The well known example that if you travel into space you'd gain let's say 5 years and people on earth 25 in the same time or so.
I just don't get it and I can't find any logic explanation.
For instance: Two twins who came to live exactly at the same moment in the year 2000 and both die on their 75th birthday at the same time. One travels into space, the other stays on earth. Earth-brother dies on earthyear 2075,space-brother dies in earthyear 3050 or so...
I know its Einstein's point but that just doesn't instantly make it correct to me.
The total velocity of our <x, y, z, t> vector will always be equal to the speed of light constant, c. You can think of something that has no physical movements as moving forward in time at the speed of light. As x, y, or z increases the magnitude of t will decrease so that the speed of light constant is always achieved.
Why this link has to hold is more complex and I cannot explain it well, but hopefully this gives some insight into time slowing as velocity increases.