Relativistic Compressor Paradox

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Discussion Overview

The discussion revolves around a thought experiment involving a relativistic train in a circular tunnel and the implications of accelerating and decelerating the train on air pressure and energy conservation. It explores concepts of relativistic effects, energy transfer, and the paradox of obtaining compressed air seemingly "for free." The scope includes theoretical physics and conceptual reasoning.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant describes a scenario where a train accelerates to 0.86 c, compressing air in a tunnel and resulting in increased pressure, suggesting this leads to "free" compressed air.
  • Another participant counters that stopping the train requires energy for deceleration, which must account for the energy used in compressing the air, asserting that energy is conserved.
  • A further elaboration introduces a scenario with a longer train and discusses the implications of stress energy during deceleration, suggesting that the rest mass of the trains changes during this process.
  • One participant warns against the idea of perpetual motion machines, emphasizing that such concepts are not permissible within the laws of physics.

Areas of Agreement / Disagreement

Participants express disagreement regarding the notion of obtaining compressed air for free and the implications of energy conservation. There is no consensus on the interpretations of energy changes during acceleration and deceleration.

Contextual Notes

Participants reference relativistic effects and energy conservation without fully resolving the mathematical implications or the specifics of the energy transformations involved. The discussion remains open to interpretation regarding the behavior of mass and energy in relativistic contexts.

jartsa
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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.
 
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jartsa said:
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.
 
PeterDonis said:
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. :confused:
 
jartsa said:
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.
 

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