Physics/Does relativistic effect of the space ship still exist if it is not accelerating?
Dear Mr. Raridon,
This question has bothered me for a long time. The famous "twin paradox" does not exist because only people on earth can make the relativistic prediction--- time dialation on spaceship, because earth is an inertial reference frame and the spaceship is not. But what will happen if the spaceship eventually stopping acceralating and flying at constant velocity close to speed of light? During this period the spaceship becomes an inertial reference frame again, can the space twin use the time dialation formula to calculate the earth time? Will the times for both earth and spaceship be same because they are both inertial reference frames now?
Looking forward to your explanation. Thanks for your time!
Here's the twin paradox.
Start with two people in the SAME inertial frame.
ACCELERATE* one of them, but not the other, away from that frame until it reaches near-light speed.
Turn around that second person -- in other words, ACCELERATE* it.
When that second person gets back to the original frame, have her DECELERATE* until she is again in the original inertial frame.
The "paradox" is that the second person will have AGED LESS than the person who never left the original frame.
Why does one of the original people age less than the other? Take a look at every word that has an asterisk after it. When one is in an accelerating frame, all the rules change! When one does the calculations rigorously, you get exactly the results noted above.
Your example is a somewhat different example: two accelerations (away from the Earth, and back towards the Earth) instead of three (no slowing down to land back on the Earth). Thus, there will be LESS difference in the age of the two people, but there will still be some.
The only difference is that, as each of them go past the other, EACH will measure the other person's clock as moving more slowly than their own, and by exactly the same amount. In other words, if BOTH are in an inertial, non-accelerating frame, then BOTH will see the exact same difference in the other frame.
However, the person whose clocks are behind the other (not just moving more slowly, but well behind the other), will be known as the person who changed velocity (ie, accelerated). This is a slight change from the usual twin paradox, but it gives the same (basic) results.