21 ms·
A delightful quirk of relativity theory
- mikewarot 5y agoThe way I think of it is we're always moving at the speed of light, through the time axis. Any normal 3d motion is orthogonal to the time dimension, so the time component shrinks ever so slightly as you move faster. Photons move only in the 3 dimensions, thus never experience time.
- lordnacho 5y agoSummary: For small angles, approximation makes it look like gradients (y/x) add simply (a+b). Similarly low velocity in relativity world makes it look like velocities just add as well. With some insight we discover how it really works, including how the approximation makes it look correct for small values.
- ramraj07 5y agoBut who was actually genuine surprised or flabbergasted that there was an extra factor that in macro real life becomes zero but is there in extreme speeds? The un-intuitiveness is typically more to do with understanding what that factor means and where it came from.
- snet0 5y agoThe insight is, in my opinion, more related to the attaching of the idea of "rotation" to space-time, and using that to explain why we can't just add velocities at high "rotations".
- glandium 5y agoRelated minute physics videos: https://youtu.be/Rh0pYtQG5wI https://youtu.be/Rh0pYtQG5wI https://youtu.be/R5oCXHWEL9A https://youtu.be/R5oCXHWEL9A The whole intro to relativity series is worth a watch.
- enriquto 5y agoI love the name of the scientist Al Unapietra. The thing is very well explained, but it's very sad to see it as a twitter thread, which is a mostly unreadable format.
- acadapter 5y agoTwitter threads are in general a very sad successor of the blogosphere.
- alfiedotwtf 5y agoSure, but you can't knock it for the speed at which cool info like this thread spread
- soneca 5y agoTwitter threads don’t bother me. The brain quickly adapts to skipping the irrelevant parts (username, like buttons, etc) and to expecting the cadency of tweets. I believe it is harder to write (due to the character limit of each text block), but, far from “unreadable”, I can read it fairly easily.
- enriquto 5y agoOh, I don't bother by the stupidly repeated usernames and dates. I just want to read the damn thing. But it is literally unreadable to me. I couldn't finish reading the thread and had to find an alternative way out of twitter. Fist trial, using my android phone with fennec fox. There is a modal that hides the content asking me to "log in"; if I close the modal I go back to the twitter homepage. Thus unreadable because I don't have a twitter account. Sometimes I have managed to read a few tweets by a "smart" combination of closing the successive modals and reloading the page, but not this time. Second trial, using my laptop with firefox browser and heavy adblocking. I can read only the first three tweets, the rest do not load due to some third-party javascript. No big deal. Third trial, now I open a "clean" firefox browser session with just ublock origin, and I manage to read about 30 tweets, until it starts talking about hyperbolic rotations. The thread obviously continues, but the sole link below it "show replies" does not work. When I click on it it says "Whoops! Something went wrong. Please try again!". Typically I wouldn't bother and stop reading. Fuck twitter. But today I really wanted to read this thread because I teach these things. Thus I learned to use nitter, which gives an interface of twitter that, even if it's equally ugly, it sort of works (in that you can actually manage to read the text). In retrospect, this is an extremely sad state of affairs. We have an excellent article which is made of a short text, a few simple formulas, and a few simple images. This could be a static html page of a handful of Kb with img tags. But it is a slow and humongous javascript monstrosity that does not even work, and may disappear at any time if twitter "bans" this user for reasons unrelated to this text.
- silvester23 5y agoI might have missed it, but is there (or do we know of) a different model for which the velocities actually add? Essentially, how do we go from slopes to angles here?
- lanternfish 5y agoIn classical Newtonian mechanics, velocities add normally a+b = c (an approximation which works near perfect for almost all velocities humans interact with). I think you might be asking a different question, though, but I'm not sure what.
- simiones 5y agoYes, he introduced it near the bottom - instead of using speeds (which are like slopes), you use "rapidities" which are the angles of the hyperbolic rotations.
- Jenny8090 5y ago[dead]
- Thomashuet 5y agoMore readable formatting: https://threadreaderapp.com/thread/1482811504424542211.html https://threadreaderapp.com/thread/1482811504424542211.html
- molbioguy 5y agoThat is so much better! Thank you.
- plucas 5y agoNote that Thread Reader loses the images attached to some of the tweets (at least for me). Edit: strike that, it was Firefox's social tracker protection blocking them. Just need to click the shield icon left of the address bar and temporarily disable it.
