Book for Special Relativity that uses Tensors

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Discussion Overview

The discussion revolves around finding books that teach special relativity using tensors, particularly for someone with a strong mathematics background but limited physics experience. Participants explore various resources and approaches to learning special relativity, including the use of tensor calculus.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant expresses a desire for books that teach special relativity using four-tensors, noting that most available resources take an algebraic/calculus approach.
  • Another participant argues that tensors are not necessary for understanding special relativity and suggests that most authors avoid using them due to the complexity involved.
  • A suggestion is made to consider general relativity texts that introduce tensors from the perspective of special relativity, with Schutz's book highlighted as a good option.
  • A participant shares a link to resources related to special relativity and general relativity.
  • One participant questions why the Lorentz transformation is not derived using trigonometric methods, suggesting that such an approach might be more intuitive than the algebraic methods commonly used.
  • A recommendation is made to refer to Landau and Lifgarbagez's book for a clearer derivation of the Lorentz transformations, which is noted as being well-regarded among the participants.

Areas of Agreement / Disagreement

Participants express differing views on the necessity of tensors in learning special relativity, with some advocating for their use while others believe they complicate the understanding of the subject. The discussion regarding the derivation of the Lorentz transformation also indicates a lack of consensus on preferred methods.

Contextual Notes

Some participants note that the complexity of tensor calculus may be a barrier for those new to physics, and there is an acknowledgment that many texts do not derive the Lorentz transformation in a way that incorporates trigonometric functions.

keebz
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Hey all!

I am a senior in college pretty much done with my mathematics major, but have had minimal physics. I'm currently self-studying special relativity with guidance from my advisor. Most of the books that I have come across use the algebraic/calculus approach such as Spacetime Physics by J. Wheeler and The Special Theory of Relativity by David Bohm. I also have Special Relativity: A Mathematical Exposition by Anadijiban Das but that one is far more mathematics than pedagogical physical explanations.

I do have Wolfgang Rindler's Intro. to Special Relativity which begins using four-tensors midway in. However, I'm just wondering if there are any other books out there like Rindler's which teach you special relativity using four-tensors and that whole complicated set of machinery usually reserved for general relativity. My search on Google and on here has not yet yielded any desirable results.

Thanks in advance!
 
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Special relativity doesn't really require tensors to understand well, and the tensor calculus/algebra usually takes some time to develop so most authors do not bother to do this for special relativity.

I think your best bet is to use a book in General relativity that starts off with Special relativity. For example, Schutz's book in General Relativity introduces tensors from the Special relativity point of view.
 
Schultz's book is a great place to start. I used it for self teaching too.
 
http://people.maths.ox.ac.uk/nwoodh/sr/index.html (SR)
http://people.maths.ox.ac.uk/nwoodh/gr/index.html (GR)
 
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Schutz's book is amazing so far, but I have a question regarding the derivation of the Lorentz transformation. All of the books I've listed above and even Schutz's just plainly state the equations of the Lorentz transformation (t', x', y', z'), or they derive it in a purely algebraic manner.

Why doesn't anyone actually derive it using trigonometry... using the infinitesimal rotation, hyperbolic sine and cosine functions, etc.? That way seems to me to be so much more intuitive than just symbolic manipulation and stating that the result is the Lorentz transformation. Same with the "Lorentz boost."
 
If you want a nicer derivation of the Lorentz transformations, refer to Landau and Lifgarbagez's book on Classical Theory of Fields (very early on, they develop SR). They do the best job from all the books I have studied and recall.
 

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