10176

The much-cited twin paradox consists of three stages: (1) the traveling twin takes off; (2) he turns around; and (3) he arrives back home. Those three events are connected by the green line segments. In this simulation, imagine that the traveling twin is moving between two walls or space stations, with the path marked in blue. The presence of these two space stations suggests three more observable events, namely, what can be seen happening at the opposite space station by the traveling twin when he is at: (4) takeoff; (5) turnaround; and (6) arrival home. You can adjust the light cone parameter to the viewpoint of each of these six events, and adjust the "beta" parameter, to see the space-time diagram in different reference frames.

DETAILS

The scale of the and axes is not given, but you may choose light-seconds and seconds or light-years and years, and so on. To see the space-time diagram for the right-bound trip, make the lower (green) leg of the trip vertical. Then for the left-bound trip, adjust the upper (green) leg of the trip to be vertical. The vertical distance between events represents the time experienced by each observer. You can see the time experienced by the stay-at-home twin by making the blue line vertical. When both legs of the twin's journey (green) are successively made vertical, you can see that the total time elapsed for the traveling twin is less than that for the stay-at-home twin. Of particular interest is the perceived distance to the opposite space station, which depends on the velocity of the twin. This phenomenon is commonly called "aberration" and is described as a shrinking of the image in the direction of acceleration. However, the actual phenomenon is not a mere shrinking of an image, but an actual increase in the distance to the visible event. As objects approach the speed of light, the image appears to move faster than the speed of light, because the light from the object arrives only shortly before the object itself. This phenomenon is called "superluminal motion".

PERMANENT CITATION

 Share: Embed Interactive Demonstration New! Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details » Download Demonstration as CDF » Download Author Code »(preview ») Files require Wolfram CDF Player or Mathematica.

Related Topics

 RELATED RESOURCES
 The #1 tool for creating Demonstrations and anything technical. Explore anything with the first computational knowledge engine. The web's most extensive mathematics resource. An app for every course—right in the palm of your hand. Read our views on math,science, and technology. The format that makes Demonstrations (and any information) easy to share and interact with. Programs & resources for educators, schools & students. Join the initiative for modernizing math education. Walk through homework problems one step at a time, with hints to help along the way. Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet. Knowledge-based programming for everyone.