A short manual to the Twin Paradox applet
It is recommended to download the applet and execute it in a command prompt with
java -jar twinparadoxon.jar
If you work with a Windows OS, you can also start the twins application with a double click on the jar file.
Setting the parameters
You can choose two parameters to supervise the effects of the twin paradoxon. First you can set the acceleration of the rocket in terms of earth acceleration g. Maximum for acceleration is 1000g. Next you can set either the time of one journey phase or the distance to the return point. With a definite acceleration, the journey time and journey distance depend of each other and are calculated each time you press the "Set Time" or "Set Distance" button.
The input in the time panel determines the time of one phase of the journey. The hole journey consists of four equal time phases. The time panel offers three possibilities to choose a time:
- Scrollbar: Moving the scrollbar changes the time parameter immediately. The unit of the scrollbar is given in years.
- Multiple Textfields: This allows a "human" kind of setting the time in common units. Don't forget to press the "Set Time" button to validate your changes.
- Single Textfield: This field can be used to enter a time in an arbitrary unit (years, days, hours, minutes, seconds). Please choose first the unit and then change the parameter value. Don't forget to press the "Set Time" button to validate your changes.
You can choose the distance that the twin will reach (single direction). First, choose the unit to set the distance (Parsec, light years, light days, light hours, light minutes, light seconds, metres). Second choose the value of the distance parameter. Don't forget to press the "Set Distance" button to validate your changes.
The contents of the diagrams are explained in the paper.
You can zoom in a diagram by pressing the left mouse button while being over the diagram, holding it and hence selecting a rectangle by dragging the mouse. By releasing the mouse button the content of the rectangle will stretch to the size of the diagram. To reset the zoom, press the left button in the upper left corner of the diagram.
Save diagram as an image
You can save each diagram as an image of type png. For this purpose press the medium button in the upper left corner of the diagram
As the diagrams aren't analytical, but based on sampling points, you can have a look at the calculated sampling points by clicking on the right button in the upper left corner of each diagram. If you like, you can save the sampling points as a text file by clicking on the little diskette in the sampling points view. The unit of the sampling points shown in that view is the unit that is shown on the axes of the diagram.
Two short examples for the Twin Applet
Example 1: Setting acceleration and travel time
First, choose an acceleration of 1g (don't forget to press "Set g"), then set a travel phase of 5 years (which means a total travel time of 20 years). Use either the time slide bar or the textfields to enter traveltime. After pressing the "Set Time" button the maximum reachable distance is calculated and displayed in the associated textfield.
With a travel phase of 5 years and an acceleration of 1g, the twin reaches a maximum distance of 1.5757389644178752e18 m. The displayed unit of the distance and the time can be easily changed with the checkboxes.
Example2: Setting acceleration and distance
Again, choose first the acceleration (don't forget to press "Set g"), for example 2g. Then choose the distance that the twin shall travel. Therefor, choose first the unit of the distance, for example light years (ly) and then the distance in that unit. Let's say 1000 light years. Press the "Set Distance" button, to see that the twin needs 3 years, 255 days,... or 3.699598958682937 years to travel one phase. That means it takes him 7.399197917365874 years (two phases) to reach the maximum distance and 14.798395834731748 years (4 phases) to make a round trip.
All contents copyright © 2006, Thomas Müller, Andreas King, Daria Adis
All rights reserved.