Reading 'Gravitation', I need more background....

[dvdt]

I've just reached the opening in chapter 2 wherein there's a brief discussion of concepts and math which should be familiar to the reader (Basic SR stuff it seems), and I'm not familiar with it unfortunately. I am familiar with future and past light cones, and the language of causality, but not the mathematics of, "Lorentz contraction, time dilation, absence of a universal concept of simultaneity... " nor am I more than glancingly familiar with, "4-Vectors in general, and the energy-momentum 4-vector, elementary Lorentz transformations, the Lorentz law for the force on a charged particle, at least one look at one equation in one book that refers to the electromagnetic field tensor..."

Obviously I have quite a lot to learn, including much of the basic math. To be clear, this is something I'm doing for personal enrichment, I don't need or expect to come out of this with the kind of skills someone studying this formally would. I'm just using 'Gravitation' as a broad guideline which helps me understand the many gaps in my knowledge I need to fill. What I'm lacking is knowledge of resources (like 'Gravitation') which can help me fill those gaps. I have access to online and offline courses (but I don't know which apply here), and I'd be more than happy to take the time to work through a textbook intended for either, but I don't know which would be helpful.

Any assistance in terms of a reading and/or course list would be extremely helpful.

 

[Vanadium 50]

It will be hard to tell you what new things you need to know if you don't tell us what old things you already know.

 

[dvdt]

It will be hard to tell you what new things you need to know if you don't tell us what old things you already know.

I see, that's a good point. In terms of mathematics I've only been formally taught through what was called "Pre-calculus". Beyond that I know what I either learned in school in classes that were frankly unrelated to STR/GTR, and what I've pieced together over years of reading books like Prime Obsession, or textbooks like Gravitation. I've come to the point where I clearly need to focus on more fundamentals of the math involved, because my knowledge is sort of the typical autodidact's mix, with holes that no one who had a formal education in the subject would have.

I would say to be fair, that I know almost nothing, that to this point I've learned in bits and pieces where I could while trying to skirt some of the more unfamiliar mathematics. I found the first chapter of Gravitation pretty comprehensible from a heuristic point of view, but even I can see the limitations of that. Clearly when all of this is generalized to a curved spacetime I'm gong to be utterly lost as well.

Does that help you get an idea of my knowledge at all?

 

[Nugatory]

Any assistance in terms of a reading and/or course list would be extremely helpful.

You aren't ready to take on MTW (or any other GR text) until you have a solid grasp of special relativity because that's where "the mathematics of Lorentz contraction, time dilation, absence of a universal concept of simultaneity" come in. So you'll want to try something like Taylor and Wheeler's "Spacetime Physics" as a stepping stone. Don't think of this as drudgery, an onerous chore to slog through before you get to the fun stuff - you will find a proper treatment of SR to be intriguing, fascinating, and fun in its own right, and the math is much less demanding.

In terms of mathematics I've only been formally taught through what was called "Pre-calculus".

That will get you through special relativity, although you'll find yourself skipping over some of the fine points. However, there is just no way of taking on MTW without the equivalent of two years of calculus: One year to cover basic single-variable differential and integral calculus, the stuff that is taught in the high school advanced placement classes in the US; and one one year for basic multi-variable and vector calculus plus a nodding acquaintance with differential equations. You can learn this on your own in much less than two years if you had a good precalculus course and you were good at it, but you'll have to learn it.

You might also consider giving up on MTW and trying Hartle's "Gravity", which is less demanding. You'll still need the calculus, but much less of it.

 

[dvdt]

You aren't ready to take on MTW (or any other GR text) until you have a solid grasp of special relativity because that's where "the mathematics of Lorentz contraction, time dilation, absence of a universal concept of simultaneity" come in. So you'll want to try something like Taylor and Wheeler's "Spacetime Physics" as a stepping stone. Don't think of this as drudgery, an onerous chore to slog through before you get to the fun stuff - you will find a proper treatment of SR to be intriguing, fascinating, and fun in its own right, and the math is much less demanding.

That will get you through special relativity, although you'll find yourself skipping over some of the fine points. However, there is just no way of taking on MTW without the equivalent of two years of calculus: One year to cover basic single-variable differential and integral calculus, the stuff that is taught in the high school advanced placement classes in the US; and one one year for basic multi-variable and vector calculus plus a nodding acquaintance with differential equations. You can learn this on your own in much less than two years if you had a good precalculus course and you were good at it, but you'll have to learn it.

You might also consider giving up on MTW and trying Hartle's "Gravity", which is less demanding. You'll still need the calculus, but much less of it.

I'm by no means wedded to any textbook or any of that, and your advice makes sense to me. If I'm getting this right, I should take some calculus courses from intro onward, focus on SR, Switch to 'Gravity', and change my thinking to something like (for me) a 4 year plan or so. This is exactly the kind of advice I was looking for, because I'm not in a rush, I just want to learn it *eventually*. I just realized a few years ago that I'd run into the limits of what I could get from heuristic summaries, and I wanted to learn more; I'm not in this to contribute to the field in any way. This sounds like a sensible way to go.

Again, thanks.