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The twin paradox is the following: if there are two twins on Earth, let's call them A and B, and B flies away and comes back at nearly the speed of light, then A has aged more than B. This occurs in A's reference frame. The paradox comes in to play when you look at the exact same situation in B's frame of reference. In this case, B sees A travel away at nearly the speed of light and come back, so therefore one would think that B would have aged more than A in B's reference frame. Relativity states that all inertial reference frames of a given situation produce the same result, yet by switching frames of reference for the above problem we get two different results, A being older in one and B being older in the other.

This paradox is resolvable, however, through the use of general relativity, as opposed to just special relativity, in the following way: For both twins to start out stationary and then have only one of them go away and come back, only one of them could have actually been acted upon by an applied force; in fact, three applied forces: one to get going, one to turn around, and one to stop. Let's say B is the twin who was acted upon by these forces. Special relativity, then, is sufficient to explain the above result in A's reference frame, since no applied force acted upon A, and A remained stationary. Special relativity is not sufficient to explain the above result from B's reference frame, however, since B was the one who had the forces acted upon them, yet A was the one to move.

General relativity gets around this problem by introducing the concept that any result obtained from a measurement made by a uniformly accelerating observer in the absence of a gravitational field, is equivalent to that of a stationary observer in the presence of a uniform gravitational field. By setting twin B stationary and introducing homogeneous gravitational fields that result in twin A's acceleration away from B, the acceleration necessary to turn A around, and the acceleration necessary to stop A when they get back, the calculation for the difference in how much each twin aged results in what we had initially found from above; that twin A has still aged more than twin B.

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Q: What is the twin paradox?
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Is the twin paradox possible if the space twin was in an inertial frames of reference?

No, if both persons are in inertial frames of reference the situation is completely symmetric so the 'paradox' does not occur. Also note that it is not really a paradox because general relativity has a conclusive answer to what happens to the twins. It is; however, not possible to set up a twin paradox-like situation with neither twin never leaving an inertial frame. This is because if they want to move apart, and come back again, they need to accelerate somehow, and the act of acceleration causes you to leave an inertial frame.


What is the difference between twin paradox and gravitational time dilation?

The twin paradox is a scenario in special relativity where one twin travels through space at high speeds and ages less than the other twin who stays on Earth. Gravitational time dilation, on the other hand, is the effect of gravity on the passage of time, causing time to run slower in stronger gravitational fields. The twin paradox is related to relative motion, while gravitational time dilation is related to differences in gravitational potential.


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