In the spirit and style of John S. Bell’s well known paper on How to Teach Special Relativity [1] it is argued, that a “Bohmian pedagogy”provides a very useful tool to illustrate the relation between classical and quantum physics and illuminates the peculiar features of the latter. The paper by Bell on How to Teach Special Relativity introduces the subject with the following remark: I have for long thought that if I had the opportunity to teach this subject, I would emphasize the continuity with earlier ideas. Usually it is the discontinuity which is stressed, the radical break with more primitive notions of space and time. Often the result is to destroy completely the confidence of the student in perfectly sound and useful concepts already acquired. 1 In the following Bell gives an account of the Lorentzian interpretation of relativistic effects, in which the Lorentz transformations are explained by a dynamical
In the spirit and style of John S. Bell’s well known paper on How to Teach Special Relativity [1] it is argued, that a “Bohmian pedagogy”provides a very useful tool to illustrate the relation between classical and quantum physics and illuminates the peculiar features of the latter. The paper by Bell on How to Teach Special Relativity introduces the subject with the following remark: I have for long thought that if I had the opportunity to teach this subject, I would emphasize the continuity with earlier ideas. Usually it is the discontinuity which is stressed, the radical break with more primitive notions of space and time. Often the result is to destroy completely the confidence of the student in perfectly sound and useful concepts already acquired. 1 In the following Bell gives an account of the Lorentzian interpretation of relativistic effects, in which the Lorentz transformations are explained by a dynamical
In this paper we introduce the new version of QTris, a board game designed to teach and learn Quantum Mechanics within the framework of Quantum Information and Computation. The key idea behind the game is that every game sequence simulates a process on a system of qubits. Thus, QTris can be effectively integrated as a pedagogical tool to teach Quantum Mechanics at high-school level following a two-state approach. After arguing in support of this latter approach, we describe QTris' basic rules and some of its possible extensions, emphasizing how the game mechanics puts in clear light key quantum concepts such as incompatibility, probabilistic measurement and unitary transformation. Moreover, we report on the results of a QTris-based educational activity which involved about 150 high-school students and provided encouraging preliminary indications that QTris can be a useful pedagogical platform to promote an immediate understanding of some key concepts of Quantum Mechanics.
Abstract It can easily be argued that a fully mature and complete knowledge of quantum mechanics should include historical, axiomatic, formal mathematical, and even philosophical background to the subject. However, for a student approaching quantum theory for the first time in a serious way, it can be the case that an approach utilizing his or her existing knowledge of, and intuition for, classical physics (including mechanics, wave physics, and electricity and magnetism) as well as emphasizing connections to experimental results can be the most pro- ductive. That, at least, is the point of view adopted in this text and can be illustrated by a focus on the following general topics:
There are two ways to teach quantum mechanics. The first way – which for most physicists today is still the only way – follows the historical order in which the ideas were discovered. So, you start with classical mechanics and electrodynamics, solving lots of grueling differential equations at every step. Then, you learn about the “blackbody paradox” and various strange experimental results, and the great crisis these things posed for physics. Next, you learn a complicated patchwork of ideas that physicists invented between 1900 and 1926 to try to make the crisis go away. Then, if you're lucky, after years of study, you finally get around to the central conceptual point: that nature is described not by probabilities (which are always nonnegative), but by numbers called amplitudes that can be positive, negative, or even complex. Look, obviously the physicists had their reasons for teaching quantum mechanics that way, and it works great for a certain kind of student. But the “historical” approach also has disadvantages, which in the quantum information age are becoming increasingly apparent. For example, I’ve had experts in quantum field theory – people who've spent years calculating path integrals of mind-boggling complexity – ask me to explain the Bell inequality to them , or other simple conceptual things like Grover's algorithm. I felt as if Andrew Wiles had asked me to explain the Pythagorean Theorem.
I distinguish between two conceptually different kinds of physical space: a space of ordinary material bodies, which is the space of points at which I could imaginably place (say) the tip of my finger, or the center of a billiard-ball, and a space of elementary physical determinables, which is the smallest space of points such that stipulating what is happening at each one of those points, at every time, amounts to an exhaustive physical history of the universe. In all classical physical theories, these two spaces happen to coincide – and what we mean by calling a theory “classical”, and all we mean by calling a theory “classical”, is (I will argue) precisely that these two spaces coincide. But once the distinction between these two spaces in on the table, it becomes clear that there is no logical or conceptual reason why they must coincide – and it turns out (and this is the main topic of the present paper) that a very simple way of pulling them apart from one another gives us quantum mechanics.
A type of mechanics will be presented that possesses some distinctive properties. On the one hand, its physical description & rules of operation are readily comprehensible & intuitively clear. On the other, it fully satisfies all observable predictions of non-relativistic quantum mechanics. Within it, particles exist at points in space, follow continuous, piecewise differentiable paths, and their linear momentum is equal to their mass times their velocity along their path. Yet the probabilities for position and momentum, conditioned on the state of the particle's environment, follow the rules of quantum theory. Indeed, all observable consequences of quantum theory are satisfied; particles can be entangled, have intrinsic spin, this spin is not local to the particle, particle identity can effect probabilities, and so forth. All the rules of quantum mechanics are obeyed, and all arise in a straightforward fashion. After this is established, connections will be drawn out between this type of mechanics and other types of quantum worlds; those that obey Bohmian mechanics, stochastic mechanics, the many worlds interpretation, and physical collapse. In the final section, a relativistic version of the mechanics will be presented.