Reddit reviews Gravitation

That reminds me of a class I took in grad school from Kip Thorne. He (co-)wrote the book on general relativity, won a bet against Stephen Hawking, and is a remarkably humble and agreeable guy. He's lecturing and writing equations on the board, and makes a mistake in writing one. It's pretty clear what the error is, but the student next to me wanted to make sure. She asks, "Why is that term (such-and-such) in that equation?"

Thorne replies, "Because I am an idiot." He corrects the equation, and continues to lecture.

The student next to me corrects her notes, but in doing so misses the next couple of sentences of the lecture. She asks, "I'm sorry, could you repeat what you just said?"

Thorne responds, "I said, 'Because I am an idiot.'"

> It'd be like if instead of gravity pulling you down, the ground was being rocketed upwards at the exact rate for you to functionally experience the same thing.

Which is exactly what's happening.

There's no gravitational force. Gravitational force is a fictitious force, just like centrifugal force. What you are experiencing is the effect of inertia, your body wants to move in a straight line in spacetime and the ground won't let it.

Source.

I was in your position just a couple of years ago, here's what I did.

Start with a mechanics course if you haven't already, it's crucial that you have a solid understanding of physics before you try to learn the advanced stuff.

Learn calc all the way through vector calc. A great resource for this is Professor Leonard (this is calc 3, but he has all of them).

Here's where I learned physics Electricity and Magnetism, I also learned special relativity and basic quantum mechanics at this point (QM is optional, but fun)

I learned linear algebra and diff eqs at this point. I used Khan Academy for this, though I'm not sure it's the best resource out there.

Next, I would recommend trying to take a class on mathematical proofs, when you are reading papers rather than watching videos you will appreciate it. I watched this series because I'm a comp sci major, but if you aren't a comp sci person, just look for a methods of proofs class.

Now it's time for the fun stuff.

Tensor Calculus is what General Relativity is founded on, I found this series to be helpful

So now it's time to get into GR.

This series from PBS Space Time is a great introduction into accurate GR. Their other stuff is great too.

This video from DrPhysicsA steps through the thoughts behind each part of the EFEs and is not the best video, but it helped me.

And that's where I couldn't find any more videos, so I used some text resources.

The book gravitation is the most commonly used textbook for GR as far as I know.

I found this article on wikipedia to be ENORMOUSLY helpful in understanding how to work a general relativity problem. It took me a few times going through it to follow it all the way, but it is great.

Where you go after this really depends on what you are trying to do with GR, personally I find Kaluza-Klein theory to be very intriguing and that leads down the road to string theory.

Good luck

Carroll

Carroll, course notes (free, I think it may be a preprint of the book)

Schutz

Wald

MTW (Some call it the GR bible)

They're all great books, Schutz I think is the most novice friendly but I believe they all cover tensor calculus and differential geometry in some detail.

Start here.

Then go here.

When you're ready for the real thing, start reading this.

If you want to become an expert, go here.

Edit: Between steps 2 and 3, get a physics degree. You need to understand basically all of physics before you can understand anything properly in General Relativity. Sorry...

Edit 2: If you really want a full list of topics to understand before tackling general relativity, the bare minimum is special relativity (the easier bit) and tensor calculus on pseudo-Riemannian manifolds (extremely difficult). I'd strongly advise a deep understanding of differential equations in general, and continuum mechanics in particular. Some knowledge of statistical mechanics and the covariant formulation of electromagnetism would be pretty helpful too. It is also essential to realize that general relativity is still poorly understood by professionals, and almost certainly breaks down at large energy densities. I strongly advise just taking a look at the first two links I posted, since that will give you an excellent and non-dumbed-down flavour of general relativity.

This question gets asked all the time on this sub. I did a search for the term books and compiled this list from the dozens of previous answers:

How to Read the Solar System: A Guide to the Stars and Planets by Christ North and Paul Abel.


A Short History of Nearly Everything by Bill Bryson.


A Universe from Nothing: Why There is Something Rather than Nothing by Lawrence Krauss.


Cosmos by Carl Sagan.

Pale Blue Dot: A Vision of the Human Future in Space by Carl Sagan.


Foundations of Astrophysics by Barbara Ryden and Bradley Peterson.


Final Countdown: NASA and the End of the Space Shuttle Program by Pat Duggins.


