Best relativity physics books according to redditors
We found 195 Reddit comments discussing the best relativity physics books. We ranked the 53 resulting products by number of redditors who mentioned them. Here are the top 20.
We found 195 Reddit comments discussing the best relativity physics books. We ranked the 53 resulting products by number of redditors who mentioned them. Here are the top 20.
"Without a bunch of jargon" is your interpretation of what Dr. Feynman said. If you read Six Easy Pieces and Six Not-So-Easy Pieces, you'll find that Dr. Feynman's actual teaching is loaded with physics jargon, and a big part of his genius lay in offering supporting intuitions for the very precise terminology physics uses.
Actual computer science—as opposed to the dressed-up vocational training that calls itself "computer science," not that there's anything wrong with vocational training—is the same way. It's mathematical, painstakingly precise, and the terminology shows it. With that said, there are Feynmans out there to help lead us through it. For example, Conceptual Mathematics: A First Introduction to Categories is a text suitable for a bright high-schooler that nevertheless will have you understanding the terms "monad," "monoid," "category," and "endofunctor" by the time you're through it, should you choose to work through it.
Quantum mechanics is quite difficult to grasp without a formal mathematical course. General Relativity is also tricky, because it involves a lot of differential geometry.
Special Relativity on the other hand is actually quite straightforward. You don't need any mathematics beyond what you do in high school, and not even all of that - it doesn't require calculus. This was my undergraduate textbook, and it's quite readable. They offer the first chapter of the older edition on their website if you want to take a look. As an example of the readability, here is the opening of the book:
>Once upon a time there was a Daytime surveyor who measured off the king's lands. He took his directions of north and east from a magnetic compass needle. Eastward directions from the center of town he measured in metres (x in meters). Northward directions were sacred and measured in miles (y in miles). His records were complete and accurate and were often consulted by the Daytimers.
And carries on in that tone. Even if you don't read everything, it's worth reading the whole "parable" in that pdf to get a good intuitive grasp of what special relativity is really about.
I personally have an issue with the idea of a singularity - i did my undergraduate dissertation on this. I dont question the existence of objects with a gravitational pull that exceeds c but i just cant wrap my head around a singularity in reality - mathematical infinities usually indicate something is wrong or incomplete in a theory. And the whole information issue makes my head hurt.
Dirac makes a reasonably interesting argument in P.A.M Dirac, ‘General Theory of Relativity’, Princeton University Press, Princeton NJ, 1996', taking the Schwarzchild case and solving Einstein's field equations from both sides of the event horizon with a non-infinite answer.
Schwarzchild's infinity in his original derivation was described as being purely mathematical in nature by both Schwarzchild himself and Einstein, and Einstein devoted an entire paper, in 1939 (A. Einstein,
Annals of Mathematics
,
40
, 922, (1939)), to discussing the nature of the Schwarzchild singularity and whether or not it existed in reality. Einstein’s conclusion was that it did
not, and the Schwarzchild singularity was a mathematical notion alone; any evidence for
such a body would have to come from direct experimental and observational data.
Schwarzchild's original paper has been translated here into English and makes for an interesting read.
Of course more recent works, including those of Hawking, would categorically deny there is any validity to such claims. I for one am still on the fence.
In answer to your question, no it is not a common school of thought at all, but does that mean you should ignore it and not make up your own mind? I think you'd also need to clarify with your professor whether he doesnt believe in the singularity, or doesnt believe in bodies that can collapse down to such a density that their gravitational pull exceeds c
Carroll
Carroll, course notes (free, I think it may be a preprint of the book)
Schutz
Wald
MTW (Some call it the GR bible)
They're all great books, Schutz I think is the most novice friendly but I believe they all cover tensor calculus and differential geometry in some detail.
Start here.
Then go here.
When you're ready for the real thing, start reading this.
If you want to become an expert, go here.
