Relativity situation. Questions.

[hedons]

Situation:

You have a bomb which will detonate if the input sample on its trigger is of a certain mass (we'll call this the critical mass).

The trigger input sample has a mass equal to 99.99% of the critical mass.

A person takes this device on spaceship which begins to accellerate towards its top speed of 99.9% the speed of light.

Will the bomb detonate?

Thanks,
Glenn

 

[JesseM]

As long as you do not accelerate too quickly (which creates G-forces) then no, the trigger input sample doesn't change in its own rest frame. Remember, velocity is all relative anyway--even if the bomb is at rest on earth, it is already moving at 99.99% of light speed in some other frame. Also, it should be noted that many physicists don't like to use the concept of "relativistic mass" at all, instead just talking about rest mass (which never changes) and relativistic momentum--see Does mass change with velocity? from the Usenet Physics FAQ.

 

[Crosson]

The problem is in considering the mass measuring device (MMD). For someone in motion relative to the bomb, everything in the bomb frame (bomb and MMD) has a momentum equal to:

$$P = m v \gamma$$

So the momentum of everything in the bomb frame (relative to the moving frame) is increased by the same factor, so any device which measured mass based on collisions would operate exactly the same as it would in the bomb's rest frame.