Reddit mentions: The best relativity physics books

It's great that you want to study particle physics and String Theory! It's a really interesting subject. Getting a degree in physics can often make you a useful person so long as you make sure you get some transferable skills (like programming and whatnot). I'll reiterate the standard advice for going further in physics, and in particular in theoretical physics, in the hope that you will take it to heart. Only go into theoretical physics if you really enjoy it. Do it for no other reason. If you want to become a professor, there are other areas of physics which are far easier to accomplish that in. If you want to be famous, become an actor or a writer or go into science communication and become the new Bill Nye. I'm not saying the only reason to do it is if you're obsessed with it, but you've got to really enjoy it and find it fulfilling for it's own sake as the likelihood of becoming a professor in it is so slim. Then, if your academic dreams don't work out, you won't regret the time you spent, and you'll always have the drive to keep learning and doing more, whatever happens to you academically.

With that out of the way, the biggest chunk of learning you'll do as a theorist is math. A decent book (which I used in my undergraduate degree) which covers the majority of the math you need to understand basic physics, e.g. Classical Mechanics, Quantum Mechanics, Special Relativity, Thermodynamics, Statistical Mechanics and Electromagnetism. Is this guy: Maths It's not a textbook you can read cover to cover, but it's a really good reference, and undoubtably, should you go and do a physics degree, you'll end up owning something like it. If you like maths now and want to learn more of it, then it's a good book to do it with.

The rest of the books I'll recommend to you have a minimal number of equations, but explain a lot of concepts and other interesting goodies. To really understand the subjects you need textbooks, but you need the math to understand them first and it's unlikely you're there yet. If you want textbook suggestions let me know, but if you haven't read the books below they're good anyway.

First, particle physics. This book Deep Down Things is a really great book about the history and ideas behind modern particles physics and the standard model. I can't recommend it enough.

Next, General Relativity. If you're interested in String Theory you're going to need to become an expert in General Relativity. This book: General Relativity from A to B explains the ideas behind GR without a lot of math, but it does so in a precise way. It's a really good book.

Next, Quantum Mechanics. This book: In Search of Schrodinger's Cat is a great introduction to the people and ideas of Quantum Mechanics. I like it a lot.

For general physics knowledge. Lots of people really like the
Feynman Lectures They cover everything and so have quite a bit of math in them. As a taster you can get a couple of books: Six Easy Pieces and Six Not So Easy Pieces, though the not so easy pieces are a bit more mathematically minded.

Now I'll take the opportunity to recommend my own pet favourite book. The Road to Reality. Roger Penrose wrote this to prove that anyone could understand all of theoretical physics, as such it's one of the hardest books you can read, but it is fascinating and tells you about concepts all the way up to String Theory. If you've got time to think and work on the exercises I found it well worth the time. All the math that's needed is explained in the book, which is good, but it's certainly not easy!

Lastly, for understanding more of the ideas which underlie theoretical physics, this is a good book: Philsophy of Physics: Space and Time It's not the best, but the ideas behind theoretical physics thought are important and this is an interesting and subtle book. I'd put it last on the reading list though.

Anyway, I hope that helps, keep learning about physics and asking questions! If there's anything else you want to know, feel free to ask.

Not really a physicist in the sense that I have a degree in anything but I am current an undergraduate doing research so I think I somewhat count.

The main reason why I became intrested in physics because, much to the annoyance of my friends, I never was satisfied to just accept that things work, I usually had to know why it worked. While it started off really being just interested in science in general, I became much more interested in physics when my parents got me this book when I was like 10. I was not able to really read most of it until I was older but even at that young age I could appreicate how amazing physics is. I mean if you tell a little kid that if he runs fast enough he is actually slowing down time how can't that kid just be amazed, especially before he understand how fast he would have to run to get that effect lol? Then throughout high school I always would just go on wikipedia and read through all of the astronomy and physics articles that I could understand. My high school education itself though was pretty shacky when it came to physics. I did not like much calc or physics and only a little chem so I became extremly scared to go to uni to major in physics. I went my entire first year of college undeclared since I was so scared that I would not be able to make it. I would have went longer undelcared but I needed to sign up to registar for the second year physics classes. Even though I was not offically a physics major I was enjoying college so much. Being surrounded by people who care about the same subject as I did was so amazing to me. I no longer felt weird and out of place for enjoying learning about the world. Even though I felt like i fit in better at college, even into most of my second year I was scared I would not be able to make it. Now though I feel so much better since I have started taking higher level classes and getting 3.5s or higher in them and also starting to do research. To me one of the best things about being a physics major at college(well probably any major really) is thinking about to over a year ago and how little was able to do compared to now. One year ago I had next to no understand of quantum mechanics, minimal understand of Special relativity, and only basic calculus knowledge. Now I feel so much more knowledgable about everything and I am amazed about how much math I ended up learning this last year. My research and physics classes have also helped me so much this last year with some personal issues I was dealing with this last 6 or so months, as it gave me something to focus on. Granted being in college also has caused a lot of stress. An "easy" class would only require 10 hours of home work a week to me right now. Due to this then I have gotten into the habit of getting minimal sleep and barely eatting during the school year since I just dont have time to do research, go to classes, do homework, and try to maintain an healthy lifestyle. Even though it makes me sound masochistic, I have in a way enjoyed being in that kind of life style as it makes me feel that I am actually earning what I am doing and I am doing this not because it is easy but because I want to go into physics.

Ninja Edit: just posted this and saw how long it was lol. Sorry if it seems a little ranty(dont know if that woud be the right word to use) but like I mentioned I have had some issues the past few months and think this was a nice little refection thing that I could do on myself about the past.

The claim that "time is exactly like space" is not true. Time is treated as a dimension in Special Relativity (SR) and General Relativity (GR), but it is very different from the "usual" spatial dimensions. (It boils down to "distance" along the time direction being negative, but that statement doesn't really mean anything out of context.) The central idea of relativity is that while the entire four dimensional "thing" (spacetime) just is (is invariant), different observers will have different ideas about which way the time direction points; it turns out to be convenient for our description of nature to respect the natural "democratic" equivalence of all hypothetical observers.

I can point you to a couple of good resources:

This
is a very good, book about SR, and some "other stuff". It's pretty mathematical, and I wouldn't recommend it to someone who isn't totally comfortable with college level intro physics and calculus.

This
is the "standard" text for undergraduate SR; it's less demanding than the above, but uses mathematical language that won't translate immediately if you go on to study GR. (I have not read this myself.)

This is the book that I learned from; I thought it was pretty good.

This is Brian Greene's famous popularization of String Theory. It has chapters in the beginning on SR and Quantum Mechanics that I think are quite good.

This is Einstein's own popularization, only algebra required. All the examples that others use to explain SR pretty much come from here, and sometimes it's good to go right to the source.

This is a collection of the most important works leading up to and including relativity, from Galileo to Einstein, in case you'd like to take a look at the original paper (translated). The SR paper requires more of a conceptual physical background than a mathematical one; the same can't be said of the included GR paper.

I don't know what your background is--the first three options above are textbooks, and that's probably much more than you were hoping to get into. The last three are not; the book by Brian Greene and the collection (edited by Stephen Hawking) are interesting for other reasons besides relativity as well. For SR, though, another book by Greene might be a bit better: this.

The Physics AS/A Levels are a funny lot of modules; I believe they're designed to be doable without any A Level-equivalent Maths knowledge, so they're riddled with weird explanations that really try to avoid maths - which often just makes everything harder in the long run. (I did AQA Physics A, but all were pretty similar as far as I gathered.)

