Now imagine you have 2 pions: one stationary on Earth called A the other accelerated to the near speed of light called B.
We do not need clocks as we do have 2 clocks on each particle: their life time. We consider that 1 unit.
- A: sees it dies in 1 unit.
- B: sees it dies in 1 unit
A: does not see B die, or if we have pions being created and dying, we will see 1xG pions, with G calculated based on the speed of B.
Now since this is a very symmetrical situation, even if we consider acceleration of B, both A and B see the other accelerating and drifting away at same speeds. In other words, if you are standing on A and consider A stationary, you see B accelerating to its speed and drifting away. By the same token, if you are standing on B, you see A and Earth and all do the same.
However, what we see in the experiments is different. We see A decays in 1 unit and B in G units from A standpoint.
In fact, if we are standing on B, we see G x pions decay in 1 unit of B.
How can we explain this despite the very symmetrical nature of the experiment?
Some points after reading comments:
I may not have been clear in my question.
My main question here is not about measuring pion life cycle. It is rather how time dilation looks like a one way street. One can imagine a particle like pion and do a thought experiment.
Take away Lab and Earth and just leave two observers on pions. The reason I brought poins in the picture was because of Don Lincoln from Fermalib explanations here:
I have watched his other videos but still not convinced why the symmetry in my thought experiment of having two observers sitting on both pions should see things differently. To me both should see the other one age slower! Then how Lincoln's explanation in first clip stands?