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Assume that we have a long Born-rigid rod with a length $L_0$ in which the speed of light is the ultimate speed for sending information. If there is a tiny missile at the right end of the missile that exerts an infinite force on the rod to move it to a significant portion of the speed of light in no time, what would be rod's left end speed?!

Indeed, when the missile is fired, the left end has not been noticed yet that the far right end of the rod has moved till a signal reaches the left one after a long time of $L_0/c$. During this time, the lab observer confirms that the rod has extremely been stretched. On the other hand, special relativity predicts that the rod should be Lorentz contracted from the perspective of the lab observer after the signal of motion reaches the left end becoming very short in length. In this case, the lab observer confirms that the left end must travel FTL even with an infinite velocity to reach close to the far right end with a tiny Lorentz contracted distance between. Where is the problem?!

Qmechanic
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Mohammad Javanshiry
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1 Answers1

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Assume that we have a long Born-rigid rod with a length 0 ... Where is the problem?!

The problem is right in the beginning. There is no such thing as a Born-rigid rod, there is only Born-rigid motion.

Even a rod made of unobtanium cannot move in Born rigid motion by being pushed on one end. However, even a rod made of jell-o can have Born-rigid motion if it is accelerated uniformly at every point along the rod. In fact, I find that often in relativity problems it is best to think of all materials as being made of jell-o.

So for your post, to make a Born rigid motion you cannot have merely one missile on the end, but rather an array of missles all along the rod whose engines are synchronized in advance to all fire at the proper time.

BioPhysicist
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Dale
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