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The Biggest Ideas in the Universe 1: Space, Time and Motion
The most trusted explainer of the most mind-boggling concepts pulls back the veil of mystery that has too long cloaked the most valuable building blocks of modern science. Sean Carroll, with his genius for making complex notions entertaining, presents in his uniquely lucid voice the fundamental ideas informing the modern physics of reality.
Physics offers deep insights into the workings of the universe but those insights come in the form of equations that often look like gobbledygook. Sean Carroll shows that they are really like meaningful poems that can help us fly over sierras to discover a miraculous multidimensional landscape alive with radiant giants, warped space-time, and bewilderingly powerful forces. High school calculus is itself is a centuries-old marvel as worthy of our gaze as the Mona Lisa. And it may come as a surprise the extent to which all our most cutting-edge ideas about black holes are built on the math calculus enables.
No one else could so smoothly guide readers to grasping the very equation Einstein used to describe his theory of general relativity. In the tradition of the legendary Richard Feynman lectures presented sixty years ago, this book is an inspiring, dazzling introduction to a way of seeing that will resonate across cultural and generational boundaries for many years to come.
Physics offers deep insights into the workings of the universe but those insights come in the form of equations that often look like gobbledygook. Sean Carroll shows that they are really like meaningful poems that can help us fly over sierras to discover a miraculous multidimensional landscape alive with radiant giants, warped space-time, and bewilderingly powerful forces. High school calculus is itself is a centuries-old marvel as worthy of our gaze as the Mona Lisa. And it may come as a surprise the extent to which all our most cutting-edge ideas about black holes are built on the math calculus enables.
No one else could so smoothly guide readers to grasping the very equation Einstein used to describe his theory of general relativity. In the tradition of the legendary Richard Feynman lectures presented sixty years ago, this book is an inspiring, dazzling introduction to a way of seeing that will resonate across cultural and generational boundaries for many years to come.
305 pages, Kindle Edition
First published September 15, 2022
1,467 people are currently reading
8,113 people want to read
About the author
Sean Carroll
35 books2,569 followersSean Carroll is a physicist and philosopher at Johns Hopkins University. He received his Ph.D. from Harvard in 1993. His research focuses on spacetime, quantum mechanics, complexity, and emergence. His book The Particle at the End of the Universe won the prestigious Winton Prize for Science Books in 2013. Carroll lives in Baltimore with his wife, writer Jennifer Ouellette.
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Displaying 1 - 30 of 227 reviews
September 22, 2022
In the brilliant Yes Minister/Yes Prime Minister TV series, an idea would be described as bold or brave it was stupid or career wrecking. In The Biggest Ideas in the Universe, Sean Carroll has done something extremely bold and brave. But - for the right audience (and we'll come back to that) - it is absolutely brilliant. A quick aside about the unwieldy title: this is the first entry in the 'Biggest Ideas' trilogy with two more to follow.
There are two broad ways to write about physics. You can take the popular science approach which is descriptive, gives context and, if done well, makes it possible to a good idea of what the science is about without bumping against the maths. Or you can write a textbook, which builds on a foundation of heavy duty mathematics. This will describe what physics is really about, but will be impenetrable to anyone without an appropriate degree. (And often exceedingly dull too.) Carroll has built a bridge between the two - something I thought was impossible until now.
Famously, Stephen Hawking was told that the audience for a book halved with every equation that was included. If this is really true, Carroll has a problem, because his book contains plenty of them. Starting simply with conservation and introducing the first equation in the definition of momentum, Carroll builds surprisingly rapidly. Not only does he approach change and dynamics using conventional analysis approaches, he also introduces Hamiltonians and Lagrangians (and, of course, partial differentials) when you are less than a third of the way through the book. By the end we've got both the special and general theories of relativity under our belt and have dealt with matrices, tensors and more.
This is astonishing - Carroll doesn't just throw in equations and loosely explain them, he gives quite detailed descriptions of where they've come from and how they are used. What we don't get, which a textbook would do, is any attempt to solve these equations or expect the reader to do anything too strenuous with them, but the amount of detail is remarkable.
Does it all work? No - almost inevitably. I have seen, for example, more approachable descriptions of the principle of least action, starting with the Baywatch Principle and least time, rather than plunging straight into least action. Yet, for the right audience (and we're nearly there), it is rarely the case that the reader is left bewildered. Carroll builds everything impressively in a way that is quite different from anything I've ever seen before.
So, the audience thing. Carroll says about equations 'they are not that scary.' He tells us he dreams of a world where 'as kids are running around at a birthday party, one parent says "I don't see why anyone thinks there should be new particles near the electroweak scale," and another immediately replies "Then how in the world are you going to address the hierarchy problem?"' I'm sorry, Sean, but dream on. It's not going to happen. There are two big problems here for a truly general audience.
One is that I think Carroll totally underestimates the depth of many people's struggle with maths. It's not so much that equations are scary for those who say they don't like maths as that they repel readers without any information going into the brain. I don't think Carroll's beautiful build of the maths underlying physics will help such people at all. The other problem is that it would be possible to absorb everything in this book and you still wouldn't get the kind of conversation Carroll envisages - getting a better understanding of how physicists do their work will not allow you to go beyond what you've learned to pose those kind of questions.
A while ago I was listening to Mark Kermode and Simon Mayo's film podcast. They had asked for a simple physics explanation of multiverses. These aren't stupid people. Yet the point at which they wen't into 'This is too complicated, it's beyond me' was when the physicist said something like 'When you think of a quantum particle like an electron'. Their minds had already blanked out. Does anyone really think that such people, intelligent but not science-oriented, would ever come round to Carroll's way of thinking?
I see the audience of this book as twofold. For people like me who have a decades old physics degree to get some nostalgic reminder of what I once knew, and for young people who are about to go to university to study physics to get a wonderful introduction to what lies beneath the mathematical slog they are about to go through and why it's all worthwhile. Any idea this will convert people who aren't already excited by physics, I'm afraid, is fantasy. But for the right people, this book is magnificent.
There are two broad ways to write about physics. You can take the popular science approach which is descriptive, gives context and, if done well, makes it possible to a good idea of what the science is about without bumping against the maths. Or you can write a textbook, which builds on a foundation of heavy duty mathematics. This will describe what physics is really about, but will be impenetrable to anyone without an appropriate degree. (And often exceedingly dull too.) Carroll has built a bridge between the two - something I thought was impossible until now.
Famously, Stephen Hawking was told that the audience for a book halved with every equation that was included. If this is really true, Carroll has a problem, because his book contains plenty of them. Starting simply with conservation and introducing the first equation in the definition of momentum, Carroll builds surprisingly rapidly. Not only does he approach change and dynamics using conventional analysis approaches, he also introduces Hamiltonians and Lagrangians (and, of course, partial differentials) when you are less than a third of the way through the book. By the end we've got both the special and general theories of relativity under our belt and have dealt with matrices, tensors and more.
This is astonishing - Carroll doesn't just throw in equations and loosely explain them, he gives quite detailed descriptions of where they've come from and how they are used. What we don't get, which a textbook would do, is any attempt to solve these equations or expect the reader to do anything too strenuous with them, but the amount of detail is remarkable.
Does it all work? No - almost inevitably. I have seen, for example, more approachable descriptions of the principle of least action, starting with the Baywatch Principle and least time, rather than plunging straight into least action. Yet, for the right audience (and we're nearly there), it is rarely the case that the reader is left bewildered. Carroll builds everything impressively in a way that is quite different from anything I've ever seen before.
So, the audience thing. Carroll says about equations 'they are not that scary.' He tells us he dreams of a world where 'as kids are running around at a birthday party, one parent says "I don't see why anyone thinks there should be new particles near the electroweak scale," and another immediately replies "Then how in the world are you going to address the hierarchy problem?"' I'm sorry, Sean, but dream on. It's not going to happen. There are two big problems here for a truly general audience.
One is that I think Carroll totally underestimates the depth of many people's struggle with maths. It's not so much that equations are scary for those who say they don't like maths as that they repel readers without any information going into the brain. I don't think Carroll's beautiful build of the maths underlying physics will help such people at all. The other problem is that it would be possible to absorb everything in this book and you still wouldn't get the kind of conversation Carroll envisages - getting a better understanding of how physicists do their work will not allow you to go beyond what you've learned to pose those kind of questions.
A while ago I was listening to Mark Kermode and Simon Mayo's film podcast. They had asked for a simple physics explanation of multiverses. These aren't stupid people. Yet the point at which they wen't into 'This is too complicated, it's beyond me' was when the physicist said something like 'When you think of a quantum particle like an electron'. Their minds had already blanked out. Does anyone really think that such people, intelligent but not science-oriented, would ever come round to Carroll's way of thinking?
I see the audience of this book as twofold. For people like me who have a decades old physics degree to get some nostalgic reminder of what I once knew, and for young people who are about to go to university to study physics to get a wonderful introduction to what lies beneath the mathematical slog they are about to go through and why it's all worthwhile. Any idea this will convert people who aren't already excited by physics, I'm afraid, is fantasy. But for the right people, this book is magnificent.
