Relativistic Spacetime Drawing Tool - Introduction

What's In The Display

Menu Bar

page1 Welcome to this drawing tool. It allows you to make simple Minkowski diagrams in time and space and then modify them. This is the first lesson, and explains how to use the tool. First, let me point out the menus along the top. If you have a Google account, you can save and share your drawings to Google Drive. Under the "View" menu you can check the "View Text" to see the text of these lessons while listening to them.

page2 If you are new to the ideas behind Einstein's relativity, you might find it easier to understand how to use this tool with the Lorentz transformation turned off. Then the drawing tool will use classical Newtonian Physics and Euclidean Geometry.

Lessons

page3 Under the "Lesson" menu you can select which lesson to view, or you can start creating your own drawing by selecting "Free Form". To view and listen to a lesson, select the lesson you want from the "Lesson" menu, and then click the play button in the audio controls. Use the audio controls to pause or seek ahead in the lesson.

Drawing Tools

page4 The buttons above the main canvas let you pick a drawing tool. You can select an item to modify it. Or you can add an event, an instant, a location, a light cone, or a time-like path.

Main Spacetime Canvas

page5 I'm going to add a few events by selecting the tool and then clicking on the main canvas. The coordinates of the main canvas are space, on the horizontal axis, and time on the vertical axis. This is an abstract tool with with units choosen so that the speed of light is 1.

page6 There are four more types of objects we can draw with this application. We can draw an instant. An instant is all of the events with the same time coordinate. This is just a horizontal line.

page7 We can draw a location. A location is all of the events with the same space cooridnate. This is a vertical line.

page8 We can draw a light cone. A light cone with only one space dimension is a pair of lines. For this application, the speed of light is one, so the slope of these two lines is 1 and -1.

page9 We can draw a time-like path. This can represent the position of an object that might accelerate. Notice that you cannot draw a path that goes backwards in time, or moves faster than the speed of light.

Edit Objects

page10 The last tool I want to talk about is the "Select" tool. If you click on any object, it will be highlighted, and you can edit its properties. Paths and locations have an Icon and can have a clock. Any object has a color and a name. You can also delete the selected object.

If you don't select an object, you can click and drag on the canvas to move the current view port.

Animation Canvas

page11 Below the spacetime canvas is the animation canvas. It shows the current time slice. You can see the current time slice as a horizontal bar in the space time canvas. Notice what happens as I change the current time using the slider near the bottom of the page. When the time slice crosses an event, we see it show up in the animation canvas.

Current Velocity

page12 Below the time controls is a velocity controller. This controls the velocity of the current view, relative to the original reference frame. Any new objects will share the current reference frame. For example, I'm going to pick the "location" tool, and then I'm going to add a train to my world that has zero velocity. Then I'm going to change the current velocity to 0.5 and add a person. If I turn on the animation, I will see the train move toward the person and pass by. However, the laws of physics are relative. That means it is just as valid to say the train moves past the person as it is to change our observer's velocity back to 0, and say that the person moves past the train.

Conclusion

page13 That's the end of the introduction. You can either listen to some lessons on relativity, or you can select "Free Form" to draw your own pictures.