With that in mind, if you're looking to study Physics further on, I'd recommend supplementing your mathematics. If you're doing Further Maths, you probably needn't bother, as the first year of any university course will bore you to death repeating everything you learnt about calculus etc.; if you're doing single Maths, I'd recommend getting confident with C1-4, and maybe purchasing the Edexcel (Keith Pledger) FP1/FP2 books to get slightly ahead before uni. They're great books, so might be useful to have for Y1 of uni and reference thereafter regardless. I was quite put off by the attitude towards Y1 maths of the Further Maths people (about half the cohort), who kept moaning about having done it all already, so found focusing in lectures a tad harder; I wish I'd bothered to read just a little ahead.

The second thing I'd recommend would be reading fairly broadly in physics to understand what aspect in particular you enjoy the most. In my experience, the students who have even a rough idea of what they want to do in the future perform better, as they have motivation behind certain modules and know how to prioritise for a particular goal, e.g. summer placement at a company which will look for good laboratory work, or even as far as field of research.

To that end (and beginning to answer the post!), books that aren't overly pop-science, like Feynman's Six Easy Pieces/Six Not-so-Easy Pieces are good (being a selection of lectures from The Feynman Lectures). Marcus Chown does a similarly good job of not dumbing things down too much in Quantum Theory Cannot Hurt You and We Need to Talk About Kelvin, and he talks about a good variety of physical phenomena, which you can look up online if they interest you. I could recommend more, but it really depends how you want to expand your physics knowledge!

E - darn, just read you're not in the UK. Oops. Mostly still applies.

In response to your request for "a book that might help" you decide on physics...

I actually hated my first exposure to physics in high school, but my freshman mechanics course really got me excited about the subject matter. The textbook we used was excellent and is called "An Introduction to Mechanics" by Kleppner and Kolenkow (link).

If you have made up your mind on classical physics, check out an introductory text on Special Relativity. There is a highly readable and mathematically completely unintimidating text by a man named Helliwell (link) that I like! I'll warn that it completely skips a tensor-based approach (which would actually be useful later on) in favor of a trivial-algebra-based approach that does miss out on some of the beauty of the subject but does manage to blow your mind if you've never seen the material before.

There are other books out there that are potentially superior, but these are the ones I like, although I will say that in my opinion nothing beats Kleppner and Kolenkow in clarity or material at its level. I hope this helps, and if it doesn't, shoot me a PM and I'll get back to you!

Good luck!

Edited: formatting, grammar.

Griffiths is the go-to for advanced undergraduate level texts, so you might consider his Introduction to Quantum Mechanics and Introduction to Particle Physics. I used Townsend's A Modern Approach to Quantum Mechanics to teach myself and I thought that was a pretty good book.

I'm not sure if you mean special or general relativity. For special, /u/Ragall's suggestion of Taylor is good but is aimed an more of an intermediate undergraduate; still worth checking out I think. I've heard Taylor (different Taylor) and Wheeler's Spacetime Physics is good but I don't know much more about it. For general relativity, I think Hartle's Gravity: An Introduction to Einstein's General Relativity and Carroll's Spacetime and Geometry: An Introduction to General Relativity are what you want to look for. Hartle is slightly lower level but both are close. Carroll is probably better if you want one book and want a bit more of the math.

Online resources are improving, and you might find luck in opencourseware type websites. I'm not too knowledgeable in these, and I think books, while expensive, are a great investment if you are planning to spend a long time in the field.

One note: teaching yourself is great, but a grad program will be concerned if it doesn't show up on a transcript. This being said, the big four in US institutions are Classical Mechanics, E&M, Thermodynamics/Stat Mech, and QM. You should have all four but you can sometimes get away with three. Expectations of other courses vary by school, which is why programs don't always expect things like GR, fluid mechanics, etc.

I hope that helps!

You sound like a great audience for the series I recommend to everyone in your position: Lenny Susskind's Theoretical Minimum. He's got free lectures and accompanying books which are designed with the sole purpose of getting you from zero to sixty as fast as possible. I'm sure others will have valuable suggestions, but that's mine.

The series is designed for people who took some math classes in college, and maybe an intro physics class, but never had the chance to go further. However, it does assume that you are comfortable with calculus, and more doesn't hurt. What's your math background like?

As to the LHC and other bleeding-edge physics: unfortunately, this stuff takes a lot of investment to really get at, if you want to be at the level where you can do the actual derivations—well beyond where an undergrad quantum course would land you. If you're okay with a more heuristic picture, you could read popular-science books on particle physics and combine that with a more quantitative experience from other sources.

But if you are thinking of doing this over a very long period of time, I would suggest that you could pretty easily attain an advanced-undergraduate understanding of particle physics through self-study—enough to do some calculations, though the actual how and why may not be apparent. If you're willing to put in a little cash and more than a little time for this project, here's what I suggest:

• Pick up a book on introductory physics (with calculus). It doesn't really matter which. Make sure you're good with the basic concepts—force, momentum, energy, work, etc.
  
  
• Learn special relativity. It does not take too long, and is not math-intensive, but it can be very confusing. There are lots of ways to do it—lots of online sources too. My favorite book for introductory SR is this one.
  
  
• Use a book or online resources to become familiar with the basics (just the basics) of differential equations and linear algebra. It sounds more scary than it is.
  
  
• Get a copy of Griffiths' books on quantum mechanics and particle physics. These are undergrad-level textbooks, but pretty accessible! Read the quantum book first—and do at least a few exercises—and then you should be able to get a whole lot out of reading the particle physics book.
  
  Note that this is sort of the fastest way to get into particle physics. If you want to take this route, you should still be prepared to spread it out over a couple years—and it will leave a whole smattering of gaps in your knowledge. But hey, if you enjoy it, you could legitimately come to understand a lot about the universe through self-study!

> Why is a photon massless and still has momentum?

Because momentum isn’t actually p = mv, as in Newtonian mechanics, but it’s really

p = ( E/c^2 ) v

For objects with a non-zero mass m, moving non-relativistically, E is approximately equal to mc^2 and then p is approximately equal to mv, the Newtonian value.

However, photons are intrinsically relativistic. They have energy even though they don’t have mass (their energy is proportional to their frequency, E = hf, where h is Planck’s constant) and, so, they also carry momentum. In fact, since their speed (in vacuum) is always c, the magnitude of their momentum, using the above results, is always p = E/c = h f/c = h/wavelength.

> Why can't anything go beyond the speed of light? (Cliché but I never really understood why despite of many videos floating on YouTube)

Please take a read at this post I wrote here some time ago, where I address that question. Please ignore the first two paragraphs as those were part of a rant.

> How does a magnetic field originate?

A magnetic field is created by electric charges in motion. Since, however, motion is relative (you’re not moving with respect to your chair but you are moving with respect to, say, the Sun), so is a magnetic field. In a reference frame where an electric charge is at rest, you’ll only measure the electric field generated by the charge. In a reference frame where the charge is in motion, you’ll observe both an electric field and a magnetic field.

—

Excellent introductory books on special relativity, in my opinion, are (in increasing order of difficulty):

Special Relativity: For the Enthusiastic Beginner

https://www.amazon.co.uk/dp/1542323517/

Special Relativity (Mit Introductory Physics Series)

https://www.amazon.co.uk/dp/B079SB3MWS/

and

Spacetime Physics: Introduction to Special Relativity

https://www.amazon.co.uk/dp/0716723271/

Einstein’s own books are pretty great too, and are now in the public domain. Search the Gutenberg project for them.

(Former) theoretical physicist here, with a few years of college teaching experience.

A lot of the recommendations provided so far by other people here emphasise a mathematical background, which is definitely important and necessary if you're going to pursue physics in the long term. However, when starting, it's easy to get sidetracked by the math and lose sight of your stated goal, thereby getting discouraged.

Therefore, my best advice is to start with a solid conceptual book and build up from there, depending on your interests and knowledge. As for the math, learn as you go until you feel that you want to dive deep into a particular subject in physics, at which point you'll know what math you'll need to learn in depth.

An excellent conceptual start is Hewitt's Conceptual Physics.

Other good starting point books are Feynman's Six Easy Pieces and Six Not-So-Easy Pieces.