June 22, 2023
I love reading about early universe physics and have since I graduated in Math/Physics in the late 1960s. Not being smart enough to pursue higher degrees, my interest in the subject matter never ceased. Most cosmology books do not offer equations to support the narrative, which is great thinking to assure potential readers are not scared off. But I always wanted to see some of the math.
Carroll provides the content and the equations and, though it took a while to get through it, the rewards were delightful. Now I have to hit the web to learn more about tensors, Hilbert Space's, and manifolds, among many more topics - which is great. For those that want to get under the covers of early Relativity and quantum physics, this is a fantastic book.
I will also have to read the book again, and maybe a third time to understand the math, but it will be worth it. It's a big gulp and a wonderful read. Much thanks, Sean. – Tom L.
Carroll provides the content and the equations and, though it took a while to get through it, the rewards were delightful. Now I have to hit the web to learn more about tensors, Hilbert Space's, and manifolds, among many more topics - which is great. For those that want to get under the covers of early Relativity and quantum physics, this is a fantastic book.
I will also have to read the book again, and maybe a third time to understand the math, but it will be worth it. It's a big gulp and a wonderful read. Much thanks, Sean. – Tom L.
September 20, 2022
16-Year-Old me would have loved this
Sean Carroll is the author of several books about physics. Although he is justly famous for his popular physics books, he is also the author of one of the best General Relativity textbooks, Spacetime and Geometry: An Introduction to General Relativity. There are equations on almost every page of Spacetime and Geometry, but very few in his previous popular physics books. I say "previous" because, with The Biggest Ideas in the Universe, that changes. Carroll argues, incontrovertibly, that without the math you don't really understand the physics. He proposes to fix that,
The Biggest Ideas series (this one is intended as the first book of a trilogy, which he likens to The Lord of the Rings -- no hubris here!) will present the Biggest Ideas in the Universe together with the math necessary to understand them. He proposes to do that using this One Weird Trick,
And,... We're Off! Starting with first-year calculus and proceeding all the way to tensor calculus, Carroll teaches you the mathematical basis of classical physics, up to and including General Relativity.
I am a 66-year-old retired professor with a PhD in Applied Mathematics. There was little here that was new to me. (But I was happy to read because Carroll is an insightful thinker who frequently manages to tell me something I already knew but didn't know I knew.) I asked myself, as one does, "Who is this book intended for?" And in a flash I realized, "I would have loved this when I was in high school." It would have been extremely challenging for sixteen-year-old me, mind-breakingly hard work, but in return I would have perceived (accurately) that I was being initiated into the Deep Magic That Makes The Universe Run. Mind blown, I'd have gobbled it down and asked for more.
There is almost nothing out there like this. Two other books come to mind, Roger Penrose's The Road to Reality: A Complete Guide to the Laws of the Universe and Leonard Susskind's The Theoretical Minimum: What You Need to Know to Start Doing Physics. The Road to Reality is to 66-year-old me what The Biggest Ideas would have been to 16-year-old me: super-challenging, but full of insight. It is not accessible to most readers. As for The Theoretical Minimum, although there is a book, it originated as a series of truly excellent YouTube lectures, and should really be consumed in that form. It is aimed higher than The Biggest Ideas: Susskind assumes his watchers are facile with basic calculus. 16-year-old me would not really have been able to follow. It's also a big time commitment. I estimate the entire series comes to well over a hundred hours of lectures. This first installment of The Biggest Ideas took me two evenings to read, perhaps six hours, or, say, twenty when the full trilogy is available.
Some of the footnotes of The Biggest Ideas were a delight. For instance, I learned that Carroll is responsible for Natalie Portman's mentioning Einstein-Rosen bridges in the 2011 film Thor. Also, one footnote is a joke that literally made me laugh out loud. I won't spoil it.
Thanks to NetGalley and Penguin Group Dutton for an advanced reader copy in exchange for a candid review.
Blog review.
Sean Carroll is the author of several books about physics. Although he is justly famous for his popular physics books, he is also the author of one of the best General Relativity textbooks, Spacetime and Geometry: An Introduction to General Relativity. There are equations on almost every page of Spacetime and Geometry, but very few in his previous popular physics books. I say "previous" because, with The Biggest Ideas in the Universe, that changes. Carroll argues, incontrovertibly, that without the math you don't really understand the physics. He proposes to fix that,
The Biggest Ideas in the Universe is dedicated to the idea that it is possible to learn about modern physics for real, equations and all, even if you are more amateur than professional and have every intention of staying that way. It is meant for people who have no more mathematical experience than high school algebra, but are willing to look at an equation and think about what it means. If you’re willing to do that bit of thinking, a new world opens up.
The Biggest Ideas series (this one is intended as the first book of a trilogy, which he likens to The Lord of the Rings -- no hubris here!) will present the Biggest Ideas in the Universe together with the math necessary to understand them. He proposes to do that using this One Weird Trick,
Most popular books assume that you don’t want to make the effort to follow the equations. Textbooks, on the other hand, assume that you don’t want to just understand the equations, you want to solve them. And solving these equations, it turns out, is enormously more work and requires enormously more practice and learning than “merely” understanding them does.
And,... We're Off! Starting with first-year calculus and proceeding all the way to tensor calculus, Carroll teaches you the mathematical basis of classical physics, up to and including General Relativity.
I am a 66-year-old retired professor with a PhD in Applied Mathematics. There was little here that was new to me. (But I was happy to read because Carroll is an insightful thinker who frequently manages to tell me something I already knew but didn't know I knew.) I asked myself, as one does, "Who is this book intended for?" And in a flash I realized, "I would have loved this when I was in high school." It would have been extremely challenging for sixteen-year-old me, mind-breakingly hard work, but in return I would have perceived (accurately) that I was being initiated into the Deep Magic That Makes The Universe Run. Mind blown, I'd have gobbled it down and asked for more.
There is almost nothing out there like this. Two other books come to mind, Roger Penrose's The Road to Reality: A Complete Guide to the Laws of the Universe and Leonard Susskind's The Theoretical Minimum: What You Need to Know to Start Doing Physics. The Road to Reality is to 66-year-old me what The Biggest Ideas would have been to 16-year-old me: super-challenging, but full of insight. It is not accessible to most readers. As for The Theoretical Minimum, although there is a book, it originated as a series of truly excellent YouTube lectures, and should really be consumed in that form. It is aimed higher than The Biggest Ideas: Susskind assumes his watchers are facile with basic calculus. 16-year-old me would not really have been able to follow. It's also a big time commitment. I estimate the entire series comes to well over a hundred hours of lectures. This first installment of The Biggest Ideas took me two evenings to read, perhaps six hours, or, say, twenty when the full trilogy is available.
Some of the footnotes of The Biggest Ideas were a delight. For instance, I learned that Carroll is responsible for Natalie Portman's mentioning Einstein-Rosen bridges in the 2011 film Thor. Also, one footnote is a joke that literally made me laugh out loud. I won't spoil it.
Thanks to NetGalley and Penguin Group Dutton for an advanced reader copy in exchange for a candid review.
Blog review.
December 29, 2022
This book states an objective that is hard to find in astro/physics books:
Most popular books assume that you don't want to make the effort to follow the equations. Textbooks, on the other hand, assume that you don't want to just understand the equations, you want to solve them. And solving these equations is enormously more work and requires enormously more practice and learning than "merely" understanding them does.
This is the first of three books that Sean is writing, all under the master title of "The Biggest Ideas in the Universe":
1. Space, Time and Motion
2. Quanta and Fields
3. Complexity and Emergence
I have read many popular physics books, and as a physics major, I have read multiple textbooks. Popular books stay away from equations. The saying goes: "each equation cuts your readership in half". Then textbooks suffer from the saying: "shut up and calculate". This book lies in the middle: lots of basic equations that are very well explained, coupled with showing why calculations with these equations actually work to describe our universe.
In the introduction he gives us an equation from Einstein that consumes this whole book. And no, it is NOT E=mc^2. Instead, it is Einstein's equation for General Relativity:
R(sub uv) - 1/2 R g(sub uv) = 8 pi G T(sub uv)
which says:
(gravity) = 8 π G × (energy and momentum)
https://www.preposterousuniverse.com/...
This equation is eventually presented once again on page 228, as eq 8.18. You really needed to understand all 237 preceding pages to feel comfortable when you arrive here.
When you look at "General Relativity" by Einstein, in Wiki:
https://en.wikipedia.org/wiki/General...
This will be the very first equation you will see.
So this equation and its understanding can help you grasp the seven Nobel Prizes where this plays a central role:
1978 - Discovery of cosmic background radiation
1993 - Binary pulsar, indirect evidence for gravitational waves
2006 - Fluctuations and spectrum of cosmic microwave background
2011 - Acceleration of the universe's expansion
2017 - Direct observation of gravitational waves
2019 - Evolution of galaxies and the universe
2020 - Theory and observations of black holes
I personally felt the hairs on my arms stand up when I reached page 228 with Einstein's field equation for general relativity (which was presented in 1915 by Einstein in a lecture to the Prussian Academy of Sciences).
