screen, field quantization re- quires 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 inter- ference patterns of light from a small distant star. The interac- tion instantly transfers the photon’s energy to a single atom of the screen. But a quantized field can contain any whole number of “excitations” (particles such as photons or elec- trons). 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 instan- taneously 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 jour- nal 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 entangle- ment experiment that should be accessible to both scientists and nonscientists. Background Figure 1 is a way to picture the creation of two-particle entanglement during an interaction. At the left and the bot- tom of the figure, we see two one-particle wave packets, i.e., two particles (remember that “particles,” i.e., field quanta, are their wave packets 2 ). The particles are initially unentangled and noninteracting, then they move near enough to create a non-negligible probability of interaction, then they separate. Quantum physics predicts that, if an interaction occurs, the packets get mixed up with each other so that, even after they no longer interact, they form a single two-particle wave packet that can’t be separated into two one-particle wave packets. Experimentally, this “entanglement” means that the particles exhibit the kind of nonlocal effects described below; theoreti- cally, it means that the particles are in a two-particle quantum state that cannot be factored into the product of two one- particle states. The figure indicates this by coloring one initial packet black and the other green. The post-interaction packets Fig. 1. When two particles interact and then separate, their quan- tum fields usually become entangled. See the text for explanation. (Reprinted by permission of Pearson Education Inc., Upper Saddle River, NJ.)