Does the wave function directly represent a state of reality, or merely a state of (incomplete) knowledge of it, or something else? This question is the starting point of this book, in which the author – a professor of philosophy – aims to make sense of the wave function in quantum mechanics and investigate the ontological content of the theory. A very powerful mathematical object, the wave function has always been the focus of a debate that goes beyond physics and mathematics to the philosophy of science.
The first part of the book (chapters 1–5) deals with the nature of the wave function and provides a critical review of its competing interpretations. In the second part (chapters 6 and 7), the author focuses on the ontological meaning of the wave function and proposes his view, which is that the wave function in quantum mechanics is real and represents the state of random discontinuous motion of particles in 3D space. He offers two main arguments supporting this new interpretation. The third part (chapters 8 and 9) is devoted to investigating possible implications. In particular, the author discusses whether the quantum ontology described by the wave function is enough to account for our definite experience, or whether additional elements, such as many worlds or hidden variables, are needed.
Aimed at readers familiar with the basics of quantum mechanics, the book could also appeal to students and researchers interested in the philosophical aspects of modern science theories.
With the rapid development of nanoscience and nano-engineering, quantum mechanics can no longer be considered exclusively the interest of physicists. Indeed, a fundamental understanding of physical phenomena at the nanoscale will require future electronic engineers, condensed-matter physicists and material scientists to master the fundamental principles of quantum theory.
Noticing that many textbooks on quantum mechanics are not meant for a wide audience of scientists, in particular those interested in practical applications and technologies at the nanoscale, the authors decided to fill this gap. In particular, they focus on the solution of problems that students and researchers working on state-of-the-art material and device applications might have to face. The problems are grouped by theme in 13 chapters, each completed by a section of further readings.
An ideal resource for graduate students, the book is also of value to professionals who need to update their knowledge or to refocus their expertise towards nanotechnologies.
Anomaly! is a captivating story of supposed discoveries that turned out not to be. The book provides an honest and not always flattering description of how large high-energy physics collaborations work, what makes experimental physicists excited, and of the occasional interference between scientific goals and personal factors such as ambition, career issues, personality clashes and fear of being scooped. Dorigo, who complements his recollections with many interviews and archival searches, proves to be a highly skilled communicator of science to the general public, as already known to the readers of his often controversial blog AQuantum Diaries Survivor. Thanks to well-chosen alternation of narration and explanation, several sections of the book read like a novel.
The main theme, as indicated by the title, is the anomalies (or outliers) that tantalised members of the CDF collaboration at Fermilab – and sometimes the external world – but ultimately turned out to be red herrings. The author uses these stories to show how cautious experimental particle physicists have to be when applying statistics in their data analysis. He also makes a point about the arbitrariness of the conventional 3σ and 5σ thresholds for claiming “evidence” and “discovery” of a new phenomenon.
Slightly off topic, given the title of the book, three chapters are devoted to the ultimately successful search for the top quark, the first evidence of which was very far from being an “anomaly”: its existence was expected in the mainstream and the “global fits” of other collider data were already pointing at the right mass range. Here Dorigo is interested in the opposite lesson: the conventional thresholds on p-values, originally motivated by the principle “extraordinary claims demand extraordinary proofs”, are hard to justify when a discovery is actually a confirmation of the dominant paradigm. (The author explicitly comments on the similarity with the Higgs boson discovery two decades later.) The saga of the top-quark hunt, which contains many funny and even heroic moments, is also an occasion for the author to elaborate on what he describes as over-conservative attitudes dominating in large teams when stakes are high.
In general, the book’s topics have clearly been chosen more by the importance of the lesson they teach than by their ultimate impact on science. Almost an entire chapter is devoted to a measurement of the Z boson mass at Fermilab, which was already known in advance to be doomed to obsolescence very soon, as the experiments at the upcoming LEP accelerator were more suited to that kind of measurement. Still, the chapter turns out to be an enthralling story, ending with a mysterious attempt by an unsporting competitor from another US laboratory to sabotage the first CDF report of this measurement at an international conference. In some other cases, the choice of topics is driven by their entertainment value, as in the case of the episode of the “Sacred Sword”, a radioactive-contamination incident that luckily ended well for its protagonists.
