[Question] About the radio signal for Twin Paradox

[cxcxcx0505]

There is an example for the radio signal for Twin Paradox from the book "Classical Dynamics of Particle and Systems, Thornton, Marion". Refer "1.jpeg", example 14.5, it said that "However, Frank continues to receive a signal every 3 years for the 8 years it takes the last signal Mary sends when she reaches the planet to travel to Frank". I cannot understand, why there is another 8 years Frank receive signal for every 3 years? Anyone can explain more about this? Thanks.

 

[Nugatory]

There is an example for the radio signal for Twin Paradox from the book "Classical Dynamics of Particle and Systems, Thornton, Marion". Refer "1.jpeg", example 14.5, it said that "However, Frank continues to receive a signal every 3 years for the 8 years it takes the last signal Mary sends when she reaches the planet to travel to Frank". I cannot understand, why there is another 8 years Frank receive signal for every 3 years? Anyone can explain more about this? Thanks.

The signal travels at the speed of light. When does the last signal sent by Mary before she reaches the planet get to Frank? She's a lot closer to the planet than to Frank when she sends that signal.

 

[ghwellsjr]

There is an example for the radio signal for Twin Paradox from the book "Classical Dynamics of Particle and Systems, Thornton, Marion". Refer "1.jpeg", example 14.5, it said that "However, Frank continues to receive a signal every 3 years for the 8 years it takes the last signal Mary sends when she reaches the planet to travel to Frank". I cannot understand, why there is another 8 years Frank receive signal for every 3 years? Anyone can explain more about this? Thanks.

I think a couple of spacetime diagrams would clear everything up for you. Here's one showing the radio signals going from Frank (blue) to Mary (Red):

As the book says, Mary receives only two signals on her way out but 18 more on her way back (counting the last instantaneous one when she gets back).

Now here's a spacetime diagram showing the radio signals going from Mary (Red) to Frank (blue):

As the book says, Frank receives 3 and a third signals during the time that Mary is traveling away (although he has no way of knowing that). He continues to see Mary's signals arriving at the same rate until 8 more years (the length of time the signal sent from Mary at her turnaround takes to get to Frank) and then he starts seeing them come in at three times his own rate for a total of six more in two of his years.

Does it all make sense now?

 

[cxcxcx0505]

Thanks all

 

[sardar]

The radio signal for the Twin Paradox is a concept that is often used to illustrate the effects of time dilation in special relativity. In this example from the book "Classical Dynamics of Particle and Systems" by Thornton and Marion, the authors are discussing a scenario where two twins, Frank and Mary, are traveling at different speeds relative to each other.

According to the theory of special relativity, time moves slower for objects that are moving at high speeds. This means that if Frank and Mary are traveling at different speeds, they will experience time differently. In this scenario, Mary is traveling at a high speed and therefore time is moving slower for her compared to Frank.

Now, let's consider the radio signals that are being sent between Frank and Mary. In the example, Mary sends a signal to Frank every 3 years. However, because time is moving slower for Mary, it takes her 8 years to reach the planet where Frank is located. This means that while Mary only sends 3 signals, Frank receives them over a period of 8 years.

To put it simply, the reason why Frank receives signals for 8 years instead of 3 is because of the difference in time between the two twins. This is a result of the effects of time dilation in special relativity. I hope this helps to clarify the concept for you.