Edit: Between steps 2 and 3, get a physics degree. You need to understand basically all of physics before you can understand anything properly in General Relativity. Sorry...
Edit 2: If you really want a full list of topics to understand before tackling general relativity, the bare minimum is special relativity (the easier bit) and tensor calculus on pseudo-Riemannian manifolds (extremely difficult). I'd strongly advise a deep understanding of differential equations in general, and continuum mechanics in particular. Some knowledge of statistical mechanics and the covariant formulation of electromagnetism would be pretty helpful too. It is also essential to realize that general relativity is still poorly understood by professionals, and almost certainly breaks down at large energy densities. I strongly advise just taking a look at the first two links I posted, since that will give you an excellent and non-dumbed-down flavour of general relativity.
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.
Upvotes for the Feynman. Parts of his lecture series on physics is quite good too. The whole thing is quite expensive, unfortunately.
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.
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.
Anti-disclaimer: I do have personal experience with all the below books.
I really enjoyed Lee for Riemannian geometry, which is highly related to the Lorentzian geometry of GR. I've also heard good things about Do Carmo.
It might be advantageous to look at differential topology before differential geometry (though for your goal, it is probably not necessary). I really really liked Guillemin and Pollack. Another book by Lee is also very good.
If you really want to dig into the fundamentals, it might be worthwhile to look at a topology textbook too. Munkres is the standard. I also enjoyed Gamelin and Greene, a Dover book (cheap!). I though that the introduction to the topology of R^n in the beginning of Bartle was good to have gone through first.
I'm concerned that I don't see linear algebra in your course list. There's a saying "Linear algebra is what separates Mathematicians from everyone else" or something like that. Differential geometry is, in large part, about tensor fields on manifolds, and these are studied by looking at them as elements of a vector space, so I'd say that linear algebra is something you should get comfortable with before proceeding. (It's also great to study it before taking quantum.) I can't really recommend a great book from personal experience here; I learned from poor ones :( .
Also, there are physics GR books that contain semi-rigorous introductions to differential geometry, even if these sections are skipped over in the actual class. Carroll is such a book. If you read the introductory chapter and appendices, you'll know a lot. On the differential topology side of things, there's Schutz, which is a great book for breadth but is pretty material dense. Schwarz and Schwarz is a really good higher level intro to special relativity that introduces the mathematical machinery of GR, but sticks to flat spaces.
Finally, once you have reached the mountain top, there's Hawking and Ellis, the ultimate pinnacle of gravity textbooks. This one doesn't really fall under the anti-disclaimer from above; it sits on my shelf to impress people.
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.
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 :)
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 should really really read this book:
Why Does E=MC^2?: (And Why Should We Care?)
http://www.amazon.com/Why-Does-mc2-Should-Care/dp/B004LQ0ICE/ref=sr_1_1?ie=UTF8&qid=1302835764&sr=8-1
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
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!
> yet to see a persuasive argument against number two
Look up Bell's Inequality.
Or this: https://smile.amazon.com/Six-Not-So-Easy-Pieces-Einstein%C2%92s-Relativity/dp/0465025269/ref=sr_1_3
Or this: https://smile.amazon.com/Quantum-Universe-Anything-That-Happen/dp/0306821443/ref=sr_1_4
Virtually no math in these that Oz's Scarecrow couldn't understand.
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.
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.
(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'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).
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.
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.
> 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.
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.
Ah yes, the extended essay, I remember an IB friend of mine telling me about his one time.
So, when it comes to realistic time travel you're limited to a few options, and with everything you read you have to keep in mind that there is scientific consensus on the issue, and the consensus is that time travel isn't possible. There aren't really multiple scientific theories on the issue, though you will be able to find science fiction accounts of the different 'models' of time travel.
If you want a serious essay about why that is you're going to need to learn a bit about relativity. There a book that I always liked by Geroch called General Relativity from A to B which is not a textbook, in that it doesn't really contain any math, but it's not a popular science book either. It might be worth a read to give you some insight into what exactly the question you're asking means, and how understanding a bit about relativity answers it.
