Originally posted by dehammer:
please explain this to me. a pair of twins get separated, one going to alpha century in a space ship. the other staying on earth.
according to what you wrote the one in the space ship will see that the person that stayed on earth is slowing down. that means that after he makes the round trip from alpha century at 3/4 light speed (about 10 years). his brother who stayed on earth will only be 4 years older while he the brother that went on the trip will be 10 years older.
the person that sees his brother leave in the space ship will see his brother slow down, and will only age about 4 years in the 10 years it takes the ship to get back.
please explain, there are only two of them. how can they both see the other not age, while they do.
Where you are going wrong here, and don't worry you are in good company (Both Sir Martin Rees the Astronomer Royal and Kip Thorne a highly respected theoretical physicist have made the same mistake in books they have written), is to think that the time dilation you observe in the framework moving with a speed v relative to you is also valid within that framework. It is not, it is only valid within your framework. Similarly owing to symmetry a person in the framework moving with a speed v relative to you will see YOU moving with a speed v relative to him. Thus he will see your time running slower relative to his time. In fact time runs at the same rate (the proper time) within both reference frames. This must be so because both reference frames are equivalent for any physical experiment; for example, the decay time of a radioactive isotope must be the same in both reference frames; although if you measure the decay time of isotopes moving relative to you, you will measure a longer time. This is why in special relativity you have a paradox. This problem can only be addressed by general relativity. The fact is that the actual times that elapsed can only be compared by coordinating the twin's clocks just before the one leaves, and then comparing them again when the twin returns. The twin that accelerated the most in the process of leaving and returning will be the youngest because gravity and acceleration are the only factors that can affect the actual clockrate.
