The Heisenberg uncertainty principle

The Heisenberg uncertainty principle is one of the most famous elements of quantum theory, not only mentioned in academic papers and described in quantum mechanics textbooks, but also present in popular treatises. Well, the fact is that " Heisenberg uncertainty principle " is a misnomer because it is neither a principle nor about uncertainties. Brian Randolph Greene, a leading theoretical physicist, mathematician, and string theorist, often mentions the Heisenberg uncertainty principle. He does so in his popular books and he did again in a recent tweet . The " Heisenberg uncertainty principle " is usually abbreviated as HUP and the first thing to clarify about it is that it is not a principle, but a theorem derived from the postulates of quantum mechanics. A derivation of this theorem can be found in book [1]. The result for two arbitrary quantum operators \( \hat{A} \) and \( \hat{B} \) associated to the observables \( A \) and \( B \) is \[ \sigma(A) \cdot \si

Steven Weinberg's mistakes

Experience shows that some people likes to rewrite history and make heroes, and when Steven Weinberg died in 2021, some obituaries could not resist the temptation. In 2005, Weinberg wrote an article titled "Einstein's Mistakes". I am not Weinberg and he was not Einstein, but I will write about Weinberg's mistakes in this post. Weinberg justified his review [1] of Einstein's mistakes in the following terms: "Perhaps most important, by showing that we are aware of mistakes made by even the greatest scientists, we set a good example to those who follow other supposed paths to truth. We recognize that our most important scientific forerunners were not prophets whose writings must be studied as infallible guides—they were simply great men and women who prepared the ground for the better understandings we have now achieved". I will not review all of Weinberg's mistakes, but only those which appear in the obituary written by Nima Arkani-Hamed: "How St

General relativity is not a field theory

There is a myth, perpetuated in physics textbooks and popular treatises, that states that general relativity is the theory of a gravitational field. The myth was started by Einstein, who often used the term gravitational field during the development of the theory. The pioneers make a lot of mistakes because the territory is unknown, but there is no reason to continue perpetuating myths a century after Albert Einstein, Marcel Grossmann, and David Hilbert developed the theory of general relativity. Let me quote a recent tweet from cosmologist Will Kinney: in general relativity, the gravitational field doesn’t really exist . Understanding that general relativity is not a field theory is not only desirable for reasons of rigor and consistency, but has profound implications for research. For example, the sad status of quantum gravity research is partially because some physicists such as Feynman and Weinberg have tried to apply quantum field theoretic methods to a theory in which there is

The modern second law of thermodynamics

The second law is one of the most popular laws of nature, because it is often discussed in popular science treatises and educative videos, but what is the more correct and general formulation of this law? According to P. W. Bridgman (1946 Nobel Prize in Physics) " There have been nearly as many formulations of the second law as there have been discussions of it ". We can find many historical verbal statements of the law, from when the science of thermodynamics was developing in the 19th century. Some examples: " A transformation whose only final result is to transfer heat from a body at a given temperature to a body at a higher temperature is impossible. " " It is impossible, by means of inanimate material agency, to derive mechanical effect from any portion of matter by cooling it below the temperature of the coldest of the surrounding objects. " " It is impossible to construct an engine which will work in a complete cycle, and produce no effect

Comments on symmetric monoidal categories by John Baez

I recently watched a talk by John Baez titled " Symmetric Monoidal Categories " [1]. Baez presents new mathematical material that he considers provides a common foundation for the description of different scientific and engineering topics, material that he considers to be a kind of " Rosetta stone ". Baez is correct that scientists and engineers like to describe processes or composite systems using diagrams: flow charts, Petri nets, electrical circuit diagrams, signal-flow graphs, chemical reaction networks, Feynman diagrams, etc. He claims that many of these diagrams fit into a common framework, the mathematics of symmetric monoidal categories, and that when we accept this achievement, we begin to see connections between seemingly different topics. Baez also claims that this new viewpoint introduces a paradigm shift in science. Let us go over all those interesting claims. My comments will focus on the scientific side of his talk. To get started, Baez says that s

Common misconceptions in physics (book)

This book does not offer an idealized view of physics, but a realistic view with its problems, inconsistencies, and limitations. Popular science books written by physicists, physics textbooks, and the professional physics literature contain misleading or easily misinterpreted claims, and such misconceptions and myths are preventing a fundamental understanding of Nature. This book identifies over two hundred common misconceptions in classical electrodynamics, thermodynamics, statistical mechanics, general relativity, quantum mechanics, and quantum field theory. The claims that the Coulomb gauge is not a physical gauge, that mass increases with velocity, that entropy is a quantity characterizing disorder, that general relativity is equivalent to the theory of a massless self-interacting spin-2 field, that molecular chaos is the source of irreversibility, that electrons and protons are sometimes particles and sometimes waves, and that relativistic quantum electrodynamics is a Lagrangian

Reviews of popular science

Books are a great way to give us knowledge: from a nontechnical introduction to some basic topic to a specialized monograph that summarizes the state of the art in a research field. It is sometimes believed that a popular book is not intended to be rigorous, but this is a mistake. Writing in popular science must be able to interest the layperson and at the same time keep the attention and never irritate the expert. Such were the talents of Humphrey Davy and Michael Faraday, the fathers of popular science lectures. If a topic is too difficult for a nonexpert audience, it is better to avoid it rather than giving the reader incorrect information. I will review popular science books in depth, with an emphasis on physical science books. In depth means that the review will be comparable in size to the original book, because the statements and equations in the reviewed book will be carefully evaluated and commented on. Reviews will be available in PRINT, EPUB (Kindle), and PDF formats. REVI