What is Reddit's opinion of Spacetime and Geometry: An Introduction to General Relativity?

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I just want to add on here that Sean Carroll is a highly, highly respected physicist too. His intro to general relativity is widely used as a graduate textbook.

https://www.amazon.com/Spacetime-Geometry-Introduction-General-Relativity/dp/0805387323

So yeah, this guy is a big deal. He knows his shit. Not saying you're implying the opposite, just a nice tidbit ��

http://www.amazon.com/Spacetime-Geometry-Introduction-General-Relativity/dp/0805387323 This book? I think I just really need a second opinion on the difference between covariant differentiation/lie derivative. so what i gather is that lie derivative is in the same point but covariant differentiation moves from point A to point B? I got einstein's gravity in a nutshell. I will check that part out to see if there is a better definition there.

Looks like it might be Spacetime and Geometry: An Introduction to General Relativity.

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I said he's not a trained Physicist nor a Cosmologist, nor any kind of scientist, so why are you citing him as an expert in Physics? And seriously, he's a really intellectually dishonest person. You should pick your intellectual heroes better.

I didn't cite him as an expert on physics, I only cited Alexander's & co paper on Arxiv for the physics side. And then I cited Craig's rebuttal of the Quantum Objection to the KCA as well as his response to Carroll for the philosophical side.

> Yes, I did, but I also read a lot from Carroll, Susskind, Hawking and others, and you know what, they all sound credible, and they are all passionate about their positions and usually they are also honest about things we just don't know yet. When you have really smart people disagreeing in science that means this is the frontier of science. Nobody disagrees about Evolution or the Geocentric model of the Solar System, because those are settled. > > Question is, why are you taking sides? Because like me, you have no deep knowledge of the field. You cite papers which you clearly never read, or understood. Why can't you just be honest about the the extent of your ignorance? >

It may be true that my knowledge isn't deep, but at least I'm not a laymen who thinks he understood things by reading deceiving popular science since I'm studying the technical side of things, I'm currently going through Carroll's textbook on GR.

I read those papers, and understood them partially.

You say: "Why are you taking sides?" Because there's currently no shred of evidence for a multiverse.

[BTW you mention all those good scientists but you seem to miss other real pioneers like Einstein (he was a deist), Schrödinger, Heisenberg, Newton... who all believed in God for rational reasons.]

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KCA and Argument from Design are as good as they get. I've read them all. But hey, if you're convinced, power to you.

Okay.

The big concepts aren't that tough. There are plenty of popular physics books that discuss the concepts. (A Brief History of Time by Stephen Hawking was my original introduction)

The math machinery that it employs requires a solid understanding of calculus, linear algebra, and differential geometry.

If you want a non-math heavy treatment check out this series of videos by Sean Carroll https://www.youtube.com/playlist?list=PLrxfgDEc2NxZJcWcrxH3jyjUUrJlnoyzX

And if you or anyone else wants a math heavy treatment (course textbook) check out Spacetime and Geometry: An Introduction to Special Relativity also by Sean Carroll

> Carroll

Are you talking about this, his lecture notes, or some other text?

https://www.amazon.com/Spacetime-Geometry-Introduction-General-Relativity/dp/0805387323

Na introducao:

> Once we become more familiar with the spirit of GR, it will make perfect sense to think of a ball flying through the air as being more truly “unaccelerated” than one sitting on a table… (which is why we feel a force on our feet as we stand on Earth).

Mais para o final:

> It’s easy to confirm with accelerometers that the ball that appears to be falling is barely accelerating at all, while the table is accelerating upward at 9.8 meters per second per second, known as 1 g. The seeming downward pull of gravity on the ball is an illusion experienced by observers around the table — who don’t believe that they’re being pushed upward either!

Here's mine: www.amazon.ca/Spacetime-Geometry-Introduction-General-Relativity/dp/0805387323

Spoiler alert: it agrees with everybody else

Yes, strictly speaking the speed of light is a factor of distance divided by time so time is a factor. But that would make the equation above E=m * (d^2 / t^2) or in si units Watts are equal to kilograms times the fraction of meters squared divided by seconds squared. You made a small error in your math, this equation simplifies out t=(m * d^2 / E)^.5 . When can put this into si units and check. s=(kilograms * meters^2 / (kilograms * meters^2 / seconds^2 )^.5 kilograms cancel as do the meters squared. Divide by a fraction moves the second numerator to the denominator so we have s=(seconds^2 )^.5 . Which means seconds are seconds. So the math is right.

