Relativistic Compressor Paradox

[jartsa]

Relativistic compressor "paradox"

Let's say we have a metro tunnel that is a circular loop with 1 m x 1 m rectangular cross section. The tunnel is 100 m long. There's a 50 m long train in the tunnel, the train fits snuggly in the tunnel. And there's air in the tunnel, at 1 atm pressure, and there are air channels connecting the tunnel to the athmosphere.

The train accelerates from 0 to 0.86 c, and becomes 25 m long, and 25 cubic meters of air is sucked into the tunnel through the air channels.

Now we plug the air channels and stop the train smoothly, the train becomes 50 m long, and air pressure increases in the tunnel, pressure will be 1.5 atm at the end.

What we did there was: We accelerated a train and some air to 0.86 c, then we decelerated the train and the air to zero velocity. AND we produced some compressed air.

So the problem is that compressed air that we got for free.

 

[PeterDonis]

So the problem is that compressed air that we got for free.

You didn't get it for free. Stopping the train requires deceleration just as starting it requires acceleration. That deceleration has to be produced using some energy source. Because the deceleration is also compressing air, it will require more energy than the acceleration did. Energy is still conserved.

 

[jartsa]

You didn't get it for free. Stopping the train requires deceleration just as starting it requires acceleration. That deceleration has to be produced using some energy source. Because the deceleration is also compressing air, it will require more energy than the acceleration did. Energy is still conserved.

Okay. Now let there be a 100 m long train in a 100 m long circular tunnel. Again we accelerate the train to 0.86 c, which makes the train 50 m long.

Then we build a train into the 50 m of empty tunnel space, we might use lego bricks to build the train. The lego bricks may be stored in the first train.

Then it's time to stop the trains. The trains at zero velocity and near zero velocity will have larger rest mass than the original trains, because of the stress energy. So deceleration from 10 km/t to zero releases more energy than acceleration from zero to 10 km/t took.

At some time during the deceleration the trains must have smaller rest masses compared to the original trains, I guess.

 

[Dale]

So deceleration from 10 km/t to zero releases more energy than acceleration from zero to 10 km/t took.

Perpetual motion machines are banned by the rules of PF and the rules of the universe.