The Twin Paradox: Triplets Edition

[greswd]

Dayum, I got to do this manually.

Why provide the LabVIEW graphing software only after we're done?

 

[ghwellsjr]

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).

Why provide the LabVIEW graphing software only after we're done?

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.

 

[greswd]

I will appreciate it

 

[ghwellsjr]

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:

Now he can make the following table to summarize his findings:

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:

And here is a table showing these findings (including the ones at the beginning and ending):

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:

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?