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Hey Crazies.
A hundred and seven years ago, Albert Einstein and David Hilbert published General Relativity.
It's the best model of gravity we have,
but university courses on it are surprisingly difficult to find.
My master's program didn't offer one, so I had to teach myself.
I had to read through all sorts of books.
Some were better than others.
Today, I want to share my experience with you in the hopes that will save you a little time and stress.
What's your experience, smarty pants.
Okay, that's a fair question. I have a master's degree in physics.
I know you mean well when you call me "doctor," but you really shouldn't.
For those unfamiliar with academia, the only difference between a master and a Ph.D.
is that a Ph.D. knows a lot more than others about a very, very, very niche topic;
and they're certified by the university in that niche topic.
But that doesn't mean that masters don't specialize. We do.
Also, it's not like we stop learning when our degree is finished.
My journey into general relativity began with my master's thesis.
The question I was trying to answer was
whether or not applying general relativity to white dwarf stars made a noticeable difference in their upper mass limit.
The answer was "yes, but not as much as I was expecting."
A negative result is still a result.
Anyway, this interest in GR continued after I got my degree.
One of my special interests is cosmology, the physics of cosmic scales.
It's a long term obsession.
GR is vitally important for that topic, so I had motivation to learn everything I could.
That involved a lot of reading and a lot of pondering.
So, where do we start?
Well, any deep journey into general relativity should start with special relativity.
The best book I've ever seen covering this is
"Special Relativity for Beginners: a Textbook for Undergraduates."
Jurgen? Jurgen?
Jurgen Freund?
It's German. You know they're going to get on me. You know it!
(Computer Voice) Jurgen Freund.
Juergen Freund? Freund?!
(Computer Voice) Freund.
Freund. Okay. Jurgen Freund.
"A Textbook for Undergraduates" by Jurgen Freund.
Jurgen Freund.
It might not be particularly colorful or look very exciting,
but it teaches you how to draw spacetime diagrams.
Granted, none of those diagrams include curved spacetime like you see in GR,
but you've got to walk before you can run, as they say.
Spacetime diagrams are important tools for visualizing relativity.
If you know how to use them, they can help you avoid your own biases.
Now, I realize not everyone can just drop a load of money on books
and you can't always find books like these in your local library.
There are some free resources available.
The Feynman lectures are a decent place to go for special relativity,
or frankly anything.
As you can see, I have the hard copies in my personal library,
but Caltech made them all available online for free.
Link in the doobly-doo.
Anyway, Richard Feynman was one of the greatest teachers of the last century.
His casual style and his emphasis on intuition are immortalized in these books.
I've referenced them while producing many of my videos.
They're a valuable resource.
Here are the chapters relevant to special relativity.
Feel free to pause and jot them down or screencap or whatever.
Unfortunately, the Feynman lectures don't come with practice problems
and practice is where the real learning begins.
That's why it's better to have at least a few textbooks like...
Freund?
That's why it's better to have at least a few textbooks like Freund somewhere in your process.
What about Wikipedia and YouTube?
When I was getting my degrees, online educational video wasn't a thing;
and Wikipedia was a very new and terribly untrustworthy thing.
But that doesn't mean they aren't useful.
Wikipedia is big on citations these days.
Sources are listed at the bottom of the page.
Those are the real power of that website, but try to limit yourself to the scientific papers.
As for online video, there are some great options for special relativity.
I have a playlist on it, though some of those videos are old and kind of embarrassing.
Minute Physics also has a great playlist where he actually built a spacetime diagram toy.
Unfortunately, these have the same problem that the Feynman lectures do:
no practice problems.
Plus, it's difficult to know who to trust.
Credentials can help, but you don't need credentials to be a good science communicator.
Checking for sources in the video description is a good first step.
If you stumble onto an educational YouTube channel
and their entire brand is defined in opposition to everyone else,
you should at least be a little skeptical.
Just a suggestion.
Crash Course has a playlist called Navigating Digital Information, if you need more help with this.
Talk about general relativity already!
Okay. Okay. Next up, we have this very popular book.
"Gravity: An Introduction to Einstein's General Relativity" by James Hartle.
Part 1 in this book is just a review of special relativity.
It might help you get used to Hartle's notation, but you can skip it if you want.
Part 2 is what makes this book so popular.
It's lighter on the math in favor of intuition.
I mean, as light as you can go on the math in GR.
Hartle tries to focus more on spacetime infinitesimals in part 2
and includes spacetime diagrams whenever possible.
This exposes the reader to some common patterns we see in general relativity...
you know, before we get into the heavy math of tensors.
Tensors and four-dimensional vectors aren't really covered until part 3.
