Time dilation when considering an object moving between two observers Consider a space ship moving from Earth to a star. If the star is in the same frame as the earth, then from the spaceship’s perspective wouldn’t both clocks on the Earth and the star have the same reading? Even if the space ship entered the star’s frame, which the example says doesn’t happen, then won’t it also have entered the Earth’s frame; since the Earth and the star are in the same frame of reference?
How can it be that the time discrepancy from Earth to spaceship and space ship to earth is same?
 A: If I reply as a physicist than I will say that your question doesn't make any sense. Cause, past, present and future exists simultaneously.
$$t = \frac{t`}{\sqrt{1-\frac{c^2}{v^2}}}$$
You can put those values inside above equation than you will get your answer.
Suppose, we(you and me) are twin I am inside earth you are traveling away.And, your average velocity is 0.4c. You came back to me after 30 years. Now, I wanna calculate your age.
$$t = \frac{30years}{\sqrt{1-\frac{c^2}{(0.4c)^2}}}$$
A: You are confusing yourself by thinking you "enter" frames, as if you visit them. A frame is a fictitious box you draw. Drawing it around a star and Earth is quite a big one, but it still works for theoretical discussions. But you never "go out" and "revisit" the frame. In this case the spaceship's frame is just a different one, where the clock on the star and Earth will nearly always have different readings. The ship's acceleration can influence the difference between these readings.
The only frame for which a clock on the star and a clock on Earth generally show the same reading, is a photon's, that travels at c. It "sees" both of these at the same time.
For all other frames, there are very limited points in time and space where information from these two clocks will show the same reading at the same time in that frame.
A: You should read about the relativity of simultaneity, as it is the cause of time dilation and length contraction, as well being the resolution of most of the so called paradoxes of SR. I will try to summarise it conceptually as follows...
If you and I are moving relative to each other, we don't share a common time axis. Instead your time axis is tilted relative to mine. That means that a plane of constant time in your reference frame is a sloping slice through time in mine, the slope being upwards in your direction of travel. Along your line of motion, all of the clocks in my frame will appear out of synch to you. In the direction you are heading, my clocks seem to be progressively ahead in time, while in the opposite direction my clocks are progressively behind in time.
It is that effect that causes time dilation.
Imagine you are walking down a corridor, and every ten seconds you pass another clock on the wall. If each clock you pass is set a second ahead of the previous one, you will get the impression that your watch is running slow, losing one second every ten seconds. In other words, you will think you are time dilated, because the time on your watch is falling further and further behind the times shown on the clocks you pass. That is not because your watch really is running slower, but because the clocks you pass are ticking at the same rate as your watch but are out of synch with your time.
The same effect happens in SR.
In the example you give, when you begin your journey, the time 'now' on the distant star in the Earth's frame is the same as the time 'now' on Earth. But that is not true in your frame. 'Now' on the distant star in your frame is several years later than 'now' on the distant star in the Earth's frame, and it is that effect which causes time dilation.