The author’s role in the book is at the same time that of an insider and of a neutral observer, attending crucial meetings and observing events unfold as a collaboration member among many others, with the remarkable exception of the final story where he plays the role of internal reviewer of one of the eponymous anomalies. In spirit and form, Anomaly! reminds me of Gary Taubes’ celebrated Nobel Dreams, but with more humour and explicit subjectivity. Although far from being scholarly, Anomaly! may also appeal to readers interested in the sociology of science or in the epistemological problem of how a scientific community finally settles on a single consensus, in the vein of Andrew Pickering’s Constructing Quarks, Peter Galison’s How Experiments End and Kent Staley’s The Evidence for the Top Quark: Objectivity and Bias in Collaborative Experimentation. The latter, in particular, is interesting to compare with the chapters of Anomaly! that narrate the same story.
This book discusses the role played by supersymmetry, and especially supergravity, in the quest for a unified theory of fundamental interactions. These are vast subjects, which not only embrace particle physics but also have ramifications in many other fields, such as modern mathematics, statistical physics and condensed-matter systems.
The author focuses on a rather specific subject: supergravity as a plausible scenario (perhaps more convincing than supersymmetry itself) for physics beyond the Standard Model. This justifies the way the author has chosen to distribute the material over the 24 chapters, for a total of 500 pages.
The first seven chapters introduce the field theories and symmetry principles on which a framework for the unification of particle forces would be based. After a short history of force unification, the author covers general relativity, Yang–Mills theories, spontaneous symmetry breaking, the basics of the Standard Model, the theory of gauge anomalies, effective Lagrangians and current algebra.
Supersymmetry is introduced next, with a short mathematical formulation including the concepts of graded lie algebras, superfields and the basic tools needed to construct (rigid) supersymmetric field theories, their multiplets and invariant Lagrangians. Non-supersymmetric grand unified theories and their supersymmetric extensions are also reviewed, investigating in particular the potential role they play in gauge coupling unification. It is surprising that the author does not discuss the original motivation for advocating supersymmetry in this context, which is related to the hierarchy problem and to the issue of naturalness of scales. No such discussion occurs in this chapter nor in the following one, devoted to the minimal supersymmetric Standard Model. The theory of supergravity and its mathematical structure, including matter couplings, is briefly exposed as well.
The second half of the book includes five chapters dedicated to the phenomenology of supergravity, covering in detail supergravity unification, CP violation, proton decay and supergravity in cosmology and astroparticle physics. In particular, supergravity inflation and supersymmetric candidates for dark matter are discussed at length. Further theories of supergravity and their connection to string theories in diverse dimensions are only briefly touched upon.
The last part of the book provides some tools, such as anti-commuting variables and spinor formalism, which are needed to write supersymmetric Lagrangians and to extract physical consequences. Notations, conventions and other miscellaneous arguments including further references conclude the volume.
The book can be considered as a valuable and updated addition to Steven Weinberg’s third volume on supersymmetry in The Quantum Theory of Fields series (2000, Cambridge University Press).
The author is a world expert on supersymmetry and supergravity phenomenology, who has contributed to the field with many original and outstanding works.
Certainly useful to graduate students in physics, the book could also prove to be a resource for advanced graduate courses in experimental high-energy physics.
This book aims to provide a self-contained and concise treatment of the main subjects in magnetostatics, which describes the forces and fields resulting from the steady flow of electrical currents.
The first three chapters briefly present the basics, including the theory of magnetic fields from conductors in free space and from magnetic materials, as well as the general solutions to the Laplace equation and boundary value problems. Then the author moves on to discuss transverse fields in two dimensions. In particular, he covers fields produced by line currents, current sheets and current blocks, and the application of complex variable methods. He also treats transverse field magnets where the shape of the field is determined by the shape of the iron surface and the conductors are used to excite the field in the iron.
The following chapters are dedicated to other field configurations, such as axial field arrangements and periodic magnetic arrangements. The properties of permanent magnets and multiple fields produced by assemblies of them are also discussed.
Finally, the author deals with phenomena where there are slow variations in current or magnetic flux. Since only a restricted group of magnetostatic problems have analytic solutions, in the last chapter numerical techniques for calculating magnetic fields are provided, accompanied by many examples taken from accelerator and beam physics.
