For Abner Shimony. Your influence on me goes well beyond physics. Knowing you and being close to you is one of the greatest privileges and pleasures in my life. Introduction Quantum mechanics is, without any doubt, a tremendously successful theory: it started by explaining black-body radiation and the photoelectric effect, it explained the spectra of atoms, and then went on to explain chemical bonds, the structure of atoms and of the atomic nucleus, the properties of crystals and the elementary particles, and a myriad of other phenomena. Yet it is safe to say that we still lack a deep understanding of quantum mechanics – surprising and even puzzling new effects continue to be discovered with regularity. That we are surprised and puzzled is the best sign that we still don't understand; however, the veil over the mysteries of quantum mechanics is starting to lift a little. One of the strangest things microscopic particles do is to follow non-local dynamics and to yield non-local correlations. That particles follow non-local equations of motion was discovered by Aharonov and Bohm, while non-local correlations – which are the subject of this chapter – were discovered by John Bell and first cast in a form that has physical meaning, i.e., that can be experimentally tested, by Clauser, Horne, Shimony, and Holt. When they were discovered, both phenomena seemed to be quite exotic and at the fringe of quantum mechanics. By now we understand that they are some of the most important aspects of quantummechanical behavior.
For Abner Shimony. Your influence on me goes well beyond physics. Knowing you and being close to you is one of the greatest privileges and pleasures in my life. Introduction Quantum mechanics is, without any doubt, a tremendously successful theory: it started by explaining black-body radiation and the photoelectric effect, it explained the spectra of atoms, and then went on to explain chemical bonds, the structure of atoms and of the atomic nucleus, the properties of crystals and the elementary particles, and a myriad of other phenomena. Yet it is safe to say that we still lack a deep understanding of quantum mechanics – surprising and even puzzling new effects continue to be discovered with regularity. That we are surprised and puzzled is the best sign that we still don't understand; however, the veil over the mysteries of quantum mechanics is starting to lift a little. One of the strangest things microscopic particles do is to follow non-local dynamics and to yield non-local correlations. That particles follow non-local equations of motion was discovered by Aharonov and Bohm, while non-local correlations – which are the subject of this chapter – were discovered by John Bell and first cast in a form that has physical meaning, i.e., that can be experimentally tested, by Clauser, Horne, Shimony, and Holt. When they were discovered, both phenomena seemed to be quite exotic and at the fringe of quantum mechanics. By now we understand that they are some of the most important aspects of quantummechanical behavior.
Thus far I have been primarily concerned with how an interpretation of quantum mechanics might, or might not, be local. This question is traditionally not sharply distinguished from the question of whether quantum mechanics is consistent with the theory of relativity. However, the two questions are indeed quite distinct, and should be recognized as such explicitly. The theory of relativity What does relativity require? As a first approximation, we may make the distinction by noting that the requirements of the theory of relativity are themselves unclear. Minimally, relativity seems to require that there be no way to distinguish one reference frame from another – i.e., that there be no experimental procedure that can determine which of two inertial observers is ‘really’ moving, or more generally that there be no way to discover an observer's absolute velocity. Most authors are willing to find in (special) relativity a stronger requirement: namely, Lorentz-invariance. They say that relativity requires that in fact there is no such thing as absolute velocity. This requirement goes beyond the minimum – it might be that there is an absolute rest frame (so that absolute velocities are given by motion relative to this frame) while there is no way to find it. (As I will discuss in chapter 9, exactly this situation occurs in Bohm's theory.)
Quantum Non-Locality and Relativity has the rare quality of being both a significant contribution to the philosophy of physics literature and a superb introduction for philosophers unacquainted with the field. Maudlin sets out to examine the implications for our understanding of the fundamental structure of space, time, and causation of what appears to be a mysterious action-at-a-distance observed in the quantum domain. Physicists and philosophers of physics have been grappling with these implications for the last half-century, and Maudlin does a remarkable job of elucidating central themes in the literature and clarifying conceptual confusions. Throughout the book, Maudlin draws out salient points from what can easily become a morass of scientific and philosophical technicalities. At the root of puzzles concerning relativity and quantum mechanics lie a few simple experimental facts. In an experimental setup in which quantum particles begin from a common source and travel in opposite directions, distant (spacelike separated) measurements of properties of the two particles are strangely correlated. These correlations have been observed, for example, in experiments which measure polarization properties of photons. A well-known theorem due to John S. (1964) expresses a constraint on the kind of correlations that measurement outcomes in this experimental setup (known as a Bell experiment) can display, in the absence of any communication between them. The surprise is that observed correlations violate Bell's theorem, meaning that the measurement events appear somehow to be influencing each other or to be otherwise connected. But there's the rub: in experiments, measurements are spacelike separated, which means they are too far apart for any force of nature travelling at or below the speed of light to traverse the distance between them in time. Faster-than-light influences seem to fly squarely (and rather quickly) in the face of everything Einstein taught us about the structure of space and time. As it is often understood, the special theory of relativity asserts that the speed of light in a vacuum is some sort of physical limit, and that matter, energy, signals, causal influence, and the like cannot travel faster than the speed of light. Do the