The wikipedia page introducing special relativity is pretty good, and should give you enough information to understand this little argument which talks about the relationship between causality, time travel and going faster than the speed of light.
You'll find in your reading that gravity and geometry are linked. And Einstein wrote down some equations which, if you solve them, tell you the geometry you get for some mass and energy distributions. Some mass and energy distributions give you really weird geometries which someone might say admit time travel. These solutions are, in the scientific community, discarded as 'unphysical'. The most famous of them is the Godel Spacetime (fair warning, that's a really technical link). Another solution of Einstein's equation is a geometry known as the Alcubierre metric which pulls space towards it in front of it, and pushes it out from behind to effectively travel faster than light, which one could call time travel (possibly). But to do so you need a large amount of negative energy, which is not something we believe to exist. Though, there's a guy at Nasa who works on it.
I think Geroch's book could serve you well, or at least help you refine your essay question into something you can talk about reasonably precisely, the other links should give you a bit of idea about what's out there in terms of actual time travel, but the consensus is that it isn't possible. As far as theories go, there's one theory, which is General Relativity, and all time travel ideas have to somehow fit inside it.
If you want to talk more about any of it, or want a hand with math/concepts behind relativity just ask. There are relativity questions here all the time, so I'm sure people would be interested in talking about it.
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.
You might want to look at this book. It's high level enough and Feynman does a good job explaining it.
I wouldn't call it subjective. But time is indeed always relative. This is what Einstein's theory was all about-- Newtonian physics always operated on the notion of absolute time, which was the same everywhere, always. That is now an old fashioned view that no one subscribes to anymore.
I think you would get a lot out of this book. It explains all of these concepts from the ground up in an amazingly intuitive way. It contains almost no equations whatsoever, and explains everything via diagrams. It's excellent, and will flesh out the picture of the relativistic nature of time, starting from the "common sense" Newtonian take, then building special, then general, relativity.
A.P. French
I recently bought Six Easy Pieces and Six No-So-Easy Pieces and both are fantastic.
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.
Mermin helped me a lot.
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!
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.
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
Spacetime and Geometry by Sean Carroll
Oh, PDF. Hmm...
J. R. Gott
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.
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
This was the most riveting and inspiring book that I have read on physics in quite awhile. The author writes it in a way that nearly anyone could understand it. In fact often times he says "skip to this page if you already understand the basics of __."
http://www.amazon.com/Why-Does-mc2-Should-Care/dp/B004LQ0ICE/ref=sr_1_1?ie=UTF8&qid=1299102838&sr=8-1
In the context of nonequilibrium thermodynamics, pattern formation in complex systems and order at the edge of chaos, several introductory/intermediate books come to mind, in particular from the Brussels' school. For a start one could go with
Prigogine - The End of Certainty
Nicolis, Prigogine - Exploring Complexity
Kauffman - The Origins of Order
For something directly from one of the giant of chaos theory, maybe one could go with
Lorenz - The Essence of Chaos
The one I read when I was a kid is The Universe and Dr. Einstein. It seemed pretty good to me.
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 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:
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!
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).
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.
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.
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!
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:
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!
> The only time travel that is possible is perception based
No, it's really something more fundamental than just perception. For example, in the classic twin-paradox setup, one twin stays on earth and observes his brother moving quickly. So, he sees his brother aging slowly. If his brother then slows down and comes back to Earth, he is actually younger than his twin. (Note that this situation is asymmetric due to the acceleration of the traveling twin - that's a whole other story if you want to get into it).
So I'd argue that it's not just a perceptual thing, time travel actually occurred. The now-younger twin has "traveled to the future" since he has aged slower than his Earthly twin. If you're interested in thinking about relativity, as it seems that you are, I highly highly recommend this book: Time Travel in Einstein's Universe. It discusses how relatively allows time travel to both the future and the past, and is written for people without a science background. (The travel to the past part is somewhat controversial - Gott (the author of that book) and Hawking argue about this)
This might help.