Hewitt's book is a more traditional textbook-style text while Feynman's books are more free-style.

From there, the Feynman Lectures in Physics are challenging but extremely rewarding reading.

Once you've gone through those, you'll be in great shape to decide on your own what you want to read/learn next.

Also, as already suggested, online resources such as MIT's Open Course are highly recommended.

Best of luck!

I don't know any good videos off the top of my head, but I'd recommend asking for an explanation of the basics of special relativity over on /r/askscience or /r/asksciencediscussion. Or you could use search bar to find old threads about the same thing. They're usually very friendly and helpful.

If you want to go more in-depth and do a little reading on the subject, I'd really recommend this book. It's short, it's not too math heavy, and it does an amazing job of making the ideas clear and obvious. It's actually the book that I learned this stuff from recently. There are also a few others in that collection that deal with other introductory physics topics.

Also, thanks for being reasonable. I don't think you need to stop posting here (not like I could stop you anyway, I'm not a mod or anything). I'm not even close to being an expert, and I still occasionally post here and on /r/askscience... but I keep it to questions rather than answers when I'm not confident that I have a good understanding of the topic.

This was the one that we used for Cosmology. It starts pretty gentle but moves into the metric tensor fairly quickly. If you don't have the maths I don't know that it'll help you to understand them but it'll definitely have all the terms and equations. As with Dirac's Principles of Quantum Mechanics, the funny haired man himself actually had a pretty approachable work from what I remember when I tried reading it.

​

This one has been sitting on my shelf waiting to be read. Given the authors reputation for popularizing astrophysics and the title I think it might be a good place to start before you hit the other ones.

What are you studying that requires tensors? Around here, you're likely to get a fairly abstract mathematical answer; tensors are often used in modern physics (especially general relativity), and physicists think about tensors in ways that, while formally equivalent, look very different to the way mathematicians think about them. If you're studying GR, you might be best reading a physics textbook so you can understand what other physicists are talking about - but make sure you come back and learn the mathematician's answer later so that you really know what's going on ;-)

Edit: I remember the introduction to tensors from Wolfgang Rindler's Introduction to Special Relativity as being quite good. It's from a physics perspective, and uses Einstein's summation convention and the like.

Also, if you're studying category theory, then the "tensors" you're encountering might not be tensors in the linear-algebraic sense at all. Category theorists like to use the tensor sign [; \otimes ;] for any product-like operator on a category; they also use the word "tensor" to mean "the left adjoint of the hom functor, if one exists". The classical tensor product is this functor on categories of vector spaces.

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.

http://deborahdrapper.com/contact-me/

I know that by now you probably dread re-runs of the BBC documentary, since it brings a spike in your email you feel obliged to reply to. I make no such demand upon your time, only that you read what I have to say and trust that I have nothing to gain from lying to you.

"Big Bang" was coined as a derogatory term by 'steady state' advocates like Fred Hoyle—who, as a man of science, finally gave his support to Big Bang theory once it could be proven, in the principal of maximum entropy, that, in fact, all matter in the universe was created in the first picosecond of space-time. What happened before the Big Bang has nothing to do with what happened after it.

What exactly prevents the above statement of fact, or something like it, from being printed in every science book dedicated to objective understanding, regardless of the reader's religious orientation, seems rather obviously to be a matter for those who, without any reasonable basis upon which to build a counter claim, deny the basic axioms of all physical processes. To learn more on these descriptions of nature which we call "laws", you might enjoy reading an accessible and entertaining book by Nobel Prize physicist Richard Feynmen called 'Six Easy Pieces'

http://www.amazon.com/Six-Easy-Pieces-Essentials-Brilliant/dp/0201408252

I noticed that in your bedtime listening you enjoy the lectures of Kent Hovind. I wondered if you are also aware that he is currently serving time in jail for refusing to render unto Caesar what is due to Caesar?

Hovind's reasons for asserting that you are being lied to about Big Bang and Natural Selection are soundly debunked in a number of videos by a YouTube user known as AronRa, who you can find at the link below.

http://www.youtube.com/view_play_list?p=126AFB53A6F002CC

Thanks for your time—and don't worry, I don't care who Victoria Beckham thinks she is either :)

You always move through time at the same rate, 1 second per second. What changes in special relativity is that we stop being able to agree on time measurements with other observers who are moving with respect to us. You can't just slap time on as an extra axis like you would with Z when moving from 2D to 3D. The very rules of geometry change when you switch from space and time to spacetime, and they do so in such a way that even though different people disagree on the amount of time that passed and the distance between things they can always agree on special quantities that are 'invariant' and we can use those invariant measurements to bridge the measurements of two observers.

In 2D when you want to know the distance between two points you can find the x position and the y position of each point and use basic trigonometry to find the distance. a^2 + b^2 = c^2 . Let's say you want to know all the points exactly one unit away from the point (0,0), you just set c = 1 and find values of a and b that still fulfill that relation. You will find that neither a nor b can be greater than 1 or less than -1 by itself, or the point will not be 1 unit away. This is relatively easy because we can freely add together the values of a and b. But what if we measured a in meters and b in miles and we didn't know how to convert those units? We could never do this basic geometric exercise, we could still refer to a given point but we could not find all the combinations where c = 1.

That is the basic problem with just tacking time on as another axis. Time is measured in seconds, and that as a unit is not compatible with meters. So we need a conversion factor in order to measure time in units of meters, it turns out the speed of light is exactly that conversion factor we need and that has some fun consequences that I don't have the time to go into. If you are interested in special relativity I highly recommend finding a copy of Spacetime Physics by Taylor and Wheeler, if you followed my argument above and have some very basic physics you should have relatively no problem with the first few chapters which should help you understand relativity much better.

> Why would you insist a human be there to observe it to make it a thing?

I didn't. I said light doesn't have a color until you look at it. While it's propagating through space, light does not have a frequency. I was merely pointing out one of the Rand quotes that exemplifies where she gets things wrong. That said, we're pretty off topic for /r/politics. :-)

That said, my complaint with Rand is how she says "Logic indicates that if existence exists, then you can infallibly deduce that the conclusions of Objectivism are correct." Except that Descartes started with exactly the same set of premises (you know, the whole "I think, therefore I am, therefore consciousness exists, therefore there must be something to be conscious of, etc" bit?) and came to the logical and inarguable conclusion that a loving God created the universe. Aristotle used "A=A" to determine that the universe had to be infinite in size (because otherwise there would have to be something outside to keep you from crossing the border, right?), that a constant force results in a constant velocity, and that heavier things fall faster than lighter things. All very logical.

I think she came to a lot of useful conclusions. But it's like the difference between saying "I agree with Jesus when he said we should be nice to people" and saying "I agree with Jesus because he's the son of god." She starts with the conclusions she wants to come to, then makes unwarranted "logical" deductions to get there, then claims that since it's "logical" you can't disagree.

> the object would then travel though the then shortest path through space

Yes. But even when the planet is there, the astronauts going in circles around the planet are still going along the shortest path through spacetime. That is what "curved space time" means. When you toss a baseball in the air, and catch it again, it just went in a straight line in spacetime (if you ignore air friction). The space ship isn't "circling the drain" of some giant funnel.

Here: http://www.amazon.com/Six-Not-So-Easy-Pieces-Helix-Books/dp/0201328429

As long as you're not feeling acceleration, you're going in a straight line. F=ma, right? (Yes, that's still true in Einstein's world.) So no force, no acceleration. You're not accelerating when you're orbiting the earth, even though you're changing direction in 3-space.

> It's like those big funnels they have that you can feed coins into.

No. It's completely and totally unlike that. What would make the coin fall down the curved funnel if the curved funnel itself is gravity? There's no "gravity outside the universe" to pull you down. That's what I was saying when I asked "what would make you slide down?"

The only way in which it's like that is that the measurements in space near mass aren't euclidean. What is the circumference of that funnel? What is the radius of the funnel? That is curved space time. The sun is about a kilometer deeper than you would calculate by dividing its circumference by Pi.