To be honest, you are still allowed to think of gravity as a force when it makes sense to do so - particle physicists like to talk about the four forces of nature, and they include gravity alongside electromagnetism and the strong and weak nuclear forces. But gravity is a different kind of force, precisely because it is universal. Gravity affects everything in the same way, unlike other forces that affect objects differently depending on their charges. That's what permits us to shift from thinking of a force propagating within spacetime to a property of spacetime itself."
The final chapter on Black Holes fully utilizes everything learned so far in this book. Most people are aware that a Black Hole has a radius of 'no return', where not even light can escape. It is called the "Schwarzschild Radius".
Einstein's equation for general relativity has this concise notation, that actually unfolds "to a blizzard of terms that would fill an entire pate's worth of mathematical symbols". Einstein himself even resorted to approximation methods, since exact solutions seemed too complicated.
That didn't deter Karl Schwarzschild: An accomplished astronomer and physicist, in 1915 Schwarzschild was serving in the German Army in World War I. He spent time on the French and Russian fronts calculating missile trajectories. But while on temporary leave he was able to attend one of Einstein's lectures to the Prussian Academy, and the became fascinated by general relativity. After returning to his war duties, in late December 1915 Schwarzschild was able to write Einstein a letter containing the first exact solution to Einstein's equation, describing the metric outside a spherical planet or star. Unfortunately Schwarzschild contracted a rare skin disease at the front, of which he died less than six months later at age forty-two. It took decades for physicists to come to terms with a mind-boggling and unanticipated implication of his discovery: the prediction of black holes in general relativity.
The rest of this Black Hole chapter uses Tensors, matrices, space-time diagrams, spherical coordinate systems and differential equations to talk about:
- gravitational time dilation
- Schwarzschild radius
- event horizon
- singularity
- Eddington-Finkelstein coordinates
- Reissner-Nordstrom solution
- Kerr solution
- area theorem
- white hole
- Hawking radiation
- white dwarf
- accretion disk
- quasar (active galactic nuclei)
- gravitational waves
I see the GR score on this book is not breaking 4 (currently) which is disappointing. The author clearly states math will be used. Einstein's field equation for gravity is in the introduction, and flipping through the book will have you viewing equations on almost every page, including 3-d graphics and matrices. You REALLY need to like both math and physics. Sean is a great audio/speaker (he has a great podcast). But you can't possibly just 'listen' to this book. There is too much you MUST see. Audio-books come with downloadable PDFs, but who actually launches these while reading the book? Get the book!
Sean Carroll had completely taken me to a full understanding of everything he told me in the introduction he would accomplish. Solid 5* for me. I look forward to volumes 2 and 3.
Most popular books assume that you don't want to make the effort to follow the equations. Textbooks, on the other hand, assume that you don't want to just understand the equations, you want to solve them. And solving these equations is enormously more work and requires enormously more practice and learning than "merely" understanding them does.
This is the first of three books that Sean is writing, all under the master title of "The Biggest Ideas in the Universe":
1. Space, Time and Motion
2. Quanta and Fields
3. Complexity and Emergence
I have read many popular physics books, and as a physics major, I have read multiple textbooks. Popular books stay away from equations. The saying goes: "each equation cuts your readership in half". Then textbooks suffer from the saying: "shut up and calculate". This book lies in the middle: lots of basic equations that are very well explained, coupled with showing why calculations with these equations actually work to describe our universe.
In the introduction he gives us an equation from Einstein that consumes this whole book. And no, it is NOT E=mc^2. Instead, it is Einstein's equation for General Relativity:
R(sub uv) - 1/2 R g(sub uv) = 8 pi G T(sub uv)
which says:
(gravity) = 8 π G × (energy and momentum)
https://www.preposterousuniverse.com/...
This equation is eventually presented once again on page 228, as eq 8.18. You really needed to understand all 237 preceding pages to feel comfortable when you arrive here.
When you look at "General Relativity" by Einstein, in Wiki:
https://en.wikipedia.org/wiki/General...
This will be the very first equation you will see.
So this equation and its understanding can help you grasp the seven Nobel Prizes where this plays a central role:
1978 - Discovery of cosmic background radiation
1993 - Binary pulsar, indirect evidence for gravitational waves
2006 - Fluctuations and spectrum of cosmic microwave background
2011 - Acceleration of the universe's expansion
2017 - Direct observation of gravitational waves
2019 - Evolution of galaxies and the universe
2020 - Theory and observations of black holes
I personally felt the hairs on my arms stand up when I reached page 228 with Einstein's field equation for general relativity (which was presented in 1915 by Einstein in a lecture to the Prussian Academy of Sciences).
To be honest, you are still allowed to think of gravity as a force when it makes sense to do so - particle physicists like to talk about the four forces of nature, and they include gravity alongside electromagnetism and the strong and weak nuclear forces. But gravity is a different kind of force, precisely because it is universal. Gravity affects everything in the same way, unlike other forces that affect objects differently depending on their charges. That's what permits us to shift from thinking of a force propagating within spacetime to a property of spacetime itself."
The final chapter on Black Holes fully utilizes everything learned so far in this book. Most people are aware that a Black Hole has a radius of 'no return', where not even light can escape. It is called the "Schwarzschild Radius".
Einstein's equation for general relativity has this concise notation, that actually unfolds "to a blizzard of terms that would fill an entire pate's worth of mathematical symbols". Einstein himself even resorted to approximation methods, since exact solutions seemed too complicated.
That didn't deter Karl Schwarzschild: An accomplished astronomer and physicist, in 1915 Schwarzschild was serving in the German Army in World War I. He spent time on the French and Russian fronts calculating missile trajectories. But while on temporary leave he was able to attend one of Einstein's lectures to the Prussian Academy, and the became fascinated by general relativity. After returning to his war duties, in late December 1915 Schwarzschild was able to write Einstein a letter containing the first exact solution to Einstein's equation, describing the metric outside a spherical planet or star. Unfortunately Schwarzschild contracted a rare skin disease at the front, of which he died less than six months later at age forty-two. It took decades for physicists to come to terms with a mind-boggling and unanticipated implication of his discovery: the prediction of black holes in general relativity.
The rest of this Black Hole chapter uses Tensors, matrices, space-time diagrams, spherical coordinate systems and differential equations to talk about:
- gravitational time dilation
- Schwarzschild radius
- event horizon
- singularity
- Eddington-Finkelstein coordinates
- Reissner-Nordstrom solution
- Kerr solution
- area theorem
- white hole
- Hawking radiation
- white dwarf
- accretion disk
- quasar (active galactic nuclei)
- gravitational waves
I see the GR score on this book is not breaking 4 (currently) which is disappointing. The author clearly states math will be used. Einstein's field equation for gravity is in the introduction, and flipping through the book will have you viewing equations on almost every page, including 3-d graphics and matrices. You REALLY need to like both math and physics. Sean is a great audio/speaker (he has a great podcast). But you can't possibly just 'listen' to this book. There is too much you MUST see. Audio-books come with downloadable PDFs, but who actually launches these while reading the book? Get the book!
Sean Carroll had completely taken me to a full understanding of everything he told me in the introduction he would accomplish. Solid 5* for me. I look forward to volumes 2 and 3.
September 26, 2022
I am familiar with Carroll's technical writings and know that he has only a cursory understanding of topics like thermodynamics, quantum mechanics, or general relativity. One day I will tell the story of a serious error in Carroll's textbook on general relativity.
With such a background, I did not expect any miracles from The Biggest Ideas in the Universe. The book is full of errors and half-truths. Moreover, expressions that are only valid for certain assumptions are presented in his book as general truths. I will only give a small sample of objections in this short review:
* He equates conservation laws to Noether's theorem, because like many other physicists, he confuses the conservation of quantity Q (expressed in mathematical form as dᵢQ = 0) with the constancy of this quantity (dQ = 0).
* Ignoring basic calculus, Carroll claims that the definite integral of a function of x is another function of x.
* He asserts that Newton's second law is invariant under time reversal, when adding a dissipative force simply breaks this invariance.
* He repeats the discredited notion that coarse-graining explains irreversibility. Furthermore, he applies to the universe a statistical mechanical definition of entropy that he cannot apply, because the definition he uses is only valid for isolated systems at thermodynamic equilibrium and the universe is not at equilibrium (e.g. there are temperature gradients in the universe).
* He claims that in the world of relativity, we define four-momentum as mass times four-velocity, when not only is this not the general relativistic definition, but it is impractical. It is better to use laboratory time for parameterizations (specially when dealing with more than one particle).
