8 ms·

An explorable explanation of relativistic spacetime

• quadcore 9y ago
  Can someone explain that to me. When the observer is in the train, he sees the right tower future? Or maybe another way of saying it, the left and right tower time are not the same? Or yet another way of saying it would be, two points of an observed moving object are not at the same position AND not at the same time? Two points of a moving object got different delta positions and delta times?
  • red75prime 9y ago
    What you see on the diagrams are pictures taken by the drone swarm which moves alongside the train. In other words the pictures show events happening on a plane of simultaneity. Observer in the train can only see events which happened in their past light cone. So they definitely cannot see right tower's future. ('They' is used as gender neutral version of gender neutral 'he')
    • quadcore 9y ago
      Why is the left tower "in the past"? Because it "goes further away" from the train? What is "going further away" determined by? Position delta? So if position delta T->pA > position delta T->pB, time offset T->pA < time offset T->pB?
      • red75prime 9y ago
        It depends on what you mean when you say "left tower is in the past". Space-time intervals are defined for the pairs of events, which are points in space-time. Left tower is not an event. In the bridge plane of simultaneity both towers lighted at -100 units of time. In the train plane of simultaneity left tower lighted at -65, right one did at -150. The values are determined by the Lorentz transformation which includes speed of the observer. So "what's in the past" depends on the positions of the events, the times of the events, and the speed of the observer.
        • quadcore 9y ago
          Wow it's so cool. So I guess the left tower lighted is not an event of the past, it will just appears differently depending on the observation frame. So let me rephrase my initial question. Why is the left tower lighted before right tower is lighted when observed from the train frame? Because the train "goes further away" from the left tower? What is "going further away" determined by? Distance delta? So, is the following correct: let two events A and B occurring respectively at positions pA and PB in the same frame, a mobile at position pM, if delta_distance(pM, pA) > delta_distance(pM, pB), then follow that observed_time(A) < observed_time(B) assuming observed_time(A) == observed_time(B) in pA and pB frame? Please note, it's not delta_position but delta_distance I've written. Also, by delta, I mean difference. (edit: I get that "distance delta" is velocity)
      • deleted 9y ago
        [deleted]
  • jules 9y ago
    From a modern perspective the relation of the time axis to the x axis is roughly the same as the relation between the x axis and the y axis. Saying that two events happened at the same x coordinate (delta x is 0) is a statement that depends on the observer. Another observer who is rotated with respect to the first will see the events at different x coordinate (delta x is not 0), because some of the x axis has been rotated into the y axis. Similarly, saying that two events happened at the same t coordinate (delta t is 0) depends on the observer. Another observer who is moving with respect to the first will see the events at different t coordinate (delta t is not 0), because some of the t axis has been "rotated" into the x axis. This notion of "rotation" only differs from ordinary rotation by a minus sign. If you rotate the xy plane around the origin then points move in a circle x^2 + y^2 = const. If you rotate in the xt plane then points move in a hyperbola x^2 - t^2 = const. Physically you "rotate" in the xt plane by accelerating in the x direction. This causes points to move along that hyperbola, which means that some delta x manifests as delta t and vice versa. We don't see that in ordinary life because we only move with respect to one another at incredibly low speeds, which corresponds to very small "rotations". Imagine a world where all creatures are facing along the x axis with only very small deviations. These creatures may think that the x coordinate has physical meaning independent of the y and z axes. They might think that there is something special about their x axis. Similarly, we are all moving with roughly the same velocity through the universe. We initially thought that there was something special about our velocity, namely, we thought that we were at rest with respect to the aether.
    • quadcore 9y ago
      edited 10 thousand times Very good explanation, thanks for your time. Still something that's unclear to me. Let say I'm observing a star moving away from me at speed of light. Will I see the star? If yes, it means that, those photon-things, have a property which I haven't. Some "move at speed of light" type of property. So now, we have two points on a line, the "value" of a photon (speed of light) and my "value" (speed x), do we? What about that? We cant call that speed because we are saying speed is relative. How do you call that property then? And what is the other bound? Cant be x right? Or another solution is that, light depends on the observer. Ok got it. 100% got it. Light both has a speed (speed being always dependent from the observer) and both has a property I havent. The key is that light has a special property I havent, but it isnt about speed. Am I correct?
