How Does Jane Receive 30 Messages from Dick in the Twin Paradox Scenario?

[bilkul_king]

hey...please answer my qustion

can someone please solve this paradox related to the twin paradox??
jane continues to be on Earth and dick goes to a planet 20 light years away at a speed of 0.8 c. Every year dick sends a message to Jane. Now for Jane due to time dilation the time taken by dick to reach the planet is 25 years and back to Earth another 25 years. Also the frequency the Jane receive the messages while dick is receding away should be equal to one message per three years and while he is coming back it should be equal to three messages per year. Now to due to length contraction dick feels that he is twelve light year away from the planet. Hence he should take 15 years to reach the planet and 15 years back to earth. That means he has sent out a total of 30 messages. Please explain tome how Jane receives these 30 messages.


I DIDN'T GET THAT.see
1) according to dick, while he receding for the 15 years he gets five messages in total in 15 yrs @ 1 msg per 3 yr
and while coming back he is receiving 3 messages per year and for 15 yrs, he will receive 45 messages
that mean a total of 50 messages which is same as the number of messages sent out by jane in 50 yrs wrt earth.


2)
now if i perform the same calculations on jane, she should get 25*(1/3) messages from dick while he is receding and 25*3 messages while he is coming back.
but that does not amount to a total of 30 messages sent out by dean.


PLZ PLZ PLZ PERFORM THESE CALCULATIONS FOR ME HERE.

AND IN A BOOK WHERE I FOUND THE QUESTION IS FOUND IT PUT AS:--

receding 25*(1/3)

because the planet is 20 lght yrs away jane on Earth continues to receive dick's msgs @ 1/3 per year FOR TWETY more years.

PLZ EXPLAIN HOW THIS STATEMENT IS VALID...

 

[OlderDan]

The calculation in #2 is not correct. Jane receives 15 messages that Dick sent while he was receding, but she does not receive all those messages while Dick is receding. He is on the way home before she receives most of them. It takes 45 years of her time to receive the first 15 messages coming to her at the rate of one every three years, and then another 5 years to receive the last 15 messges coming to her at the rate of 3 per year.

 

[bcoats]

space-time diagram

Drawing a space-time diagram should help improve your understanding. I drew one as a quick example...in Paint, so please excuse the crudity. The traveler is moving at v=.8c. Earth is sending one signal every year. The dotted lines represent the signals from earth, except from the line through the origin which simply represents the line x=ct, to which the others should be parallel and equidistant. The solid lines represent the traveler's path to a fixed point 4ly away from earth, and back. You can see how he will receive only one on the journey out, then the other eight on the way back. Likewise, you can draw lines for the signals being sent out by the traveler (perpendicular to his path), and visualize the rate at which the Earth receives the signals.