* Contrary to his claims, instantaneous action-at-a-distance is fully compatible with relativistic theories. In fact, an instantaneous version of Maxwell's theory of electromagnetism has recently been developed (Instantaneous action-at-a-distance representation of field theories; 1993; Physical Review E 48, 4008; R. A. Villecco).
* He confuses the two principles of equivalence: weak and strong.
* He claims that the energy-momentum tensor in general relativity sums up everything we want to know about the "energy-like characteristics" of a collection of matter, radiation, "or anything else". This is not true, because the tensor lacks the "energy-like characteristics" of gravitation itself, which produces the well-known energy problem in general relativity, a problem Carroll neglects to mention.
* And so on.
With such a background, I did not expect any miracles from The Biggest Ideas in the Universe. The book is full of errors and half-truths. Moreover, expressions that are only valid for certain assumptions are presented in his book as general truths. I will only give a small sample of objections in this short review:
* He equates conservation laws to Noether's theorem, because like many other physicists, he confuses the conservation of quantity Q (expressed in mathematical form as dᵢQ = 0) with the constancy of this quantity (dQ = 0).
* Ignoring basic calculus, Carroll claims that the definite integral of a function of x is another function of x.
* He asserts that Newton's second law is invariant under time reversal, when adding a dissipative force simply breaks this invariance.
* He repeats the discredited notion that coarse-graining explains irreversibility. Furthermore, he applies to the universe a statistical mechanical definition of entropy that he cannot apply, because the definition he uses is only valid for isolated systems at thermodynamic equilibrium and the universe is not at equilibrium (e.g. there are temperature gradients in the universe).
* He claims that in the world of relativity, we define four-momentum as mass times four-velocity, when not only is this not the general relativistic definition, but it is impractical. It is better to use laboratory time for parameterizations (specially when dealing with more than one particle).
* Contrary to his claims, instantaneous action-at-a-distance is fully compatible with relativistic theories. In fact, an instantaneous version of Maxwell's theory of electromagnetism has recently been developed (Instantaneous action-at-a-distance representation of field theories; 1993; Physical Review E 48, 4008; R. A. Villecco).
* He confuses the two principles of equivalence: weak and strong.
* He claims that the energy-momentum tensor in general relativity sums up everything we want to know about the "energy-like characteristics" of a collection of matter, radiation, "or anything else". This is not true, because the tensor lacks the "energy-like characteristics" of gravitation itself, which produces the well-known energy problem in general relativity, a problem Carroll neglects to mention.
* And so on.
October 9, 2024
In the introduction section, Sean Carroll asserts that they are two types of science books.
The first is the popular science book. In this book, science is elucidated using metaphors and analogies, formulas are the anathema, details are hand waved away, scientists are elevated into larger than life personalities.
The second is the academic book. In this book, the objective is to train the reader to solve any question related to the subject matter. Comprehensiveness is the target as this type of book seeks to build a catalogue of techniques and a body of problems that the reader is expected to repetitively attempt in order to gain complete mastery of the domain.
The author says that he wants to write a third type of book. One that straddles the border between the two. Where the focus in not on entertainment or mastery but understanding.
Where formulas are not anathema or expressed in their full gory detail but discretion is used to strip all the superfluous components to achieve bare minimum required to achieve cognizance of the topic.
You get the idea.
This is the first of a three book series.
The first book is on classical mechanics - that is, the stuff you learned (or never could learn) in high school physics & maths.
The second is on quantum mechanics, the fun world of Schrodinger's cat and Einstein's spooky action at a distance.
I'm not really sure what the third one is supposed to be on (something about complexity and emergent systems).
So does the author achieve his goal?
Yes, he does. This is the kind of book that exemplifies, through its absence in high school curricula, why school classes are mostly boring. You give me this book and maybe, just maybe I would have been far more interested in maths and physics than I was in school.
The chapter on the non-intuitive concept of spacetime is one of the best intuitive simplifications of this concept.
If have any kids or siblings or niblings who are entering high school, this is the perfect book to gift them.
The first is the popular science book. In this book, science is elucidated using metaphors and analogies, formulas are the anathema, details are hand waved away, scientists are elevated into larger than life personalities.
The second is the academic book. In this book, the objective is to train the reader to solve any question related to the subject matter. Comprehensiveness is the target as this type of book seeks to build a catalogue of techniques and a body of problems that the reader is expected to repetitively attempt in order to gain complete mastery of the domain.
The author says that he wants to write a third type of book. One that straddles the border between the two. Where the focus in not on entertainment or mastery but understanding.
Where formulas are not anathema or expressed in their full gory detail but discretion is used to strip all the superfluous components to achieve bare minimum required to achieve cognizance of the topic.
You get the idea.
This is the first of a three book series.
The first book is on classical mechanics - that is, the stuff you learned (or never could learn) in high school physics & maths.
The second is on quantum mechanics, the fun world of Schrodinger's cat and Einstein's spooky action at a distance.
I'm not really sure what the third one is supposed to be on (something about complexity and emergent systems).
So does the author achieve his goal?
Yes, he does. This is the kind of book that exemplifies, through its absence in high school curricula, why school classes are mostly boring. You give me this book and maybe, just maybe I would have been far more interested in maths and physics than I was in school.
The chapter on the non-intuitive concept of spacetime is one of the best intuitive simplifications of this concept.
If have any kids or siblings or niblings who are entering high school, this is the perfect book to gift them.
March 9, 2024
Great refresh in essentials of physics explaining the progress of concepts and giving insights behind equations. I don’t think it is easily comprehensible as Sean Carroll claims though as it gets pretty complicated and even complex in the first chapter on conservation laws. Overall it’s a nice guided tour in various vectors of time and space. Later on relativity the gravity the of situation eventually pulls you into black holes…
October 31, 2022
I learned about this book from a radio interview with the author and it was pitched as one for a general audience. I am well-educated and able to grasp difficult concepts but I could not understand the explanations of the equations here from the start. Admittedly, my background in math and science is weak. If you don't have a strong math background, if you never took calculus, I would not bother with this book.
I would not give it a negative review if the introduction did not tell me the book is "meant for people who have no more mathematical experience than high school algebra, but are willing to look at an equation and think about what it means."
I looked at the equations on pages 13 and 14, and reread pages 11-15, over and over again. The author says: "It is easy to add two vectors together. Just imagine placing the beginning of the second vector at the end of the first, so we define a third resulting vector by traveling down the first and then the second." Which is the first vector and which is the second? Where are the beginnings and the ends of the vectors? How do you travel down a vector? I have studied and studied those diagrams and the words do not connect with the pictures for me at all. I read for another ten pages or so and then gave up. It is very dense and too hard to understand to be a satisfying read.
It may be a great book for people who understand it, but if, like me, you are intelligent and well-educated but have no more mathematical experience than high school algebra, I don't think you'll enjoy this book.
I would not give it a negative review if the introduction did not tell me the book is "meant for people who have no more mathematical experience than high school algebra, but are willing to look at an equation and think about what it means."
I looked at the equations on pages 13 and 14, and reread pages 11-15, over and over again. The author says: "It is easy to add two vectors together. Just imagine placing the beginning of the second vector at the end of the first, so we define a third resulting vector by traveling down the first and then the second." Which is the first vector and which is the second? Where are the beginnings and the ends of the vectors? How do you travel down a vector? I have studied and studied those diagrams and the words do not connect with the pictures for me at all. I read for another ten pages or so and then gave up. It is very dense and too hard to understand to be a satisfying read.
It may be a great book for people who understand it, but if, like me, you are intelligent and well-educated but have no more mathematical experience than high school algebra, I don't think you'll enjoy this book.
June 21, 2024
This book is aimed at the physics-curious, intending to fill a very empty gap between textbooks with lots of equations you actually have to solve and physics books for the lay reader that have no equations at all and pretend that that's OK.
The book gives you the important equations, explains them but doesn't force you to do anything that would feel a bit too much like physics homework. This is a great approach, and just right for those of you like me that always feel unsatisfied by popular science books that tend to oversimplify things, tell half truths or come up with incomprehensible analogies.
To give a concrete example, I've amused myself recently with a few physics questions at a high school level. There is nothing I like more than time spent on an inclined plane, with oscillating springs and swinging pendulums - but it was only after a few months that I found out that I could have been having just as much fun with a Laplacian or even a Hamiltonian. For reasons which are unfathomable to me these things are kept secret from anyone under the age of eighteen, but if I had known about them when I was younger, physics would have been much easier and my conceptual understanding much better. This book introduces both in the first few chapters and explains them very well.
I also read through the sections on Reimann geometry and on special and general relativity, and for the first time ever I felt that I understood them.
I didn't of course, but at least it felt as if I did and I am reasonably certain that if I spent about three to five hours a day for the next few years studying advanced calculus I might be in with a chance, and I can't say better than that.
The book gives you the important equations, explains them but doesn't force you to do anything that would feel a bit too much like physics homework. This is a great approach, and just right for those of you like me that always feel unsatisfied by popular science books that tend to oversimplify things, tell half truths or come up with incomprehensible analogies.
