Question Regarding the Twin Paradox

[Nitin Gupta]

Homework Statement

In the twin paradox suppose the twins are named Dick and Jane. And they both are 20 years old.Dick takes off on a voyage at a speed of 0.8c to a star 20 light years away.Lets say that both the twins send each other signals once a year while Dick is away.How many signals does Jane receive?

Homework Equations

This problem is from the book "Concepts of Modern Physics" by Arthur Beiser. I have understood the part about how many signals are receive by Dick. And I am utterly at a loss to explain the signals received by Jane.

The Attempt at a Solution

Since for Jane the total journey by Dick is 50 years (25 going and 25 returning). And by relativistic calculations each twin receives 1 signal per 3 years while they are being separated and they receive 3 signal per year when Dick is returning. So while Dick is on his way to reach the star Jane should receive (25/3) = 8 signals.But the book mentions that Jane receives ( (25+20)/3 ) = 15 signals while Dick is journeying to the star. I can't understand where this 20 came from.

 

[SammyS]

Homework Statement

In the twin paradox suppose the twins are named Dick and Jane. And they both are 20 years old.Dick takes off on a voyage at a speed of 0.8c to a star 20 light years away.Lets say that both the twins send each other signals once a year while Dick is away.How many signals does Jane receive?

Homework Equations

This problem is from the book "Concepts of Modern Physics" by Arthur Beiser. I have understood the part about how many signals are receive by Dick. And I am utterly at a loss to explain the signals received by Jane.

The Attempt at a Solution

Since for Jane the total journey by Dick is 50 years (25 going and 25 returning). And by relativistic calculations each twin receives 1 signal per 3 years while they are being separated and they receive 3 signal per year when Dick is returning. So while Dick is on his way to reach the star Jane should receive (25/3) = 8 signals.But the book mentions that Jane receives ( (25+20)/3 ) = 15 signals while Dick is journeying to the star. I can't understand where this 20 came from.

From Dick's point of view, how far is the journey ?

 

[Nitin Gupta]

From Dick's point of view, how far is the journey ?

According to him the journey is 15 years going and 15 years returning... total 30years

 

[SammyS]

According to him the journey is 15 years going and 15 years returning... total 30years

So, Dick sends 15 signals while he journeys to the star. Of course, Jane will not receive some of these until Dick is on his return portion of the journey.

 

[Mayank Bhandare]

Probably this could help!

https://www.physicsforums.com/insights/geometrical-view-time-dilation-twin-paradox/

The answer lies straight down in the last diagram.

 

[akash244]

But anyone get this that where the 20 years come from??

 

[phyzguy]

But anyone get this that where the 20 years come from??

Yes. Calling the bginning (when Dick sets off on his journey) year 0, in what year does Jane receive the last signal sent by Dick on his outward journey? This signal was sent just as Dick is arriving at the star. If this isn't clear, try drawing a space-time diagram.

 

[kuruman]

So, Dick sends 15 signals while he journeys to the star. Of course, Jane will not receive some of these until Dick is on his return portion of the journey.

The problem states that

... both the twins send each other signals once a year while Dick is away.

If Dick is away for 30 years of his time (post #3 to which I agree), he must send out 30 signals, all received by Jane before they are reunited. Here $\gamma=5/3$ which means that Dick's signals are $\Delta t = 12\times (5/3)=20$ months apart in Jane's frame. Now, also in her frame, the trip is 50 years or 600 months long. This checks because $600/20=30$ signals.

On edit:
I just noticed that this thread is about 5 years old.

 

[PeroK]

I just noticed that this thread is about 5 years old.

In whose reference frame?