Aimed at undergraduates in physics and electrical engineering, the book includes not only basic explanations but also many references for further study.
By R Peron, M Colpi, V Gorini and U Moschella (eds)
Springer
This book, a collection of expert contributions, provides an overview of the current knowledge in gravitational physics, including theoretical and experimental aspects.
After a pedagogical introduction to gravitational theories, several chapters explore gravitational phenomena in the realm of so-called weak-field conditions: the Earth (specifically, the laboratory environment) and the solar system.
The second part of the book is devoted to gravity in an astrophysical context, which is an important test-bed for general relativity. A chapter is dedicated to gravitational waves, the recent discovery of which is an impressive experimental result in this field. The importance of studying radio pulsars is also highlighted.
A section on research frontiers in gravitational physics follows. This explores the many open issues, especially related to astrophysical and cosmological problems, and the way that possible solutions impact the quest for a quantum theory of gravity and a unified theory of the forces.
The book’s origins lie in the 2009 edition of a school organised by the Italian Society of Relativity and Gravitation. As such, it is aimed at graduate students, but could also appeal to researchers working in the field.
This book is a collection of essays on various physics topics, which the author aims at presenting in a manner that is accessible to non-experts and, specifically, to non-physics science and arts students at the undergraduate level. The author is motivated by the conviction that understanding fundamental concepts of other subjects facilitates out-of-the-box thinking, which can result in making original contributions to one’s chosen field.
The selection of topics is very personal: some basic-physics concepts, such as standards for units and oscillation theory, are placed next to discussions about general relativity and the famous twin paradox. The author uses an informal style and has particular interest in dispelling some myths about science.
The final chapters cover topics from his area of research, atomic and optical physics, focusing on the Nobel Prizes assigned in the last two decades to scientists in these fields.
Even though the use of equations is kept to a minimum, some mathematics and physics background is required of the reader.
Raw Data is a scientific novel that explores the moral dilemmas surrounding the accidental discovery of a case of scientific misconduct within a top US biomedical institute.
The choice of subject is interesting and unusual. Scientific misconduct is not an unprecedented topic for scientific novels, but the focus is usually on spectacular frauds that clearly violate the ethos of the scientific community. This story depicts a more nuanced situation. Readers may even find themselves understanding, if not condoning, the conscious decision of one of the co-protagonists to cheat.
This character chooses to “cut a corner” out of fear of being scooped, to satisfy an unreasonably picky reviewer who had requested an additional control experiment that she deems irrelevant. The stakes for her career are huge because she is competing with other groups on the same research line, and publishing second would cost her a great deal academically. When a co-worker accidentally finds hints of her fabrication and immediately alerts the laboratory’s principal investigator, both find themselves in a bitter no-win situation. “Doing the right thing” has a significant cost, but any other option potentially entails far worse consequences for their careers and their reputations.
Along the way, the author illustrates vividly how people in research think, feel, work and live. Work–life balance in science, especially for young female researchers, is a secondary theme of the book. Overall, the portrait of academia is not a flattering one, but definitely faithful. As someone who works in high-energy physics, I learnt about day-by-day practices in the biomedical sector and how it differs from mine. Although the author focuses on her own area of the scientific environment, some descriptions of “postdoc life” are quite general.
This relatively short novel is followed by a long Q&A section with the author, a former biomedical researcher who left the field after some considerable career achievements. There she makes her opinions explicit about several of the topics, including the “publish or perish” attitude, work–life balance, scientific integrity, and what she perceives as systemic dangers for the academic research world.
Although the author clearly made an effort to simplify the science to the minimum needed to understand the plot (and as a reader with no understanding of microbiology I found her effort successful), I am not sure that a reader with no previous interest in science would be hooked by the story. The book is well written, but the plot has a slow pace and, while Springer deserves credit for publishing it, the text contains many typographical errors.
Overall, I recommend the book to other scientists, regardless of their specialisation, and to the scientifically educated public who may appreciate this insider view of contemporary research life.