An Astronaut's Guide to Life on Earth: What Going to Space Taught Me About Ingenuity, Determination, and Being Prepared for Anything by Chris Hadfield.


You Are Here: Around the World in 92 Minutes: Photographs from the International Space Station by Chris Hadfield.


Space Shuttle: The History of Developing the Space Transportation System by Dennis Jenkins.


Wings in Orbit: Scientific and Engineering Legacies of the Space Shuttle, 1971-2010 by Chapline, Hale, Lane, and Lula.


No Downlink: A Dramatic Narrative About the Challenger Accident and Our Time by Claus Jensen.


Voices from the Moon: Apollo Astronauts Describe Their Lunar Experiences by Andrew Chaikin.


A Man on the Moon: The Voyages of the Apollo Astronauts by Andrew Chaikin.


Breaking the Chains of Gravity: The Story of Spaceflight before NASA by Amy Teitel.


Moon Lander: How We Developed the Apollo Lunar Module by Thomas Kelly.


The Scientific Exploration of Venus by Fredric Taylor.


The Right Stuff by Tom Wolfe.


Into the Black: The Extraordinary Untold Story of the First Flight of the Space Shuttle Columbia and the Astronauts Who Flew Her by Rowland White and Richard Truly.


An Introduction to Modern Astrophysics by Bradley Carroll and Dale Ostlie.


Rockets, Missiles, and Men in Space by Willy Ley.


Ignition!: An Informal History of Liquid Rocket Propellants by John Clark.


A Brief History of Time by Stephen Hawking.


Russia in Space by Anatoly Zak.


Rain Of Iron And Ice: The Very Real Threat Of Comet And Asteroid Bombardment by John Lewis.


Mining the Sky: Untold Riches From The Asteroids, Comets, And Planets by John Lewis.


Asteroid Mining: Wealth for the New Space Economy by John Lewis.


Coming of Age in the Milky Way by Timothy Ferris.


The Whole Shebang: A State of the Universe Report by Timothy Ferris.


Death by Black Hole: And Other Cosmic Quandries by Neil deGrasse Tyson.


Origins: Fourteen Billion Years of Cosmic Evolution by Neil deGrasse Tyson.


Rocket Men: The Epic Story of the First Men on the Moon by Craig Nelson.


The Martian by Andy Weir.


Packing for Mars:The Curious Science of Life in the Void by Mary Roach.


The Overview Effect: Space Exploration and Human Evolution by Frank White.


Gravitation by Misner, Thorne, and Wheeler.


The Science of Interstellar by Kip Thorne.


Entering Space: An Astronaut’s Oddyssey by Joseph Allen.


International Reference Guide to Space Launch Systems by Hopkins, Hopkins, and Isakowitz.


The Fabric of the Cosmos: Space, Time, and the Texture of Reality by Brian Greene.


How the Universe Got Its Spots: Diary of a Finite Time in a Finite Space by Janna Levin.


This New Ocean: The Story of the First Space Age by William Burrows.


The Last Man on the Moon by Eugene Cernan.


Failure is Not an Option: Mission Control from Mercury to Apollo 13 and Beyond by Eugene Cernan.


Apollo 13 by Jim Lovell and Jeffrey Kluger.


The end

Far from it, he's also one of three authors of one of the most famous GR books.
https://www.amazon.co.uk/Gravitation-Physics-Charles-W-Misner/dp/0716703440

Since you're helping me in my thread, I'll help you in yours.

Try Gravitation, by Misner, Thorne and Wheeler. It offers a very intuitive (i.e not many proofs), geometric introduction to differential geometry.

Gravitation by Misner/Thorne/Weeler is not bad.

The math is more in depth than can be covered in a single post; there are ginormous volumes dedicated to the subject.

For cosmological models the typical solution to Einstein's field equations is the FLRW metric. In the case of expansion and the balloon analogy which gets bandied about the important part is to see how points on an expanding surface all move away from each other, not that the surface is closed. The FLRW metric involves a parameter k which is linked to the amount of mass-energy in the universe. If the quantity of mass-energy is small the overall structure of the universe is closed like the surface of the balloon. If the mass-energy exactly equals a certain critical value then the universe is flat and open, essentially an infinite plane. If the mass-energy is larger than the critical value then the universe has a hyperbolic shape which, it turns out, is quite hard to visualize.