> Originally I was attempting to use an analogy to explain how the universe works irrespectively of human belief structure.

Yes. It works that way regardless of human belief. But by the same logic, you can't look at how the universe works and deduce from that human beliefs. And humans don't work the same way regardless of human beliefs - if you're delusional, the world isn't the same for you as it is for most others. It doesn't matter if the universe says "you have inalienable rights to not be taxed", if there's never been a society in all of human history that didn't impose taxes forcefully, eh? Personally, when logic disagrees with reality, I go with reality, because that means something in your logic is wrong.

In your scenario, you are traveling at the speed of light (speed of light is called "c" from here on out); this is impossible since you have mass and can't possibly travel at the speed of light.

Lets use your idea with a slightly different example. You would think that if you are traveling at 0.75c (aka 3/4 of the speed of light) and fire a bullet forward with a velocity of 0.75c then the bullet will be traveling 1.5c (faster than the speed of light)... but this is not how velocity addition works.

Velocities don't add like 10+10=20, but have a more complicated form called relativistic velocity addition:

vtotal=(v1+v2)/[1+(v1*v2)/c^2]

This is especially important at velocities that start to apporach the speed of light (let's say 0.2c and faster) and it is negligible at every day speeds like driving your car or flying in a plane.

With the correct formula and using the numbers in the example above;

v=(0.75c+0.75c)/[1+(0.75c*0.75c)/c^2_]
v=0.96c

You can try any combination of numbers for v1 and v2 between 0 and 1c but you will never get a result greater than c. This velocity addition equation is a result of Einstein's Special Relativity.

Relativity also affects momentum and energy giving different values than would be expected using Newtonian classical mechanics at these very high velocities. Time and the length of your moving space craft are both distorted. Furthermore, a person in the space craft and a person at rest (with respect to the spacecraft) may not even agree on the order of two events when they are observed by both people. This gif is a Minkowski diagram that shows the effect of the shifted worldline at relativistic velocities and its effect on the observation of simultaneous events.

A great resource and starting point for learning special relativity is a book called It's About Time: Understanding Einstein's Relativity.

All the video sources I'm finding seem... spotty, but Richard Feynman's lectures on physics are the best in my opinion. He starts out with the basic foundations modern physics and progresses into much more difficult territory. They're well written, and definitely a good read for anyone who wants a basic understanding of physics.

I have these copies of his lectures which I like because they split up the easy and the hard topics in to separate books. But this is just personal opinion, and there are many, many copies of his works out there.

1. Physics does not say. The closest we can come is "what if the mirror were made of light", and in that case it would just go on ahead of the light forever and nothing would be reflected. (But wait! you say. Wouldn't an observer on the mirror see the light coming at c, like every observer? You're right, but you forget that an observer moving at c also sees the universe contract to a point and does not experience the passage of time. So really, they can't be trusted.)
   
   
2. I think you would see it moving at about 57% normal speed and most of the previously-visible light would be shifted out of the visible spectrum (you'd see yourself in UV, which is usually dimmer anyway, without the doppler shift), but I don't actually know how this works for reflected light vs. emitted light, and it seems to me the effect might be stronger for reflected light (as in a mirror). It would also be dimmed by a similar factor.
   
   
3. Let me clarify. The 'continuous stream of light' I talked about would have to be coming from you at a single moment, not over time. That is, you'll never see yourself at a standstill because there has to be new light coming in constantly (in order for you to keep seeing the image indefinitely), but that new light has to have all been emitted at the one time of the 'snapshot' you're seeing (or else it would show you moving). So even without considering relativity, it's clear that if you're seeing yourself slowed down 2x, you'll be 2x dimmer (since the light has to be spread out over twice as much time).
   
   If you're interested, go check out the fairly old book Mr. Tompkins in Wonderland -- it's sometimes hard to find books about this that explain the ideas without oversimplifying things or getting major things wrong, with the result that people are left with a bunch of perfectly reasonable unanswered questions or impressions of paradoxes where there are none. You can get the book (bundled with another of Gamow's books, which you should ignore) here.
   
   If you have a good math background and are willing to work through things slowly and logically (it won't be easy, but it will answer every one of these questions), you can try Feynman's lectures on the subject. You can get them most cheaply as Chapter Three of Six Not-So-Easy Pieces.
   
   Contrary to what physicists will tell you, Feynman is not the clearest teacher (his books are a lot more popular with physicists than with their students) but this is because he will never simplify anything to the point of teaching you something that's wrong (which you later have to unlearn when you advance a level). So sometimes this means he teaches things in strange orders (relativity before basic mechanics), or he looks at complicated parts of simple problems which most teachers would ignore. But if you're willing to go slowly, stick to it, and follow the math of each example carefully, by the end of a Feynman chapter you will have a better understanding of that area of physics than the average university physics student.
   
   The Wikipedia page on special relativity is also a good place to start.

Entirely depends on the level of comprehension you're looking for. For an advanced layman understanding there are a lot of books out there at different levels. It also depends on how much you want to learn. An overview by reading things like Six Easy Pieces or A Brief History of Time would probably help with comprehension of some later stuff. Off the top of my head I can't think of anything which would help directly with the questions you want answered but the books will be there.

On the other hand if you want to understand more completely as well as the links in drunkenwizzard's post there's this. Its by a theoretical physicist and has the aim of getting someone completely up to speed to the extent that you would in principle completely get it. If it looks like a lot its because it is, but there isn't really any way around the fact that theoretical physics is quite difficult. Either way its going to be a challenge so...good luck

Richard Feynman's popular works are a great way to 'click' on a lot of physics. Books like 6 Easy Steps. I'm not sure what level they expect you to be at already, but Feynman was an outstanding teacher, one of the world's best in my opinion.

It is a fairly simple concept that you can easily look up and read up in more detail about (I suggest http://www.amazon.com/Time-Travel-Einsteins-Universe-Possibilities/dp/0618257357 which includes a very good explanation).

It is simply a statement of probability. If you are a random human (and guess what -- you are), it is most probable that you will come into existence when there are more humans than when there are less humans (assuming you are not in some way "special"). If you don't understand this bit, don't waste your time reading further, as that is fundamental.

Gott expresses the principle in terms of confidence levels (as a percentage). e.g. We can be 95% sure we are in the middle 95% of the span of human existence, or we can say we are 50% sure were in the middle 50%. So confidence in the prediction drops as the prediction becomes more narrow.

It makes total sense, and I can't help you if you do not understand the concept (or are unwilling to read one of the many sources that describe it).

The current well-documented rise of human population is completely irrelevant to what we are describing (and is likely to be constrained by resource constraints and disease, anyway). You would have to be pretty nuts to think human population can grow geometrically forever, whilst it has a finite resource base.

Edit: You may also want to try and find this article: http://www.nature.com/nature/journal/v363/n6427/abs/363315a0.html

You're welcome!

To be honest, I went out of my way to take courses in Tensor Analysis and Differential Geometry before I started learning GR, and I can't say it was that useful. It didn't hurt, but if your interest is just in learning GR, then most introductory GR textbooks teach you what you need to know. I'd recommend Schutz as a good book with tons of exercises, or Carroll ,partly because his discussion of differential geometry is more modern than that of Schutz.

c is called the speed of light, but really it's the speed limit of the universe. Landau and Lifshitz give a beautiful explanation in their famous textbook series (not for the inexperienced) as to why it makes sense for there to be a "speed limit."

> However, experiment shows that instantaneous interactions do not exist in nature. Thus a mechanics based on the assumption of instantaneous propagation of interactions contains within itself a certain inaccuracy. In actuality, if any change takes place in one of the interacting bodies, it will influence the other bodies only after the lapse of a certain interval of time. It is only after this time interval that processes caused by the initial change begin to take place in the second body. Dividing the distance between the two bodies by this time interval, we obtain the velocity of propagation of the interaction.