To give a concrete example, I've amused myself recently with a few physics questions at a high school level. There is nothing I like more than time spent on an inclined plane, with oscillating springs and swinging pendulums - but it was only after a few months that I found out that I could have been having just as much fun with a Laplacian or even a Hamiltonian. For reasons which are unfathomable to me these things are kept secret from anyone under the age of eighteen, but if I had known about them when I was younger, physics would have been much easier and my conceptual understanding much better. This book introduces both in the first few chapters and explains them very well.
I also read through the sections on Reimann geometry and on special and general relativity, and for the first time ever I felt that I understood them.
I didn't of course, but at least it felt as if I did and I am reasonably certain that if I spent about three to five hours a day for the next few years studying advanced calculus I might be in with a chance, and I can't say better than that.
October 16, 2022
I love the niche this series is targeting:
Though I've had more math education than that, I've also forgotten a lot of it, so this sounded like the perfect level of explanation for me.
How successful is this attempt to make physics accessible? Until the last two chapters - on gravity and black holes - I think it does pretty well. I had to reread and think about things a few times, but the effort paid off. I suspect I would have needed to invest significantly more time to really follow the final chapters, but I at least gleaned a little from them. I'm looking forward to the next two volumes.
Cool stuff. My mind was blown a little bit by the explanation of why gravity follows an inverse-square law. It's so simple yet somehow I'd never heard it before: the inverse-square law is a consequence of the fact that in 3-dimensional space, the area of a sphere is proportional to the radius squared.
I also enjoyed the explanation of why "almost every oscillating system is approximated by a simple harmonic oscillator", which relies on just a little algebra and calculus showing that typically only the squared term in the potential energy function will be significant.
Taxonomy. Carroll explains that physical theories can be categorized as either classical or quantum and also as relativistic or non-relativistic. This book discusses both kinds of classical theories (including Newtonian mechanics and general relativity) but leaves quantum mechanics for a future volume.
He also contrasts local theories with global theories. As I understand it, the difference is whether you make predictions directly based on a single data point, or by using a rule to select from all the predictions that are consistent with a set of data points. Two examples he discusses are Newtonian mechanics and Lagrangian mechanics: they both make identical predictions about the path an object will follow. In the former, you find this path by applying a formula based on the object's state at one point in time. In the latter, you consider all possible paths between the object's states at two points in time and choose the one that minimizes a specific quantity.
Geometry. A few years ago I'd just moved to a new city and was also trying - or at least, aspiring - to beef up my math skills, so I signed up for a local math meetup. I bought the book they were reading at the time, Tensor Analysis on Manifolds, despite not knowing what a tensor or a manifold was or why anyone would need to analyze them. (I never went, and the book has been collecting dust.)
After reading Carroll's chapter on geometry, now I sort of know! A manifold is a way of describing a space, potentially a non-Euclidean space (one that's curved, where parallel lines can intersect or diverge). To fully specify the curvature of a manifold, all you need is a function called a line element that tells you the length of the curve between any two given points. A matrix called a metric tensor is a compact way to express the same information as the line element. This is relevant to physics, of course, because relativity tells us that spacetime is not actually Euclidean, and we need a way to talk about precisely what it is instead.
Relativity. Carroll's discussion of coordinate time vs proper time was illuminating for me:
And things get weird because:
So instead of the Pythagorean theorem's sum-of-squares, proper time is calculated using the difference of squares of coordinate time and distance (equation 6.2, page 152):
(The same fact can be expressed in a metric tensor by having "a minus sign for the timelike direction. A metric with this kind of minus sign is called Lorentzian...")
Thus, you experience more time if you sit still from 6pm to 7pm than if you leave on a round-trip journey at 6pm and arrive back where you started at 7pm. Carroll's explanations do a good job of making this weird aspect of reality seem somewhat less mysterious.
(crossposted from https://brokensandals.net/reviews/202...)
The Biggest Ideas in the Universe is dedicated to the idea that it is possible to learn about modern physics for real, equations and all, even if you are more amateur than professional and have every intention of staying that way. It is meant for people who have no more mathematical experience than high school algebra, but are willing to look at an equation and think about what it means.
Though I've had more math education than that, I've also forgotten a lot of it, so this sounded like the perfect level of explanation for me.
How successful is this attempt to make physics accessible? Until the last two chapters - on gravity and black holes - I think it does pretty well. I had to reread and think about things a few times, but the effort paid off. I suspect I would have needed to invest significantly more time to really follow the final chapters, but I at least gleaned a little from them. I'm looking forward to the next two volumes.
Cool stuff. My mind was blown a little bit by the explanation of why gravity follows an inverse-square law. It's so simple yet somehow I'd never heard it before: the inverse-square law is a consequence of the fact that in 3-dimensional space, the area of a sphere is proportional to the radius squared.
If we draw a sphere centered on the sun, the lines of force all pass through that sphere. If we draw another sphere with a bigger radius, the same lines will pass through it, but they will be more spread out—fewer lines will pass through any fixed area of the sphere.
I also enjoyed the explanation of why "almost every oscillating system is approximated by a simple harmonic oscillator", which relies on just a little algebra and calculus showing that typically only the squared term in the potential energy function will be significant.
Taxonomy. Carroll explains that physical theories can be categorized as either classical or quantum and also as relativistic or non-relativistic. This book discusses both kinds of classical theories (including Newtonian mechanics and general relativity) but leaves quantum mechanics for a future volume.
He also contrasts local theories with global theories. As I understand it, the difference is whether you make predictions directly based on a single data point, or by using a rule to select from all the predictions that are consistent with a set of data points. Two examples he discusses are Newtonian mechanics and Lagrangian mechanics: they both make identical predictions about the path an object will follow. In the former, you find this path by applying a formula based on the object's state at one point in time. In the latter, you consider all possible paths between the object's states at two points in time and choose the one that minimizes a specific quantity.
Geometry. A few years ago I'd just moved to a new city and was also trying - or at least, aspiring - to beef up my math skills, so I signed up for a local math meetup. I bought the book they were reading at the time, Tensor Analysis on Manifolds, despite not knowing what a tensor or a manifold was or why anyone would need to analyze them. (I never went, and the book has been collecting dust.)
After reading Carroll's chapter on geometry, now I sort of know! A manifold is a way of describing a space, potentially a non-Euclidean space (one that's curved, where parallel lines can intersect or diverge). To fully specify the curvature of a manifold, all you need is a function called a line element that tells you the length of the curve between any two given points. A matrix called a metric tensor is a compact way to express the same information as the line element. This is relevant to physics, of course, because relativity tells us that spacetime is not actually Euclidean, and we need a way to talk about precisely what it is instead.
Relativity. Carroll's discussion of coordinate time vs proper time was illuminating for me:
Now there are two distinct notions of what is meant by "time." One notion of time is as a coordinate on spacetime. Spacetime is a four-dimensional continuum, and if we want to specify locations within it, it's convenient to attach a nunmber called "the time" to every point within it. That's generally what we have in mind when we think of "6 p.m." and "7 p.m." Those refer to values of a coordinate on spacetime, labels that help us locate events. Everyone is supposed to understand what we mean when we say "meet at the restaurant at 7 p.m."
But, says relativity, just as the distance as the crow flies is generally different from the distance you actually travel between two points in space, the duration of time that you experience along your world line generally won't be the same as the universal coordinate time. You experience an amount of time that could be measured by a clock that you carry with you on the journey. This is the proper time along the path. And the duration measured by a clock, just like the distance traveled as measured by the odometer on your car, will depend on the path you take.
And things get weird because:
In space, a straight line describes the shortest distance between two points. In spacetime, by contrast, a straight path yields the longest elapsed time between two events.
So instead of the Pythagorean theorem's sum-of-squares, proper time is calculated using the difference of squares of coordinate time and distance (equation 6.2, page 152):
(The same fact can be expressed in a metric tensor by having "a minus sign for the timelike direction. A metric with this kind of minus sign is called Lorentzian...")
Thus, you experience more time if you sit still from 6pm to 7pm than if you leave on a round-trip journey at 6pm and arrive back where you started at 7pm. Carroll's explanations do a good job of making this weird aspect of reality seem somewhat less mysterious.
(crossposted from https://brokensandals.net/reviews/202...)
August 13, 2024
Trigger Warning: VERY spooky equations🫣🫣🫣
September 21, 2022
If you like physics I'd say run out and read this one right away. Sean Carroll is one of my favorite science authors and this is his best work. What I like about this one is that he gets into the mathematical tools that physicists actually use. He explains them at a conceptual level, such that even if you still can't solve the kinds of equations he's talking about you can still see how they work. The major tools of modern physics - Newtonian mechanics, Lagrangian mechanics, Hamiltonian mechanics - are all here. He takes up a unique space straddling popular science book and university textbook, which is hard to do but I think he does it quite well.