Interestingly, the parameter k is really close to the critical value which determines the large scale structure of the universe. Current data points to k being larger than the critical value, so our universe would have a hyperbolic geometry. This parameter also is linked with the eventual fate of the universe. If the data is correct and k is larger than the critical value then gravitation will never be able to entirely stop the universe's expansion and we will all eventually die cold and alone. If k is smaller than the critical value then gravity will win and we will all die packed tightly into a glorious inferno.

The well-worn copy of Hyperspace by Michio Kaku has a special place in my bookcase. Right next to Gravitation.

> Whoa whoa whoa... Who said that?

Almost all cosmologists. General relativity doesn't require "space" to exist as a static playing field on which other things dance around; its brilliance is that it shows how space and time can be warped and twisted in areas of high mass density.

The big bang actually brought space into existence, blown up something like a balloon. Actually, the correct metaphor is the surface of a balloon. When you inflate it more, where does the extra surface come from?

A truly complete answer requires an understanding of general relativity. This 1200 page textbook starts with heavy mathematics and gets steadily more difficult. I'm not trying to stonewall, but it's way too complicated to summarize here.

Basically, the entire concept of time is pretty complicated around black holes and the big bang. It changes place with space. The expression "before the big bang" might not make sense, like how if you walk north, you'll reach the north pole. If you keep walking, you'll be going south. Even though you never turned around.

And when we get really close to the big bang, all our current theories break down. For reasonably large, slow, and light things, classical Newtonian physics is all you need. At high speeds, you need special relativity, which isn't too difficult. As things get smaller, this gets less accurate until you need quantum mechanics to understand what's going on.

When things are very heavy, you need general relativity to understand what's going on.

The big bang was both very small and very massive, requiring both. And unfortunately, they're currently incompatible in a very fundamental way. They can't both be right, and probably neither one is.

The problem is, the conditions under which the disagreements become apparent are the insides of black holes, which not really accessible to human scientists. Particle accelerators like the LHC get as close as any human technology can.

The frustrating thing is that we've been unable to find the slightest error in either theory, but there has to be an error somewhere!

[Edit: spelling fix.]

1215 pages 5.7 pounds
That could work...

John Wheeler trivia: the textbook he and Misner and Thorne put together is both the largest text book (also known as the phone book) and the most readable book with thousands of tensors in it I have ever seen. Seeing it is out of print is nearly as strange as it would be to see Feynman's lectures out of print.

Kip Thorne (the T in MTW) was a science consultant for the film. They got it pretty right dude. Yeah the whole [spoiler](#spoiler, "Inside the black hole") part isn't scientific, but it was adequately explained and motivated. If you can't handle something like that science fiction, as a genre, is not for you. Everything else was based on real physics and far more accurate than we could ever have hoped for. They ignored the gravitational red shift so that we could see anything... because it's a movie. That's fairly reasonable. And [spoiler](#spoiler, "The ship left in orbit when they went down to the wave planet should have experienced just about the same time dilation as the people on the surface"). But that seems like a minor nitpick.

Yes, it does hold. Mass-energy is the typical term used when talking to laypeople, but physicists tend to use natural units (\hbar=c=k_{B}=eV=1) which means that mass and energy are equal, not just equivalent. E=m, instead of E=mc^2, since c=1. (E^2 =m^2 c^4 +p^2 c^2 becomes E^2 =m^2 +p^2 for high velocities, for the pedantic.) So the terms are interchangeable, as long as you're using the right system of units.

The actual theory (the Alcubierre metric) is a solution to the Einstein Field Equations (the complex system of nonlinear partial differential equations that make up general relativity). However, since these are differential equations they can have many solutions, and indeed many different solutions have been found. It is not known which solution (if any) is correct for the real world. In general, it can't be known for certain until a full theory of quantum gravity is discovered. Indeed, the existence of "Dark Energy" is one of the indications that the theory is slightly wrong. It may be explainable as a modification of the theory or may actually be some sort of negative mass-energy, but at the moment we have no way to tell. Again, we need a complete theory of quantum gravity.


