What is Minkowski diagram: Definition and 34 Discussions

A spacetime diagram is a graphical illustration of the properties of space and time in the special theory of relativity. Spacetime diagrams allow a qualitative understanding of the corresponding phenomena like time dilation and length contraction without mathematical equations.
The history of an object's location throughout all time traces out a line, referred to as the object's world line, in a spacetime diagram. Points in spacetime diagrams represent a fixed position in space and time and are referred to as events.
The most well-known class of spacetime diagrams are known as Minkowski diagrams, developed by Hermann Minkowski in 1908. Minkowski diagrams are two-dimensional graphs that depict events as happening in a universe consisting of one space dimension and one time dimension. Unlike a regular distance-time graph, the distance is displayed on the horizontal axis and time on the vertical axis. Additionally, the time and space units of measurement are chosen in such a way that an object moving at the speed of light is depicted as following a 45° angle to the diagram's axes.

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  1. L

    I Question about the Minkowski diagram

    In the case of two rulers of equal rest length moving past one another ibex posted the minkowski diagram and I have a question about the one diagram that follows the following comment by him: Note that, in the primed frame, "State 2" is after "State 3"! This is the relativity of simultaneity...
  2. R

    Minkowski diagram, where to put an event

    I drew the Minkowski diagram, but I'm not sure if this is correct. From what I drew the angle between x and ct ##\approx 0## then the event is "inside" the light ray and will eventually reach A.
  3. cianfa72

    I Clarification on Rindler coordinates definition

    Hi, starting from this post Basic introduction to gravitation as curved spacetime I would ask for a clarification about Rindler coordinates. From this wiki entry Rindler coordinates I understand that the following transformation (to take it simple drop ##y,z##) $$T = x\sinh{(\alpha t)} ...
  4. fee_de

    B Understanding Spacetime Diagrams from "Reality is not What it Seems

    I'm reading a book called "Reality is not what it seems: the journey to quantum gravity" by Carlo Rovelli and I'm struggling to understand this diagram that is part of the chapter about special relativity. https://i.stack.imgur.com/JgBDJ.jpg Before this image Rovelli writes: "It's not...
  5. jk22

    B Should the 'time' axis of a Minkowski diagram be time's imaginary unit?

    Since the metric is euclidean in coordinates ##(ict,x)## it can be drawn in a plane, but if the metric is ##diag(1,-1)##, can both axis still be drawn in a plane ?
  6. F

    B Any interest in a spacetime diagram generator?

    Hi, I've written a script-based spacetime diagram generator. I have no idea if it has any value for anyone besides myself—you may have access to better tools than I do. When I looked for spacetime generators, I only found some very limited web tools and one downloadable program that wasn't much...
  7. S

    B Minkowski Diagram: Expanding Universe

    Is this how you would draw the Minkowski space diagram with space expanding, (without acceleration or black holes) ?
  8. I

    I Hash marks on minkowski diagram

    I'm confused as to how far apart the hash marks should be on a minkowski spacetime diagram that shows the rocket frame overlapped over the lab frame. Should the hash marks that represent space in the rocket frame be spaced apart exactly the same length as the hash marks that represent space in...
  9. Destroxia

    Special Relativity - Length Contraction

    1. Homework Statement Why does the non-relative simultaneous frame have an additional term of ##v \Delta t## along with the contracted length ## L ## for ## \Delta x ##? 2. Homework Equations ## L + v \Delta t = \Delta x ## ---- (1) ## \Delta x = \gamma \Delta x' = \gamma L_{\star} ## ----...
  10. stickman76

    I Graphic Anim of Special Theory of Relativity: Exploring Interrelationships

    There is a relationship between each of the mathematical values in each of the paradoxes with regard to each observers. There is obviously also a relationship between every situation we study in the Special Theory of Relativity. The Lorentz Transformations obviously prove this. So, I began to...
  11. Pushoam

    Minkowski Diagram and Mathematica

    Homework Statement [/B]Homework Equations Mathematica The Attempt at a Solution I want to plot the diagram using Mathematica. I saw on the net there is some kind of programming needed for this. Do I need to learn programming for doing this? If yes, how to learn it?
  12. Pushoam

    I Calibration of Minkowski Diagram: Explaining Invariance of S^2

    Can anyone please illustrate highlighted part? Can anyone please explain me how invariance of s^2 is useful in characterization of events? I didn't understand the highlighted part i.e. how to determine velocity of S' relative to S?
  13. J

    I Explore Time Dilation in Minkowski Diagrams

    Hello, I noticed something peculiar when looking at the Minkowski Diagram and I'm not sure how to interpret this. Let observer A be the reference frame for the diagram and B someone who travels with respect to A. The red line is the displacement of light over time. The blue, yellow and green...
  14. Divy Jain

    I Interactive Minkowski Diagram Tool

    I've made a Interative Minkowski Diagram Tool, http://divykjain.github.io/IMD You can add events, connect events and add world lines. Lorentz transformation for moving frames also present. I've added support for frame velocities equal or greater than light speeds(but the animations are a mess...
  15. Powergade

    Minkowski diagram: angles.