February 3, 2025
Very disappointing. Who is the audience for this book? Laymen will feel that the author glossed over many things because (rightly so) they don't have the necessary background expertise. Physicists may like this book because they will "fill in the blanks". Two Einstein quotes came to me while reading this book: (i) You don't really understand something unless you can explain it your grandmother": but conversely (ii) Everything should be made as simple as possible, but not simpler.
We have gas inflation, food inflation, and now book review inflation. You don't rate this book a 4 or 5 because the author tried doing something that is very difficult. You rate the book based on the output.
As a side issue - an excellent book on Special Relativity is the classic Spacetime Physics by Taylor and Wheeler.
We have gas inflation, food inflation, and now book review inflation. You don't rate this book a 4 or 5 because the author tried doing something that is very difficult. You rate the book based on the output.
As a side issue - an excellent book on Special Relativity is the classic Spacetime Physics by Taylor and Wheeler.
March 16, 2025
This book consists of Sean Carroll giving you a super quick crash course on classical mechanics, building up to an outline of the basic concepts in general relativity. He outlines the relevant math but without assuming the reader knows anything about it, so he uses basic language and clearly makes an effort to make everything as intuitive and accessible as possible.
I like his approach. I appreciate that he keeps it super basic but still focuses on the math and the structure of the theory. I think (haven't tried yet) that this book creates a good foundation for maybe looking at more serious GR books. At the very least, it gets rid of some of the intimidation factor by at least introducing the basic concepts (both physical and mathematical) very nicely.
That said, it was a tiring read for me and took me a super long time to finish. The first tiring thing: parts of the book were boring for me because it was covering stuff I already know. However I didn't want to skip it because even on these sections, occasionally Carroll drops some insight or intuition that I've never thought about, so I still get to learn something. So basically I was slogging through every word in case he does drop some interesting insight for me. That's on me
The second tiring thing: I found a lot of the stuff he writes confusing. How do I put this?? The language he uses isn't necessarily confusing (in fact Carroll goes to decent lengths to be precise), but I don't see how the things he says follow from the foundation he gives us. Which is probably fine and I just need to look at a textbook if I want everything to make sense.
Overall good book, would recommend to anyone interested in the topic (physics background or not).
I like his approach. I appreciate that he keeps it super basic but still focuses on the math and the structure of the theory. I think (haven't tried yet) that this book creates a good foundation for maybe looking at more serious GR books. At the very least, it gets rid of some of the intimidation factor by at least introducing the basic concepts (both physical and mathematical) very nicely.
That said, it was a tiring read for me and took me a super long time to finish. The first tiring thing: parts of the book were boring for me because it was covering stuff I already know. However I didn't want to skip it because even on these sections, occasionally Carroll drops some insight or intuition that I've never thought about, so I still get to learn something. So basically I was slogging through every word in case he does drop some interesting insight for me. That's on me
The second tiring thing: I found a lot of the stuff he writes confusing. How do I put this?? The language he uses isn't necessarily confusing (in fact Carroll goes to decent lengths to be precise), but I don't see how the things he says follow from the foundation he gives us. Which is probably fine and I just need to look at a textbook if I want everything to make sense.
Overall good book, would recommend to anyone interested in the topic (physics background or not).
January 13, 2023
This is a very good book. I'm just not entirely clear who the best audience for it is. I think I would have loved it late in high school, because Carroll explains things with actual equations attached, though I would have missed many of the key insights (I would not have appreciated the motivation for the Lagrange density, for example...).
And I really like the book now, as someone with a PhD in physics but who doesn't work in mechanics or relativity. It provided me with some good insight about why Lagrangian and Hamiltonian approaches are so useful, and appropriate in different places, as well as good insight about how to think correctly about special and general relativity. I think most books now avoid talking about mass increasing with velocity, and correctly limit themselves to rest mass, energy, and momentum, but it's still standard to talk about "length contraction". Carroll explains why this isn't the best way of thinking about it. Likewise basic discussions of black holes (e.g., Astrophysics in a Nutshell) will give the Schwarzschild metric and show that proper time intervals go to zero compared to coordinate time intervals at r=2GM, but won't discuss the coordinate singularity at the event horizon or give you coordinates that allow you to go into the black hole, as Carroll does here.
Do be a bit cautious, though, as even someone as careful and clear as Carroll has the occasional mistake. E.g., on page 197 he says the components of a vector are "the projections of the vector along each axis", which is only true for an orthonormal basis. He talks in this same chapter and elsewhere about coordinate systems that aren't orthogonal—relativity is famous for them being common, unlike quantum mechanics—so he really should know better.
And Carroll also doesn't really know who the audience for his book is. He technically introduces everything in this book, from one-dimensional calculus to partial derivatives of tensors, but no one could actually learn these things from his book. Carroll was an excellent teacher back in the day (I had him for a class at the University of Chicago), but I don't think he ever taught intro physics, and I don't think he's been teaching formal classes much at all for decades (he was a research professor at Caltech, and I'm not sure he'll be teaching in his new position at Hopkins, but it won't be intro physics if he does). So he really does not understand what it takes to truly teach these topics (aside from GR, which he is experienced at teaching). For example, on page 14 he blithely shows the reader how to add vectors, which I guarantee you will only help remind those who already know how to do so, or a small percentage of very bright people. Same for a lot of the basic mechanics, which as someone who does teach intro physics routinely, I can assure you will not really sink in as given here.
So I was hoping maybe this would be an excellent book for an upper-level undergrad. Someone who knows a lot of basic physics, has seen Lagrangian mechanics, some special relativity, but not general relativity. And I think maybe that is the best audience for the book, although such students will have little patience for the sections explaining what a derivative is.
As I was reading the book, I was trying to think of some way to design a capstone course around it (and the forthcoming companion books on other areas of physics). And I'm not sure I can. Because this book is intentionally an odd duck. It's more technical than a popular-level book. It has equations, including the Einstein equation and even the geodesic equation (albeit in the appendix, for the latter). But it's intentionally not a textbook, and is not designed to teach someone how to do any of this physics and really use the equations. There are no examples, no exercises, and precious little derivation (unless it's something quick that gives good insight—there are some of those, and I appreciated them). So maybe I could create a course like this, but it would require a lot of supplementation and effort on my part.
But maybe this book is aimed at the most beautiful kind of learning, for most people. Deep enough to get some real understanding of things (if there are no equations, you're not actually looking at the physics). At the same time, quick and light enough to be something many people can take on, unlike even an undergraduate physics degree.
So in the end I come down highly in favor of the book, despite or maybe even because of the uncomfortable and lonely place it has in the set of physics books.
And I really like the book now, as someone with a PhD in physics but who doesn't work in mechanics or relativity. It provided me with some good insight about why Lagrangian and Hamiltonian approaches are so useful, and appropriate in different places, as well as good insight about how to think correctly about special and general relativity. I think most books now avoid talking about mass increasing with velocity, and correctly limit themselves to rest mass, energy, and momentum, but it's still standard to talk about "length contraction". Carroll explains why this isn't the best way of thinking about it. Likewise basic discussions of black holes (e.g., Astrophysics in a Nutshell) will give the Schwarzschild metric and show that proper time intervals go to zero compared to coordinate time intervals at r=2GM, but won't discuss the coordinate singularity at the event horizon or give you coordinates that allow you to go into the black hole, as Carroll does here.
Do be a bit cautious, though, as even someone as careful and clear as Carroll has the occasional mistake. E.g., on page 197 he says the components of a vector are "the projections of the vector along each axis", which is only true for an orthonormal basis. He talks in this same chapter and elsewhere about coordinate systems that aren't orthogonal—relativity is famous for them being common, unlike quantum mechanics—so he really should know better.
And Carroll also doesn't really know who the audience for his book is. He technically introduces everything in this book, from one-dimensional calculus to partial derivatives of tensors, but no one could actually learn these things from his book. Carroll was an excellent teacher back in the day (I had him for a class at the University of Chicago), but I don't think he ever taught intro physics, and I don't think he's been teaching formal classes much at all for decades (he was a research professor at Caltech, and I'm not sure he'll be teaching in his new position at Hopkins, but it won't be intro physics if he does). So he really does not understand what it takes to truly teach these topics (aside from GR, which he is experienced at teaching). For example, on page 14 he blithely shows the reader how to add vectors, which I guarantee you will only help remind those who already know how to do so, or a small percentage of very bright people. Same for a lot of the basic mechanics, which as someone who does teach intro physics routinely, I can assure you will not really sink in as given here.
So I was hoping maybe this would be an excellent book for an upper-level undergrad. Someone who knows a lot of basic physics, has seen Lagrangian mechanics, some special relativity, but not general relativity. And I think maybe that is the best audience for the book, although such students will have little patience for the sections explaining what a derivative is.
As I was reading the book, I was trying to think of some way to design a capstone course around it (and the forthcoming companion books on other areas of physics). And I'm not sure I can. Because this book is intentionally an odd duck. It's more technical than a popular-level book. It has equations, including the Einstein equation and even the geodesic equation (albeit in the appendix, for the latter). But it's intentionally not a textbook, and is not designed to teach someone how to do any of this physics and really use the equations. There are no examples, no exercises, and precious little derivation (unless it's something quick that gives good insight—there are some of those, and I appreciated them). So maybe I could create a course like this, but it would require a lot of supplementation and effort on my part.