For anyone actually wanting to learn about this sort of thing in detail, try the following, in order:

http://www.amazon.com/Gravity-Post-Newtonian-Relativistic-Eric-Poisson/dp/1107032865
http://www.amazon.com/Gravitation-Physics-Charles-W-Misner/dp/0716703440/

Both are graduate level texts (it's a graduate level theory) and require a thorough understanding of differential equations. And differential geometry, and all the more basic physics on which they build of course. The first book starts with some very good material on Newtonian gravity, but you'll still want to have had at least a year of undergraduate physics to start. The theory is simple, but the solutions are very complicated.

>The song is a wave of vibrating air molecules

The "song" is not a vibrating air molecule. I can sing the same song back to you and it would be different vibrations, but the same song. The song can sung be a different person, but it is still the same song. The song can be stored as a series of 1's and 0's but when played will still be the same song but the vibrations of the air molecules will be different because it was stored digitally.
Songs and words can be represented physically, but this does not mean they are physical themselves. Is the "law" is a physical object? Are "crimes" physical objects? Can you point out where scientists have discovered the crime atom? Concepts, abstractions are not physical and it is childish to pretend they are.

>Beauty is mathematical patterns loosely related to the golden ratio.

Wow, and people say us scientists are cold and unpoetic. There's really no way for me to go here if you truly believe this.

>It is called "materialism"

Materialism does not dictate that abstract concepts must be physical. What materialism does say is that there is only nature. There is no supernatural or unnatural. What exists exists. The physical universe is entirely physical.

>However, what you're talking about is not abstraction. It is closer to the theory of the "universals."

A 'universal' is an abstraction. Just as a word is not a physical object neither is a property of such a word.

>I do not have a belief on this matter.

If you honestly can't comprehend the difference between something real and something abstract then you do have a belief on the matter and my arguements will fall on deaf ears since they presuppose abstractions.

>No, you are not. If you were taking your information straight from the OT, you would know that you speak absolutely nonsense.

It is helpful to point specifically what I said was wrong rather than just declare it. Did god or did he not flood the earth? Was this a real flood and not a 'metaphorical' flood? Were Noah and his family the only human surivors? Simple yes or no questions.

>Anyway, prove your statement that God had to break the laws of physics to cause the flood.

You need to answer what the flood is first. I can ask this question to a hundred different christians and get a hundred different answers, which version are you subscribing to?

>Yes, but it is not my job to figure out how God did it.

You can start by telling me what he did first, then we can deduce the possible ways of doing this.

>I don't know what you mean by clear exchange of mass

Electrons have mass. Also energy is mass.

>No. The word 'universe' is defined to encompass all that is physically real,

Then you and I and astrophysics are using different definitions. The universe is defined to be everything that exists.

>Your argument falls flat on the fact that many scientists defend (and are attempting to prove with good chance) the existence of the multiverse,

The argument doesn't fall flat because scientists are not infalliable. Also, good luck to them searching for a multiverse (though it would be undetectable by definition), Copenhagen interpretation FTW.

>it is certainly not a strange idea for science that something outside of our Universe exists.

It is a strange idea precisely because there is no evidence for it. Even the string theorists have yet to make an experimental prediction. They are like the aetherists of yesteryear.

>Aging is measurable. If they are not aging, then they are immortal. It is verifiable.

And what if they are aging so slowly that it cannot be verified above uncertainty that they are aging? Better to put a hard limit on it, say 500 years?

>No more hunger and preventable diseases...

Well this is your version of utopia though it hits pretty close to any mark that I would measure to be a good interpretation. One world government though? I doubt tea-party activists would call that utopia.
But whatever it's a workable definition. I don't think it'll ever be achieved, not because there is no supernatural but because of human nature. Maybe we could do it with a bigger planet and a lot of robots. Or mind control, would that count?

>Yes. I do not consider it true resurrection because we have very little control over the outcome

We'll have very little outcome over the football results but it's still football. Certain techniques make the outcome more likely, but there is no such thing as certainty and it certainly isn't random that using, say, a defibrillator has a better chance of starting someone's heart than not.

>I want an absence of time-limit.

We'll we've advanced to the point of minutes.

>As long as there is a body left, in reasonable condition, it should be doable 100% of the time.

The devil is in the details, define 'reasonable'. Right now a limiting factor is nerve tissue damage which is currently impossible to reverse.
Still though, the techique is only getting better.

>Supernatural souls do not exist. It is greek pagan mythology.