> We note that this velocity should, strictly speaking, be called the maximum velocity of propagation of interaction. It determines only that interval of time after which a change occurring in one body begins to manifest itself in another. It is clear that the existence of a maximum velocity of propagation of interactions implies, at the same time, that motions of bodies with greater velocity than this are in general impossible in nature. For if such a motion could occur, then by means of it one could realize an interaction with a velocity exceeding
the maximum possible velocity of propagation of interactions.

Basically, if there wasn't a universal speed limit, then interactions could occur instantaneously over any distance. Events in distant galaxies billions of light-years away could affect us immediately. This is not how we observe nature to work, so their must be a speed limit. Now, everyone must agree on that speed limit all the time, or else it's not really a speed limit. Working out the full implications of that gives us special relativity.

Now the question is, why should light travel exactly at that speed limit? Because it's massless. To quote L&L again:

> Experiment shows that the so-called principle of relativity is valid. According to this principle all the laws of nature are identical in all inertial systems of reference. In other words, the equations expressing the laws of nature are invariant with respect to transformations of coordinates and time from one inertial system to another. This means that the equation describing any law of nature, when written in terms of coordinates and time in different inertial reference systems, has one and the same form.

When he talks about "inertial reference systems" he's talking about a system of stuff all moving together at constant velocity. So no matter where you are, and no matter how fast you're moving, physics looks the same everywhere. Another way to put it is that there's no way to say whether I'm standing still and you're moving, or you're standing still and I'm moving. Physics looks identical in either case, so one statement is as good as the other.

What does this have to do with massless particles moving at the speed of light? If something is moving at less than the speed of light, then it must have a co-moving reference frame. That is, there is some vantage point (some speed and direction of motion) in which that thing is at rest. But if we were able to get into the co-moving reference frame of a massless particle, then we would see it have no mass and no momentum, hence no energy at all. It wouldn't be there! So some observers would say there is a particle, and others would say there's not. There would be a disagreement about physical observables based on reference frame, which contradicts the principle of relativity. Now it is possible for a massless particle to move at exactly the universal speed limit because everyone always agrees on that speed, so no matter what reference frame you're in, you'll always see it moving exactly at that speed limit. This also implies that a massive particle can never move at the universal speed limit.

Edit: fixed some typos.

The analogy holds up well enough for things like gravitational lensing. But yea, just gotta be careful. It's meant to help you understand the highest-level qualitative concept, not to be predictive.

And, for the record /u/benisbrother, there are GR resources available for the layman which are as accurate as they can possibly be. General Relativity: From A to B by Robert Geroch is one of them that uses almost no math, but details the entire theory geometrically in 2d and 3d spacetime (where you sacrifice spatial dimensions rather then the temporal one, and work in projections). It relies very heavily on the geometry of projected lightcones to build intuition, which works remarkably well. I literally mean visual geometry; drawing lines and curves. The writing is fantastic, the figures are fantastic... anyone interested in this thread should give it a go.

i have done a lot of research into this area. people in this thread are a bit shortsighted in my opinion. here are some references that do exactly what you ask and what they state can't be done:

• the einstein theory of relativity: a trip to the fourth dimension by lillian lieber - by a mathematics professor
  
  
• general relativity from a to b by robert geroch - a well known mathematical physicist
  
  
• a journey into gravity and spacetime by john wheeler - that's the advisor of richard feynman and kip thorne and co-author of gravitation by misner, wheeler, thorne
  
  
• discovering relativity for yourself by sam lilley - the author taught relativity to adult students for many decades
  
  
• flat and curved space-times by george f.r. ellis and ruth m. williams - note this book references the books by lilley and geroch in the preface or introduction (can't remember which)
  
  also, the popular science book black hole by marcia bartusiak is a great account of some of the history of general relativity with respect to the acceptance of black holes. none of the books above are popular science though. they describe real physics in real ways.
  
  there are more, but i think this is a good start. have fun!

Ahh... I like you!

Great question!

The answer to this is actually extremely complicated. In fact, energy conservation is actually not true in general relativity. If you are interested in reading about this, check out Sean Carroll's blog entry on the topic. He's a well known cosmologist at Caltech who wrote a textbook on general relativity.

Yes, Bryson's is a good one. I'd also recommend some classic books: 1. The Universe and Dr. Einstein. 2. About any book written by George Gamow, like One Two Three . . . Infinity. 3. Thinking Physics. I think all these books are quite motivating.

Hartle: http://www.amazon.com/Gravity-Introduction-Einsteins-General-Relativity/dp/0805386629/ref=sr_1_7?ie=UTF8&qid=1420630637&sr=8-7&keywords=general+relativity

Pretty introductory, not a ton of math but enough to satisfy most undergrads. Includes a section on introductory Tensor Calculus.

Carroll: http://www.amazon.com/Spacetime-Geometry-Introduction-General-Relativity/dp/0805387323/ref=sr_1_3?ie=UTF8&qid=1420630637&sr=8-3&keywords=general+relativity

Probably the best intermediate book, does GR at an intermediate level. Includes several chapters on the math needed.

Wald: http://www.amazon.com/General-Relativity-Robert-M-Wald/dp/0226870332/ref=sr_1_2?ie=UTF8&qid=1420630637&sr=8-2&keywords=general+relativity

Covers GR at a fairly advanced level. More rigorous books exist, but are not appropriate for a first course.

Well a good intro. textbook is Fundamentals of Physics by Halliday, Resnick, and Walker. This is a full freshman physics book, so it has a little bit of everything, but I used it a lot through my entire undergraduate degree.


Had a class that technically required Theory of Relativity by Pauli but the teacher used their own notes so I never read the book.


My favorite book that deals with relativity is Exploring Black Holes by Taylor and Wheeler. Took an undergrad class where this was the main textbook and loved it.

You are welcome to think of it as a vector analogy, it will make "sense" if you understand vectors. Every particle is of length of c, that is a constant. c is a vector (direction) and is fundamental to all particles. Your c is always projected along your time axis. When you move in space, your c is tilted compared to the other c's around you. That means that temporal projection of your c vector onto their time axis is shorter. Or if you wish, their projection of their c vectors onto your axis is shorter. The particles on the front of your body and the rear of your body are at different times, relative to other times. Just draw your a one meter length on their x axis and rotate it so that it is moving in their frame, it is easy to see that the ends are at different times. Your spacial projection of your particles onto other spatial axis is also shorter.

This conceptual model correctly summarizes special relativity. It is not the normal way it is taught but it is a well known alternative. See Special Relativity Visualized.

Enjoy your journey through space - time.

A list of several GR books (mostly lecture notes from classes)

Einstein's 1920 relativity book (notation is a bit old fashioned)

Or Pauli's book (written at age 21 the bastard), which can be bought for ~$4 on amazon used which appears to be under copyright still though google search seems to show available for free download.

I have Pauli/Einstein books and find them less useful than modern books.

I learned GR as an undergrad using F&N and liked it for being short and to the point + Schaum's book on Tensor Analysis, which can be obtained for ~$35 and ~$5 on amazon used.

Was referring to this book and this one specifically. They are lectures by Feynman, yes. I'm assuming that they are pieces taken from that huge collection, but I'm not 100% sure of that. He was a wonderful teacher though, and if you have any interest in the subject, you should check it out.

For Statistical physics I would second the recommendation of Pathria. Huang is also good.

For electromagnetism the standard is Jackson. I think it is pedagogically terrible, but I was able to slowly make my way through it. I don't know of a better alternative, and once you get the hang of it the book is a great reference. The problems in this book border from insane to impossible.

So that's the basics. It's up to you where to go from there. If you do decide to learn QFT or GR, my recommendations are Itzykson and Carroll respectively.

Good luck to you!

Looks like your question has been answered, but I have a book recommendation:

http://www.amazon.com/Why-Does-mc2-Should-Care/dp/0306817586

I think you'll enjoy it. It explains the answers you've asked for and a lot more, in a pretty approachable way.

