About

A spacetime diagram showing the location of three events.

Simultaneity Spacetime Diagram

The Simultaneity Spacetime Diagram model uses light-trajectories to show the effect of relative motion when observing (recording) events in special relativity.   In the default scenario, an explosion (an event) at the center of a right-moving stick occurs at t=0 and the arrival of the explosion light signal at each end is recorded.  The arrival event at the left end occurs before the arrival event at the right end because the stick is moving.  How do the location and time of these events change if they are observed in a reference frame (the Other Frame) in which the stick is stationary? 

The Simultaneity Spacetime Diagram model was written for the study of special relativity using spacetime diagrams.  Initial conditions, such as the locations of the explosion and the detectors, can be adjusted by dragging before the simulation is run. The slider can be used to change the speed of the stick.  A third view shows the stick and the wavefront in space.  More importantly, a checkbox allows users to compare the predictions of Galilean and special relativity in order to observe how the assumption of a constant speed of light leads to the relativity of simultaneity.

The Simultaneity Spacetime Diagram model is distributed as a ready-to-run (compiled) Java archive.  Double clicking the ejs_sr_SimultaneitySpacetimeDiagram.jar file will run the program if Java is installed.  Other special relativity programs are also available.  They can be found by searching the OSP Collection for special relativity.

References:

• "The Twin Twin Paradox: Exploring Student Approaches to Understanding Relativistic Concepts," Sébastien Cormier and Richard Steinberg, The Physics Teacher, (in press).

• Spacetime Physics 2nd ed, Edwin F. Taylor and John Archibald Wheeler, W. H. Freeman (1992).

• A Travelers Guide to Spacetime, Thomas Moore, McGraw-Hill Science (1995).

Credits:

The Simultaneity Spacetime Diagram model was created by Wolfgang Christian using version 4.3 of the Easy Java Simulations (EJS) authoring and modeling tool.  You can examine and modify a compiled EJS model if you run the program by double clicking on the model's jar file.  Right-click within the running program and select "Open EJS Model" from the pop-up menu to copy the model's XML description into EJS.  You must, of course, have EJS installed on your computer.

Information about EJS is available at: <http://www.um.es/fem/Ejs/> and in the OSP ComPADRE collection <http://www.compadre.org/OSP/>.

A spacetime diagram showing the location of three events.

Understanding Spacetime Diagrams

One of the most useful ways to analyze objects moving in one dimension in special relativity is with spacetime diagrams.  In a spacetime diagram, time is plotted on the vertical axis and position is plotted on the horizontal axis.  A stationary particle produces a vertical trajectory in this diagram as time advances.  An object moving with constant velocity produces a straight line trajectory with slope equal to 1/velocity.  The unit of time on a spacetime diagram is chosen to be the time it takes for light to travel one unit of length.  This choice of units puts time and space are on an equal footing.  For example, if the unit of time is one year, then the unit of distance is one light year 9,460,730,472,580.8 km. If the unit of length is one foot, then the unit of time is approximately one nanosecond.

A spacetime diagram is an important visualization tool in special relativity because the speed of light is a universal constant.  Consequently, light is always represented by a line with unit slope. The two red lines in the simulation represent light traveling to the right and left along the stick after the explosion at t=0.  In special relativity, the slope of these lines is always plus or minus one because light travels one unit of distance in one unit of time in all reference frames.  The yellow line in the spacetime diagram shown should not be confused with a spatial view of the stick.  The vertical axis is time (not space) and the thickness of the line was chosen for visibility.  The length of the line does, however, represent the length of the stick in the chosen reference frame.  Points on a spacetime diagram represent events and are drawn as small circles for visibility.

In order to compare the predictions of special relative and Galilean relativity, the Simultaneity Spacetime Diagram model also shows a pseudo-spacetime diagram in which speed of light obeys the principles of Galilean invarience.  The home reference frame is assumed to be a special reference frame such that the speed of light is the same to the right and left.  According to Galileo and Newton, an observer traveling with a right-moving meter stick will measure a smaller speed for light traveling to the right and a larger speed for light traveling to the left.  Countless experiments have shown that this classical physics concept of an absolute space and an absolute time is incorrect.

Exercise

When we are dealing with moving reference frames, we must modify our idea of simultaneity to include the idea that events that are simultaneous in one reference frame are not simultaneous in another reference frame.  This is perhaps one of the most important things to keep in mind when considering the apparent paradoxes that arise in special relativity.  Almost all of these apparent paradoxes can be understood by remembering that events simultaneous in one reference frame are not simultaneous in another reference frame.

Set the stick velocity to +0.2 and drag the light source in the home frame to a location such that the right- and left-traveling light reach the detector at the same time.  Use geometric (spacetime) arguments to predict if the right or left detector will be the first to detect the explosion.  Does your argument depend on the length of the stick?  Check your prediction in the other reference frame.

Questions

Run the model with different stick velocities and compare the Home and Other spacetime diagrams.  What changes and what remains constant in each of these spacetimes when the velocity is changed?  You can right-click within a diagram to make a snapshot if you wish to compare spacetime diagrams with different initial conditions.

Repeat the spacetime comparison if Galilean invariance is assumed.  What changes and what remains the same?

Translations

Code	Language		Translator	Run

Software Requirements

Credits

Wolfgang Christian - Davidson College; This email address is being protected from spambots. You need JavaScript enabled to view it.

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