So there are no souls or spirits in christian mythology? If your body doesn't go heaven then what does?

>As long as it is not a machine.

Details, devil, what is a 'machine'? If a machine is that which is created by man then the task is impossible by definition.
Would you allow a new form of bacterial life created artificially in a lab as an acceptable result?

>They are achievable and measurable. They are not easy.

They are getting close to being measurable, clearly defined conditions need to be stated from the beginning or else these definitions could change and we could never acheive the result.

>This has been found multiple times. And whenever it happens, they find an excuse to why the dating doesn't match.

This can't be true. There is a nobel prize out there waiting for anyone who can disprove along standing scientific theory. Einstein got one for disproving Newtonian physics.
If I had such evidence that evolution was false I would be shouting it from the rooftops because it would be one of the greatest discoveries ever and would advance our knowledge.
If by 'excuse' do you perhaps mean 'reason'? Show me the best three pieces of such evidence.

>No, it is not true, sorry

Roman examples aside. Do we not celebrate winter solstice? Have we not named our days of the week after Norse and pagan gods? Do you have a starsign?
Our culture is a melting pot of those that came before it.

>Your argument is basically, "if something doesn't exist already, then it cannot ever exist."

Not something, but basically yes as applies to time and space. You cannot say there was nothing and then there was time because 'then' is a temporal concept that cannot exist without time and you may as well say 'always'.

>Citation needed.

Well you can start with Gravitation is you want the details, or you could probably find it all in some of Hawkings pop-sci books

>No. Answer the question. By 'evolution' you mean M.E.S. or the basic premise of the theory?

You're confusing two arguments here. I was using evolution as analogy for something you know to true, this was before I knew I was talking to a creationist.
So instead of biology lets use geology. Just to double check, you know the Earth is an oblate spheriod yes? OK, imagine you are talking to a flat-earther and he demands absolute proof that the Earth has no edge, what do you say to him?

>...there is demonstrable evidence that M.E.S. is wrong.

Another topic for another day.

>It is the Bell's Theorem.

Just Bell's theorem not 'the', and it is a rival idea to the probability interpretation of quantum mechanics so hated by Einstein. In every experiment so far, QM holds perfectly. Though there are some limitations on what experiments can be done and it will be interesting to see if anything comes of this.
(Here's](http://www.springerlink.com/content/r23275410u4p5q72/) a good paper on the incompatibility will non-local realism theories like Bell's and QM

>I wouldn't go as far as saying that such important premise of QM 'doesn't make any sense.'

What doesn't make sense is something being both non-local and non-casual in the same experiment at the same time.

>Virtual particles are only demonstrably non-causal if locality is assumed to be true. The problem is that locality is independently demonstrably not true.

Yes, and non-locality depends on classical causality being true, which it demonstrably isn't at the QM scale.

>First, it is possible to prove a negative.

You can never prove the non-existence of something, you can only show where it doesn't exist

>You should not attempt to prove him wrong. You should request of him the proof that he is right.

Yes!

>There is a wall behind me.

I never said how far behind you, or how large the elephant was, or whether the elephant can go through walls. Here is the problem in proving a negative. All you can say at this point is there is no visible evidence of an elephant behind you, but is absense of evidence really evidence of absense?

>Virtual particles only violate causality is locality is assumed as true, as far as I know. Unfortunately I don't have access to the journal.

Well this is splitting hairs a little. Newtonian physics only works if you assume locality is true or causality is true (and you usually assume both). Virtual particles exist, they do not on their own violate locality but they do violate classical causality.

I know this isn't exactly what you wanted, but Gravitation by Misner, Wheeler and Thorne ranks among mankind's most brilliant scientific achievements. This book is a tour-de-force of GR, with deep insights in every chapter, though some parts are a little out of date. You may be able to get a used copy for cheap.

Try this:
http://www.amazon.com/Gravitation-Physics-Charles-W-Misner/dp/0716703440/ref=sr_1_1?s=books&ie=UTF8&qid=1314236758&sr=1-1

I'm not a physicist, but this book seems like a standard text, and I found it to be an excellent resource.

Many reasons, plus I own this book.

https://www.amazon.com/Gravitation-Charles-W-Misner/dp/0716703440

There's a great book on Amazon called Gravitation that explains it pretty well.