Six Easy Pieces and Six Not-So-Easy Pieces are both great introductory books that explore the fascinating essentials of Physics. Feynman is a lucid and captivating science teacher.

> They are the least problematic because essentially magic is involved, its hand waving and saying "Yeah its there because its always been there"

No, they're least problematic because there are no causality issues at all. All this forth and back through wormholes and black holes creates a closed time like curve where the actions of an object traveling in time and interacting with itself leads back into exactly this path.

Also there's not really a bootstrapping problem. To our minds this looks like violating common sense, because we're so used to the arrow of time. However common sense never works very well with this kind of physics.

But on a quantum level such closed time like curves are formed from nothing all the time: virtual particle / anti-particle pairs forming and destroying themself, if you look at the equations the anti-particle is actually a "normal" particle moving backwards through time.

There's also an excellent pop-sci book, written by a theoretical physicist, that deals with all things time-travel, focusing on how this works in the Einstein view (general relativity) of the universe. I highly recommend reading it. The case of closed loop bootstrapping is covered exhaustively and even discussed as a possibility for how the universe may have come to be in the first place: Amazon link: http://www.amazon.com/Time-Travel-Einsteins-Universe-Possibilities/dp/0618257357

Enjoy the course! I'm an amateur with an interest in relativity. Most tests of GR are tests of the Schwarzschild metric. Check out Orbits in Strongly Curved Spacetime. The BASIC code for plotting orbits in Schwarzschild geometry is the 2nd link in the 1st reference. Also I highly recommend the books Exploring Black Holes and Relativity Visualized.

Fortunately, special relativity isn't that mathematically intensive. If you took college algebra and trigonometry, it will be familiar to you. If you took calculus, it will be mathematically easy. Although the concepts are certainly difficult.

This book presents it at a very simple level.

This book and this book present some very interesting physics at a layman level. I'd suggest it to anybody curious about topics such as relativity.

Any decent introduction to special relativity should cover it. I don't know how technical you are, though. If you're mathematically inclined, Taylor and Wheeler's Spacetime Physics is an awesome book. A lot cheaper and pretty accessible would be Relativity: A Very Short Introduction

I'm a big fan of reading historical physics papers. I have this extremely well-annotated version of Newton's Principia, this collection of Schrödinger's original QM papers, and this fairly easy to find collection of relativity papers (mostly Einstein). Oh yeah, and these Dirac lectures.

Besides that, I just use my university subscription to find old papers, which is usually successful if they were published in English or sufficiently famous. I would say that I have a lot of "classic" papers saved just through finding them on Google Scholar or whatever. I could try to go through and list them, but I'd say it's mostly "usual suspects" plus important papers from my own interests (condensed matter/stat mech/QFT).

I recommend this book: http://www.amazon.ca/Spacetime-Physics-Taylor-Archibald-Wheeler/dp/0716723271

We covered it as part of a 3rd year physics course. It's actually very accessible, and prefers to provide good explanations (and help you to learn how to resolve apparent paradoxes) instead of lots of mathematical exercises.

I think most have provided the standard intro to GR textbooks at this point, so I'll make a vote here for Flat and Curved Spacetimes by Ellis and Williams. The illustrations, examples, and exercises in there are quite enlightening for one encountering SR and GR for the first time. Also, the annotated bibliography at the end of each chapter is an excellent resource to guide one to more advanced reading.

His primary point is sound. The light speed limit isn't a limit in the frame of the traveler.
The Taylor and Wheeler classic: http://www.amazon.com/Spacetime-Physics-Edwin-F-Taylor/dp/0716723271 is relevant here.
You can get around where you will in as short a time as you like given the ability to scoot. I recall programming a solver for this just outta high school and being astounded that most places in the universe are reachable even at a modest 1g. But you'd need mountains of fuel to with ungodly conversion ratios and nevermind the shielding to make it. ... And then, if you went too far, in what kind of place would you be arriving? It looks like a big crunch is out, so you just might run yourself early into a big rip?

You could do that, but I reckon that wouldn't be the most helpful thing.

Here's what I want you to do. Pick up this guy right here:

Book.

Read it all the way through, without thinking about your own paper too much. Take the papers on their own merit. Don't look up another book to help you, don't say "Well, ____ showed this to be wrong." Take the papers on their own merits, and work through the arguments on their own.

Actually, when I say "read", I mean "work through". I want you to be able to show how they go between each equation, and why. It's a short book, with short papers, but they are not easy. If you think you've got it intuitively, you probably haven't. Anything Einstein leaves as an "exercise for the reader" or waves away as "basic algebra", I want you to do, on paper. Until it's solved. It should take you several weeks.

Once you've done that, think about your paper again. Think about if it stands up to the same sort of criticism and analysis as the papers you will have just finished. Think about if there are any new points you need to make.

How does that sound?

Epstein also has a great book called Relativity Visualized that goes great with Thinking Physics.

If you want to learn more about special relativity, I suggest you read this textbook. My half semester special relativity class used this book, and I think a highschool student with a good background in classical mechanics should be able to go through most of it.

If you had gone over the site, you would have noticed that I address your objection, which is a silly one. If you think you can use proper time tau to parametrize time t as a way of showing that t is a variable, I've got a bridge to sell you. Time is time. What's good for the gander is good for the goose. If you think that you can use tau to show that t is a variable, you must first show that tau can change. You would need a meta-tau for your tau, and a meta-meta-tau and so on, ad infinitum.

Not all relativists are as dumb as you though. Here is a quote from "Relativity from A to B" by Prof Geroch at the U. of Chicago.

>"There is no dynamics within space-time itself: nothing ever moves therein; nothing happens; nothing changes. [...] In particular, one does not think of particles as "moving through" space-time, or as "following along" their world-lines. Rather, particles are just "in" space-time, once and for all, and the world-line represents, all at once the complete life history of the particle.

From Relativity from A to B by Dr. Robert Geroch, U. of Chicago

If that does not shut you people up, nothing else will. I tried. Besides, your intelligence compared to someone like Karl Popper is obviously miniscule. He was smart enough to understand that time cannot change by definition. You're just a pompous ass. Those who are voting you up are ass kissers. Now vote this down, AKs. LOL.

There's a book about this... its both excellent and terrible at the same time ... The book does a great job explaining some points, it really gets down to your level and treats you like a kid (this is a good thing).. but then it makes giant leaps of logic leaving you wondering what the heck just happened. I read it like 3 time and still don't understand parts of it. Why does E=mc^2?

Halliday & Resnick would be my recommendation. We used their Physics, Parts 1&2 when I was a student, not their Fundamentals of Physics, which seems to be a different book (and the two books were published simultaneously for a while; I was never sure what the difference was).

If you want individual books, try Kleppner & Kolenkow for mechanics, and Purcell for E&M. Those are often used in honors sections of freshman physics, since the problems tend to be a bit harder. There's also Newtonian Mechanics by A.P. French, which was used for freshman mechanics at MIT for a while (not sure if it still is). French's introductory books on Special Relativity and Quantum Physics are also good. But for relativity my favorite intro-level book is Spacetime Physics by Taylor & Wheeler.

That's right. I think theory of relativity is rarely explained well and in detail. I can recommend "It's About Time: Understanding Einstein's Relativity" by N. David Mermin as a book that helped me gain a better understanding of it.

I guess I'm frustrated because you're completely wrong and people are agreeing with you. The level of scientific illiteracy in these comments is disturbing. It's good that you recognize that you could be wrong and that you've actively tried to find out. I would recommend Why e=mc^2? (and why should we care?) as an excellent and accessible book exploring these topics.

One helpful way of learning is discussing our understanding of the ideas after we read about them. That's one thing that really helped me.

