This tutorial is a visual study of the familiar Pole in the Barn Paradox. If you have not run the simulation application before, please read the System Requirements document at http://relativitysimulation.com/Documents/SystemRequirements.html.
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 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 “Launch” 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 and that is what this tutorial is for.
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. The list may vary. Scroll to and select Pole in the Barn.
In a few seconds, you will see a green pole and a red barn 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 Pole in the Barn, the example is loaded with you, the observer, looking at the barn from above. To get a ground level view, in the X- Navigation group, click the Clockwise button about 9 times and then, in the Y- Navigation group, click the Counterclockwise button about 6 times.
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. Note that 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 Pole in the Barn example, clicking Run will start the pole moving toward the barn. This example has a rule that pauses the simulation to alert the user when the pole hits the sensor on the back wall of the barn.
Click OK to close the message window. Notice that the run button now says continue. Click Continue. The pole continues thru the back wall of the barn. At the same time, another rule triggers the barn door to close. If the barn door encounters the pole while closing, it will stop (jam) before it completely closes. But in this case, the door successfully closes behind the pole.
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.
Switching Reference Frames
One of the objectives of this simulation is to give you the opportunity to observe the movement of objects from different reference frames. You can do this whenever the simulation is stopped and reset. If you have selected the Pole in the Barn example, for instance, it is initially inserted into the scene with you, the observer, in a default reference frame. This default also happens to be the reference frame of the barn. That is, the barn is at rest with respect to you and the pole is moving. Just below the Examples List is another selection box labeled Observer Reference Frame. The default is identified there. Click Reset. (If Reset is not active, try clicking Stop first.) Then Click the down arrow of the reference frame selection box and select Pole. (The numbers after the object names are generic IDs useful if you have more than one of the same objects in the scene.)
Now it is the pole that is at rest and the barn is moving. Notice that the pole has lost is relativistic length contraction. It is longer. The barn, on the other hand, has acquired length contraction. It is foreshortened. Physicists believe that certain events in the world must be independent of the reference frame from which they are observed. So, even though velocities, positions and geometries are different as observed from different reference frames, if the door closed successfully in one reference frame it must do so in all others. But how can such a long pole get thru the short barn before the door closes? This is the reason the example is called a paradox. Run the simulation. Notice that the pole does indeed make it thru. (You may want to use the navigation buttons to get a better view.)
Now, someone grounded in Newtonian physics might conclude that the program has been “fixed”. The door no longer starts its closure when the pole hits the back wall. It starts much later. This is a case of the Relativity of Simultaneity. To better understand this characteristic of Special Relativity, this example is provided with the ability to show clocks at strategic locations. The next section on Viewing and Changing Object Properties explains how to run the simulation with the clocks showing.
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 object’s 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 the Pole in the Barn example inserted there will be one tab for the barn and one for the pole. Make sure that the Relativistic checkbox is checked and that the pole is selected as the observer reference frame. Click Reset. Then click the properties tab for the pole. You will see several sets of information. At the top left are miscellaneous properties that may include fields for the name of the object, description, rigidity, dimensions, color, mass and charge. Just below them is an area for specifying signaling. Signaling is covered in the Twins tutorial. Notice that the length of the pole is .8 long. That’s 80,000,000m 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 is a section on clock properties, acceleration plans and itineraries. In this simulation the pole has two clocks. Below is a set of properties entitled Initial Conditions with respect to Observer. And then a set entitled Current Relativistic Conditions with respect to Observer. Notice that the initial translation for the pole is x = -40,170,000m, y = 0m and z = -10,000,000m. Since the origin of the coordinate system is the center of the scene, the scale for the scene is very large indeed! The pole’s initial velocity is zero m/s. All its rotations are 0 degrees, meaning it is inserted into the scene with the same orientation as originally drawn. Notice that the current conditions are identical to the initial. The pole is at rest with respect to you. For now, just click the checkbox Check to Show All Clocks.
Then click the simulation tab. If you have been doing navigation, click the Reset Navigation button. You will see pole and barn again plus two clocks. One will be positioned at each end of the pole.
Now, click on the properties tab for the barn. Notice that the barn is 40,000,000m deep. Its initial velocity is -260,000,000 meters/second in the x-direction. The barn also has two clocks. Again click the checkbox Check to Show Clocks. Now when you go back to the simulation, you will see two more clocks, one at the back of the barn and one at the front.
The clocks don’t have numbers. They don’t show exact time. They are intended to show relative time between them. Look at the clocks on the pole. If you have set the pole as the observer’s reference frame, the hands on both clocks are straight up. All clocks in an observer’s reference frame always read the same time. But the hands on the barn clocks are not straight up and they do not agree. The time in a reference frame moving with respect to an observer depends upon the clock’s position in and the velocity of that reference frame. In particular, notice that the reading on the clock at the front of the barn trails the reading on the clock at the back. Run the simulation until the barn hits the pole and the simulation pauses by itself. Notice that the two clocks on the barn have been running at half the rate of the two on the pole. Moving clocks run slow. Since the two barn clocks have been running at the same rate, they have maintained their difference in reading with respect to each other.
When the massage appears and the simulation pauses, it means that the pole has hit the sensor at the back wall of the barn and the sensor has told the barn door to close. But the sensor says close at the time as indicated by the clock on the back wall. That is not the time for the front of the barn and the door. The door will close when the time at the front of the barn reads what is currently the time for the back wall. Make a note of the position of the clock hand at the back wall then click Continue to resume the simulation. Watch the clock at the front of the barn and notice that the door does indeed begin to close when the clock at the front of the barn reads the noted time. The pole has cleared the barn entrance and the door closes successfully. Length Contraction, Time Dilation and Relativity of Simultaneity combine to produce consistent results for observers in both reference frames.
The pole and the barn are sized such that the relative velocity of 259,600,000 meters/second between them will demonstrate the resolution of the Pole in the Barn Paradox. This program allows you to change the size or initial velocity of any object but you must be in the default reference frame to do so. Click Reset and Reset Navigation. Switch back to the default reference frame. Then go back to the properties tab for the pole. Increase the velocity in the x-direction to 2.8. (Note: When you change position or velocity parameters you must click the Apply Changes button at the top of the page.)
Return to the simulation and switch reference frames to the pole. Now the barn is even more contracted. You might instinctively think that this change will result in the door failing to close. Try it. (You may have to click the Right button some to see the closing.) The door closes with room to spare.
To better understand why, click Reset and switch back to the default reference frame. (Click Reset Navigation too.) Now the pole is the highly contracted object.
Run the simulation. Note how easily the highly contracted pole clears the front of the barn before the door starts to close.
Click Reset and go to the properties tab for the Pole. Set the velocity of the pole to 2.3 in the x-direction. Make sure to click the Apply Changes button.
Then return to the simulation. Switch reference frames to that of the pole. Now, with the reference frame set as the pole, the barn is deeper.
Yet, when you run the simulation, the door catches a piece of the pole and jams.
Click Reset and switch back to the default reference frame. Note how the not so contracted pole cannot clear the front of the barn before the door closes.
Go back to the properties for the pole. On the upper left side is a dimensions table. The default length of the pole is 80,000,000meters. Try making the length of the pole longer or shorter and rerun the simulation. In all these cases, whether the door closes successfully or not, the behavior observed from either the pole or the barn should always be consistent for a given relative velocity and dimension.