Your next jump, however, goes a little to far. Time is not a property of matter, but there is a relationship between matter (specifically mass) and time. And there is a relationship matter (specifically mass) and distance. The difference is fine but it is important. There is nothing inherently time like about matter (or anything inherently matter like about time) but if matter and time both exist then they cannot help but to interact with and effect each other. I have heard professors liken the two two a coin. Time (and space) on one side and mass on the other. But I don't like this analogy. A coin is still one thing. The head and the face are properties of one thing: a coin. Rather it is like trying to roll between a 7 and a 12 using six sided dice. It takes two of them. They aren't physically connected but you need both to achieve the result. So if you know about mass and time you can say something about distance. If you know about distance and time you can say something about mass.

The mechanism we use to make these relationships is relativity. This is, in fact, the basic point behind relativity. But you need to accept two additional pieces of information. Mass doesn't work by itself but rather it gives rise to a force called gravity. In this case, gravity really is a property of matter. Also, you have to accept as /u/shadydentist says that c, the speed of light in a vacuum is a constant no matter what. And, for that matter, dentist's point does stand, because relativity is tied to time and because time is a part of the speed of light and because the speed of light is fixed time is not a property of matter I'm just trying to explain why they are right.

For time itself this relationship is in its simple form t=tsub0 / (1- (v^2 / c^2 ))^.5 . Or in English as best I can this means the time you claim an event occurred and the time a different resting frame (some one moving faster than you or positioned near a lot more mass than you - we'll come back to that latter point in a second because the equation is messier) are related but different. Specifically, the time you claim something occurred is proportional to the time it took to occur in the reference frame divided by the square root of 1 minus their velocity relative to you divided by the speed of light squared. Okay, a few interesting points. First, both of you are absolutely correct. The time you both think it took to happen is really the time it took to happen even though this describes two different times. Second, their speed is measured relative to yours but you both agree on what the speed of light is no matter how fast you are going. This is really different than normal speeds. Lets say you are on a train that travels as fast as a bullet. I fire a gun next to the train next to you. You see the bullet "hang" in the air as you both travel forward at the same speed. You say the bullets speed is zero. I see both you and the bullet go wizzing away and I say you are both moving at bullet speed. But if we both turned on a flashlight we would both exactly agree on the speed of light. Finally, when their speed relative to yours is very small then the fraction v^2 / c^2 is 0. 1-0=1 and something divided by 1 is itself. So when their speed is relatively close to yours you both essentially agree on how long it took for something to happen. Keep in mind for you intuition that the speed of light is some 300,000,000 m/s 671,000,000 mph so its a takes a good bit of speed for you to be relatively apart relative to the speed of light.

More on that idea laid out here.

Okay. I promised to lay out the relationship between time and mass for simplicity's (a little bit of simplicity) lets say the radial velocity is about the same - you are both traveling at the same speed just one in space and one on a planet. This will let me drop the radial component and save us a bit of headache.

delta time (sub you) = ((1 - (2 * gravitational constant * (sum of all masses) / (sum of all distances of all masses from them * c^2 )) * delta time (sub them)). Okay so what does this mean? Well, if the sum of the masses near them is very small then 1 - 0 / anything is 1 so when neither of you are near any mass and you are traveling the same speed you agree how much time time takes. If the things they are near has a lot of mass then you see their temporal ticks as traveling less far into the future as each of your ticks...their clock slows down according to you who is not near any mass. Also, if they are very close to their massive objects then 1 - anything / a very large number is very close to 0 and again you see their ticks not ticking very far into the future relative to yours but if they are far away from mass and you are not near any mass then you both think time is going the same speed. 1- a number / a very large number is very close to 1.

So mass definitely plays a part in the way time operates but is not itself a property of time.

More information here

I reworked the gravity equation to use proper units and drop the radial tensor from the version presented here any mistakes in the algebra are strictly my own.

My school uses Sean Carroll's book. It has very strong reviews from both me and my classmates. At least for the opening chapters.