When it comes to the big bang, it is primarily about the expansion of space. The existence of matter is kind of a happy-accident that still needs explaining. Basically, during the big bang, there were particles and their anti-particles being created and colliding with one another and turning into pure energy. These should have annihilated each other completely, canceling them out. Instead, matter seems to have won out. Finding out the answer to that is one of the big questions facing physics these days.

I can admit that your ideas sounds good and seem consistent. The problem is that they aren't at all reflective of reality.

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 🙂

Six Easy Pieces: Essentials Of Physics Explained By Its Most Brilliant Teacher

by Richard Feynman

Spacetime Physics is the best introduction to special relativity I know. It will get your mind through the unintuitive parts if you give it time.

ok, the thing is you cannot expect to be able to tackle relativistic quantum field theory without a very solid knowledge of relativity (among other things). A very good introductory textbook to special relativity is Taylor's and Wheeler's, and also Rindler's spends more time explaining tensors and indices.

If you're willing to buy a book, Helliwell is a great one. We used it in my special rel class, and some of the reviews mention self-studying from it too.

It's not particularly small, but Relativity Visualized by Lewis Carroll Epstein is mostly pictures and is an awesome book.

Edit: by the description of the cover, maybe it's Thinking Physics, also by Epstein?

The Feynman Lectures are an excellent way to learn the baiscs of physics. I'd suggest the OP pick up Six Easy Pieces and Six Not-So-Easy Pieces, both put together from excerpts from his Lectures. Consider them the starter version for lay-people.

I recently bought Six Easy Pieces and Six No-So-Easy Pieces and both are fantastic.

I just want to start by saying that in order to fully understand how Relativity, and Special Relativity, work that you will need to be able to understand the physics and mathematical concepts behind the theory. If you would like to do this, I recommend a book that we used when I studied this on the undergraduate level: Spacetime Physics by Taylor and Wheeler.

You should be able to understand most of this book with minimal understanding of calculus.

That said, I'll endeavor to explain this without confusing the issue. I did mention previously (you may want to look at the other post and my response there) that yes, an object's velocity does affect how it experiences time. That said, the difference between how two frames of reference experience time is typically insignificant. I mentioned somewhere (this thread or the other one) that if you traveled in an airplane you'd be younger than someone standing on the surface of Earth. You won't be days or even full seconds younger - you'd have to be in the airplane a "long time" and be going decently fast to even be a full second younger than the Earth observer.

I mention this because you must remember that GPS systems must be extremely precise. This is the same with your computer. Your computer does not have a little atomic clock in it, but there are other clocks that your computer periodically synchronizes with. Your computer and GPS systems do not have little atomic clocks in them, but it is very important to keep these devices in sync with other devices - even more so if the the devices are on a network (and both computers, if you are connected to the internet, and GPS systems are on networks). As an anecdote, when I was working in IT at my University there were some services that would kick a fit if the host computer's system time did not match the synchronized time (i.e. if the host computer was a few minutes, or more, different from the synchronized/network time).

I would like to say that the major cause for the need for periodic synchronization has very, very little to do with relativity and much, much more to do with "lost time" (i.e. increasing error). Every measurement has a margin of error. For an atomic clock this margin of error is 10^-9 seconds. For most of the clocks you purchase at at a store, or the components in a GPS or host computer, the margin of error is several orders of magnitude higher than that. These clocks therefore "lose time" more quickly and need to be synchronized.

Also, you could say that Earth travels around Sun at a given speed and that Sun travels around the galactic core at a given speed. But you must also remember that if Sun is traveling around the galactic center, so is Earth. Think of this as being similar to swinging a ball around on a string and then walking around in a circle in your living room. The ball would have two directions of motion - one around you and the other around the room.

This means that both Earth and Sun, for the purposes of this discussion, can be considered the same frame of reference as the Earth-Sun system travels around the galactic core. This means, again for the purposes of this discussion, that the Earth-Sun system experience time in the same way (since they are both in the same frame of reference).

In a similar way, when you talk about the the galaxy moving through the universe, it is the Earth-Sun-Milky Way system you must consider. Just like we considered both Earth and Sun to be in the same frame of reference, the Earth, Sun, and Milky Way would be in the same frame of reference (at least for the purposes of this discussion).

So although there is no absolute time, remember that some objects are in the same frame of reference with respect to other objects - it depends on what your frame of reference is and what systems you are looking at/your margin of error.

Now there is more to relativity than just speed. There is gravity as well. Time dilation occurs both when an object is in a strong gravitational field and also when it is traveling at a significant fraction of the speed of light in a vacuum (remember that the observed speed of light is not constant in all media). This has actually been observed with the planet Mercury. There was a time when it was theorized that an extra planet, nicknamed Vulcan, had to exist in order for Mercury's orbit to be the way it appeared. This would only have been required with Newtonian motion (an approximation of relativity when applied to slow moving objects, or what we observe here on Earth), but was resolved by relativity. For some more information about this I direct you to Wikipedia's article about Mercury. The section named "Advance of perihelion" includes information about Mercury's orbit and Vulcan. Note that other planets, such as Venus, Earth, and etc. are far enough from Sun that this is not observable in the same way it is with Mercury.

Satoshi invented a new idea. They are an authority in describing the concept, just like Einstein with space-time and relativity or Pythagoras and his geometrical theorem. Yes, once the concept is understood by others it can be refined, improved, or modified, but if you want to know what the idea of relativity is there's hardly anyone that can describe it better than Einstein.

In the case of Bitcoin, we have a socioeconomic concept, an idea, an invention, a eureka moment. One that was had by Satoshi (whoever they are), and then described for the first time in a revolutionary whitepaper (a design document). The name "Bitcoin" has since been misleadingly attached to software implementations of the idea. But of course implementations can differ from design, and once those differences are fundamental, the implementation should no longer carry the name of the design. Otherwise you could say that the "Pythagorean Theorem" is "A=1/2bh" or "C=(pi)r-squared" simply because that's what your organisation is now insisting.

The one I read when I was a kid is The Universe and Dr. Einstein. It seemed pretty good to me.

Einstein understood why it worked pretty damn well. I've read Relativity by Einstein which is his own account not just of what the Special and General theories of Relativity say, but how he came up with them. Try to actually know something before you condescend like this next time.

Eh, I'm not sure if that's true. One of my undergrad professors wrote a book on the subject, which is one of my favorite science books ever: Time Travel in Einstein's Universe. Although Hawking disagrees, it seems that time travel (to the past) isn't inconsistent with anything we currently know about relativity.

However, it does seem very likely that it will not be possible to change the past - that is, the only stable solutions to Einstein's equations are those in which the time-travel is self-consistent. So things like The Time Traveler's Wife, LOST, or Harry Potter (3), not Back to the Future.

Time to go back to my book on relativity (despite my failure, it really is a very good book). I seem to be able to understand each concept of relativity in isolation, but I always go wrong in putting them all together and analysing a real situation... never know which part of the theory is applicable. Practice makes perfect, I suppose!

Thanks for the reply!

Griffiths E&M is a common E&M textbook for physics undergrad. It's common enough that you should be able to find the solutions online. A good contrasting approach is Landau. He typically takes a more elegant or straight forward approach to solve problems and doesn't have many (if any?) brute force problems.

Yes, he proved it, which is the entire reason why Einstein is so famous in the first place. Here's an excellent introductory textbook on the subject if you're not afraid of the math.

General relativity is the most iron-clad, battle-tested theory in all of science, along with quantum mechanics. None of its predictions have been proven false yet. Just last fall, one of the Einstein's predictions, gravitational waves, was proven to be true by an experiment called LIGO (Laser Interferometer Gravitational-Wave Observatory).

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.

He's also an author. That specific book titled " Why Does E=mc^2 " breaks the equation and relativity down to an understandable topic and you don't have to do the math, unless you want to.

He's got a few other books out that are on my wishlist. I really enjoyed the one listed above, I've read it twice so far. Will probably read it again this weekend.