But maybe this book is aimed at the most beautiful kind of learning, for most people. Deep enough to get some real understanding of things (if there are no equations, you're not actually looking at the physics). At the same time, quick and light enough to be something many people can take on, unlike even an undergraduate physics degree.
So in the end I come down highly in favor of the book, despite or maybe even because of the uncomfortable and lonely place it has in the set of physics books.
October 7, 2022
This book was a Godsend for me personally, which- to adapt a quip for Bertrand Russell- is pretty chic for an atheist.
I've been reading popular physicist authors since Brian Greene's Fabric of the Cosmos while in high-school. More recently, I've read all of Carroll's and Greene's books as well as Max Tegmark, Carlo Rovelli, Stephen Hawking, Steven Weinberg, David Deutsch, and Michio Kaku. As enlightening as they all have been to understanding the concepts at the forefront of physics, and giving competing interpretations, there was something deeply missing: equations. Sure you can grasp the concept of the equation for General Relativity by the famous John Wheeler quote, "Spacetime tells matter how to move; matter tells spacetime how to curve."But I wanted to understand what the symbols meant within this masterpiece and the most eloquent equations of physics at large.
After hearing Tegmark rave about how influential The Feynman Lectures on Physics had impacted him personally, I decided to pick up a copy several years ago. As I had taken 2 courses on Physics for Majors in undergrad, much of Feynman's work was a refresher. Oddly, the two pillars of modern physics- Quantum Mechanics and General Relativity- were no where to be found in my physics courses. And I admittedly struggled to make it deep into Feynman's 3rd book in the lecture series on Quantum Mechanics. As Carroll explains, texts are written with the intent that you will be solving equations.
The Biggest Ideas in the Universe has been a perfect solution to bridge the gap between my understanding of physics through popular science writing and the Feynman Lectures. It's sole purpose is to help one understand the equations without adding the complexity of solving them. I'm extremely grateful Carroll wrote this book and I look forward to the other two in the series.
Just as Feynman opened his lecture series by captivating the reader with the line, "If we were to name the most powerful assumption of all, which leads one on and on in an attempt to understand life, it is that all things are made of atoms, and that everything that living things do can be understood in terms of the jigglings and wigglings of atoms", Carroll takes ambitions to the next level, opening by imagining a world where people openly discuss physics at parties.
I'm slightly skeptical of this happening anytime soon. For example, his review of calculus was extremely helpful, but FOR ME. It was an important refresher, having been removed from my undergrad calculus course for 15 years. I have reservations in thinking the person with no background knowledge would grasp hold so quickly.
Regardless, I love the ambition of Carroll. This work is revolutionary for those of us who desire to understand what the most famous equations in physics are telling us. Thank you Sean!
I've been reading popular physicist authors since Brian Greene's Fabric of the Cosmos while in high-school. More recently, I've read all of Carroll's and Greene's books as well as Max Tegmark, Carlo Rovelli, Stephen Hawking, Steven Weinberg, David Deutsch, and Michio Kaku. As enlightening as they all have been to understanding the concepts at the forefront of physics, and giving competing interpretations, there was something deeply missing: equations. Sure you can grasp the concept of the equation for General Relativity by the famous John Wheeler quote, "Spacetime tells matter how to move; matter tells spacetime how to curve."But I wanted to understand what the symbols meant within this masterpiece and the most eloquent equations of physics at large.
After hearing Tegmark rave about how influential The Feynman Lectures on Physics had impacted him personally, I decided to pick up a copy several years ago. As I had taken 2 courses on Physics for Majors in undergrad, much of Feynman's work was a refresher. Oddly, the two pillars of modern physics- Quantum Mechanics and General Relativity- were no where to be found in my physics courses. And I admittedly struggled to make it deep into Feynman's 3rd book in the lecture series on Quantum Mechanics. As Carroll explains, texts are written with the intent that you will be solving equations.
The Biggest Ideas in the Universe has been a perfect solution to bridge the gap between my understanding of physics through popular science writing and the Feynman Lectures. It's sole purpose is to help one understand the equations without adding the complexity of solving them. I'm extremely grateful Carroll wrote this book and I look forward to the other two in the series.
Just as Feynman opened his lecture series by captivating the reader with the line, "If we were to name the most powerful assumption of all, which leads one on and on in an attempt to understand life, it is that all things are made of atoms, and that everything that living things do can be understood in terms of the jigglings and wigglings of atoms", Carroll takes ambitions to the next level, opening by imagining a world where people openly discuss physics at parties.
I'm slightly skeptical of this happening anytime soon. For example, his review of calculus was extremely helpful, but FOR ME. It was an important refresher, having been removed from my undergrad calculus course for 15 years. I have reservations in thinking the person with no background knowledge would grasp hold so quickly.
Regardless, I love the ambition of Carroll. This work is revolutionary for those of us who desire to understand what the most famous equations in physics are telling us. Thank you Sean!
February 7, 2023
[Imported automatically from my blog. Some formatting there may not have translated here.]
I've read a couple of Sean Carroll's pop-science books (The Big Picture and Something Deeply Hidden) over the past few years, so when this new one became available at Portsmouth Public Library, I grabbed it.
Now, science books aimed at the masses will often shy away from math. Sometimes their authors will acknowledge and excuse this by pointing out the relevant market forces: their publishers' research shows that each equation in a book will decrease sales by X percent, or something. But (I assume) Carroll successfully persuaded his publisher to let him math it up in this book, so good for him. This book is volume one of a projected trilogy; the next one will be subtitled Quanta and Fields, and the last Complexity and Emergence. I'm on board.
But this book concentrates on "classical" physics. He starts off slow, describing Newtonian mechanics, conservation laws, aided by basic calculus. Moving on to Lagrangian mechanics and the principle of least action. And then Hamiltonian mechanics. All do an approximately fine job of describing non-relativistic motion of macroscopic bodies.
But then we edge into Einsteinian insights, the interplay between space, time, mass, and energy. And then (watch out!) the notion of curved spacetime, which quickly invokes (eek!) tensor notation, the better to introduce General Relativity. And before you know it, we're hip deep in Riemann and Ricci and all that stuff. To a point where (if you've been following along, nodding your head) you can appreciate beauty of the Einstein equation (I'm not sure how this will appear on Goodreads):
Rμν - ½Rgμν = 8πGTμν
And we wind up with a good (but quick) discussion of black holes (they're hairless!), event horizons, naked singularities, accretion disks, gravitational waves and the like.
I must confess that, even though I was a physics major decades ago, I got lost at a certain point. I think to actually know this material, you have to take courses from smarter people, doing problem sets along the way. There's no shiny magic path to understanding. But (on the other hand) I learned a good deal at the fuzzy territory between "yeah, this is simple, I get this" and "whoa, what's going on here?"
November 5, 2022
This book was challenging but useful to read. I'm endlessly fascinated by modern understandings of how the universe works, so I regularly add a book like this to my reading list.
The most difficult aspect was the importance of math in Carroll's exploration of classical and quantum physics. Immediately the dust rose from my buried college fling with introductory calculus, and it reached nightmare proportions when matrix algebra entered the picture about 2/3 of the way through.
Now, Sean Carroll promised there would be value in embracing the math, and there was. It was extremely interesting to see how skilled mathematicians mined equations to make predictions of actual phenomena for which devising detection methods would yield startling new understandings.
Was it worth the effort? I think so, though I felt like I was holding on to a cliff edge with my fingernails to stay engaged with the math. At some point, I definitely slipped from the ledge, especially as the variables multiplied and matrix algebra brought back traumatic memories of a graduate level statistics course.
I read through to the end and, because the last chapter is on black holes, was rewarded with some brand new ideas.
The most difficult aspect was the importance of math in Carroll's exploration of classical and quantum physics. Immediately the dust rose from my buried college fling with introductory calculus, and it reached nightmare proportions when matrix algebra entered the picture about 2/3 of the way through.
Now, Sean Carroll promised there would be value in embracing the math, and there was. It was extremely interesting to see how skilled mathematicians mined equations to make predictions of actual phenomena for which devising detection methods would yield startling new understandings.
Was it worth the effort? I think so, though I felt like I was holding on to a cliff edge with my fingernails to stay engaged with the math. At some point, I definitely slipped from the ledge, especially as the variables multiplied and matrix algebra brought back traumatic memories of a graduate level statistics course.
I read through to the end and, because the last chapter is on black holes, was rewarded with some brand new ideas.
October 10, 2022
A wonderful volume from Carroll. As Carroll states, there are few books that are intermediate between popular science and textbook, and I think he fills this role here really well. I appreciate having the equations (and their explanations) even if we do not set about solution methods. The author is also an excellent presenter of information and it is easy to read, and Carroll does an excellent job of explaining the most important ideas in compelling ways.
