The Largest Concepts within the Universe: House, Time, and Movement

Pretty advanced but well written
It’s over my head but I’m picking up the terms and I did have some moments of insight.

Readable overview of some major ideas in classical mechanics and beyond
Space Time and Motion is Sean Carroll’s first book in his new series on the biggest ideas in physics. This one discusses mainly ideas the are the foundation of classical mechanics from Newton to Einstein. The book is minimal in equations and intended for the general audience and I believe it follows his podcasts which I have not listened to. Nonetheless the author does communicate the ideas quite effectively and clears up some concepts that are often glossed over in physics textbooks in the pursuit of trying to give an understanding of the foundations of physics rather than just present calculation tools. Overall the book is pretty good but I prefer Leonard Susskind’s approach to this which uses more equations but gives the reader a deeper picture into the same material.
The book covers 9 major topics some of which follow naturally from one another while others could deserve their own book. The author starts with discussing the ingredients of physics and begins with conservation. he highlights how physicists use terms and what their meaning is and the remarkable properties that enable us to make predictions . Starting with conservation the author describes conservation of momentum and energy. He also lays the foundation of abstraction by describing how physicists drop most assumptions and focus on bare essentials to find patterns using a spherical cow joke to make the point. From there the author moves on to dynamics and in particular change. Forces are introduced with gravitation and the author starts to weave in some basic math like how physicists describe dynamical change with functions of time and differential and integral calculus to capture continuous changes. Simple mathematical concepts like taylor series are introduced and the author also tackles ideas like Hamiltonian mechanics and phase space. The treatment of momentum as independent of position is well done and the author does a good job giving the abstraction intended for Hamiltonian mechanics rather than just the benefits it delivers in calculation. The author then moves on to space and eventually spacetime. Given the author’s first published book was a general relativity textbook, this is an area of deep expertise for him. The chapters on geometry, differential and Riemannian are well written and interpretable, albeit condensed for anyone to really get that much out of. The move into general relativity proper with the metric tensor along with write ups on covariant derivatives are also well done. The author gives the fundamental ideas that provided Einstein with the tools to construct a theory of gravity and that is a definite accomplishment. He then ventures into Schwarzschild’s solution, then Kerr and tackles black holes as the final chapter.
Overall the book is readable but not that deep. It does give a reasonable picture of the big ideas in physics but given the length of the book and the breadth of topics it is inevitably superficial. As mentioned I believe Susskind’s books to be more realistic in their attempt to give the bare minimum to understand the bare minimum of these topics and it requires three books of slightly longer length to cover this one book. Nonetheless it is better than many popular physics books and is not without any merit. I find the author’s subsequent work much more disappointing and unable to deliver on its goals, but this slightly hits the target.

My kind of physics book
This book is a welcome relief from the many popular books on physics and other science topics which assume that books won’t sell unless they create analogies with phenomena which a third grader can relate to.
In this book Carroll writes for intelligent, educated adults who had a good comprehension of calculus and geometry 30 or 40 years ago but eventually choose a career path that led elsewhere. Medicine in my case. So Carroll undertakes to begin at the beginning, giving a review of important math topics in a few pages. For anyone who has never taken a course in calculus or linear algebra in their lives, his book will be rough going. But for readers who only need a refresher, the book is a wonder. One thing I really enjoyed early on are the subtle connections Carroll makes in physics and math, where he points to a deeper, hidden understanding of certain topics. My college professors were too obsessed with proofs and exercises to point these out.
The book moves at a brisk pace but Carroll isn’t writing a text book, he follows a rather quirky path which makes each page interesting, if not fascinating, pages worth pondering and enjoying.
There is one improvement I would suggest, expressing more concepts in terms of units. For me anyway, thinking about the units involved in a concept often leads to quicker understanding. For example, early on when he’s discussing oscillators, he uses the common symbol ω, the angular velocity. But he never seems to mention that ω is radians/second. Anyone who hasn’t studied much physics would have difficulty here.

Sean Carroll (não confundir com seu homõnimo, o excelente biólogo) lançou-se a uma empreitada ousada: explicar os fundamentos da física sem subtrair suas bases matemáticas ao leitor não especializado. Nas suas próprias palavras: trata-se de fazer com que o(a) leitor(a) não especializado(a) COMPREENDA os fundamentos conceituais e matemáticos da física, SEM que isso faça dele ou dela um(a) físico(a). A despeito da clareza com que o autor explica cada conceito e formulação matemática, trata-se de um livro de leitura árdua, especialmente na sua parte final.
Na parte inicial, em que são apresentadas sucessivas interpretações e matematizações da mecânica clássica, um conhecimento básico de Cálculo (que felizmente possuo) habilita a leitura do livro sem maiores tropeços.
A parte final, que apresenta a geometria de Riemann e suas implicações para a Teoria da Relatividade Geral não são nada simples, ainda que os leitores estejam em ótima companhia. O próprio Einstein estudou o tema em detalhe ao longo de anos, até dominar e, finalmente, encontrar as equações que melhor expressassem seus conceitos (o que ocorreu quase em paralelo com o tratamento das operações com a geometria de Riemann e com os Tensores, por parte de Hilbert, um dos maiores matemáticos da época). Esta não é uma seção nada simples para os não físicos, e de pouco valem conhecimentos básicos de Cálculo e de geometria clássica. Ambos fornecem subsídios, mas não elucidam um paradigma conceitual e matemático substancialmente diverso. Ainda assim, há de se reconhecer que o autor se esforça em ser sempre claro e lança mão de recursos gráficos, modelos simplificados etc…
Não conheço outro livro escrito para não especialistas tão detalhado e preciso. O verdadeiro “tour de force” que exige a sua leitura, se mostra frutífero.

Viele Themen werden hier völlig anders erklärt als in Lehrbüchern und öffnet einem so die Augen. Dass eine “Gerade” in der vierdimensionalen Raumzeit beispielsweise der Weg mit der größten Eigenzeit ist, macht Phänomene die sonst mit Zeitdilatation und Längenkontraktion beschrieben werden, viel einleuchtender.