- #1
ShreyasR
- 88
- 2
The first thing we learn in relativity is that what we measure is relative motion, i.e., with respect to a particular frame of reference. The values of position, velocity, acceleration differs with the frame of reference chosen.
When we go on, we come across time dilation. The theory mentions that "a moving clock(1) tics slower than a clock(2) at rest". The terms "moving" and "rest" actually creates a lot of ambiguity.
Even if it is mentioned that this is explained with respect to the frame of reference in which the clock(2) is fixed at the origin of a coordinate system taken as the reference, and clock(1) is moving, clock(1) ticks slower than clock(2).
Using this, the "Twin paradox" is explained.
"Consider a pair of twins "A" and "B"(age 20). Let "B" blast off in a spaceship on Jan 1st 2013, moving at about 2.8x10^8 m/s, close to the speed of light, and return to Earth on Jan 1st 2023. The observations of "A" are:
"B" is in the spaceship.
"B" and spaceship are moving away at 2.8x10^8 m/s.
"B"'s clock ticks slower.
After "B" returns to the earth, "A" would be physically 30 years old, and "B" would physically be about 21 years. In other words, To "A", it seems that "B" is 9 years younger. In this situation, obviously, it should appear to "B" that "A" is 9 years older than "B".
If the same theory is explained with a frame of reference in which the spaceship of "B" is taken as the origin (B is at rest), the observations are:
"A" is on the earth.
"A" and Earth are moving away at 2.8x10^8 m/s.
"A"'s clock is ticking slower,
And hence, after "B" returns to the earth, "B" would be physically 30 years old, and "A" would physically be about 21 years. In other words, To "B", it must seem that "A" is 9 years younger. In this situation, obviously, it should appear to "A" that "B" is 9 years older than "B".
The theoretical results obtained from the first case is exactly opposite to that of the second case.
Now my question is, as the theory of relativity itself is quite ambiguous, have I not understood it properly, or is there something wrong with this twin paradox?
If there is something wrong with my explanation, please correct it line by line.
When we go on, we come across time dilation. The theory mentions that "a moving clock(1) tics slower than a clock(2) at rest". The terms "moving" and "rest" actually creates a lot of ambiguity.
Even if it is mentioned that this is explained with respect to the frame of reference in which the clock(2) is fixed at the origin of a coordinate system taken as the reference, and clock(1) is moving, clock(1) ticks slower than clock(2).
Using this, the "Twin paradox" is explained.
"Consider a pair of twins "A" and "B"(age 20). Let "B" blast off in a spaceship on Jan 1st 2013, moving at about 2.8x10^8 m/s, close to the speed of light, and return to Earth on Jan 1st 2023. The observations of "A" are:
"B" is in the spaceship.
"B" and spaceship are moving away at 2.8x10^8 m/s.
"B"'s clock ticks slower.
After "B" returns to the earth, "A" would be physically 30 years old, and "B" would physically be about 21 years. In other words, To "A", it seems that "B" is 9 years younger. In this situation, obviously, it should appear to "B" that "A" is 9 years older than "B".
If the same theory is explained with a frame of reference in which the spaceship of "B" is taken as the origin (B is at rest), the observations are:
"A" is on the earth.
"A" and Earth are moving away at 2.8x10^8 m/s.
"A"'s clock is ticking slower,
And hence, after "B" returns to the earth, "B" would be physically 30 years old, and "A" would physically be about 21 years. In other words, To "B", it must seem that "A" is 9 years younger. In this situation, obviously, it should appear to "A" that "B" is 9 years older than "B".
The theoretical results obtained from the first case is exactly opposite to that of the second case.
Now my question is, as the theory of relativity itself is quite ambiguous, have I not understood it properly, or is there something wrong with this twin paradox?
If there is something wrong with my explanation, please correct it line by line.