This tutorial is a visual study of two dimensional motion as observed from different reference frames.†
Please Note:† Relativity is built on and modifies Newtonian Physics.† These tutorials do not attempt to teach the user Newtonian Physics.† They assume the user already knows Newtonian Physics.
If you have not run the simulation application before, please read the System Requirements document at
If you are comfortable that your system satisfies the requirements, or just want to try it and see what happens, go to http://relativitysimulation.com and click the ďLaunchĒ button.† The first time you run the application, it may take a minute or two to load.† When it is successfully loaded, you will see the blank simulation scene below.†
The above picture was taken on a computer running Internet Explorer 8 on Windows Vista.† What you see on your computer may vary.† Notice the two checkboxes at the bottom center of the simulation window.† Simulations may be run using either Newtonian or Relativistic physics.† The default is Relativistic, but in order to understand the way that Special Relativity changes the way objects are observed in two (and three) dimensional this tutorial will guide the user though some Newtonian simulations too.
Selecting a Predefined Example
At the bottom right is a selection box labeled Examples List.† Clicking the selection box will display a list of examples.† The easiest way to use the application is to select a predefined example from this Examples List.† Your list may vary.† Scroll to and select Two Dimensional Motion Ė Velocity Addition.†
In a few seconds, you will see three blue particles, one green and two red inserted into the scene.† After the scene is populated with an example, new tabs will appear above the scene.† The tabs will be explained in the section on Viewing and Changing Object Properties.
Navigating through an Example
At the bottom left of the scene are navigation buttons.† These buttons allow you to look around the scene.† The buttons are in three groups with a reset button above.† The Reset Navigation button will cancel all navigation commands and present the scene to you as first inserted.† Buttons in the X-Navigation group affect your view by changing your orientation with respect to the x-axis of the scene.† Similarly, there are buttons for the y-axis and z-axis.† Clicking the Left button, for instance, will move the objects in the scene a bit to the left.† If your browser is not showing you as much of the scene as you would like, clicking the Out button will zoom you out a bit and show you more.† To view the scene from a different angle, try clicking a Clockwise or Counterclockwise button.† If you have selected a Two Dimensional Motion example, you are looking at a set of particles in a two dimensional plane.† The green particle and the blue one above it are on the Y-axis.† To verify this, in the Y-axis group, click the Clockwise button a few times.†††
Click Reset Navigation.† Then try clicking the Clockwise or Counterclockwise buttons in the X-axis and Z-axis groups.† Click Reset Navigation again to return to the default view.
Running an Example
To run an example, at the bottom of the scene, click the Run button.† When running, the objects in the scene will move according to the velocities and rules specified for them in their respective properties tabs.† If you have inserted objects into the scene yourself instead of selecting an example, the objects are initially inserted with no velocity and no rules.† So clicking the run button will not do anything.† If you have selected the Two Dimensional Motion example, clicking Run will start the three blue and two red particles converging on the green.†
Stopping an Example
If a scene is running, you will notice that the Run button has changed its name to Stop.† Click it to stop the simulation.
Continuing an Example
When stopped, the Stop button will change its name to Continue.† Click it to continue the simulation from where it stopped.
Resetting an Example
Clicking the Reset button will reset the objects in the scene to their initial positions ready to run again.† Click Stop and Reset now to make sure the simulation is ready for the next section.
Switching between Relativistic and Newtonian Simulations
Note that the green particle is spherical.† All the other particles are contracted by a factor of 50% in the direction of their motion.† Make sure the simulation is stopped and reset and click on the Newtonian checkbox.† This will set the simulation to Newtonian physics where there is no contraction due to relative velocity.† Note that all the particles are now spheres.† Click Run and note that the red and blue particles still converge on the green.† The Newtonian simulation gives the same results as the Relativistic for this reference frame.†
Stop and reset the simulation.† Then run it again and make sure to stop it before the particles converge.†
Viewing and Changing Object Properties
When an object is inserted into the scene, it is provided with its own tab above the scene.† The tabs allow you to view and change some of the objectís properties.† When you are running a Newtonian simulation, clicking a properties tab will show you the Newtonian properties.† When running a Relativistic simulation, clicking a properties tab will show you the Relativistic properties for the same object.† If you have been following these instructions and have a Two Dimensional Motion example inserted there will be one tab for each particle. †Make sure that you are running a Newtonian simulation by verifying that the checkbox labeled Newtonian at the bottom of the scene is checked.† Then click the properties tab for CenterParticle.† (The number suffix provides a unique ID when you have more than one particle in the scene.)† You will see several sets of information.† At the top left are miscellaneous properties that may include fields for Id, name, description, rigidity, dimensions, color, etc.† Notice that the sphereís radius is .015.† Thatís 1,500,000m in this simulation.† All of the objects in all the examples have very large sizes so as to exaggerate the time and contraction differences predicted by Special Relativity.† To the right are sections for attached clocks, acceleration plans and itineraries.† The tutorial Pole in the Barn uses attached clocks.† The tutorial Bells Spaceships uses an acceleration plan.† Below is a section labeled Initial Conditions with respect to Observer.† The sphereís position and velocity are zero.† Below the initial conditions is a section entitled Current Conditions with respect to Observer.
