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I have been asked to retitle this question and I have been asked to edit the question to adhere to mainstream physics. And I simplified it. So here it is:

Two cars approach each other at the same constant speed relative to earth. Special theory of relativity (SPR) tells us that the clocks inside each car will run slower than an identical clock at rest. Most importantly, the clocks inside each car run at the same (slower) rate because they are traveling at the same speed. SPR also tells us that whenever relative motion exists between two inertial frames of reference, the approaching clocks will run at different rates. Yet in this case the approaching clocks run at the same rate (as demonstrated above). How can SPR explain this paradox?


marked as duplicate by dmckee Aug 7 '16 at 19:36

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    $\begingroup$ You're falling back onto the idea of absolute time by saying "the clocks run at the same rate". That happens to be true in the Earth's frame, but there's nothing special about that frame. Different observers can disagree on which clocks are running faster or slower. $\endgroup$ – knzhou Aug 7 '16 at 19:28
  • $\begingroup$ For more information, just search for 'time dilation'. I think a good half of the results will be about this same paradox. $\endgroup$ – knzhou Aug 7 '16 at 19:29
  • $\begingroup$ In SR all velocities are relative. You are free to assume which clock is at rest and which is moving. So I am allowed to say that the car on our right is at rest, the Earth's clock is approaching it at $v$, and the left car is approaching the right car at $2v$ and the Earth's clock at $v$. In this situation all assumptions concerning the speeds of the clocks will change. Which only adds to the paradox. That's Special Relativity ... $\endgroup$ – bright magus Aug 7 '16 at 19:33
  • $\begingroup$ Master question on time dilation: physics.stackexchange.com/q/241772. And the next thing you're going to want to ask about is covered by the "twin paradox". Please read before asking. $\endgroup$ – dmckee Aug 7 '16 at 19:34
  • $\begingroup$ The twin paradox is obvious, one twin accelerated and one twin did not. The car question is fundamentally different since both cars have identical acceleration/speed. That both cars experience the same slower clock rate has been proven experimentally. No disagreement there. That SR predicts a different clock rate for the two approaching cars is the unanswered paradox. Conclusion - relative motion does not always result in relativistic effects. $\endgroup$ – M. Pope Aug 7 '16 at 19:54