Special Relativity Train Scenario

In summary, the engineer who built the tunnel saves money by constructing a shorter tunnel that still encompasses the full length of the train when the train moves at relativistic speeds.
  • #1
kasha
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Assume there is an engineer who built a tunnel, tunnel length is 10m, and we have a train its length is also 10m...so the tunnel can encompasses the entire length of the train.

But if we assume that train is a light express train, it always comes through the tunnel at relativistic speed, let's say train speed = 0.8c, relative to the observing engineer.
So the civil engineer who built the tunnel, watches the train gets shorter due to special relativity (Train length relative to the standing engineer is 5m).

Does it make sense to say: since the train crosses the tunnel at relativistic speed close to the speed of light, so the engineer can build a shorter tunnel (length 5m) and tunnel can still encompasses the full length of the train?!? Engineer has saved money on the lower cost shorter tunnel.!
 
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  • #2
If the only constraint on the tunnel length is that the entire train has to fit into the tunnel at some instant of time in the tunnel's rest frame, then yes, the tunnel could be built shorter if the train were guaranteed to be moving at relativistic speed. However, I don't see how any actual tunnel would have this as its only constraint. Tunnel lengths are determined by what must be tunneled through, not by what's going to be passing through the tunnel.
 
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  • #3
You may want to google for "pole-barn paradox" - the path you're on is going to take you there pretty quickly.
 
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  • #4
PeterDonis said:
If the only constraint on the tunnel length is that the entire train has to fit into the tunnel at some instant of time in the tunnel's rest frame, then yes, the tunnel could be built shorter if the train were guaranteed to be moving at relativistic speed. However, I don't see how any actual tunnel would have this as its only constraint. Tunnel lengths are determined by what must be tunneled through, not by what's going to be passing through the tunnel.

You are right...there is no actual implementation of my scenario. Tunnel Height is more realistic constrain than the tunnel length. but couldn't come up with a scenario that would utilize the Tunnel Height, because the tunnel height would be unchanged relative to the train operator since the train moves on the x-axis whereas the tunnel's height is y-axis.

Thanks a lot
 
  • #5
Nugatory said:
You may want to google for "pole-barn paradox" - the path you're on is going to take you there pretty quickly.

Oh wow...never heard of that paradox, but that makes much more sense than by training fitting in a tunnel :-)

Got all the answers I was looking for: http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/polebarn.html

Many Thanks
 

1. What is the "Special Relativity Train Scenario"?

The Special Relativity Train Scenario is a thought experiment used to illustrate the principles of special relativity, a theory in physics that describes the relationship between space and time. In this scenario, a train is traveling at a high speed relative to an observer on the ground, and the observer observes certain phenomena that appear to violate common sense or classical laws of physics.

2. What is the significance of the Special Relativity Train Scenario?

The Special Relativity Train Scenario is significant because it helps us to understand the principles of special relativity, which have been confirmed by numerous experiments and are essential to our understanding of the universe. It also challenges our intuitive understanding of space and time, and shows us that there are certain phenomena that can only be explained by special relativity.

3. What are some key concepts to understand in the Special Relativity Train Scenario?

Some key concepts to understand in the Special Relativity Train Scenario include time dilation, length contraction, and the relativity of simultaneity. Time dilation refers to the phenomenon where time appears to pass slower for objects moving at high speeds, while length contraction refers to the shortening of objects in the direction of motion. The relativity of simultaneity refers to the idea that events that appear simultaneous to one observer may not appear simultaneous to another observer in a different frame of reference.

4. How does the Special Relativity Train Scenario relate to Einstein's theory of special relativity?

The Special Relativity Train Scenario is a thought experiment that was first proposed by Albert Einstein in his theory of special relativity. The scenario helps to illustrate the key principles of this theory, including the constancy of the speed of light, the relativity of simultaneity, and the concept of time dilation and length contraction.

5. Are there any real-world applications of the Special Relativity Train Scenario?

Yes, there are several real-world applications of the Special Relativity Train Scenario. One example is the Global Positioning System (GPS), which relies on the principles of special relativity to accurately calculate and account for the time dilation effects of satellites moving at high speeds. Special relativity also plays a crucial role in particle accelerators and in the development of technologies such as nuclear power and nuclear weapons.

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