The textbook

The World According to Quantum Mechanics

Publisher’s blurb:

An invalu­able sup­ple­ment to stan­dard text­books on quantum mechanics, this unique intro­duc­tion to the gen­eral the­o­ret­ical frame­work of con­tem­po­rary physics focuses on con­cep­tual, epis­te­mo­log­ical, and onto­log­ical issues. The theory is devel­oped by pur­suing the ques­tion: what does it take to have mate­rial objects that nei­ther col­lapse nor explode as soon as they are formed? The sta­bility of matter thus emerges as the chief reason why the laws of physics have the par­tic­ular form that they do.

The first of the book’s three parts famil­iar­izes the reader with the basics through a brief his­tor­ical survey and by fol­lowing Feynman’s route to the Schrödinger equa­tion. The nec­es­sary math­e­matics, including the spe­cial theory of rel­a­tivity, is intro­duced along the way, to the point that all rel­e­vant the­o­ret­ical con­cepts can be ade­quately grasped. Part II takes a closer look. As the theory takes shape, it is applied to var­ious exper­i­mental arrange­ments. Sev­eral of these are cen­tral to the dis­cus­sion in the final part, which aims at making epis­te­mo­log­ical and onto­log­ical sense of the theory. Piv­otal to this task is an under­standing of the spe­cial status that quantum mechanics attrib­utes to mea­sure­ments — without drag­ging in “the con­scious­ness of the observer.” Key to this under­standing is a rig­orous def­i­n­i­tion of “macro­scopic” which, while rarely even attempted, is pro­vided in this book.

Publisher’s web­site

Chapter 1: Prob­a­bility: Basic con­cepts and the­o­rems [PDF]


From the Preface:

Having explained why inter­pre­ta­tions that try to accom­mo­date clas­sical intu­itions are impos­sible, Dieks[1] goes on to say:

How­ever, this is a neg­a­tive result that only pro­vides us with a starting-​​point for what really has to be done: some­thing con­cep­tu­ally new has to be found, dif­ferent from what we are familiar with. It is clear that this con­struc­tive task is a par­tic­u­larly dif­fi­cult one, in which huge bar­riers (partly of a psy­cho­log­ical nature) have to be overcome.

Some­thing con­cep­tu­ally new has been found, and is pre­sented in this book. To make the pre­sen­ta­tion rea­son­ably self-​​contained, and to make those already familiar with the sub­ject aware of meta­phys­ical prej­u­dices they may have acquired in the process of studying it, the format is that of a text­book. To make the pre­sen­ta­tion acces­sible to a wider audi­ence — not only stu­dents of physics and their teachers — the math­e­mat­ical tools used are intro­duced along the way, to the point that the the­o­ret­ical con­cepts used can be ade­quately grasped. In doing so, I tried to adhere to a prin­ciple that has been dubbed “Einstein’s razor”: every­thing should be made as simple as pos­sible, but no simpler.

This text­book is based on a philo­soph­i­cally ori­ented course of con­tem­po­rary physics I have been teaching for the last ten years at the Sri Aurobindo Inter­na­tional Centre of Edu­ca­tion (SAICE) in Puducherry (for­merly Pondicherry), India. This non-​​compulsory course is open to higher sec­ondary (stan­dards 10–12) and under­grad­uate stu­dents, including stu­dents with neg­li­gible prior expo­sure to clas­sical physics.

(I con­sider this a plus. In the first sec­tion of his bril­liant Cal­tech lec­tures, Richard Feynman[2] raised a ques­tion of con­cern to every physics teacher:

Should we teach the cor­rect but unfa­miliar law with its strange and dif­fi­cult con­cep­tual ideas…? Or should we first teach the simple … law, which is only approx­i­mate, but does not involve such dif­fi­cult ideas? The first is more exciting, more won­derful, and more fun, but the second is easier to get at first, and is a first step to a real under­standing of the second idea.

With all due respect to one of the greatest physi­cists of the 20th Cen­tury, I cannot bring myself to agree. How can the second approach be a step to a real under­standing of the cor­rect law if “philo­soph­i­cally we are com­pletely wrong with the approx­i­mate law,” as Feynman him­self empha­sized in the imme­di­ately pre­ceding para­graph? To first teach laws that are com­pletely wrong philo­soph­i­cally cannot but impart a con­cep­tual frame­work that even­tu­ally stands in the way of under­standing the cor­rect laws. The damage done by imparting philo­soph­i­cally wrong ideas to young stu­dents is not easily repaired.)

The text is divided into three parts. After a short intro­duc­tion to prob­a­bility, Part 1 (“Overview”) fol­lows two routes that lead to the Schrödinger equa­tion — the his­tor­ical route and Feynman’s path-​​integral approach. On the first route we stop once to gather the needed math­e­mat­ical tools, and on the second route we stop once for an intro­duc­tion to the spe­cial theory of relativity.

The first chapter of Part 2 (“A Closer Look”) derives the math­e­mat­ical for­malism of quantum mechanics from the exis­tence of “ordi­nary” objects — stable objects that “occupy space” while being com­posed of objects that do not “occupy space.” The next two chap­ters are con­cerned with what hap­pens if the objec­tive fuzzi­ness that “fluffs out” matter is ignored. (What hap­pens is that the quantum-​​mechanical cor­re­la­tion laws degen­erate into the dynam­ical laws of clas­sical physics.) The remainder of Part 2 covers a number of con­cep­tu­ally chal­lenging exper­i­ments and the­o­ret­ical results, along with more con­ven­tional topics.

Part 3 (“Making Sense”) deals with the onto­log­ical impli­ca­tions of the for­malism of quantum mechanics. The penul­ti­mate chapter argues that quantum mechanics — whose validity is required for the exis­tence of “ordi­nary” objects — in turn requires for its con­sis­tency the validity of both the Stan­dard Model and the gen­eral theory of rel­a­tivity, at least as effec­tive the­o­ries. The final chapter haz­ards an answer to the ques­tion of why stable objects that “occupy space” are com­posed of objects that do not “occupy space.” It is fol­lowed by an appendix con­taining solu­tions or hints for some of the prob­lems pro­vided in the text.

Ulrich Mohrhoff
August 15, 2010

1. [↑] Dieks, D.G.B.J. (1996). The quantum mechan­ical world­pic­ture and its pop­u­lar­iza­tion. Com­mu­ni­ca­tion & Cog­ni­tion 29 (2), pp. 153–168.

2. [↑] Feynman, R.P., Leighton, R.B., and Sands, M. (1963). The Feynman Lec­tures in Physics I, Addison–Wesley, pp. 1–2.