[HN Gopher] Show HN: Relativity: A Modern Primer
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Show HN: Relativity: A Modern Primer
Author : fferen
Score : 174 points
Date : 2021-09-05 02:29 UTC (20 hours ago)
(HTM) web link (ramp-book.com)
(TXT) w3m dump (ramp-book.com)
| Deutscher wrote:
| Would you mind making this available as an EPUB?
| musgravepeter wrote:
| I had a quick look and this seems like a solid, concise intro to
| GR.
|
| The article https://people.carleton.edu/~nchriste/PTO000041.pdf
| gives an overview of the ways and books to learn GR. It does not
| cover some more recent intro books.
|
| If you like "physics first" then I am a big fan of Hartle's book.
| drewolbrich wrote:
| @fferen Thank you for sharing your work. This is an excellent
| resource.
|
| If you don't mind, I have a question.
|
| If I drive in a straight line on the Earth's surface without
| stopping and I ignore mountains and oceans and other obstacles,
| then after 16 days, I will arrive at my starting point.
|
| Why is this?
|
| It's because the Earth is a sphere.
|
| This is a nice satisfying answer, whereas x^2+y^2+z^2=r^2, while
| perfectly accurate, is arguably less satisfying.
|
| Given this context, my question is, for special relativity, why
| do time dilation and length contraction happen?
|
| Ideally, I'm looking for an answer that has the same satisfying
| intuitive flavor as "Because the Earth is a sphere", or at least
| is suggestive of that kind of answer.
| cygx wrote:
| _Given this context, my question is, for special relativity,
| why do time dilation and length contraction happen?_
|
| Place two rulers right next to each other, and their length
| scales will agree. Now, place them at an angle, and have one
| ruler measure the other by orthogonal projection. Each of the
| observers represented by the rulers will conclude that the
| other one has 'contracted' by a factor given by the cosine of
| the angle.
|
| Now, add a third ruler to complete the triangle. To go from one
| vertex to the opposite one, you can either follow along a
| single ruler, or via a bent path along two rulers. The symmetry
| has been broken, and the bent path will be objectively longer -
| that's the twin 'paradox'.
|
| Things are more complicated than that because Minkowski space
| is non-Euclidean (for example, less time will pass for the
| travelling twin, ie the bent path will be the 'shorter' one),
| but if you want a simple analogy, I think that's a pretty
| decent one...
| fferen wrote:
| Thanks! I don't believe these two concepts are related. You get
| back to the same point because the earth is _globally_ a
| sphere. However, time dilation and length contraction are
| _local_ concepts: they happen even for very small motions.
|
| I guess a global object in spacetime analogous to a sphere in
| space is the hyperboloid t^2 - x^2 = r^2. Moving on this
| hyperboloid corresponds to changing boost velocity. But unlike
| a sphere, it is not closed, so moving in one direction does not
| get you back to the same point.
|
| May add to this answer later.
| drewolbrich wrote:
| Apologies, I didn't mean to suggest that the two concepts are
| related.
|
| For SR, I'm looking for an answer to "why?" that only has
| same satisfying flavor as the sphere question. I want the
| same "aha!" feeling.
|
| For example, if I stand up from the sofa and walk across the
| room and come back and sit down next to my friend, I want a
| deep intuitive sense that of course it must be the case that
| less time has passed for me than the amount of time that my
| friend has experienced. Why does this happen?
|
| An answer like "t'=t/sqrt(1-v^2/c^2) describes what happens",
| while correct, is not satisfying.
|
| Similarly, if I wave my hand in front of my face, I want it
| to seem obvious to me that less time must have passed for my
| hand than for the rest of my body.
|
| Given your experience writing the book, you must have
| developed an intuitive sense for the behavior of the effects
| of relativity and why they happen, so I am wondering how you
| would translate that into words for a general audience.
|
| Imagine the context where a random person with a minimal math
| background at a party was to ask you why less time passes in
| the sofa scenario, using an actual sofa to demonstrate it.
|
| They stand up and walk away from you and return and sit back
| down next to you and they want you to explain to them why
| less time has passed for them. They want you to explain why
| the room around them got shorter in the direction that they
| were walking.
|
| These are effects that, while undetectably small, really
| happened.
|
| They want to know why.
|
| How would you answer their question?
| mhh__ wrote:
| I'm not sure a satisfactory answer necessarily exists here. The
| earth _is_ a sphere, but you are asking a question about a
| mechanical action whereas time dilation and friends are
| fundamental statements about the nature of measurement itself.
| Koshkin wrote:
| That's exactly what often troubles students of special
| relativity - why should a physical quantity be defined by the
| way you are trying to measure it. (The mass is the mass, for
| example, no matter what device you construct to measure it.
| In special relativity, on the other hand, the very notion of
| time interval seems to be tied to observing how light travels
| between mirrors.)
| richardw wrote:
| Not the expert you're looking for but here's my intuitive
| reasoning: Because light will always be moving at the speed of
| light for you. You move at 0C. As you speed up, time slows down
| to preserve that.