- bradstewart 5y agoAm I crazy, in that I actually like Twitter threads for this sort of thing--at least in the hands of a capable author? When threaded correctly (as this one is), its easy to follow. And the requirement to condense and split thoughts into tweet-sized chunks creates natural breaks to pause and consider the content before continuing. I find the cadence of "each thought is a tweet" provides a nice rhythm. Sure, you can do this with paragraphs in a blog post. But Twitter works equally well in my mind!
- actually_a_dog 5y agoYou may actually have something there. The average word length in English is approximately 5 letters, which gives you an average of about 56 words per tweet. That's roughly 5-6 solid sentences, which is... one good paragraph. It probably didn't work as well before they raised the character limit from 140 to 280.
- snet0 5y agoI think this was one of the few good Twitter threads. Each Tweet was a kind of step from the previous, towards the next. The only thing I think would be improved by having this in blogpost form is more interact-able visuals, equations and similar.
- MattPalmer1086 5y agoLovely explanation. Builds up from simple angles and suddenly makes what seemed weird in relativity actually kind of obvious. I particularly like how the model you choose to describe things can make the same phenomenon easy or hard to understand.
- alfiedotwtf 5y agoMy favourite example of this is planet epicycles vs ellipses around the Sun :)
- jabl 5y agoHeh, small world. I met Markus Deserno when I was visiting MPI-P for a few weeks some, uh oh, 15(?) years ago, working on coarse grained molecular dynamics for polymer physics. Nice chap.
- thesz 5y agoI cannot help but add a reference to a conformal geometric algebra here: https://en.wikipedia.org/wiki/Conformal_geometric_algebra https://en.wikipedia.org/wiki/Conformal_geometric_algebra Why? Because it describes movement as rotation from the infinitely far away point (a special basis vector there). And "coordinates" there are somewhat self-normalizing, because there is a special basis vector that keeps coordinates' squares. And, of course, it is investigated as a tool to think about relativistic coordinates, linking my comment to a tweet part that says "wrong tools can obscure things".
- formerly_proven 5y ago> Because it describes movement as rotation from the infinitely far away point Doesn't this also work in normal geometry as the length of a translation goes to zero and the distance to the rotation's origin goes to infinity... because a big circle looks like a straight line up close?
- thesz 5y agoExactly. CGA has special point e_{inf} which is infinitely far away from any other regular point (with regular euclidian coordinates) and linear movements are rotations around that point.
- doctoboggan 5y agoI like this, but it doesn't completely remove the "unintuitivenes" of relativity. For example, why do we measure in fractions of light speed? What happens when we are already rotated all the way to light speed and then fire another bullet? I guess there are other ways to reason about this, but it still doesn't feel intuitive to me.
- OscarCunningham 5y agoLightspeed has infinite rapidity, so when you add on the rapidity of a bullet you just get lightspeed again
- gowld 5y agohttps://en.wikipedia.org/wiki/Rapidity https://en.wikipedia.org/wiki/Rapidity That's amazing, and it was well explained in 1908! Yet students today are learning a horrific bastardized version of it. Physics is absolutely terrible when courses and books try to to remove the "complicated" math, and in its place they put something more complicated and ambiguous. Teach the math! It's like Greenspun's Tenth Rule, but for math: "Any sufficiently complicated scientific theory contains an ad hoc, informally-specified, bug-ridden, slow implementation of half of Complex Analysis."
- codeflo 5y agoIt’s important that the “angle” isn’t directly the fraction of c, but tanh^-1(v/c). This number is also called “rapidity”, and goes to infinity as v -> c. Yes, hyperbolic angles aren’t limited to [0, 2 pi). You can’t rotate all the way to lightspeed, that would be rotation by an infinite angle. For any finite angle (i.e. speed below c), you can always add the angle of the bullet to get a new (finite) angle.
- d-d 5y ago
- fknorangesite 5y agoI look forward to your Nobel prize.
