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WiFO215
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Does anyone know of any book that treats special relativity from a mathematical standpoint? I want to learn SR before starting to read Schutz/ Hartle/ Carrol.
anirudh215 said:Does anyone know of any book that treats special relativity from a mathematical standpoint? I want to learn SR before starting to read Schutz/ Hartle/ Carrol.
qspeechc said:Ok, I did some research and I found https://www.amazon.com/dp/9810202547/?tag=pfamazon01-20, but I haven't read it.
Landau said:I'm sorry, I haven't read it myself, only browsed though it. Are you a mathematics/physics student? Do you know SR from a phycisists' point of view?
George Jones said:There also is
https://www.amazon.com/dp/1441931023/?tag=pfamazon01-20.I echo what Landau wrote. By "mathematical," do you mean "quantitative, but still from a physics point of view," or do you mean "written in a style suitable for a mathematics course?"
I just noticed what exactly you're asking here. Schutz's GR book contains one of the best introductions to SR, so I think you should probably start with that one.anirudh215 said:Does anyone know of any book that treats special relativity from a mathematical standpoint? I want to learn SR before starting to read Schutz/ Hartle/ Carrol.
Fredrik said:I just noticed what exactly you're asking here. Schutz's GR book contains one of the best introductions to SR, so I think you should probably start with that one.
etc. so he clearly defines his math, and then explains how physicists (intuitively) think about them.Minkowski spacetime is a 4-dimensional real vector space M on which is defined a non-degenerate, symmetric, bilinear form g of index 1. The elements of M will be called events and g is referred to as a Lorentz inner product of M.
I agree. In fact, I don't think anyone hates that "definition" as passionately as I do. It's been about 15 years since I took classes where that definition was used, and I still get angry when I think about it. It's not just that it's a stupid and obsolete definition. It's also that the books I had to read back then as well as all the teachers I had always stated the definition in a way that doesn't make sense. Would it have killed them to say e.g. "an assignment of four functions [itex]v^\mu:M\rightarrow\mathbb R[/itex] to each coordinate system..." instead of "something"??anirudh215 said:See, what I find out of place is that after reading Linear Algebra, Analysis etc. from math textbooks, I find the treatment given in most physics books quite odd. Instead of simply calling vectors as part of some vector space, they have all these round-about definitions like "a vector is something that transforms properly". Why go into linear transformations and other mappings just to define the same thing??
This is actually very natural. I mean, it's the mathematical structure that we use to represent real-world concepts "space" and "time", so I think the name is very appropriate. Also, it's not just "a simple 4-D space", because even though the vector space structure is defined exactly the way we would do it for a Euclidean space, it doesn't have an inner product, and is equipped with a bilinear form that isn't positive definite instead.anirudh215 said:They have all these weird connotations. A simple 4-D space that you might encounter all the time in an Algebra book is given some funny hokey name, "spacetime". Yeesh.
There's a very good reason why the word "curved" is used, and you'll find the same terminology as well as an explanation of the terms in the best math books. (This one has to be the best).anirudh215 said:They'll add "spacetime is curved" to sound more fancy. It's just a different metric, dammit! I'd find it so much easier if I could avoid all this weird stuff. This is why I'm looking for a book written on the math side.
Fredrik said:But I have some good news for you. Schutz explains tensors really well, if I remember correctly. He defines them as multilinear functions, defines their components in a basis for the vector space (and it's dual space), and derives the formula for how the components associated with one basis are related to the components associated with another basis, i.e. how the components "transform".
Special Relativity is a theory developed by Albert Einstein that describes how objects move in space and time, especially at high speeds. It is based on two postulates: the laws of physics are the same for all observers in uniform motion, and the speed of light in a vacuum is constant for all observers regardless of their relative motion.
Special Relativity differs from classical mechanics in several ways. In classical mechanics, time and space are absolute and do not change based on an observer's perspective. In Special Relativity, time and space are relative and can be affected by an observer's motion. Additionally, Special Relativity takes into account the effects of high speeds and the constant speed of light, while classical mechanics does not.
The mathematical treatment of Special Relativity involves using the Lorentz transformation equations to convert measurements of time and space between different reference frames. This includes the dilation of time and contraction of space at high speeds, as well as the addition of velocities. The equations also account for the constant speed of light and allow for the calculation of relativistic momentum and energy.
Special Relativity is applied in many real-world situations, such as in the design and operation of particle accelerators, GPS systems, and satellites. It is also important in understanding the behavior of objects at high speeds, such as in space travel. Special Relativity has also been used to make predictions and testable hypotheses in other areas of physics, such as quantum mechanics and cosmology.
Yes, Special Relativity is still a valid theory and is widely accepted in the scientific community. It has been extensively tested and its predictions have been confirmed through experiments and observations. However, it is important to note that Special Relativity is a classical theory and does not account for the effects of gravity, which are described by Einstein's general theory of relativity.