| random314 wrote:
| While this might not be the answer you are looking for, but I
| can present an argument about why time dilation must be true to
| explain electromagnetism. The experiment produces apparently
| paradoxical equations that simply happen to work out fine.
| Trying to explain this experiment forces us to accept special
| relativity.
|
| https://en.m.wikipedia.org/wiki/Moving_magnet_and_conductor_...
| motohagiography wrote:
| Every question I have is predicted on ignorance of the complete
| picture, but I have dozens of questions. This is the perfect
| format for going through and re-formulating and re-writing it in
| ones own notes to hack through it.
| monday_ wrote:
| This is great and way better then the more long-winded textbook
| explanations. Math is around for a reason and it's good to see it
| at work by compressing a lot of material into still readable
| format.
|
| Sure hope there's a similar primer on QFT.
| Koshkin wrote:
| I can recommend https://nononsensebooks.com/qft/ (as well as
| the rest of this excellent series of books).
| monday_ wrote:
| Thanks!
| wanderingmind wrote:
| This is fantastic. I always wanted to learn relativity. But
| almost all the books I borrowed were so deep targeted towards
| students who will think about that day in and out.
|
| I think a lot of avenues of core sciences need books like these
| that are deeper than popular science but are accessible to
| someone who is not doing it for a living.
| oefrha wrote:
| (Physicist here.) Looked at TOC, then skimmed some chapters.
| The special relativity part of the book is about as deep and
| denser than most undergraduate introductions, with less
| motivations and intuitive discussions. The general relativity
| part is dense by necessity (after all 95% of it is differential
| geometry, no way around it), and this book apart from being way
| more condensed isn't in any way diluted.
|
| It's a compact book of essentials for mathematically minded
| people*. It's not a shallower-than-textbooks accessible
| introduction one step up from pop science.
|
| * If you only ever took some linear algebra and calculus for
| engineering students, this probably doesn't describe you.
| fferen wrote:
| This is fair enough. Hopefully some will still find it
| useful. I will note that I took a special relativity course
| in university that did things the "slow and intuitive" way,
| and many years later realized I still had some fundamental
| misconceptions about it. Eventually learned it the right way
| mostly by osmosis. More examples and motivation doesn't
| necessarily lead to correct understanding.
| oefrha wrote:
| > Hopefully some will still find it useful.
|
| Yes, I definitely think it will be useful for
| mathematically minded people who don't find the "slow and
| intuitive" approach helpful. However, I suspect the fact
| that it is posted to HN where most of the audience would be
| people who only took some math for engineering students and
| that "popular physics book" is even mentioned on the
| homepage (it clearly says "unlike", but for most textbooks
| this comparison isn't even needed) might give rise to the
| misconception that it's between pop science and other
| textbooks in terms of depth, as the root of this thread
| seems to demonstrate.
| ericbarrett wrote:
| I recommend Sean Carroll's "Biggest Ideas in the Universe"
| series on YouTube for modern physics. He's a professor at
| CalTech. Each is 60-90 minutes with an accompanying 60-90
| minute Q&A--don't miss the latter, they're just as interesting.
| You won't get a PhD after watching them but he gets a lot
| mathier than e.g. a Kurzgesagt video while only assuming a high
| school education (basic calculus, trig, vectors).
| chisquared wrote:
| I quite like this lecture series, and I normally hate learning
| from YouTube videos:
| https://www.youtube.com/playlist?list=PLFeEvEPtX_0S6vxxiiNPr...
| Koshkin wrote:
| Dr. Schuller's lectures is one of the few recordings of this
| kind on YouTube that I can listen to without getting
| irritated by one thing or another. (Another one being the
| widely known physics lectures by L. Susskind.)
| MathMonkeyMan wrote:
| Just read a textbook. It's not easy, but it's what you want:
|
| - rigorous treatment of the material
|
| - no bullshit fluff
|
| - exercises that you can do to think about the material and
| test your comprehension (often 50-100% of the answers are
| available online)
|
| - systematic treatment used to train real physicists
|
| In my experience, it's all about the homework. The rest just
| supports that.
| powera wrote:
| I'm not sure who this is supposed to be useful to; I'm not sure
| how anybody can understand it unless they have completed an
| undergraduate degree in math AND already have a solid conceptual
| understanding of relativity.
|
| It is _extremely_ dense.
| jvvw wrote:
| For those of us with that background, it looks like it might be
| really useful though. I've only had a brief look so far, but as
| somebody who took all the pure courses in my maths degree, I've
| been looking for something a bit like this!
| dieselerator wrote:
| That seems a reasonable complaint.
|
| For relativity with more explanation and not much math I
| suggest
|
| Relativity (The Special and the General Theory) by Albert
| Einstein, 1916. Translated to English: ISBN 0-517-029618
|
| I think the book is still in print, and new and used copies are
| cheap if you shop around.
|
| It is good reading if you want the details explained step by
| step.
| mhh__ wrote:
| That describes the usual general relativity student though.
| BeetleB wrote:
| > I'm not sure how anybody can understand it unless they have
| completed an undergraduate degree in math AND already have a
| solid conceptual understanding of relativity.