- irthomasthomas 5y agoThis would be more fun in a blog post. Twitter is a fucking horrible format for a complex analysis of special relativity. That aside, my favourite quirk from relativity is this: "The more you move in space, the less you move in time." Like relativity in general, it sounds simple enough, but it's consequences are profoundly shocking. (That is, if you take the time to understand it, and don't leap to the conclusion that you know relativity better than Einstein or Penrose ;) Take the case of two people on Earth, one stationary and one travelling past in a car. They each have a different reference frame, and a different set events which make up their present. Now imagine that there is an alien government in Andromeda debating a possible invasion of Earth. In the reference frame of the person on Earth who is moving, the debate is still going on. But, in the reference frame of the stationary person, it is a day or so later in Andromeda, and the invasion fleet is already on it's way! In nature there is no absolute reference frame we can call base reality, and both observers reference frames are equally valid. Then the outcome of the invasion debate is a foregone conclusion. How can there be any room for free will in the deliberations of the alien government? This is the crux of the Andromeda Paradox and the Reitdijk-Putnam-Penrose argument. BTW: "Notice that neither observer can actually "see" what is happening in Andromeda, because light from Andromeda (and the hypothetical alien fleet) will take 2.5 million years to reach Earth. The argument is not about what can be "seen"; it is purely about what events different observers consider to occur in the present moment." https://en.wikipedia.org/wiki/Rietdijk%E2%80%93Putnam_argument https://en.wikipedia.org/wiki/Rietdijk%E2%80%93Putnam_argume... More info https://en.m.wikipedia.org/wiki/Relativity_of_simultaneity https://en.m.wikipedia.org/wiki/Relativity_of_simultaneity Edit: If you know of any serious alternatives to the 4D spacetime/ block universe theory then I would love to read it. Rescuing free-will from the jaws of spacetime would be cool!
- Ma8ee 5y agoIsn't the whole point that talking about "the present moment" about something very far away isn't particularly meaningful when simultaneity for spatially separated events depends on the observer?
- awb 5y agoCorrect, check the criticisms on the Wikipedia page: https://en.m.wikipedia.org/wiki/Rietdijk%E2%80%93Putnam_argument#Criticisms https://en.m.wikipedia.org/wiki/Rietdijk%E2%80%93Putnam_argu...
- stared 5y agoIn the topic of special relativity, I wholeheartedly recommend recently published "Unusually Special Relativity| by Andrzej Dragan (https://www.amazon.com/Unusually-Special-Relativity-Andrzej-Dragan/dp/1800610807 https://www.amazon.com/Unusually-Special-Relativity-Andrzej-...). It starts from basic high-school mathematics but covers many paradoxes and puzzles. Some might challenge ordinary students, who know the formula but didn't stretch their minds on "what if" questions. It includes cases where velocity is higher than the speed of light - as there are a few caveats on "nothing can travel faster than light". Also, this "velocity addition for v<<c" is covered in the first chapter. I read its draft almost 20 years ago (back then, it was a collection of notes in Polish) and didn't find anything remotely close to it in English. Later, I had the pleasure of attending his course. Also, Andrzej Dragan is a notorious individual, primarily known in photography (https://andrzejdragan.com/ https://andrzejdragan.com/). To the point that there are posts on "how to Draganize a picture".
- messe 5y agoAn interesting quirk of this, is that the description of the path of a particle under constant proper acceleration in special relativity is mathematically very close to that of a simple harmonic oscillator. Now, just as you can use rotation in the complex plane (i^2 = -1) to describe a simple harmonic oscillator in 2D space, x + iy = e^(it) It's possible to use a rotation in the split-complex plane[1] (j^2 = 1) to describe the motion of a particle undergoing constant proper acceleration, x + jt = e^(ajτ)/a - 1 [2] This is because multiplying by e^(jτ) preserves the split-complex modulus (|x+jt|^2 = (x + jt)(x - jt) = x^2 - t^2), which is equivalent to the Minkowski norm. Expanding the above gets you, x = cosh(aτ)/a - 1 t = sinh(aτ)/a which are the more traditional expressions you would typically see. [1]: https://en.wikipedia.org/wiki/Split-complex_number https://en.wikipedia.org/wiki/Split-complex_number [2]: There's a line of reasoning that allows you to write this down almost immediately, or in maths-speak makes it trivial, but I can't remember it at the moment. I spent a good deal of time thinking about this for a university assignment years ago in order to avoid spending 2 minutes doing an integral.