You'll definitely want to read Einstein's original papers on the Special Theory of Relativity and related work. Dover has a cheap paperback edition of them translated to English, but they're available all over the place.

They're accessible enough for an undergraduate, and yet they're still some of the most profound works in all of physics' history.

No worries dawg, this book is really great for building relativistic intuition :)

https://www.google.co.uk/url?sa=t&source=web&rct=j&url=https://www.amazon.co.uk/Spacetime-Physics-Introduction-Special-Relativity/dp/0716723271&ved=2ahUKEwixufTdkv_dAhVHIcAKHaOJDQ4QFjAKegQIABAB&usg=AOvVaw1hmY1kwBnhsQdHYLk-r_fk

You might want to look at this book. It's high level enough and Feynman does a good job explaining it.

If you're in the mood for a book, Why Does E = MC Squared is a really good and accessible explanation.

This might help.

I found it quite interesting.

This scenario is written about in the book Why does e=mc^2 and why should we care?

Good book; a bit heady at times.

Try reading Relativity Visualized by Epstein. It does not use any complex math and explains this in a very clear way.

http://www.amazon.com/Relativity-Visualized-Lewis-Carroll-Epstein/dp/093521805X

I've heard very good things about [General Relativity from A to B]
(https://www.amazon.com/General-Relativity-B-Robert-Geroch/dp/0226288641/ref=sr_1_1?ie=UTF8&qid=1499632748&sr=8-1&keywords=general+relativity+from+A+to+B) by Robert Geroch, but haven't read it myself.

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)

The album art of the Strokes album freaked me out for a minute because the same image is on the front of my Special Relativity text book.

http://www.amazon.com/Ideas-That-Shaped-Physics-Frame-Independent/dp/0072397144

Upvotes for the Feynman. Parts of his lecture series on physics is quite good too. The whole thing is quite expensive, unfortunately.

You might want to try Taylor and Wheeler it is an introduction to the basics of GR whose math prerequisite is calculus.

Mermin helped me a lot.

Probably too late for you to read this but I actually have a book to suggests that spends quite some time dealing with this very subject.
http://www.amazon.com/Why-Does-mc2-Should-Care/dp/0306817586

Spacetime and Geometry by Sean Carroll

Oh, PDF. Hmm...

J. R. Gott

Your Inner Fish

How to Teach Physics to Your Dog

The Universe and Dr. Einstein

The Code Book: The Science of Secrecy from Ancient Egypt to Quantum Cryptography

Find a book called The Universe and Dr. Einstein.

Time Travel in Einstein's Universe.

Why Does E=mc2 by Brian Cox, Jeff Forshaw

The Goldilocks Enigma by Paul Davies

>Okay, so I wouldn't bother going back in time. If there is no reason for something to happen, and you just said that I would have to go back in time because, as you admit, if I didn't have to, then it doesn't make any sense, then you accept that time travel, as described by just about every movie, is simply a silly notion.

Yeah, no. I didn't say that there wasn't a reason for the thing to happen, I said that I didn't know what the reason was.

> If my going back in time to get a car is dependent entirely on whether or not I have that car in my garage (which I think would be the criteria for any fiscally responsible person in existence)

Yeah, see, this is your mistake. Sorry, but all your fancy pants attempt at using formal logic did was make you look even more confused. You never actually explained why any of my scenarios were logically inconsistent (all three directly addressed your false assumption), you basically just moaned that you didn't like them. Probably because you don't like causal loops. Which is a failing of your mental faculties, not a fault with time travel.

If you need convincing that causal loops are not "silly", you should read up on closed timelike curves, which are what physicists call time travel when it happens within the general theory of relativity. There is a book called Time Travel in Einstein's Universe that might be of use to you. It discusses scenarios like this. They can be modelled mathematically, and so assuming ZFC is consistent, they do not lead to a paradox.

But of course, I'm sure to you the combined efforts of some of physics' finest minds are just some "lackluster explanation". Which I gather from context means "thing I refuse to understand".

Read this in high school it touches on ethics in a future society that uses these matter recreaters to teleport people. For example teleporting from an ambulance stretcher to a hospital bed instantly and how a group of people develops that thinks the soul or ghost gets left behind.

My undergraduate GR course used Spacetime and Geometry by Sean Carroll, which has a discussion of gravitational lensing in section 8.6. The problem is that the discussion there is built on the rest of the book, which is on the mathematically rigorous side of things. Also, it is kind of expensive, but you might be able to find it in a library.

This should keep you busy, but I can suggest books in other areas if you want.

Math books:
Algebra: http://www.amazon.com/Algebra-I-M-Gelfand/dp/0817636773/ref=sr_1_1?ie=UTF8&s=books&qid=1251516690&sr=8
Calc: http://www.amazon.com/Calculus-4th-Michael-Spivak/dp/0914098918/ref=sr_1_1?s=books&ie=UTF8&qid=1356152827&sr=1-1&keywords=spivak+calculus
Calc: http://www.amazon.com/Linear-Algebra-Dover-Books-Mathematics/dp/048663518X
Linear algebra: http://www.amazon.com/Linear-Algebra-Modern-Introduction-CD-ROM/dp/0534998453/ref=sr_1_4?ie=UTF8&s=books&qid=1255703167&sr=8-4
Linear algebra: http://www.amazon.com/Linear-Algebra-Dover-Mathematics-ebook/dp/B00A73IXRC/ref=zg_bs_158739011_2

Beginning physics:
http://www.amazon.com/Feynman-Lectures-Physics-boxed-set/dp/0465023827

Advanced stuff, if you make it through the beginning books:
E&M: http://www.amazon.com/Introduction-Electrodynamics-Edition-David-Griffiths/dp/0321856562/ref=sr_1_1?ie=UTF8&qid=1375653392&sr=8-1&keywords=griffiths+electrodynamics
Mechanics: http://www.amazon.com/Classical-Dynamics-Particles-Systems-Thornton/dp/0534408966/ref=sr_1_1?ie=UTF8&qid=1375653415&sr=8-1&keywords=marion+thornton
Quantum: http://www.amazon.com/Principles-Quantum-Mechanics-2nd-Edition/dp/0306447908/ref=sr_1_1?ie=UTF8&qid=1375653438&sr=8-1&keywords=shankar

Cosmology -- these are both low level and low math, and you can probably handle them now:
http://www.amazon.com/Spacetime-Physics-Edwin-F-Taylor/dp/0716723271
http://www.amazon.com/The-First-Three-Minutes-Universe/dp/0465024378/ref=sr_1_1?ie=UTF8&qid=1356155850&sr=8-1&keywords=the+first+three+minutes

It sounds like you want to understand both GR and the standard model of particle physics. For an intro to GR, try Sean Carroll's book or lecture notes. For the standard model, try Srednicki's book (there is a preprint PDF available from the author).

You should have a solid understanding of both GR and the standard model if you want to try to explain the weakness of gravity through beyond-SM or beyond-GR theories. There are no compact extra dimensions in the SM or GR, so what you're talking about is already beyond-SM / beyond-GR. The type of model which tries to combine gravity and standard model forces via compact extra dimensions is called a Kaluza-Klein model and it's been around for a long time (1921!). The more modern ideas about explaining the weakness of gravity through extra dimensions are e.g. DGP models or RS models or cascading gravity ... they seem kind of contrived to me, but there's no accounting for taste.

I just wanted to point out one thing, not necessarily settle any arguments. Einstein's equation you wrote is a bit wrong. It should be E=mc2+(1/2)mv2. I think this is right, although I am a bit tired and too lazy to double check (sorry). Anyways, the reason we only remember the E=mc^2 part is because if a relatively small object (for example 1kg) is at zero velocity, then there is a huge amount of energy involved in the total mass. Theoretically, it could power a city for 100 years. This was the ground breaking part, and it lead physicists to discover the atomic bomb -> a lot of energy in little mass.

*This book is the source of what I (brutally) said.