    1. Homework Statement In a diagram where I have two observers (one still (A) and one moving with a "v" velocity (B)), where the two parts disagre in the simultaneity of events, how can I prove that the angles of the B person axis that are put in the A person axis are equal. (/alpha=/beta , in...
  16. jannesvanpoppelen

    B Understanding Minkowski Diagrams in Special Relativity

    Something that has been bothering me for a while is this question. As seen from this Minkowski diagram,http://imgur.com/GkBN2HQ , the angle between x and x' is equally big as the angle between ct and ct'. I really can't seem to figure out why this is, although I think it has to do with the...
  17. G

    I Minkowski diagrams without scales on axes

    Hi. I have seen quite a lot of demonstrations of time dilation and length contraction that used standard Minkowski diagrams WITHOUT any scales on the axes at all. If I understand them correctly they seem to directly compare lengths, which would imply (I think) that the scaling on the ##ct/x##...
  18. J

    Axes of the Minkowski diagram

    Hello, First of all, I'm sorry since I bet there are quite a few threads about this but I still have a bit of a hard time wrapping the axes of the Minkowski diagram around my head. I understand very well that, to have the speed of light traveling at a 45 degree angle in a space-time diagram...
  19. DiracPool

    Intergalactic Space & the Minkowski Diagram

    Couple of questions as to how to interpret the Minkowski diagram when it comes to intergalactic space. 1) To begin, I'll make some pre-assumptions to the question, which you may correct if I'm wrong: 1a) Within any given galaxy, the distances between it's constituent stars is roughly equal...
  20. A

    Plotting Minkowski diagram for 2 simultaneous accelerating

    Homework Statement two objects are at rest in an inertial reference frame. Two objects accelerate simultaneously in the same direction until reaching half the velocity of light and then halt simultaneously. The two objects are initially connected by a thread just long enough to cover the...
  21. DiracPool

    Minkowski diagram questions

    I had some questions about how to understand the Minkowski diagram better: 1) One thing that I hear characterizes a light ray or a photon is that it "experiences no time." That is, it's time dilation is so extreme that at the "null lines" or light cone lines at the 45 degree mark, the...
  22. Adrian555

    Types of Rotations - Hi Everybody, Ask Your Questions Here

    Hi everybody, This is my first post, so I apologise for all the possible mistakes that I can make now and in the future. I promise that I'll learn from them! My question is the following: It's well-known the relationship between two pair of cartesian axes when a circular rotation is made...
  23. Ibix

    Interactive Minkowski diagrams tool

    This is a little toy I put together that I thought might be of interest: http://ibises.org.uk/Minkowski.html It's an interactive Minkowski diagram. You can add events and connect them up with straight-line paths, then Lorentz boost either to a specified velocity or to the rest frame of a...
  24. M

    Minkowski diagram, what does observer see.

    Suppose we have a spacetime diagram like this: Red lines indicating light travel from the moving object to the observer. Object is moving at the speed of 0.8c. At this speed we have: Lorentz factor 1/√(1 - v2/c2)=1/0.6=1.66(6) Relativistic Doppler effect √((1 + β) / (1 - β)) = 3 My question...
  25. 7

    Length contraction and Minkowski diagram

    Hello, in my other topic members on the forum helped me to understand time dilation by using Minkowski spacetime diagram. Now i would also need some assistance with explaining length contraction in Minkowski spacetime diagram. I have observer Žiga in his frame ##x,ct## and observer Ranja...
  26. 7

    Time dilation and Minkowski diagram

    After i figured out how to show length contraction in this topic. I tried to use a similar way to show time dilation in Minkowski diagram. Time dilation means that time interval between two events is the shortest in the frame in which those two events happen in same place. We call this frame its...
  27. 3

    Minkowski diagram - the angle between axes

    I was reading through my textbook and it said that the angle between the axes of two inertial frames, one stationary and one moving at velocity v is supposed to be tan^-1(v/c). I assumed this would be easy to show, but after spending a couple of hours on this probably trivial problem, I can't...
  28. M

    Orthogonal diretion on the Minkowski diagram

    I have a trivial question: Let assume a world sheet of a time-like spherical shell in Minkowski space-time. On the 2D-Minkowski diagram (R,T), where R is the radius and T is the time, the world line is represented by a time-like curve. Let assume that the shell collapse and its 4-velocity is...
  29. K

    Minkowski diagram frame scale comparison

    Homework Statement Draw a clearly labelled “Minkowski spacetime” diagram illustrating two events ((1) a farmer firing his laser gun at his cow, which is sitting along his positive x-direction, and (2) the cow dying) as observed by two observers (S at rest in the farmer’s and cow’s frame, and...
  30. P

    Beginner's Minkowski diagram / space-time interval question

    Good morning, We are trying to understand Special Relativity through internet, and we would like to ask a couple of questions about the subject. We plan to post more questions as more doubts arise. Both doubts concern the Minkowski space-time diagram. First doubt: in the temporal dimension...
  31. L

    Minkowski Diagram for Twin Paradox

    In the twin paradox, if B moves away from A at constant high speed what would the minkwoski diagram look like in the frame of A and in the frame of B. well in the frame of A. if B starts next to A i.e. at O and is moving at close to c to begin with the world line of B will just be a straight...
  32. M

    Relativity in Minkowski Space and Minkowski Diagram

    hi :smile: I'm working on "Relativity on Minkowski Space and Minkowski Diagrams" as my undergraduate project. I have some references for my project but I want to make it perfect. May you introduce me some cool stuff (references, interestings, topics to work on & etc.) about this topic...
  33. P

    Draw Minkowski Diagram: x-axis 0-5m, ct-axis 0-5m

    draw a minkowski space-time diagram for s and s' showing x- and ctaxis as well ass the x'- and ct'-axis. the x-axis and ct axis will span from 0-5m. everwhere x'-axis ct'=0 and likewise for ct'-axis x'=0. [(v=0.6c)(t=t'=0, x=x'=0)] so any way I start out with drawing ct and x. like a normal...