Twin Paradox: Difference between revisions
No edit summary |
No edit summary |
||
| Line 10: | Line 10: | ||
Here is how to think about the situation. Think about two twins who are exactly the same age, and consider the situation where one twin travels by spaceship to and from a planet a distance D away at a velocity (v). The twin traveling on the spaceship does not immediately have a velocity v, but has to accelerate. We could say the twin accelerates very quickly, and thus spends almost the entirety of the trip at a constant velocity. However, the twin who stays on the planet does not need to accelerate, because he is not leaving the planet. Of course, one could argue that according to the twin on the spaceship, the twin on Earth “appears” to be accelerating backwards, but in reality, the only observer who had to experience a force to accelerate was the one on the spaceship. As a result of the twin on the spaceship accelerating, this twin changed inertial reference frames, and thus is the twin who is actually in motion. This means we can apply the time dilation equation to the scenario of the twins, with t being the time for the round trip according to the twin on earth, and to being the time according to the twin on the spaceship. | Here is how to think about the situation. Think about two twins who are exactly the same age, and consider the situation where one twin travels by spaceship to and from a planet a distance D away at a velocity (v). The twin traveling on the spaceship does not immediately have a velocity v, but has to accelerate. We could say the twin accelerates very quickly, and thus spends almost the entirety of the trip at a constant velocity. However, the twin who stays on the planet does not need to accelerate, because he is not leaving the planet. Of course, one could argue that according to the twin on the spaceship, the twin on Earth “appears” to be accelerating backwards, but in reality, the only observer who had to experience a force to accelerate was the one on the spaceship. As a result of the twin on the spaceship accelerating, this twin changed inertial reference frames, and thus is the twin who is actually in motion. This means we can apply the time dilation equation to the scenario of the twins, with t being the time for the round trip according to the twin on earth, and to being the time according to the twin on the spaceship. | ||
<math>\Delta t = \frac{\Delta t}{2}</math> | <math>\Delta t = \frac{\Delta t}{\sqrt{1 - \frac{v^2}{c^2}}}</math> | ||
===A Computational Model=== | ===A Computational Model=== | ||
Revision as of 17:54, 28 October 2024
Chaz Sporrer Fall 2024
Short Description of Topic
The Main Idea
Special relativity has created the idea of time dilation, in which the clock of an observer in motion will move slower than the clock of the observer at rest relative to the object. However, in each observer`s inertial reference frame, it will appear that they are motionless and that it is really the other observer who is moving. This means that each observer will think that their clock is moving faster than that of the other observer. This creates a problem, because only one clock can truly move faster than the other. This problem is known as the twin paradox. Though it is called the twin paradox, it is not actually a paradox. Thus, one observer`s clocks does actually move faster than the other`s.
A Mathematical Model
Here is how to think about the situation. Think about two twins who are exactly the same age, and consider the situation where one twin travels by spaceship to and from a planet a distance D away at a velocity (v). The twin traveling on the spaceship does not immediately have a velocity v, but has to accelerate. We could say the twin accelerates very quickly, and thus spends almost the entirety of the trip at a constant velocity. However, the twin who stays on the planet does not need to accelerate, because he is not leaving the planet. Of course, one could argue that according to the twin on the spaceship, the twin on Earth “appears” to be accelerating backwards, but in reality, the only observer who had to experience a force to accelerate was the one on the spaceship. As a result of the twin on the spaceship accelerating, this twin changed inertial reference frames, and thus is the twin who is actually in motion. This means we can apply the time dilation equation to the scenario of the twins, with t being the time for the round trip according to the twin on earth, and to being the time according to the twin on the spaceship.
[math]\displaystyle{ \Delta t = \frac{\Delta t}{\sqrt{1 - \frac{v^2}{c^2}}} }[/math]
A Computational Model
How do we visualize or predict using this topic. Consider embedding some vpython code here Teach hands-on with GlowScript
Examples
Be sure to show all steps in your solution and include diagrams whenever possible
Simple
Middling
Difficult
Connectedness
- How is this topic connected to something that you are interested in?
- How is it connected to your major?
- Is there an interesting industrial application?
History
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.
See also
Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?
Further reading
Books, Articles or other print media on this topic
External links
Internet resources on this topic
References
This section contains the the references you used while writing this page