# Question Regarding the Twin Paradox

• Nitin Gupta
In summary, the twin paradox involves two twins, Dick and Jane, who are both 20 years old. Dick travels at a speed of 0.8c for a total journey of 30 years (15 years going and 15 years returning). Both twins send each other signals once a year while Dick is away. According to relativistic calculations, Jane should receive 8 signals while Dick is on his way to the star. However, the book mentions that she receives 15 signals. This is because in her frame of reference, the trip is 50 years long and Dick's signals are 20 months apart. This results in a total of 30 signals being received by Jane before they are reunited.
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.

Nitin Gupta said:

## 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 ?

SammyS said:
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

Nitin Gupta said:
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.

Last edited:
Nitin Gupta
But anyone get this that where the 20 years come from??

akash244 said:
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.

SammyS said:
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
Nitin Gupta said:
... 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:

kuruman said:
In whose reference frame?

SammyS, phinds, DrClaude and 1 other person

## What is the Twin Paradox?

The Twin Paradox is a thought experiment in special relativity where one twin travels through space at high speeds while the other remains on Earth. When the traveling twin returns, they have aged less than their twin on Earth, leading to a paradox.

## Why is it called the Twin Paradox?

It is called the Twin Paradox because it involves two identical twins, one of whom travels through space at high speeds and returns to Earth at a later time, resulting in a difference in their ages.

## Is the Twin Paradox a real phenomenon?

No, the Twin Paradox is a thought experiment and not a real phenomenon. It is used to illustrate the concepts of time dilation and the relativity of simultaneity in special relativity.

## How does the Twin Paradox demonstrate the concept of time dilation?

The Twin Paradox demonstrates time dilation by showing that time passes slower for the traveling twin due to their high-speed travel, as observed by the twin on Earth. This is due to the fact that time is relative and can be experienced differently by observers in different frames of reference.

## What is the resolution to the Twin Paradox?

The resolution to the Twin Paradox lies in the fact that the traveling twin experiences acceleration and deceleration when changing direction, which causes them to experience time differently than the twin on Earth. This resolves the paradox and explains the difference in their ages upon the traveling twin's return.

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