- captainmuon 5y agoThe description of relativistic movement by hyperbolic rotations is really neat. One way I like to think of it is that moving with respect to some other observer puts you into a different "world", where the x and t axes are rotated towards each other. You can see from the diagrams that for example different events happen in different orders in both "worlds". And this is not just due to signal propagation, but there really is no "true" ordering if the events are sufficiently separated. Bit there is one thing I never understood, even though I have a PhD in physics. Why does relative movement put you into a different "world"? Or more precise, why does relative movement correspond to a lorentz boost? That is not a piori neccessary. A stupid example is a laser pointed to the moon. If you flick it quickly, the spot can move faster than light over the ground. But you can also imagine mass moving independent of boost. You have a rock at x=0, t=0. At t=1, cut it and paste it at x=1. At t=2, cut it and paste it at x=2. Now make the time steps infintely small. It is moving (in the sense of dx/dy>0) but not moving (in the sense of v or ß = 0). My intuition is, if you look at electromagnetism, it takes some time for a changing electric field to create a magnetic field, and for the magnetic field to create an electric field. This is what Einstein meant when he said, time exists so that not everything happens at once. If you think of a relatively moving object - and I'm thinking of it completely in terms of EM for the sake of simplicity - what happens is that the fields are propagating. One field creates the next field not at the same space but slightly in front. So the whole thing is rotated towards the x axis. The "time" vector does not point completely in the time direction, but in the space direction. This gives you time dilation as well as the subjective experience of an intertial frame (because you are just moving forwards in time, but not in space from your POV). I think this microscopic perspective shows why motion must == boost. But does anybody here know if there is a canonical answer to this question? Edit: I just realize this is basically electromagnetism of moving bodies which Einstein already solved in 1905 :-) but I still find it hard to wrap my head around
- alde 5y agoIt is interesting that "real" observations of relativistic objects are quite different from what you expect them to be. For example, a cube passing by at relativistic speed would appear as if it is rotating towards you. This allows you to see some of its sides which you normally wouldn't [1]. [1] https://en.wikipedia.org/wiki/Terrell_rotation https://en.wikipedia.org/wiki/Terrell_rotation
- perryizgr8 5y agoThis is just the most basic consequence of relativity. It's not a "delightful quirk". It's literally the first thing you learn when you study the theory.
- topaz0 5y agoMarkus Deserno is a fantastic scientist in my field, and always gives the best talk at the conference.
- pmontra 5y agoUnrolled for sanity of readers https://threadreaderapp.com/thread/1482811504424542211.html https://threadreaderapp.com/thread/1482811504424542211.html I don't know if I admire more the mastery of science of the author or the willpower necessary to write those posts on such a wrong medium for them. Worse than one twit per paragraph, only MMSes.
- ngcc_hk 5y agoQuite a good description of “𝙇𝙤𝙧𝙚𝙣𝙩𝙯 𝙩𝙧𝙖𝙣𝙨𝙛𝙤𝙧𝙢𝙖𝙩𝙞𝙤𝙣𝙨”. Still hard to understand intuitive, but sort of understand “logically”. Btw the blog site is so much better.
- walnutclosefarm 5y agoNot a fan of doing this via twitter, but otherwise a beautiful exposition. Deserno is a gifted teacher.
- krupan 5y agoSome people hate tweet threads like this, but I feel like it really forces concise communication and arranging thoughts into small but complete chunks. I’ve never put my thoughts into this format, but I would guess it’s actually pretty difficult and requires some careful planning to do it well, especially for a challenging topic like this. Thanks for sharing this to hacker news, sohkamyung!
- gowld 5y agoIt's like Power Point presentation. Forcing everyone to read at the same pace, waiting for the point to show up, instead of skimming to the part they need to read.
- everyone 5y ago
- cletus 5y agoThis is too longwinded (and a Twitter thread ugh). I'll repeat an analogy I read somewhere else. Everything in the universe moves at constant speed through (four-dimensional) spacetime. To simplify the analogy we'll just consider two dimensions: space (x-axis) and time (y-axis) with your spacetime vector being of constant length. At rest your spacetime vector is (0,1). You speed up to 10% of light speed and your spacetime vector is approximately (0.1, 9.99) so you're moving slightly slower through time. What I like about this analogy is it constrains your space vector to the speed of light. Warp Bubble Andys like to pump negative values for energy and mass into equations to rationalize something they want to be true: that faster-than-light travel is possible. To me, this is just a fundamental lack of understanding about the domain of a function. Velocity is no different. I firmly believe it's bounded by [0,c). Values outside of that range just don't make sense are as such undefined. Garbage in, garbage out.
- renewiltord 5y agoHaha, 'una pietra' is 'ein stein'. Very amusing. Love the format too. I felt things sort of click in my head. The angle in this world being the important thing is dope. Dude, this hecka cool!
- SavantIdiot 5y agoNow I don't know what "rotation" means. After reading that thread, the phrase "rotating through spacetime" is still just gibberish. It sounds like he's trying to solve a physics problem backwards by making the units match: because the Lorentz transformation is a hyperbolic rotation matrix with a trig property applied, somehow it is a rotation? That just perverts the word "rotation".