# Special Relativity Train Scenario

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.!

## Answers and Replies

Related Special and General Relativity News on Phys.org
PeterDonis
Mentor
2019 Award
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.

kasha
Nugatory
Mentor
You may want to google for "pole-barn paradox" - the path you're on is going to take you there pretty quickly.

kasha
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

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