Thanu Padmanahhan's book, Sleeping Beauties in Theoretical Physics is a great find. It's reasonably accessible for a technical tome on theoretical physics, it has an interesting framework that makes the connections between chapters on very different subjects coherent, and it covers a number of interesting topics, including ones that I'd thought I'd have references to in other books but my knowledge of them must have come from papers.
The feature that Padmanabhan uses to categorize physics is similar to the one used by Griffiths in his Introduction to Electrodynamics: a cube has eight vertices, and each of these vertices is a type of physical theory. Each of the eight vertices has one of three Boolean values: gravitation, relativity, and quantum. If the effect is accounted for, the value is on, if not, it's off. The vertex where they are all off is Newtonian Mechanics (without gravity) and the far vertex is a Theory of Everything (or somesuch, he calls it something else). Turning gravity off is like setting the gravitational constant equal to zero, turning relativity off is like setting the speed of light to infinity, and turning quantum mechanics off is like setting Planck's constant equal to zero.
So, I could make a list of the different vertices:
The most interesting statement in the introductory chapter is that GQM is a theoretically unpopular zone, and very poorly developed, despite being one step away from the TOE and possibly holding clues to it (or, I assume it would, even if it's boring to the high-powered mathematical physics wizards).
Sleeping Beauties touches on most of these topics (perhaps being short on the TOEs), showing up with some interesting takes on different phenomena, many of which I knew (rainbows and mirages, Thomas precession), many of which I didn't realize (the connection between Thomas precession and the Foucault pendulum), and many I had never touched on in my life (gravitational bending of the electric field). The twenty-six chapters have at least twenty-five topics and are each worthy of attention, especially those where he's making connections either between the vertices of his scheme or between subjects that seem disparate (but really aren't).
But, it's not for people who avoid mathematics.
The very first chapter of content, "The Emergence of Classical Physics," is an example of this. It tries to show how minimization principles in classical physics are explained by the limit of quantum mechanics. This uses Wigner functions to show that the action is the phase of the quantum mechanical wave function, and so classical particles follow trajectories that follow paths where the wave function's phases isn't cancelled out by neighboring paths (just like in Feynman's QED: The Strange Theory of Light and Matter). Obviously, if you're not up on the quantum mechanics or the calculus of variations, you might not see why this is so awesome. Speaking of QED, chapter 17, "If Quantum Mechanics is the Paraxial Optics, Then..." does something similar by applying the results of chapter 16's investigation of the transformation from wave optics to ray optics to discuss how quantum particles move in quantum field theory. Including why you must include trajectories for your particles that go backward in time. It's all the same process.
That is probably the most obvious recurring theme in the book: by understanding how a theory can be derived from a more fundamental theory, mysterious things like minimization principles can be made to make sense. That is, if you know how to turn off one of the switches, then you can better understand why things occur in the lower level theories -- and where those theories might lead you astray.
I therefore heartily recommend this book, and hope you both read and like it, but it does require an investment in mathematics to realize its physical returns.
The feature that Padmanabhan uses to categorize physics is similar to the one used by Griffiths in his Introduction to Electrodynamics: a cube has eight vertices, and each of these vertices is a type of physical theory. Each of the eight vertices has one of three Boolean values: gravitation, relativity, and quantum. If the effect is accounted for, the value is on, if not, it's off. The vertex where they are all off is Newtonian Mechanics (without gravity) and the far vertex is a Theory of Everything (or somesuch, he calls it something else). Turning gravity off is like setting the gravitational constant equal to zero, turning relativity off is like setting the speed of light to infinity, and turning quantum mechanics off is like setting Planck's constant equal to zero.
So, I could make a list of the different vertices:
- (0,0,0) Newtonian Mechanics
- (1,0,0) Newtonian Gravity
- (0,1,0) Special Relativity
- (0,0,1) Qunatum Mechanics
- (1,1,0) General Relativity
- (1,0,1) Gravitational Quantum Mechanics
- (0,1,1) Quantum Field Theory
- (1,1,1) Theory of Everything
The most interesting statement in the introductory chapter is that GQM is a theoretically unpopular zone, and very poorly developed, despite being one step away from the TOE and possibly holding clues to it (or, I assume it would, even if it's boring to the high-powered mathematical physics wizards).
Sleeping Beauties touches on most of these topics (perhaps being short on the TOEs), showing up with some interesting takes on different phenomena, many of which I knew (rainbows and mirages, Thomas precession), many of which I didn't realize (the connection between Thomas precession and the Foucault pendulum), and many I had never touched on in my life (gravitational bending of the electric field). The twenty-six chapters have at least twenty-five topics and are each worthy of attention, especially those where he's making connections either between the vertices of his scheme or between subjects that seem disparate (but really aren't).
But, it's not for people who avoid mathematics.
The very first chapter of content, "The Emergence of Classical Physics," is an example of this. It tries to show how minimization principles in classical physics are explained by the limit of quantum mechanics. This uses Wigner functions to show that the action is the phase of the quantum mechanical wave function, and so classical particles follow trajectories that follow paths where the wave function's phases isn't cancelled out by neighboring paths (just like in Feynman's QED: The Strange Theory of Light and Matter). Obviously, if you're not up on the quantum mechanics or the calculus of variations, you might not see why this is so awesome. Speaking of QED, chapter 17, "If Quantum Mechanics is the Paraxial Optics, Then..." does something similar by applying the results of chapter 16's investigation of the transformation from wave optics to ray optics to discuss how quantum particles move in quantum field theory. Including why you must include trajectories for your particles that go backward in time. It's all the same process.
That is probably the most obvious recurring theme in the book: by understanding how a theory can be derived from a more fundamental theory, mysterious things like minimization principles can be made to make sense. That is, if you know how to turn off one of the switches, then you can better understand why things occur in the lower level theories -- and where those theories might lead you astray.
I therefore heartily recommend this book, and hope you both read and like it, but it does require an investment in mathematics to realize its physical returns.
Math is boring. *blink*
ReplyDeleteBut seriously, though, all I ever needed to know about physics I learned from The Dancing Wu Li Masters.
*blink*
(I imagine you've seen this: https://xkcd.com/1861/)
I hadn't seen that. I haven't regularly looked at any comic since I left California.
DeleteIt is good, though. I was just thinking about this when writing a lecture for an introductory talk about electricity and magnetism: students always want to know what the electric field is, but what it is isn't helpful at the elementary level. My graduate E&M class started there, a little too much towards the math side to be helpful with it ("electromagnetism is the result of a spin-1 scalar boson"), but even there the knowledge wasn't helpful.
So, how do you express something about virtual photons to a class of students who aren't ready to do anything with it, probably never will be ready, and even if they decide to go for it, will need another six years of math and physics to understand what's going on?
Well, you draw a cartoon...