Congratulations, you're not the only one who misread the hadith. Even Dr; Brown had a reaction close to yours, and I think he puts it nicely;

> Why not follow the rule that Muslim scholars followed? "If you hear a hadith think of it what is most pious, what is closest to guidance, what is most fitting of the Prophet." You may find wisdom. And this is something that is a very interesting case, you all heard this hadith that's in sahih bukhari and sahih muslim of: khulikat almar’ato min dil’ine la tastaqimo laka ’ala tariq, women - and then there's different versions of the hadith after that and I'll give you one version, women were created from a rib, 'a bent rib', rib is crooked, and they will never straighten for you, speaking to a man, "laka", they will never straighten for you, ... if you want to enjoy them enjoy them as they are crooked, ... if you try to straighten out you break them. Now, when I first read this hadith I thought this is very sexist, this is obviously made up, y'know arabs are sexists, and y'know muslims are sexists, and everyone in the past is sexist, and so this came out of arab muslims people in the past we were sexists and they made this up because they wanted it as a way to oppress women. That's what I thought. And I thought this is really .. I don't have to go and defend this hadith and people gonna come and tell me y'know how can a Muslims believe this, and I'm willing to bet I'm not the only person who had that's reaction [he repeated it twice]. And then one day I was watching just some comedian Comedy Central or HBO Comedy or something and a comedian ... got in into his little "Men understand things this way" and "women understand things that way". And I thought y'know it's funny how these seems to be part of every comedian routine y'know "Men they think of money like this" - "Women they about money like that" and of course anytime bunch of guys get together I guarantee you they will sit in and talk about the nature of marriage and how women are, and how they deal with women, and I don't know because I'm not a women and I have never been able to sneak into any of these gatherings, but I assume that may be the case with women. They sit around and talk about how .. why men are like this, why men are like that. And there's a hole industry of books, very successful books, not only commercially but also I think useful for people's lives that tells men how to be better husbands by not always thinking like men but also seeing the world as women. So men - and I'm not revealing any trade secrets - but men generally consider women to be irrational, they consider their brains to be not straight, and sometimes they do really stupid things, this is ... by the way I have no trouble going to court and saying that the majority of men think like this. What is this hadith saying? It's saying, ... from your perspective (men) women are crooked, you can sit around and try to straighten them out, you can sit around and tell them why aren't you more like me, you can sit around and tell them why don't you see the world the way I do? Or you can accept that's the way they are, that they're different from men and try to accommodate them, and try to enjoy life with them in that way. Which is, as far as I can tell from ... reading these books [relationships self-help ones] that's exactly what these books are trying to tell you which is don't sit around and change the way your spouse and to expect it to act like a men and women don't except your husband to act like a women, and they say that you have to understand how these two genders generally view the world differently and seeing that difference accommodate and this enables you to live a happier more peaceful and more productive life. So suddenly I realized then judging this hadith all the time, and in fact it did then making a point not only the comedians make tons of money off constantly ... but also that the most respected relationships self-help books also teach you. Now I'm not trying to say this is a mu’jiza [a miracle] ... 

Taken from this lecture from 51m43s.

First thing that came to mind was this textbook I used an an astrophysics student concerning General Relativity.

Actually, this makes sense! cf: General Relativity these texts from undergrad Spacetime and Geometry and Gravity.

Ok, so I would recommend Carrol's Spacetime and Geometry http://www.amazon.com/Spacetime-Geometry-Introduction-General-Relativity/dp/0805387323

If you are feeling more up to snuff with tensor calculus and mathematical analysis and can wade your way through R_n analysis, (in terms of problem solving and approaches), then go for Wald's Genearl Relativity http://www.amazon.com/General-Relativity-Robert-M-Wald/dp/0226870332

edit: warning: both of those books are graduate level. Any GR is only taught at grad level, but I took GR with Wald (yep the guy himself) my 3rd year with similar background to yours. You will be fine, but its going to be a lot of head beating against the wall. Some of that stuff is really complex and will possibly require more than one source to understand. JUST the book may not be enough. I would even recommend you talk to your local GR prof and see if you can send him questions as you work through this; I cant imagine any good professor refuse to help you in this way, as long as you dont send a question every 5 minute and they are actually substantial.

also, anything else you would be stepping lower than carrol and i would advise against it if you wanted to get a good grasp of mathematical approaches and rigorous proofs (especially Wald in this case)