|
| The prerequisites are clearly listed:
|
| > Prerequisites: vector calculus and classical mechanics
|
| Do you not find this accurate?
|
| (Note that classical mechanics means the typical physics
| undergrad classical mechanics - where you know diff eq and
| things like Lagrangians and calculus of variations).
| pvg wrote:
| The same can be said for, say, Lifshitz & Landau's textbooks. A
| little bit closer to earth, Axler's _Linear Algebra Done Right_
| is well-liked and popular but of relatively little use to
| people trying to do linear algebra right for the fist time.
| goldenkey wrote:
| I disagree. Most of relativity comes from the fact that all
| objects have an average velocity of their fundamental
| constituents. The highest average velocity is C, when the
| object is a beam of electromagnetic energy. This is why it
| takes infinite energy to accelerate an object to the speed of
| light, you can add more photons to it, but the average will
| always be less than C, you just get it slightly closer.
|
| The reason for time dilation and the other facets of relativity
| pretty much come down to the fact that objects either move or
| change, but cannot do both simultaneously. One can think of
| time passing inside a spacecraft or object as internal
| movement, as oppose to the external movement of the spacecraft
| throughout the cosmos. Each bit of energy provides h (Planck's
| constant) action, a measure of change of state. The more the
| object allocates toward external movement in space, the less it
| can allocate for internal movement / internal changes, which is
| what observer time really is. Even though I say external vs
| internal, I am not violating relativity. The reference frames
| are relative, we do not need an absolute reference frame.
|
| Doubly special relativity deduces most of these elegant
| derivations by assuming there is a smallest quanta of energy
| possible, but nonetheless, these concepts can be derived just
| by understanding the role of mass as loops of energy, energy as
| an allowance for change of state, and time as the usage of
| energy for internal change of state, and movement as the usage
| of energy for external change of state.
|
| Relativity is just the consequence of energy's connection to
| information and movement.
|
| https://en.wikipedia.org/wiki/Doubly_special_relativity
| Koshkin wrote:
| > _average velocity of their fundamental constituents_
|
| An interesting (if unusual) viewpoint; I wonder if this could
| lead to (a more realistic) quantum gravity.
|
| > _objects either move or change, but cannot do both
| simultaneously_
|
| This does make time slowing down inside a moving object kind
| of obvious. (I wonder if this description based on
| action/energy quantization turns out to be equivalent, at a
| certain level, to the essentially geometric picture of the
| classical relativity.)
| goldenkey wrote:
| It is indeed a very geometrical picture since position is
| just as much of a state as spin is. Position just has a few
| huge dimensions as its degrees of freedom. We don't know
| _yet_ whether position is continuously valued or discrete.
|
| Gravity being quantum would most likely indicate that
| position is also discrete.
|
| Since all energy, being allocated for external movement or
| just internal time, produces the same amount of gravity, it
| appears that the act of any state change induces gravity.
| Einstein never really gave a physically understandable
| reason for why all change causes gravitation, but it's
| likely similar to a ship in water. If the ship is rocking
| really fast, the waves that emanate from it can pull
| objects towards it. The rocking is just state change and
| even for a rest mass, we know that it's a loop of energy,
| there really is no static storage of mass.. it's a process
| of energy containment and cyclic change.
| AnimalMuppet wrote:
| Um, no. That is not how any of that works.
|
| For instance, your second paragraph: No, objects move or
| change at the same time, just at different rates. And an
| object can be moving in one frame of reference, and _only_
| "changing" (time passing) in another.
| goldenkey wrote:
| I made my point clear, the amount of change of state that
| an object can produce over time, is given by its energy.
| This is because action equals joule-seconds, so energy
| equals actions per second. Just because you can change your
| frame to see change differently (ie. stationary) doesn't
| invalidate the point. This principle applies just as well
| even as the frame is changed.
|
| https://en.wikipedia.org/wiki/Action_(physics)
| fferen wrote:
| Any particular suggestions? Although it is compact, I have
| tried to carefully choose the wording and arrange the sections
| so each concept builds on the last. Also, I intentionally avoid
| unnecessary mathematical abstraction; for example, the abstract
| definition of manifolds using coordinate charts, and tangent
| vectors as differential operators. This really tripped me up
| when trying to learn GR from standard textbooks.
| [deleted]
| powera wrote:
| Maybe call it "The Mathematics of Relativity"?
|
| It works well as an outline from my point of view, but I
| think you have to assume the reader already understands the
| Lagrangian in classical physics (which is a stretch for even
| the comparatively well-educated Hacker News audience). Also,
| somewhere around 3.5 it gets too dense with material I don't
| already know. (Christoffel symbols? Riemann curvature
| tensor?)
|
| And then in the General Relativity section, there's simply
| too much material covered for any of it to be explained in
| depth beyond the necessary equations. I would drop the fluids
| (at a minimum) to give more space for other topics.
| mhh__ wrote:
| Needham's latest book might be a good source of intuition to
| "borrow" from for geometry.
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