Gaining a Better Understanding of Special Relativity

[Al68]

He says that in the case of the twin paradox,we can tell which person is moving,as opposed to other situations in SR where due to relative uniform motion,we can't tell which person is moving and which isn't---but this is again,not due to any breach of the laws of SR,but it is due to a common sense explanation,that a massive nonliving object like a star can't move all of a sudden. If we lacked this common sense,or if the star had the capability to move,like a giant living object,we could not have told who actually is moving.

Every star in the sky is "moving". Unless you mean "accelerating" instead of moving. In that case, of course an observer could tell if he accelerated even if he couldn't feel it (because he was a robot with no accelerometer, for example) because his change of motion would be relative to not just one star, but every star in the universe. He could tell he wasn't at rest in an inertial frame because every other object in the universe would have accelerated (relative to him) with no force acting on them.

 

[JesseM]

I was actually assuming the ideal case where the acceleration is instantaneous and its perception is negligible.

Even if we assume non-ideal accelerometers which can't detect this, you could detect the acceleration in other ways. Suppose in the middle of a rocket you let go of a ball, and since everything inside is weightless the ball just hangs there, not moving closer to any of the walls (from the perspective of a frame where the rocket is moving, the ball is moving inertially with the same velocity). But now if the rocket instantaneously accelerates, since no part of it is in contact with the ball the acceleration is not imparted to the ball, so the ball continues to move inertially at the same velocity as before, meaning from the perspective of an observer in the rocket the ball has suddenly stopped being at rest relative to the walls and is now moving towards one of the walls at great speed.

What do you think of the rest of the explanation--do you approve of it?

Looks fine to me.

 

[Urmi Roy]

Even if we assume non-ideal accelerometers which can't detect this, you could detect the acceleration in other ways. Suppose in the middle of a rocket you let go of a ball, and since everything inside is weightless the ball just hangs there, not moving closer to any of the walls (from the perspective of a frame where the rocket is moving, the ball is moving inertially with the same velocity). But now if the rocket instantaneously accelerates, since no part of it is in contact with the ball the acceleration is not imparted to the ball, so the ball continues to move inertially at the same velocity as before, meaning from the perspective of an observer in the rocket the ball has suddenly stopped being at rest relative towards the walls and is now moving towards one of the walls at great speed.

Hmm...It seems that if we analyse with a little bit of logic,there may be loads of ways to detect acceleration! Thanks for this particular idea.

Looks fine to me.

I'm really grateful,it's a big load off my mind,now!

 

[Urmi Roy]

Sorry to bother you all with this thread after a long time,but I have some small,but essential points to clear up...

1.Is it that in the real world a velocity of greater than 'c' is not attainable or any velocity greater than or equal to c is not attainable?

2. Since the lorentz contraction factor depends on the square of the ratio of the relative velocity by the velocity of light,is the magnitude of length contraction independant of the direction of relative motion?

3. In the formula for the addition of velocities,the lorentz factor(gamma) cancels out--does this imply anything very important?
(I mean the formulae derived in the page http://theory.uwinnipeg.ca/mod_tech/node137.html)