Spacetime physics
Collaboration on the First Edition of Spacetime Physics began in the mid-1960s when Edwin Taylor took a junior faculty sabbatical at Princeton University where John Wheeler was a professor. The resulting text emphasized the unity of spacetime and those quantities (such as proper time, proper distance, mass) that are invariant, the same for all observers, rather than those quantities (such as space and time separations) that are relative, different for different observers. The book has become a standard introduction to relativity. The Second Edition of Spacetime Physics embodies what the authors have learned during an additional quarter century of teaching and research. They have updated the text to reflect the immense strides in physics during the same period and modernized and increased the number of exercises, for which the First Edition was famous. Enrichment boxes provide expanded coverage of intriguing topics. An enlarged final chapter on general relativity includes new material on gravity waves, black holes, and cosmology. The Second Edition of Spacetime Physics provides a new generation of readers with a deep and simple overview of the principles of relativity.
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- Taylor & Wheeler's Spacetime Physics is similar. They emphasize the importance of frame invariant representations. (I highly recommend the first edition over the second edition, the second edition was a massive downgrade.)
Kip Thorne was also heavily influenced by this geometric approach. Modern Classical Physics by Thorne & Blandford uses a frame invariant, geometric approach throughout, which (imo) makes for much simpler and more intuitive representations. It allows you to separate out the internal physics from the effect of choosing a particular coordinate system.
- > I'm very sure that you are wrong here
What actual textbooks on relativity have you studied? If you haven't studied any, I would strongly suggest doing so before being this confident about your beliefs about relativity. Many pop science sources (including, unfortunately, books by physicists who should know better but who can't help themselves when there are no other experts peer reviewing their work) will say the kinds of things you're saying about photons "not experiencing time", but you won't find a textbook or peer-reviewed paper that says them, because such misstatements are weeded out. Sean Carroll has a set of free online lecture notes [1] that make a good start (they're more focused on GR than SR but they have an introductory section that covers SR). Taylor & Wheeler's Spacetime Physics [2] is a good introductory textbook as well.
The fundamental physical point here is that timelike objects (objects with positive rest mass that follow timelike worldlines) and lightlike objects (objects with zero rest mass that follow null worldlines) are different things, and the concept of "experienced time" or "proper time" (the latter is the correct technical term) only applies to timelike objects. The mathematical basis for this is that timelike worldlines can be parameterized by arc length, and arc length along a timelike worldline corresponds to elapsed time on a clock following that worldline. Null worldlines, however, cannot be parameterized by arc length at all, so the fact that arc length along them is zero does not mean lightlike objects "experience no time", it means that the whole concept of "experienced time" doesn't even work for them: it's mathematically invalid since it requires parameterizing the worldline by arc length.
Another way of seeing the fundamental difference is to look at how Lorentz transformations act on timelike and null vectors. Lorentz transformations hyperbolically rotate timelike vectors: that means the transformation changes which way in spacetime the vector points, without changing its length. But Lorentz transformations do not rotate null vectors: they dilate them, meaning they increase or decrease all components of the vector by the same factor, without changing its direction in spacetime.
This means that a null vector is not a "limiting case" of any set of timelike vectors as far as the Lorentz transformations are concerned; null and timelike vectors are simply two disconnected sets of vectors with respect to Lorentz transformations. Which in turn means that the common pop science image of objects "experiencing less time" as they move faster and faster, until photons moving at the speed of light "experience no time" in the limit, is not correct: it is not a valid description of what is actually happening in the math. Lorentz transformations don't change the length of timelike vectors at all, so they don't change the "experienced time" along them. The apparent "time dilation" of an object that is moving relative to you is due to the angle in spacetime between your worldline and the object's worldline, not to any property of the object's worldline itself. But the "angle" here is a hyperbolic angle, and the hyperbolic angle between your worldline (you being a timelike object) and any null worldline (i.e., any worldline of a light ray or photon) is infinite--in other words, mathematically ill-defined.
In short, pop science authors who make claims like "photons don't experience time" are putting an interpretation on the fact that a photon's worldline has zero length in the Minkowski metric that is not justified by anything in the actual math. They do it, unfortunately, because they believe (quite possibly correctly) that saying things like that, even if they're wrong, will sell more books than trying to teach their readers the actual science.
- I've always had a fondness for Taylor and Wheeler's "Spacetime Physics".
- Taylor’s and Wheeler’s “Spacetime Physics” is quite approachable and easy to read introduction to Special Relativity that has hardly any math beyond basic algebra.
- I will also recommend reading "Spacetime Physics" by Taylor and Wheeler (Feynman's PhD advisor). Excellent discussion in a kind of old school style (which is how I like it).
- My personal recommendations for an undergraduate course in physics (based in large part off of my own undergrad curriculum):
Foundations:
1. Newtonian Mechanics by A.P. French (https://archive.org/details/NewtonianMechanics/mode/2up). This will give you a good foundation for what is to come.
2. Spacetime Physics by Taylor & Wheeler --- first edition if you can find it! It is much, much better than the second! Special relativity is conceptually strange, but mathematically pretty easy, so you can jump right into it after learning Newtonian mechanics. Have a little fun!
3. Electricity & Magnetism by Purcell. This book is a little unusual in that it derives magnetism from the laws of special relativity. This is the more natural approach than just asserting the laws of magnetism since magnetism is fundamentally a relativistic phenomenon.
4. Waves by Crawford. (https://archive.org/details/Waves_371/mode/2up) A bit hard to find in print, but a really excellent textbook. Waves are a fascinating topic because they come up in every area of physics, so a course focused around them has a huge number of applications.
5. Introduction to Quantum Mechanics by Griffiths. The best introduction to the topic you will find!
6. Thermal Physics by Kittel & Kroemer. I haven't actually found an introductory book on statistical physics that I'm crazy about, but this one isn't too bad.
That should last you some time. But once you're through with those and are looking for more, then here are some advanced topics:
7. Analytical Mechanics by Hand & Finch. This will teach you advanced Newtonian mechanics --- in particular Lagrangian and Hamiltonian dynamics. There is a chapter on chaotic dynamics towards the end, too. Another option here is Classical Mechanics by Goldstein.
8. Introduction to Electrodynamics by Griffiths. More advanced E&M than Purcell. If you want to go further, then there's always Classical Electrodynamics by Jackson.
9. Principles of Quantum Mechanics by Shankar. This spends more time on the mathematical foundations of QM than Griffiths does and goes into the path integral formalism and touches on relativistic QM towards the end of the book.
10. A First Course in General Relativity by Schutz. There are arbitrarily advanced texts on GR, but I'd recommend starting off with something friendly like Schutz.
11. An Introduction to Elementary Particles by Griffiths. Not super advanced mathematically, but it's a good thing to read over to prepare you for more advanced QFT texts. The first chapter is especially good as a history of the development of particle physics.
12. Quantum Field Theory in a Nutshell by Zee.
13. Modern Classical Physics by Thorne & Blandford. This is a tour de force. It's an enormous book but it really touches on everything that is left out by the above books. It covers optics, fluid dynamics, statistical physics, plasma physics, and more. (I'm currently reading through it and have only gotten through 6 chapters, but it's really an incredible textbook.)
14. Statistical Mechanics: Entropy, Order Parameters, and Complexity by Sethna. This is a really fun book, but almost all the material is in the problems.
Finally, and most importantly --- remember that physics is not a spectator sport! You must do problems. A lot of them --- and hard ones, too!
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