The Barn Paradox and Superluminal Communication

Discussions of superluminal communication and the paradoxes raised therein always involved unsatisfying (to me) examples about space ships and Andromeda and impending doom, but it turns out that the (real) paradoxes raised by superluminal communication can be easily merged with the Barn Paradox.

The Barn Paradox

Assume an Olympic-level sprinter with a 20m pole that, through dint of great training, is able to run 80% of the speed of light. We have cunningly designed the doors of a 20m barn to register when the ends of the pole hits them. Label the front end of the pole Pf and the back end Pb, and the barn doors Bf and Bb.

From the sprinter’s point of view, the barn is length contracted and will only be 20m * 0.60 = 12 meters long, so the pole will not fit into the barn. The ordering of the events will be:

whereas from the barn’s point of view, the pole is length contracted to only 12m long and the ordering of the events is:

Note that the ordering of the events appears different in the different reference frames: to the pole vaulter, the front door of the barn closes after the back of the barn has been hit, whereas to a barn observer, the front door of the barn closes before the back of the barn has been hit.

A Murder Mystery

Let us say that we try and make a murder mystery of this (which, incidentally, is how this whole article came about). A villain has put the pole vaulter’s loved one at the back end of the barn and has cunningly designed a mechanism such that when the front door closes (i.e., Pb leaves Bf), a laser will fire at the back end of the barn. But there is one chance to save her: if the back end of the barn is touched (Pf touches Bb), then we shall put up an ablative shield to save the sprinter’s paramour.

Fortunately, she is untouched. From the barn’s point of view, the shield goes up at 25 (t*c) and she is hit by the laser only afterwards at 35 (t*c). From the pole vaulter’s point of view, the shield goes up at 15 (t*c) and she is hit by the laser at 37 (t*c).

Phew!

Superluminal Communication

But now postulate a fiendish device that is able to communicate instantly, bypassing speed of light limits. When the front door of the barn closes, we will send a signal to the back of the barn telling a bomb to go off. The bomb is only disarmed when the back of the barn is touched by the pole. What happens then?

From the pole vaulter’s point of view: the bomb is disarmed at 15 (t*c), so even though the bomb is triggered at 25 (t*c), our heroine is safe. However, from the barn’s point of view: the front door is closed, and the bomb triggered, at 15 (t*c), which is before the back of the barn is hit at 25 (t*c). Therefore, the heroine dies.

So, the addition of faster-than-light communication turns the (fake) Barn Paradox turns into a (real) Barn Bomb Paradox.

[1] Ladder Paradox (Wikipedia)
[2] The Pole-Barn Paradox

Discussion

Comments are moderated whenever I remember that I have a blog.

Anwar Shiekh | 2009-05-02 19:12:54

You are assuming instantaneous in each frame which would yield the ability to talk back in time; a possible resolution (no paradox) is that things are instantaneous in only one frame. The same problem appears in quantum theory with the instantaneous collapse of the wave-function.

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Anwar Shiekh | 2009-05-02 22:38:13

The pole and barn paradox can be taken a lot further, by racing a spring into the barn and trapping it. This maneuver converts a Lorentz contraction into a real compression and now one has energy in a compressed spring. This has many interesting consequences, including no man sized wormholes, no negative Casimir energy and even hints at the 1/r and r potentials of Nature's forces. Can. J. Phys., 70, 458, 1992 Concerning the possibility of a preferred frame where things are instantaneous http://arxiv.org/pdf/0901.1475

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