I found it quite interesting.
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.
Epstein also has a great book called Relativity Visualized that goes great with Thinking Physics.
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.
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.
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.
Since you've apparently read Greene, you should move to Prigogine. We've got whole new ways to cook with eggs and entropy now.
The link is his most accessible book, written 20 or so years after his Nobel in Chemistry. But if you've worked with quantum mechanics and are already familiar with quantum operators and associated notation/conventions, From Being to Becoming is a really accessible formal intro, written for an academic audience but necessarily academics in his field.
I think you are getting it.
If you want to understand all the cool, weird stuff including about the order of events, time changing, space shrinking and momentum changing read Spacetime Physics. It is easy to understand and comprehensive.
As for modern physics texts any of these should be fine but I have only glanced at them: Thornton and Rex, Krane, Bernstein, Fishbane, and Gasiorowicz
I read through Taylor and Wheeler's Spacetime Physics and it is really good if you want a lot of conceptual discussion of special relativity, not as much mathematics involved but honestly the math doesn't get too gnarly in SR anyways so conceptual might be the better approach to the topic. Unfortunately it only goes over SR, and not any of the other modern topics.
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.
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 universe evolves and it does it through a process of selection called self-organization.
Self-organisation is not "a process of selection"! Further to which, it is no indicator for determinism. One of the most important figures in the field was Prigogine, a guy who explicitly rejected determinism and held the libertarian position on free will. Here's a pop-science book for you.
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.
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.
You might want to try Taylor and Wheeler it is an introduction to the basics of GR whose math prerequisite is calculus.
If you're in the mood for a book, Why Does E = MC Squared is a really good and accessible explanation.
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
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
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.
Read the original papers. Einstein went way beyond Minkowski, Lorentz and Poincare's papers (some of which were published after Einstein). The other pioneers never made the paradigm shift that time is relative and there is no aether and their theories were fundamentally incomplete. See: http://en.wikipedia.org/wiki/Lorentz_ether_theory
Einstein also beat Hilbert to developing GR -- Einstein's importance in developing the theory for SR, equivalence of mass and energy, GR, photo-electric effect, recognition of spooky-action at a distance in ordinary quantum mechanics, and brownian motion cannot be minimized.
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.
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.
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?
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
This book really helped me in my modern physics course for the relativity section
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 🙂
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.
>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".
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.
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.
We use Special Relativity by French.
> 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
> Special relativity in a single reddit comment? That doesn't work.
Sure it does:
https://www.amazon.com/Special-Relativity-M-I-T-Introductory-Physics/dp/0393097935
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.
Find a book called The Universe and Dr. Einstein.
Time Travel in Einstein's Universe.
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.
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.
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.
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.
>QM
Definitely pick up Feynman's QM and Path Integrals, a step towards particle physics after Griffith's.
>QED (nontechnical)
QED: The Strange Theory of Light and Matter By Mr. Feynman. Written for the layperson, so if your just starting out it would be VERY advanced yet VERY easy to understand and really gives you a feel of modern physics to entice you in the classical studies.
>GR
I picked up Dirac's book last week and I have to say it is most succinct. I've tried one other GR book and various online sources and they all were terrible and I made zero progress. Dirac is crazy good.
And also: THE LAGRANGIAN IS IMPORTANT! That is all.
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?
Why Does E=mc2 by Brian Cox, Jeff Forshaw
The Goldilocks Enigma by Paul Davies
A mostly-serious answer: Paul Dirac's book, which provides a relatively complete treatment, in 84 pages.
Six Easy Pieces: Essentials Of Physics Explained By Its Most Brilliant Teacher
by Richard Feynman
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)
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.
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
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.