Chapter 4 deals with Quantum Mechanical (QM) phenomena. The first section describes the first attempts at quantization of energy, momentum, angular momentum, etc. We start with Plank's solution to the black-body problem, introducing the concept of photons: discrete packets of electromagnetic energy. We show how Plank's description of black-body radiation is perfectly fit by the cosmic microwave radiation, providing the strongest evidence for the Big-Bang at the origin of the Universe. We then describe Bohr's solution to the paradoxical stability of atoms, introducing quantization of angular momentum (or action) and correctly predicting the energy levels of the hydrogen atom. We show how Einstein used Plank's idea to explain the photo-electric effect (an effect exploited in CCD cameras and solar cells) and how he used Bohr's understanding of energy levels in atoms to provide an intuitive explanation of Plank's law. Einstein insight opened the way to the field of spectroscopy and the development of the laser. In the second section, following the lead of Dirac, we show that QM is equivalent to Linear Algebra in the space of complex functions (which describe the state of the system). We show that Schrödinger's equation is a natural consequence of that description, once the relation between energy and frequency established by Plank (for photons) and de Broglie (for particles) is taken into account. In the context of the chiral ammonia molecule we discuss the queerness of QM which describes physical systems as superposition of states (such as left and right chirality state of a molecule, dead and alive cat). We show that this queerness is nonetheless supported by experiments and is behind much of our technology: masers and lasers, atomic clocks, semiconductors (diodes, transistors, etc.). In the following section we introduce the representation of operators in QM (the equivalent of matrices in linear algebra): momentum, position, energy, etc. which correspond to measurements on the system. We show that the non-commutability of some operators (common with matrix operations) leads to Heisenberg uncertainty principle: the position and momentum of a particle cannot be determined with absolute precision. We discuss the solution of Schrödinger's equation for free particles demonstrating their equivalence with EM phenomena: particles undergo refraction and diffraction, exemplifying the particle/wave duality inherent to QM systems. We discuss QM tunneling and its use in the Scanning Tunneling Microscope. In the following section we study Dirac's equation: the successful attempt by Dirac to unify QM with Einstein's relativity, with the resulting prediction of anti-particles and spin. We then solve for the energy levels of electrons in the hydrogen atom (from Schrödinger's equation) and show that the existence of spin profoundly affects the behavior of electrons in an atom: they cannot share the same energy level, a rule known as Pauli's exclusion principle. Pauli's principle is central to the understanding of the chemical properties of atoms and fully explains Mendeleev's periodic table of the elements. In the next section we discuss along with two exactly soluble systems (diatomic rotational and vibrational levels), various approximations used to study systems (e.g. molecules) for which there are no analytical solutions. In particular, we introduce Pauling's variational approach, Hückel molecular orbital theory and time independent perturbation theory. We apply those approaches to determine the energy levels in alkenes, in multi-electron atoms and in systems under constant electric or magnetic field (such as in Magnetic Resonance Imaging). In the last section we discuss time dependent perturbation theory. We use it to establish the rules allowing for transitions between energy levels and revisit Einstein description of absorption/emission phenomena.
Dad I understand that light is emitted when an atom decays from an excited state to a lower energy state. Feynman That's right. Dad And light consists of particles called photons. Feynman Yes. Dad So the photon ‘particle’ must be inside the atom when it is in the excited state. Feynman Well no. Dad Well how do you explain that the photon comes out of the atom when it was not there in the first place. Feynman (Physics Teacher 1969) I'm sorry. I don't know I can't explain it to you. INTRODUCTION As was stated in Chapter 1, spectroscopy is a study of the interaction of matter with radiation. In order to understand their mutual interaction, we must therefore characterize both radiation and matter. The starting point is quantum mechanics, because the origin of quantum mechanics was based on unexplained phenomena related to both the nature of electromagnetic radiation and that of matter. In fact, quantum mechanics owes its birth to some puzzling results of spectral and other experiments. We may say that “spectroscopy is quantum mechanics in action.” We therefore begin our study of quantum mechanics with a recapitulation of its postulates. An understanding of the postulates is also essential for our development of the time-dependent perturbation theory and also forms the basis for the connection between theory and experiment. Indeed, spectroscopy is the experimental verification of the laws of quantum mechanics. Quantum mechanics is based on a few postulates (from the Latin postulatum ), meaning a truth that does not need any further proof, because it is obvious by itself, and its success lies in the fact that no experiment till date has proved it wrong. There is no agreement of how many axioms one needs to describe the machinery of quantum mechanics; however, the six given below is an acceptable number.
The theory of Quantum Mechanics is one of the mainstay of modern physics, a well-established mathematical clockwork whose strength and accuracy in predictions are currently experienced in worldwide research laboratories. As a matter of fact, Quantum Mechanics laid the groundwork of a rich variety of studies ranging from solid state physics to cosmology, from bio-physics to particle physics. The up-to-date ability of manipulating single quantum states is paving the way for emergent quantum technologies as quantum information and computation, quantum communication, quantum metrology and quantum imaging. In spite of the impressive matemathical capacity, a long-standing debate is even revolving around the foundational axioms of this theory, the main bones of content being the non-local effects of entangled states, the wave function collapse and the concept of measurement in Quantum Mechanics, the macro-objectivation problem (the transition from a microscopic probabilistic world to a macroscopic deterministic world described by classical mechanics). Problems that, beyond their fundamental interest in basic science, now also concern the impact of these developing technologies. Without claiming to be complete, this article provides in outline the living matter concerning some of these problems, the implications of which extend deeply on the connection between entanglement and space-time structure.
During the 1960s, Bell produced his seminal work on the foundations of quantum theory, first showing that, contrary to von Neumann’s argument, hidden variable theories were allowed but then that they had to be non-local. Thus, he showed that quantum theory did not respect local causality, and he outlined experiments that could be used to test whether the assumption of local realism was true in quantum theory: Bell’s theorem, or Bell’s inequality, or Bell’s inequalities. His work was followed up by John Clauser, Abner Shimony, Michael Horne, and Richard Holt, who produced the CHSH inequality. Bell had moved to CERN, where he worked on the theory of neutrino experiments, and on nuclear and elementary particle physics, making crucial suggestions concerning the use of gauge theory for each type of physical force and also producing the Adler–Bell–Jackiw anomaly, or the ABJ anomaly.