One of the most intriguing works in the philosophy of science is Wigner’s 1960 paper titled “The Unreasonable Effectiveness of Mathematics in the Natural Sciences”. Indeed the fact that so many natural laws can be formulated in this language, not to mention that some of these represent the most precise knowledge we have about our world, is a stunning mystery.
A related question is whether mathematics, which has largely developed overlapping or in parallel with physics, is constructed by the human mind or “discovered”. This question is worth asking again today, when modern theories of fundamental physics and contemporary mathematics have reached levels of abstraction that are unimaginable from the perspective of just 100 years ago.
This book is a collection of essays discussing the connection between physics and mathematics. They are written by the winners of the 2015 Foundational Questions Institute contest, which invited contributors – from professional researchers to members of the public – to propose an essay on the topic.
Since it appears primarily as a subject of the philosophy of science rather than of science itself, it is not a surprise that there are conflicting viewpoints that sometimes reach opposite conclusions.
A significant point of view is that the claimed effectiveness of mathematics is actually not that surprising. This is because we process information and generate knowledge about our world in an inadvertently biased way, namely as a result of the evolution of our mind in a specific physical world. For example, concepts of elementary geometry (such as straight lines, parabolas, etc) and the mechanics of classical physics are deeply imprinted in the human brain as evolutionary bias. In a fuzzy, chaotic world, such naive mathematical notions might not have developed, as they wouldn’t represent a good approximation to that world. In fact, in a drastically unstructured world it would have been less likely that life had evolved in the first place, so it may not seem such a surprise that we find ourselves in a world largely governed by relatively simple geometrical structures.
What remains miraculous, on the other hand, is the effectiveness of mathematics in the microscopic realm of quantum mechanics: it is not obvious how the mathematical notions on which it is based could be explained in terms of evolutionary bias. Actually, much of the progress of fundamental physics during the last 100 years or so crucially depended on abandoning the intuition of everyday common sense, in favour of abstract mathematical principles.
Another aspect is selection bias, in that failures of the mathematical description of certain phenomena tend simply to be ignored. A prime example is human consciousness – undoubtedly a real-world phenomenon – for which it is not at all clear whether its structure can ever be mapped to mathematical concepts in a meaningful way. A quite common reductionist point of view typical of particle physicists is that, since the brain is essentially chemistry (thus physics), a mathematical underpinning is automatic. But it may be that the way such complex phenomena emerge completely obfuscates the connection to the underlying, mathematically clean microscopic physics, rendering the latter useless for any practical purpose in this regard.
This raises the issue of the structure of knowledge per se, and some essays in this book argue that it may not necessarily be hierarchical but rather scale invariant with some, or many, distinguished nodes. One may think of these as local attractors to which “arrows of deeper explanation” point. It may be that only locally near such attractors does knowledge appear hierarchical, so that, for example, our mathematical description of fundamental physics is meaningful only near one particular such node. There might be other local attractors that are decoupled from our mathematical modelling, with no obvious chains of explanation linking them.
On a different tack, a vehemently dissimilar and extreme point of view is taken by adepts of Tegmark’s mathematical universe hypothesis, which has been directly addressed by various authors. This posits that there is actually no difference between mathematics and the physical world, so the role of mathematics in our physical world appears as a tautology.
Surveying all the thoughts in this collection of essays would be beyond the scope of this review. Suffice it to say that the book should be of great interest to anybody pondering the meaning of physical theories, although it appears more useful for scientists rather than for the general public. It is not an easy read, but the reader is rewarded with a great deal of food for thought.
The aim of this book is to provide undergraduate students taking classes in the physical sciences with the fundamental-mathematics tools they need to proceed with their studies.
In the first part the author introduces core mathematics, starting from basic concepts such as functions of one variable and complex numbers, and moving to more advanced topics including vector spaces, fields and operators, and functions of a complex variable.
The second part shows some of the copious applications of these mathematics tools to physics. When introducing complex physics laws and theories, including Maxwell’s equations, special relativity and quantum theory, the author tries to present the material in an easily intelligible way. The author also emphasises the direct connection between the conceptual basis of these physics topics and the mathematical tools provided in the first part of the text.
Two appendices of formulas conclude the book. A large number of problems are included but the solutions are only made available on a password-protected website for lecturers.
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