# Special Relativity: Train in Tunnel Paradox Solved

• I
• Agalal1
In summary, the conversation is about a person looking for examples and resources to learn about the classic train in a tunnel paradox from special relativity, but they are advised to specify their level of knowledge and research on their own before asking for help. The conversation also suggests searching for the "barn and pole paradox" and using specific numeric values to make the calculations easier.
Agalal1
Hello, I was wondering if anyone could set up and solve a classic train in a tunnel paradox from special relativity with unique values for multiple observers including time space diagrams. Thanks

That's not what PF is for. Once you've made an attempt at it we will provide help and feedback. But we aren't here to do your work for you.

Ibix said:
That's not what PF is for. Once you've made an attempt at it we will provide help and feedback. But we aren't here to do your work for you.
well i was hoping for different examples i can learn from, would be great if anyone can link me a pdf or a book with examples and answers with space time diagrams

Agalal1 said:
well i was hoping for different examples i can learn from, would be great if anyone can link me a pdf or a book with examples and answers with space time diagrams

You'd be better to post what level your physics and maths are and how you are currently learning SR. There are lots of textbooks out there and many threads of recommendations on here.

Agalal1 said:
classic train in a tunnel paradox from special relativity

Which is not an "A" level question. Thread level changed to "I".

Agalal1 said:
classic train in a tunnel paradox
You might also try searching via e.g. Google for "barn and pole paradox." I would be surprised if this does not find some numeric examples.

If you choose to measure distances in light-seconds and time in seconds the speed of light will come out to be 1. Now you can take the speed of the train to be ##\frac{4}{5}=.8## so the ##\gamma## factor will come out ##\frac{5}{3}## and the length of the train to be one light-second.

With these numeric values you'll find that the arithmetic comes out to be really easy.

## 1. What is the Special Relativity: Train in Tunnel Paradox?

The Special Relativity: Train in Tunnel Paradox is a thought experiment that illustrates the concepts of special relativity, which is a theory developed by Albert Einstein to explain the relationship between space and time. In this paradox, a train is moving at a high speed through a tunnel, and an observer outside the tunnel sees the train as shorter than it actually is. However, an observer inside the train sees the tunnel as shorter. This paradox raises questions about the relativity of space and time, and how they are perceived by different observers.

## 2. How is the Special Relativity: Train in Tunnel Paradox solved?

The paradox is solved by understanding the principles of special relativity. According to this theory, the perception of space and time is relative to the observer's frame of reference. In the case of the train in the tunnel paradox, both the observer outside the tunnel and the observer inside the train have different frames of reference, which leads to their different perceptions of the train and the tunnel. By taking into account the relative motion and the speed of light, the paradox can be resolved.

## 3. What is the role of the speed of light in the Special Relativity: Train in Tunnel Paradox?

The speed of light is a constant in the universe and is the same for all observers, regardless of their frame of reference. This means that no matter how fast an observer is moving, the speed of light will always be the same. In the paradox, the speed of light plays a crucial role in resolving the paradox because it helps to explain the different perceptions of the train and the tunnel by the observers.

## 4. How does the Special Relativity: Train in Tunnel Paradox relate to Einstein's theory of relativity?

The Special Relativity: Train in Tunnel Paradox is a thought experiment that illustrates the principles of special relativity, which is a part of Einstein's theory of relativity. This theory states that the laws of physics are the same for all observers, regardless of their relative motion. The paradox helps to demonstrate the concepts of time dilation and length contraction, which are fundamental principles of special relativity.

## 5. What are some real-world applications of the Special Relativity: Train in Tunnel Paradox?

The Special Relativity: Train in Tunnel Paradox has many real-world applications, especially in the field of modern physics. It is used to understand the behavior of particles at high speeds and to develop technologies such as GPS systems, which rely on the principles of special relativity to function accurately. The paradox also helps to explain the behavior of objects in space, such as the bending of light around massive objects like black holes.

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