Relativistic Fireworker: Exploding Rockets at V=C/2

[japam]

suppose an imaginary fireworker that launches rockets at a v=c/2 ( could be any velocity, but near light), and the rockets are programmed to explode at certain time T
according to relativity there must be a certain delay in the explosion seen from the fireworker frame , and he should see the explosion at T*(2/sqrt3), or also that means that the explosion really occurs ((2/sqrt3) -1) seconds after T

However he could reason also in this way: he knows the rocket has traveled during T*(2/sqrt3) at c/2 velocity, hence, multipliyng , the rocket is now at
c*T/sqrt3 meters from home, dividing this for c, he obtains that the explosion ocurred T/sqrt3 seconds after T

so, my question is, if there is something wrong in this argument and where?

 

[Valerie Park]

Yes, there is something wrong in this argument. The fireworker cannot reason in this way because the speed of light is not constant in all frames of reference. According to the theory of relativity, the speed of light is always the same in all inertial frames of reference. This means that the fireworker's frame of reference is moving relative to the rocket's frame of reference, and thus the velocity of light seen from the fireworker's frame is different than the velocity of light seen from the rocket's frame. Therefore, the fireworker cannot use the speed of light as a measure of distance traveled in his own frame of reference.

 

[sir-pinski]

Your reasoning is correct, and there is nothing wrong with your argument. The delay in the explosion seen from the fireworker's frame is due to the fact that the speed of light is constant in all frames of reference. This means that the rocket, which is traveling at a speed of c/2, will take longer to reach its destination (where it explodes) in the fireworker's frame compared to an observer who is stationary with respect to the rocket.

The time dilation effect, which is the basis of the fireworker's reasoning, is a consequence of the constancy of the speed of light. It is a fundamental principle of relativity and has been verified experimentally. Therefore, there is nothing wrong with your argument and it accurately describes the situation in the fireworker's frame.