Physics/Seeming paradox in special relativity
You were skipping my question, i didn't ask a homework question, it is a paradox in relativity
"Suppose an object "O" is travelling towards me at 90%
speed of light which is placed at 1hr c away, then how
much time in "MY Clock" would it take to reach me?
I calculated it to be 1hr and 6 mts, am i right?
But on the other hand I'm the once who is moving
towards the object so by time dilation I'll reach there in
26.16mts, which one is the correct answer?"
Three things you need to be aware of:
1) The intro you read should be clear: "Please do not waste your time by asking a question that comes out of ANY kind of academic, professional, or business matters."
2) What you read as you typed out your question should also be clear: 'If I conclude the question involves any of these; I simply click "I believe this is a homework question." This will occur even if the question is not homework, or even if you are not a student'.
I had hoped these statements would make it clear to people what types of questions I will or will not answer. If there were a button for me to push that said, "I believe this question involves academic, professional, or business work"; I would have pressed that button. Unfortunately, the only button I have is "I believe this is a homework question."
2) When I make a decision on whether or not a question involves academic or professional work, I use what I call the "Duck Test." Namely, "If it looks like a duck, walks like a duck, and quacks like a duck; I don't care how much you insist it's a horse, I'm going to conclude it's a duck." To me, "Which one is the correct answer?", along with exact numbers you gave in your question, is pretty much saying, "I need to make a choice between these two numbers." I conclude this is VERY unlikely to be anything but something you need to know for some kind of academic work.
However, I'll give you the benefit of the doubt, and resolve the paradox. By waiting several days to do so, I've removed any help this gives to you if it is academic work, but done you not one bit of harm if it isn't.
You have two observers, approaching each other at a constant rate of 90% of the speed of light. They've synchronized their clocks such that, when they are one light-hour apart from each other, it is time zero.
Because NEITHER of these observers can claim to be at rest in an absolute frame, EACH of them views THEMSELVES as at rest, with the other moving towards them at .9c Thus, BOTH of them will measure the time as 66 minutes when they reach the other. However (and this is the resolution of the paradox), each will ALSO see the OTHER observer's clocks as having expended about 26 minutes of time. Please note that the clock in the other frame will not "seem" or "appear" to be running more slowly, each of them WILL BE running more slowly. Thus, neither observer can know if s/he is standing still and the other observer is moving, or vice versa, or if they are both moving at .45c, or any other combination -- all they can know is that the two frames are approaching each other at .9c
So, bizarre as it may sound, BOTH answers are correct. You will see 66 minutes expended on YOUR clock, but you will only see 26 minutes expended on the other person's clock.