• CuriousSkeptic 9y ago
  I’ve been trying to learn all this stuff lately. One thing that bothers me though, that perhaps someone here can help with. In Minkowski diagrams you set things up to have rays as diagonal lines. But this way of illustrating things suggests that light moves in time. But they should really not be interpreted as that since they essentially define the limit of the time dimension. So I was thinking that I would like to have another illustration of things where light moves in 90-degree angles instead to fix this. Are there some specific, established ways to do this?
  • archgoon 9y ago
    I'm not entirely sure what your objection is; light does move in time.
    • CuriousSkeptic 9y ago
      Still learning ;) But IIUC, could you send a clock along 45-degree angles in a minkowski diagram it would not measure any time. But perhaps there is time there relative to an observer at 0-degrees? But what does that even mean then? If that observer sent a photon towards a mirror, would the photon have aged when returned to the sender?
      • soVeryTired 9y ago
        You can make your statement more accurate by saying that a clock will measure vanishingly little time as you get sufficiently close to the 45 degree line. But the 45 degree line isn't achievable. (Note I've made the same inaccuracy further up the page. Sometimes it's just easier to drop the epsilons and speak informally.) Physicists are precise people :)
        • fjsolwmv 9y ago
          Mathematicians are precise people. Physicists just assume their series converge :-)
  • QAPereo 9y ago
• mjfl 9y ago
  beautiful work. To anyone who is interested in really understanding relativity deeply without intimidating math, I recommend Tim Maudlin's book: "Philosophy of Physics: Space and Time".
  • Koshkin 9y ago
    > without intimidating math While having nothing against the book or its author, I must point out that ultimately it is "math in which we trust" (even experimental science leaves room for interpretation); philosophy, on the other hand, gives us no choice but to trust the philosopher!
    • dvt 9y ago
      Not exactly sure what you mean. The foundation of philosophy is logic. Also the idea that "math in which we trust" is kind of bizzare, as mathematics is an axiomatic system. So really, it's the axioms in which we trust. But that also opens a whole can of worms, because some axioms are kind of weird and controversial (like the Axioms of Choice, Replacement, Regularity). Not to mention that any for any system (> Peano Arithmetic) you can't have your cake and eat it, too; sound, complete, consistent: pick two.
      • hackinthebochs 9y ago
        I think the point was simply that there is no understanding of physics without the math, as the math is the only accurate description of the physics involved. Admittedly, "trusting math" was a poor phrasing.
        • Koshkin 9y ago
          We can trust math because it is trivially verifiable. Its relation to physics is somewhat complicated (e.g. verifying physics is not as trivial), and yes - you can understand a lot about physics without math - by combining direct observation with trusting the "philosopher".
      • 9y ago
• dvt 9y ago
  This is amazing! I remember having to study and draw some of these diagrams in an undergraduate Philosophy of Space & Time class.
• z3t4 9y ago
  As a kid there was a military air base in the neighboring city, so fighter jets passed our home regally. It was always fascinating that the sound and the plane where on different locations. You could always hear them but it was hard to spot the actual plane in the sky. Now imagine if they jets where going faster then light and that light was a bit slower so we could see them. That would mean the visible position would be different then the physical position of the plane ...
  • joshvm 9y ago
    There are some weird edge cases in physics where you can move faster than the speed of light. We don't have any means, yet, to move faster than light in a vacuum, but light slows down as it enters materials (0.75c in water, for example). One effect is Cerenkov radiation, which is light emitted when a charged particle moves through a medium faster than light does. You see this in nuclear reactors. It's basically a 'photonic' boom that happens in the wake of the moving charge. Your scenario works for things that are far enough away that the travel time of the photon is significant. Another poster mentioned the Sun. While that example is wrong (the Sun moving), it's true that if the Sun was whisked out of existence, we wouldn't know about it for 8 minutes. An example of this is supernovae in very distant stars. We see the flash of the explosion many years after it happened.
  • SiempreViernes 9y ago
    Or you know, just things far away moving at normal speeds, like also happens with sound. The sun for example is not physically in the place it appears to be due to the 8 minutes of light travel time and the fact it moves about one diameter in two minutes.
    • aisofteng 9y ago
      >moves about one diameter in two minutes Not in its own reference frame.
      • SiempreViernes 9y ago
        Uh, maybe the sun prefers to use the galactic standard of rest? Did you think of that? Maybe it likes to think of itself as an active and healthy star that takes care of itself and puts in the hours on the treadmill? Anyway, I was talking about the motion on the sky, not in an arbitrary reference system.
• mrfusion 9y ago
  I always wondered how a database would know which transactions to commit first in a relativistic world?