If you donít see it, click the scrollbar on the right side of the window.†
As long as the CenterParticle is at rest with respect to you the observer, its current condition will be the same as its initial.† Click on the tab for the EastParticle. Note that the initial and current velocity of this particle is -260,000,000 meters/second (westerly).†
If you have been following the tutorial and ran the simulation a little and then stopped it, you will notice that the current translation is not the same as the initial.† It, along with the other particles, is converging on the green particle.† Click on the tabs for the WestParticle and examine its velocity.† It is 260,000,000m/s (easterly).
If you like, click on the tabs for the other particles and satisfy yourself that the particles will indeed converge as the simulation demonstrates.† Then go back to the simulation.
Switching Reference Frames
One of the objectives of this simulation is to give you, the observer, the opportunity to see the movement of objects from different reference frames.† You can do this whenever the simulation is stopped and reset. †Click Reset.† Just below the Examples List is another selection box labeled Observer Reference Frame.† The default reference frame is identified there.† This is also the reference frame of the green particle.† This means that the green particle is at rest with respect to you and all the others are moving.† Click the down arrow of the reference frame selection box and notice that all the particles are listed there.† Select the EastParticle. (The number is a generic ID to help you keep track in case you have more than one particle with the same name.)†
Run the simulation and note that the EastParticle is now at rest and the other particles converge on it.†
Click on the tabs for the various particles and satisfy yourself that the velocities have changed in accordance with Newtonian physics.† Note that the WestParticle velocity is 520,000,000m/s eastward.† Thatís greater that the speed of light.† Light travels at 300,000,000 m/s.† That canít happen in Relativistic physics.† The composite speeds of the North and NorthWest particles are also greater than the speed of light.
Switching reference frames among moving objects will result in the objects changing velocities and position relative to you, the observer.† In Newtonian physics, even if none of the objects have a velocity greater than the speed of light initially, switching reference frames can result in one or more objects having a relative velocity greater that the speed of light.†† Click the simulation tab to return to the simulation.† Run and Reset the simulation until the reasons for these greater than light velocities are obvious.† In order for WestParticle, all the way over on the left, to participate in the convergence all the way over on the right, it must have a very large velocity.† The same argument applies for the NorthParticle at the top of the scene, though to a lesser extent.† Click Reset and try changing reference frames to the other particles and running the simulation.† Physicists believe that certain events in the world must be independent of the reference frame from which they are observed.† So, even though velocities and positions are different as determined from different reference frames, the particles always converge together.† Reset the simulation again and switch to the default reference frame.† Then click the Relativistic checkbox.† Note that the contraction of the spheres returns.† Change reference frames to the EastParticle.† If you lose sight of all the particles, click the Out button until they are all within you view.
You may feel that the new position of the particles with respect to the EastParticle is unexpected.† Run the simulation, the EastParticle is at rest with respect to you and the others move with respect to it.† But all the particles still converge.† After youíve done this a few times you will realize the reason for the new position of the particles.† Take the WestParticle.† If it had stayed in the same position relative to the EastParticle, it would have needed a velocity greater than the speed of light to join in the convergence.† Since it couldnít do that in Relativistic physics, it had to start off closer.† You can check the Relativistic starting velocities and translations of the particles by paging through the tabs.
Initial and Current Time are included in the object properties.† For Newtonian physics, this seems a waste.† Time is absolute and every object has the same initial time and current time.† But for Relativistic physics, every object has its own Proper Time that is a function of its position and velocity with respect to the observer.† You, the observer, have your own time too.† Reset the simulation and review the time of the various objects in their respective tabs.† The simulation is designed to start at observer time = zero.† This is an arbitrary choice on the part of the program.† Any object that is in the observerís reference frame must have the observerís time as its Proper Time.† Any object that is not in the observerís reference frame, but starts at the origin of the observerís reference frame must also have the observerís initial time as its Proper Time.† Run the simulation and Stop it before the convergence.† Review the time of the various objects again.† Time passes for all objects but not at the same rate.† Time for you, the observer and any object in your reference frame, passes at the fastest rate.† Time for other objects passes at slower rates depending upon the relative velocity of the object with respect to you.† Click Reset. †Then switch reference frames to the EastParticle.† Review the times again.††† Now the EastParticle ís initial Proper Time is zero.† But CenterParticleís Proper Time is still zero because it is at the origin of all reference frames.†