If you enjoy physics-popular, amateur, or professional-then I think you will enjoy this book. My only complaint is my perennial one with physics books that cover Noether's theorem, is that it implies a one-to-one correspondence between specific [continuous] symmetries and specific conservation laws that the theorem does not say exists in general. But that is just a nitpick in a truly excellent book.
If you enjoy physics-popular, amateur, or professional-then I think you will enjoy this book. My only complaint is my perennial one with physics books that cover Noether's theorem, is that it implies a one-to-one correspondence between specific [continuous] symmetries and specific conservation laws that the theorem does not say exists in general. But that is just a nitpick in a truly excellent book.
December 20, 2022
To make anything of this you'd better be on familiar terms with calculus, personally I'm not, so my prejudice is founded on ignorance, rather than extrapolated from an advanced ability to critique high level mathematical concepts.
We're looking at degree level mathematics here, unless you're some kind of savant...but you can still understand what's going on at a lesser level, to an extent where your efforts are not completely in vain.
We're looking at degree level mathematics here, unless you're some kind of savant...but you can still understand what's going on at a lesser level, to an extent where your efforts are not completely in vain.
January 8, 2023
I had few glimmers of understanding while reading this book. The author tried to get me to follow along as he manipulated metrics and tensors; then also found it necessary to remind me that the square root of a term can be a plus OR minus value, and that “momenta” is plural for momentum. :-|
Who exactly was this book written for?! I do feel that I understand spacetime, gravity, and black holes marginally better after reading it, but not because of all the equations!
Who exactly was this book written for?! I do feel that I understand spacetime, gravity, and black holes marginally better after reading it, but not because of all the equations!
November 3, 2022
Not What I Expected
Way more high level math than I expected. I should have researched it more before buying. I love Sean's work but I wasn't looking for a deep dive into math.
Way more high level math than I expected. I should have researched it more before buying. I love Sean's work but I wasn't looking for a deep dive into math.
April 14, 2023
Would never recommend for someone who is unwilling to read slowly, think deeply, break your brain, re-read, and still struggle. This was a fascinating read for me but definitely a slow go to ensure I was understanding. I can’t count the number of times I had to backtrack to re-read concepts. By the end I felt I actually understood a large majority of it (except metrics and tensors and that). The mathematical formulas were hard to wrap by brain around, but when it was brought into the physical realm showing the real world consequences of those mathematical formulas I was much better able to comprehend them. I’ll definitely be reading the follow up when it comes out to delve even further into the world of physics.
April 3, 2024
Does not shy away from the maths, but without going into the nitty gritty details. Each chapter builds on top of the previous one in a nice progression and explains the historical context, principles involved and challenges. Won't give you an undergraduate diploma, but it is a very enjoyable read.
February 17, 2024
I had to listen to most chapters twice, and to follow on the kindle book, but it was worth it! 😅 To me this was similar and slightly more accessible than the 'Theoretical Minimum' series, which is now easier for me to follow. I look forward to the other volumes in this series!
April 24, 2023
This falls closer to a 2.5/5, but I'm rounding down for reasons I'll explain below.
I want to preface this by saying that I'm currently in Calc II, and I've read a few surface-level astrophysics books, the kind of which was described in the intro by Carroll. That is to say that I'd like to think I'm not completely ignorant to this particular subject, and was in fact very excited by the concept of this book.
However the reason I gave a 2.5 and rounded down was because I believe that this book failed to deliver on its whole premise, which was again outlined in the intro.
Like I said, I'm currently in Calc II and have taken basic physics before. In the intro, Carroll stated that you didn't need more than basic high school algebra to understand this book - which in my opinion was just flat-out untrue (or I'm more of a blockhead when it comes to math than I realized). Despite reading and rereading passages, I found myself bewildered for the majority of this book. Carroll would outline some complicated mathematical concept, and then go "so OBVIOUSLY based on /this/ we can make /that/ assumption - " when, no! It really isn't that obvious! (I STILL have no idea what a metric tensor is.)
I really wanted to like this book, but I simply couldn't get into it. I learned a lot of interesting terms, and the final few sections about black holes were absolutely fascinating, but I can already tell that none of the more complicated underlying concepts are going to stick.
I guess the bottom line is - Carroll assumed too much of his reader's ability to understand his technical jargon.
I want to preface this by saying that I'm currently in Calc II, and I've read a few surface-level astrophysics books, the kind of which was described in the intro by Carroll. That is to say that I'd like to think I'm not completely ignorant to this particular subject, and was in fact very excited by the concept of this book.
However the reason I gave a 2.5 and rounded down was because I believe that this book failed to deliver on its whole premise, which was again outlined in the intro.
Like I said, I'm currently in Calc II and have taken basic physics before. In the intro, Carroll stated that you didn't need more than basic high school algebra to understand this book - which in my opinion was just flat-out untrue (or I'm more of a blockhead when it comes to math than I realized). Despite reading and rereading passages, I found myself bewildered for the majority of this book. Carroll would outline some complicated mathematical concept, and then go "so OBVIOUSLY based on /this/ we can make /that/ assumption - " when, no! It really isn't that obvious! (I STILL have no idea what a metric tensor is.)
I really wanted to like this book, but I simply couldn't get into it. I learned a lot of interesting terms, and the final few sections about black holes were absolutely fascinating, but I can already tell that none of the more complicated underlying concepts are going to stick.
I guess the bottom line is - Carroll assumed too much of his reader's ability to understand his technical jargon.
January 3, 2023
→ 5 stars (★★★★★)
starting off 2023 with an amazing read!
this book is nonfiction and explores key physics concepts in both an expert and accessible manner; Sean Carroll provides more scientific depth than merely a philosophical discussion of physics concepts, but he does an excellent job of explaining the main ideas and equations without it reading like an academic textbook. his writing is eloquent, amusing, and unpretentious, despite the obvious extent of his knowledge and intelligence.
as a third-year university student studying engineering and physics, i found some of the simpler content to be an enjoyable review and the more complex content to be a mentally-stimulating challenge. overall, i feel that anyone who is interested in physics (particularly space, time, and motion) would enjoy this book, regardless of whether they have multiple STEM degrees or only some high school math/science courses under their belt.
i tabbed so many fascinating passages in this book as i read it, and i will definitely be rereading it in the future!
starting off 2023 with an amazing read!
this book is nonfiction and explores key physics concepts in both an expert and accessible manner; Sean Carroll provides more scientific depth than merely a philosophical discussion of physics concepts, but he does an excellent job of explaining the main ideas and equations without it reading like an academic textbook. his writing is eloquent, amusing, and unpretentious, despite the obvious extent of his knowledge and intelligence.
as a third-year university student studying engineering and physics, i found some of the simpler content to be an enjoyable review and the more complex content to be a mentally-stimulating challenge. overall, i feel that anyone who is interested in physics (particularly space, time, and motion) would enjoy this book, regardless of whether they have multiple STEM degrees or only some high school math/science courses under their belt.
i tabbed so many fascinating passages in this book as i read it, and i will definitely be rereading it in the future!
November 6, 2022
I really enjoyed this. The aim of the book is to provide a middle ground between the sort of “pop science” we get in podcasts, etc. that doesn’t ask the consumer to try to understand the mathematical foundations of what they’re hearing on one side and the hard work physicists do on the other side.
It’s a rigorous book because the author argues you really do need to understand some mathematical formulas to really grasp why these concepts exist and why things behave in the way that they do, and sets out to make those formulas accessible.
The first several chapters I thought were really successful at doing so and would have received 5 stars from me, but somewhere along the way the math started going over my head and even when re-reading pages it became harder to process what I was reading.
That being said I always reading books about this sort of thing and it was a fun break from my usual fare; I’d definitely recommend giving this a shot.
It’s a rigorous book because the author argues you really do need to understand some mathematical formulas to really grasp why these concepts exist and why things behave in the way that they do, and sets out to make those formulas accessible.
The first several chapters I thought were really successful at doing so and would have received 5 stars from me, but somewhere along the way the math started going over my head and even when re-reading pages it became harder to process what I was reading.
That being said I always reading books about this sort of thing and it was a fun break from my usual fare; I’d definitely recommend giving this a shot.
January 26, 2023
First of a planned trilogy. The hook with this is that it explains a lot of science stuff with the math. Most pop science books skip the math. I enjoyed that aspect of it and did feel like it helped my understanding of the concepts, though by no means am I an expert in math now. The idea is more that you have a better understanding of the math, rather than that you'll now be able to solve all the problems yourselves. So, I still find the math confusing, but I think I understand it better than I did. And I'm looking forward to the other books in the series.
October 12, 2022
If you like science books you will like portions of this book. If you like math, you will like this book. I love the science, and while I like math, it’s a bit much here. It makes the book read more like a text book and the math is convoluted mathematician level math. Overall I definitely enjoyed it, but the author is writing to a very narrow window of readers.
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