  • fjsolwmv 9y ago
    You don't need relativity, this problem is already answered by distributed systems that lack TrueTime clock guarantees. Today have to make arbitrary and inconsistent choices. (Or "eventually consistent", but then you lose some level of resolution in your ordering of moments) Related, this classic economic article: https://www.princeton.edu/~pkrugman/interstellar.pdf https://www.princeton.edu/~pkrugman/interstellar.pdf
  • philipov 9y ago
    Relativistic systems still behave causally; What observers can't agree on is how much time passes between events. The database is just another observer, so it would commit the transactions in the order that light-rays arrive. The requirement to preserve causality is why there is an upper bound on the speed of information, so that all observers can still agree on the order of events.
• adamnemecek 9y ago
  If you are interested in this, check out the formalization of space time in geometric algebra. It kinda makes sense! (i.e. more sense than in other formalisms) https://en.wikipedia.org/wiki/Spacetime_algebra https://en.wikipedia.org/wiki/Spacetime_algebra
• chriswarbo 9y ago
  This is quite nice, although I think I'm too familiar with to topic to know whether it's actually useful to someone trying to learn this stuff :) Although I think that "explorable explanation" is a bit of a grand claim for this sort of thing. The explanations (the connections, reasons, mechanisms, etc.) are given in the text, which isn't any more "explorable" than a book; whilst the "explorable" parts (the graphs/diagrams) aren't really "explanations" since they have no depth: the relationships are hard-coded, so the user can only adjust some parameters and get told what the "answer" is for that parameter. Many years ago I tried to make a more in-depth "explorable explanation" of some concepts from thermodynamics, using the Smalltalk-based EToys system. I did this by setting up many small simulations, e.g. of "atoms" bouncing around in containers, of pistons and thermometers, of falling weights, etc. The behaviour (scripts, methods, etc.) of each object could be inspected, and mostly involved simple stepped-integral scripts like those in games (update position based on velocity, update velocity based on acceleration, etc.). "Measurements" would be taken of the aggregate behaviour, e.g. of a piston's position, and plotted against some other parameter (time, pressure, velocity, etc.), to produce graphs which (hopefully) demonstrate the relationship described by the text. These were "explorable" since the user had complete control to inspect and modify the dynamics of the simulations and see what happens. Unfortunately I ended up abandoning the project once it maxed-out the RAM of my OLPC XO-1, since I was no longer able to load and save it :(
• xixixao 9y ago
  I have to add that although there are quite a few great resources explaining special relativity, resources explaining general relativity, beyond focusing on describing the math behind it, are few and far between. Anyone's got a contradicting example?
  • catnaroek 9y ago
    I learnt a lot from “Introducing Einstein's Relativity” by Ray d'Inverno and “A First Course in General Relativity” by Bernard Schutz. However, they are by no means leisurely reads. You need to be prepared to expand your mind (both your physical intuition and mathematical technique) and work very hard (you don't learn just by reading theory, you need to solve exercises and perform long calculations).
  • jperras 9y ago
    General relativity is, fundamentally, the study of the metric tensor: it is the object that connects the geometric representation of space and time with mass and energy. Different metric tensors can produce wildly different results, from flat space to black holes to bubbles in space time that provide inertial reference frames that can travel "faster" than than the speed of light. You could spend your entire life studying small variations in metric tensors. Some people do. More simply: 1. Light travels from point A to point B via the shortest path. 2. In the absence of mass (aka where the Minkowski metric applies), the shortest path is a "straight line". 3. In the presence of mass (where a non-trivial metric exists), space itself curves. Light, which follows the shortest path between two points, must follow this curved space. As a lower-dimensional analogy, think of what a "straight" line means on the surface of a sphere[1]. The shortest path between two points is, by definition, a "straight" line, but if the space itself that the path is embedded in is curved, then when viewed from a higher dimension (i.e. on the surface of the sphere it's straight for you, but if you were in space) it would appear curved. The analogy fails when you attempt to think about it in higher dimensions, since humans have a very difficult time perceiving anything greater than the standard 3+1 spatial & time dimensions. But the math still holds. Light will always travel in a straight line, it just so happens that gravity redefines what "straight" actually means. 1. http://mathworld.wolfram.com/GreatCircle.html http://mathworld.wolfram.com/GreatCircle.html
• catnaroek 9y ago
  Explanations of special relativity, explorable or otherwise, are dime a dozen. Try explaining general relativity in this fashion. Try explaining cosmology in this fashion.