The Villain's Fate: Alive or Dead?

[Adam Lewis]

Hi, I brought this up in physics class a while ago but didn't get a very satisfactory response...

A train moving at some ridiculous velocity near that of light is watched by two observers. The first is a circa 1885 villain who twiddles his moustache nefariously from aboard the train (and in its reference frame). The second is a member of the Secret Service, sent to stop the villain. Unfortunately for Great Brittania, she has arrived too late, and can only watch helplessly from Earth's reference frame as the train zips by.

The villain's evil plot is to destroy the train, thus killing himself and destroying vital documents implicating the organization he is a member of in various crimes. He plans to do this by simultaneously detonating two bombs. Each bomb is on a different face of the train, but at opposite ends, as pictured (the exclamation points are bombs, the asterixes train).

_________________ !
--------------------******************----------------------------------------
__________________*______(villain)______*
---------------------******************----------------------------------------
_____________________________________!

_________________________(agent)Now, the effect of detonating a single one of these bombs ought to be to rotate and derail the train. However, given that the bombs are of exactly equal power, it is feasible to imagine that if both were detonated at the same time, the rotations would cancel out and the train would not derail.

Suppose, then, that the villain explodes the bombs at the exact moment when the bombs are horizontally equidistant with respect to the agent. In that case, the villain ought to witness simultaneous explosions, so the train will not derail and he will not die. The agent, however, should see one bomb detonate before the other, resulting in a very derailed train with a very dead villain on top. Is the villain alive or dead?

 

[Dale]

The experiment is poorly specified. How fast does the shockwave from each bomb travel? How long after the arrival of the first shockwave does it derail unless the second shockwave arrives?

Once you specify the problem fully you will find that both frames agree on the outcome.

 

[DocZaius]

If I understand the question correctly, it relies on disagreement of simultaneity possibly leading to an observer seeing something looking to be physically impossible.



The train paradox is another example of simultaneity disagreement at first seeming to imply logical inconsistencies but when looked at closely enough, remaining logically consistent.

 

[Fredrik]

Wouldn't these two bombs rotate the train the same way? The problem would make more sense if you e.g. had a bomb behind the train and one in front of the train (not on the sides). When the villain sets them off simultaneously in the train's frame, they cause the front of the train to slow down a bit and the back of the train to speed up a bit. Let's say there's a third bomb in the middle, connected to a speedometer, and that it's rigged to explode if its speed relative to the ground changes significantly.

In this version of the problem, the bomb in the middle will not explode. This is obvious when you consider what's going on in the train's frame. In the ground frame however, the bomb at the rear explodes first. So doesn't the shock wave from the rear reach the middle of the train first? It would if it had the same speed in the ground frame as the shock wave from the bomb at the front, but we have to do relativistic addition of velocities to find out what the speeds are. If the speed of the shock waves in the train's frame is u, then their speeds in the ground frame are (u+v)/(1+uv/c²) and (u-v)/(1-uv/c²), where v is the train's velocity. These speeds are not the same.

 

[tiny-tim]

The agent, however, should see one bomb detonate before the other, resulting in a very derailed train with a very dead villain on top. Is the villain alive or dead?

Yes, he does see one bomb detonate before the other - but he also sees the agent, still nefariously twiddling his moustache, very cleverly moving at almost the speed of light away from the earlier detonation and towards the later detonation so as to be exactly at the point where the two detonations meet!

Hey - why does the bad guy have to win? Couldn't you have put the agent on the ground, villainously watching as the Secret Service member, who has a PhD in the Lorentz-Fitzgerald contraction (so it would have to be 1889), cleverly cheats death, leaps off the train, and fells the villain from behind with one blow of his new-fangled lawn-tennis racquet, shouting "How's that for a secret service"?

God save the Queen!