Time Dilation & My paradox explained.

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I wanted to post this for my friends here to read. It is an e-mail exchange between my self and a Physics Professor at one of the major universities. (I have blanked his name to preserve his privacy.)

It goes to the issue of time dilation I posted earlier and it is obvious I overlooked something.

Following is the exchange in its entirety:

Dear Dr. _____:
] I have submitted the following scenario to several people in the field
] of Relativistic Study and as yet have received no answer for what
] appears to me to be a paradoxical situation in time dilation. It's a
] twist on the old "Twins" paradox but goes a bit further in a way the
] original does not address.
] Can you help?
] --
] An astronaut leaves Earth for a journey circling our solar system at a
] velocity significantly near enough the speed of light to cause a very
] noticeable dilation in time, relative to his counterparts on Earth. He
] makes many circumnavigations of the Sun and is always in view from Earth
] at least by telescope. He also has a telescope aboard and is always able
] to view the Earth. This does not have to be an orbital flight in the
] classic Newtonian sense as that would require a very large Solar orbit
] radius at said velocity. We can allow it to be if you wish however, if
] we stipulate that the telescopes are very powerful. Suffice to say that
] our astronaut has a powered craft such as Boussard Ramjet or any
] hypothetical propulsion method you choose that is capable of sustaining
] a lengthy journey. The only condition is that the astronaut is always
] directly visible from Earth and vice versa, and is travelling at near c
] velocities. It follows then that if he can observe the Earth, he can
] likewise observe the Sun.
] He returns to Earth after we have monitored his progress for, say, 50
] years. Due to time dilation, the journey only lasted 10 years for him
] however and his age reflects this.
] During this period, we obviously witnessed ourselves revolve around the
] Sun 50 times. How many revolutions of the Sun did our astronaut witness
] the Earth perform?

{The good Dr.'s response.}

That is an invariant answer, and all observers will agree. Now if you
want to DEFINE a year by the number of revolutions of the earth around
the sun, then by definition, he is 50 years old. However, if he takes a
clock with him ( and his own biology is a type of clock), then he will
find that for him, each orbit of the earth around the sun takes much
less that the 3X10^7 seconds that an earthbound observer will claim each
revolution takes. Since they take much less time, he can still fit 50 of
them into the 10 years that he is travelling.

] {Lee again}

] Regardless of the answer, how can this be?
] Even further, we were able to count the number of revolutions he made
] around the Sun. (Obviously a GREAT number at c during "our" 50 years.)
] How many did he count for HIMSELF, relatively speaking?

{The Dr.}

The same number. Again the length of time that each revolution took
would be different for him and for the earth bound observer.
End of exchange.

How easily we (I) forget the simple details when setting up a hypothetical scenario.

Well first let me say I am glad to see you are familer with the theory on the subject. I too have problems keeping Realitity in mind sometimes. Time dilation is for some reason harder for me to keep a mental hold on than say lenth contraction or relativity of simultanetiy. If you are formiluar with these very closly realated topics (he way the lenths of thing look different form two different veiwing fames)it may help to think back on them to get a grasp on time dilation whin you start to get lost in a complex situation. Anyway it works for me, it kind of gives me a solid place to organize my thoughts. Sorry about the spelling.