The Twin Paradox: Triplets Edition

In summary, Charles has a paradoxical experience in which he simultaneously observes his brother Adam and his brother Bob travel away in rocketships and return a year later. Adam and Bob are the same age, but Charles perceives Adam to be older because he is in a reference frame in which time dilation has already taken place.
  • #141
Dayum, I got to do this manually.

Why provide the LabVIEW graphing software only after we're done? :tongue2:
 
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  • #142
greswd said:
Dayum, I got to do this manually.
It's not that hard. Start by making a table like I did in post #92 and #93 (page 6).
greswd said:
Why provide the LabVIEW graphing software only after we're done? :tongue2:
Yes, otherwise, you won't appreciate it. But my software doesn't do non-inertial frames. It allows you to define a triplet scenario (speed and length of time for the traveling triplets) and draws the diagram in the inertial triplet's rest frame and then it uses the Lorentz Transformation to redraw it at whatever speed you want the new IRF to be moving relative to the original IRF.

When I did the non-inertial rest frames, it was all done by cut-and-paste in Paint and I have only done this one on graph paper.
 
  • #143
I will appreciate it :smile:
 
  • #144
Here is a diagram repeating the one from post #140 but showing just a pair of radar signals emitted by Red as he measures the distance to Blue:

attachment.php?attachmentid=61974&stc=1&d=1379598027.png

Now he can make the following table to summarize his findings:
Code:
Radar   Radar   Calculated   Calculated    Blue's
Sent    Rcvd      Time        Distance      Time
  0       0        0             0            0
  4      16       10             6            8
 16      28       22             6           32
 32      32       32             0           40
Remember that the Calculated Time is determined by adding the Radar Sent and Rcvd times together and dividing by two and the Calculated Distance is determined by subtracting the Radar Rcvd time from the Radar Sent time and dividing by two. If you want, you can include as many more samples from post #140 as you want. For completeness, I have included the readings at the beginning and at the ending (even though those radar signals are instantaneous).

Now here is another diagram repeating the one from post #140 but showing just a few of the radar signals emitted by Red as he measures the distance to Black:

attachment.php?attachmentid=61975&stc=1&d=1379598875.png

And here is a table showing these findings (including the ones at the beginning and ending):
Code:
Radar   Radar   Calculated   Calculated   Black's
Sent    Rcvd      Time        Distance     Time
  0       0        0             0           0
  1      16        8.5           7.5         4
  4      28       16            12          16
 16      31       23.5           7.5        28
 32      32       32             0          32

Now we are ready to construct the non-inertial rest frame for red as he determines the distances to Blue and Black:

attachment.php?attachmentid=61976&stc=1&d=1379599832.png

You can confirm that this diagram represents the findings from the two tables and any additional samples you want to include.

If you want, you can download the diagram and draw in radar and/or Doppler signals (along 45-degree diagonals) for all three observers and confirm that this diagram conforms to all my other diagrams in terms of what each observer sees of the other observers. All the diagrams that I have drawn are equivalent and contain the same exact information.

Any questions?
 

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<h2>1. What is the Twin Paradox: Triplets Edition?</h2><p>The Twin Paradox: Triplets Edition is a thought experiment in physics that explores the concept of time dilation and its implications for identical triplets who experience different rates of time due to their relative motion.</p><h2>2. How does the Twin Paradox: Triplets Edition work?</h2><p>In this thought experiment, one triplet stays on Earth while the other two travel at high speeds in opposite directions. When they return, the triplet who traveled at a higher speed will have aged less than the one who stayed on Earth, creating a paradox as they are all genetically identical.</p><h2>3. What is the significance of the Twin Paradox: Triplets Edition?</h2><p>The Twin Paradox: Triplets Edition highlights the effects of time dilation and the relativity of time in different reference frames. It also challenges our understanding of the concept of aging and the perception of time.</p><h2>4. Is the Twin Paradox: Triplets Edition possible in real life?</h2><p>While the thought experiment is possible in theory, it is not possible to observe in real life as the speeds required for noticeable time dilation are not achievable by humans. However, the effects of time dilation have been observed in experiments with atomic clocks and high-speed particles.</p><h2>5. What are the implications of the Twin Paradox: Triplets Edition?</h2><p>The Twin Paradox: Triplets Edition has implications for the concept of time travel and the possibility of traveling to the future by traveling at high speeds. It also challenges our understanding of the nature of time and its relationship to space.</p>

1. What is the Twin Paradox: Triplets Edition?

The Twin Paradox: Triplets Edition is a thought experiment in physics that explores the concept of time dilation and its implications for identical triplets who experience different rates of time due to their relative motion.

2. How does the Twin Paradox: Triplets Edition work?

In this thought experiment, one triplet stays on Earth while the other two travel at high speeds in opposite directions. When they return, the triplet who traveled at a higher speed will have aged less than the one who stayed on Earth, creating a paradox as they are all genetically identical.

3. What is the significance of the Twin Paradox: Triplets Edition?

The Twin Paradox: Triplets Edition highlights the effects of time dilation and the relativity of time in different reference frames. It also challenges our understanding of the concept of aging and the perception of time.

4. Is the Twin Paradox: Triplets Edition possible in real life?

While the thought experiment is possible in theory, it is not possible to observe in real life as the speeds required for noticeable time dilation are not achievable by humans. However, the effects of time dilation have been observed in experiments with atomic clocks and high-speed particles.

5. What are the implications of the Twin Paradox: Triplets Edition?

The Twin Paradox: Triplets Edition has implications for the concept of time travel and the possibility of traveling to the future by traveling at high speeds. It also challenges our understanding of the nature of time and its relationship to space.

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