The upside to that is that the reader isn't scared away.
The downside is Einstein's equation isn't covered until you're almost at the end of the book,
which seems silly to me.
Overall, Hartle is a good place to start on the fundamentals of GR,
but you should be wary of the practical applications of this book.
Back when I was going through my grad work, I noticed that this graph didn't match these equations.
I actually emailed the author
and then he told me that the graph was made by somebody else at a different school.
Just because it's in a book, it doesn't mean it's correct.
If writing my own book has taught me anything,
it's that authors are not infallible.
Thankfully, early readers of the e-book version caught most of my mistakes
and I was able to fix them before releasing the hard copy.
But that's enough shameless self-promotion for one video.
The next book on our list is this one.
"Spacetime and Geometry" by Sean Carroll.
Yes, that Sean Carroll.
Like usual, this book begins with a review of special relativity.
But don't skip chapter 1.
This review chapter is written as a special case of general relativity.
Tensors are introduced almost immediately.
You need to read it.
This approach is more rigorous, but it could easily scare away anyone new to GR.
That's why you should read and work through the practice problems and Hartle first.
When you finally get to the Carroll book, it hopefully won't feel so overwhelming.
The rigor in here will also fill in many of the gaps left in Hartle.
It's even a good reference text as you can see from the wear and tear on my copy.
Sean Carroll has also made some resources available for free online.
There's a 24 page "no nonsense introduction" available on his own website
and 238 pages of lecture notes from a first course on GR
available on archive dot org.
Links in the doobly-doo.
Both of which are written in the same style as his book.
Beyond that, there are really only two more books in a relativist's library.
"General Relativity" by Wald;
and "Gravitation" by Misner, Thorne, and Wheeler.
I never would have gotten through my master's thesis without the Wald book.
It's a textbook, so it's organized in a way that makes sense to read from front to back.
Unfortunately, it does lean heavily into the math without asking forgiveness,
but that means it's going to cover a lot of the nuance in GR.
Wald is also a place you want to go for practical applications
like white dwarfs, black holes, and cosmology.
It corrected a lot of those application issues I found in Hartle,
which is odd because Hartle referenced Wald.
"Gravitation" is a completely different story.
Also known as the "Big Black Book," it's the ultimate compendium for general relativity.
But it is not a textbook. It is a reference only.
This book is not meant to be read front to back.
It's almost 1300 pages.
The way this book was written and organized lends more to research than learning.
It not only has a standard index; but also lists of all tables, figures, and boxes within the book.
The text formatting makes important information pop off the page for easy discovery.
This is a book you use when you need to find specific information.
It's not a book where you learn the basics.
It's a beast!
But, remember, you need to go beyond the reading.
It's really easy to read a book and think you understand, not realizing there are holes in that understanding.
Do the problems at the end of each chapter in the textbooks I've mentioned.
Practice is key. You might not retain it otherwise.
You could also try to explain it to someone else and have them ask you questions.
Write down the questions you couldn't answer and then look for those answers.
That seems like a lot of work.
Yeah, general relativity is a lot of work.
Can't I just watch some YouTube videos?
Okay. If you absolutely must have the info in video form
and you want more than just a passing understanding,
you're going to need to go beyond EDUtainment.
Not even my videos are enough.
You need to be watching pure education content
like DrPhysicsA's playlist on special and general relativity,
or eigenchris's multiple playlists on tensors.
Links in the doobly-doo,
but you need to think of them like tutorials rather than lectures.
If you want to retain the material, work through it yourself.
You're not just absorbing knowledge. You're learning a new skill.
Kind of like the ones you can learn on Skillshare.
Skillshare is an online learning community with thousands of inspiring classes
for anyone who wants to explore their creativity or learn new skills.
To help me produce this video, I worked through a class by Marques Brownlee.
In "YouTube Success: Script, Shoot, & Edit" with MKBHD,
he explains his entire process from pre to post-production.
Of course, I've been doing this for a while, so I'd already figured out some of his suggestions.
But this video was going to involve camera shots that were a bit outside my wheelhouse,
so it was helpful to see how much planning went into his shots.
If video production isn't your thing, Skillshare also has classes on photography, animation, productivity, and more.
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If this sounds like something you might be interested in, check out Skillshare.
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It also let Skillshare know you heard about them for me, which helps out the channel.
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Let us know in the comments.
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And until next time, remember, it's okay to be a little crazy.
Why doesn't the distance between the ships contract?
Because we defined the scenario that way.
I defined "acceleration in the same fashion" as the distance is maintained from the inertial observer's point of view.
If it's not maintained in your mental picture, then we're talking about two different scenarios.
Anyway, thanks for watching.