# Time dilation & Pions - Why Both Stationary and Moving Pions Should not See the Same Result?

One of the proofs for time dilation is how pions travel further than they should as their lifetime expands due to their travelling near speed of light.

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?

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:

Relativity: how people get time dilation wrong

Einstein's Clocks

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?

First of all, when one particle accelerates you do not have symmetric situation. The physics in accelerated frame is different, there are suddenly new pseudoforces which are not present in an inertial frame. You are right, that if observer on B only observers position, he sees the other pion accelerate. But he can observer other things also, like the mentioned pseudoforces, which breaks the symmetry.

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 poins decay in 1 unit of B.

You say this is experimental result, but from which experiment? It does not seem right. If both pions A and B are inertial, then A should see B living longer than A and so should B see A living longer. They would not agree on how many A lifetimes the pion B lives as you are claiming.

• Symmetrical in the sense that A sees B accelerate in the same way (in a diff direction of course) B accelerates. You can be on A observing B accelerating or on B observing A accelerating. The fact that one is on Earth does not make it different! Experiments here: en.wikipedia.org/wiki/Experimental_testing_of_time_dilation As well as explained here: youtube.com/watch?v=Txv7V_nY2eg Aug 17 '20 at 6:40
• @TheITGuy Symmetry in the sense you mentioned is not symmetry of physical laws. You asked "How can we explain this despite the very symmetrical nature of the experiment" and I told you if one of the pion is accelerated, the nature of experiment is not symmetrical at all. Aug 17 '20 at 9:18
• @TheITGuy ok, I watched the video and read the wiki page, I have not seen any mentioning of "if we are standing on B, we see G x poins decay in 1 unit of B." This is simply wrong. Both (in this case inertial) pions will see each other decay in G units of their lifetime. But keep in mind the statistical nature of lifetime and that you really need beam of pions instead of one pion as annav explained. Aug 17 '20 at 9:49
• Thanks for your comments. Watch this one: youtube.com/watch?v=svwWKi9sSAA Based on this Lincoln calculates time seen from B should see A decay 1/Gth of the unit, right? On the point of symmetry, if symmetry is violated when B is accelerated, how so? Are you saying the direction of acceleration makes the difference? Because from B standpoint, A accelerates too, on a different direction. If we stand on B, then how things become different from when we are standing on A? Everything is the same no matter whether you stand on A or B except that A is with Earth! Aug 17 '20 at 23:28
• @TheITGuy "Everything is the same no matter whether you stand on A or B..." it is not. As I said, in an accelerated frame there are additional pseudoforces which are not present in inertial frame. This means accelerated frame is not equivalent to inertial one. Aug 18 '20 at 4:09

We do not need clocks as we do have 2 clocks on each particle: their life time. We consider that 1 unit.

Pions are quantum mechanical entities. They do not have clocks. They are mathematically described by a complex number wavefunction $$Ψ$$ which has the mathematical information on the probability of the given pion to decay ,given by $$Ψ^*Ψ$$ , real numbers, so observable. To see probabilities one has to accumulate a statistically significant number of pions at a given energy , i.e. in a given inertial frame. In the inertial frame of a pion at rest is the lifetime of the pion found in the PDG tables.

So the possible experiments are:

1. pions at rest, and register the time t from their creation ( in an interaction,) to their decay.

2. create a beam of pions at a given momentum and energy (four vector) and register the number of pions at the time from the creation of the beam to the number remaining after certain time intervals, to get a lifetime plot. It is a much more complicated experiment to get the lifetime from cosmic rays, but it can be done as an exersize for students.

Pions cannot "see" each other, they can only interact with various possible forces. Your experiment treats pions as classical particles obeying relativistic equations, but they are not, they follow quantum mechanical relativistic kinematics which only predict probability distributions.So it is a science fiction experiment.

• Well, I was not really talking about true clocks but rather thought experiment clocks. Imagine you are on a pion and see it decay in 2.6 x 10-8 seconds. I consider that to be a unit of time for the observer on the poin. No other clocks needed. Just the lifecycle of poins. Aug 17 '20 at 6:49
• Please see this clip. youtube.com/watch?v=Txv7V_nY2eg Dr Lincoln mentions there is a real experiment involving poins! Aug 17 '20 at 6:52
• It is pions not poin, which you keep writing wrong. Of course there aref experiments with pions, even as exercise for masters students as the one in the link I give. But the way to see their lifetime and time dilation is through quantum mechanical equations . Aug 17 '20 at 6:55
• A similar experiment is done using mu-mesons and is available on youtube (I am not able to link it here for some reason but I have given the name) :'Time Dilation : An Experiment With Mu - Mesons (1962)' . There explanation should probably clear your doubts.Pay careful attention to the fact that in the frame of reference of mesons coming from above the length contraction of mountain is considered while time dilation is given emphasis for the mesons in the Lab as they 'look' at the upcoming mesons.
– Lost
Aug 17 '20 at 8:51
• @TheITGuy A pion at rest does not have a fixed decay time, it isn't like an alarm clock. The time it takes to decay is a statistical thing, as per usual with quantum events. A (charged) pion has a mean lifetime of ~26.033 ns, in other words, it has a half-life of ~18.045 ns. So if you start with 1,024,000 pions (at non-relativistic speeds, relative to the lab frame), after 180 ns you'd expect that around 1000 of them won't have decayed yet. Aug 17 '20 at 14:24

I think I see where you're coming from. Let me try to restate the problem in maybe a more precise way.

In this scenario a pion decays exactly 1 unit of time after its creation (in the frame of the pion). There's no probabilistic element.

According to the observer on earth, at a particular moment pion A pops into existence at rest in the lab and pion B pops into existence high up in the atmosphere traveling at a high speed toward the ground.

According to this observer, the "clock" attached to pion B is ticking slowly and so pion B lives longer than pion A. The observation is that at the moment pion A decays pion B is still alive.

This seems like a paradox since the observation "A dead, B alive" seems like a physical invariant. I.e. an observer attached to pion B will also see pion A decay while pion B is still alive. In fact, let's set up the experiment so that pion A decays at the exact moment the two pions meet. Then we really have a local measurement that observers traveling with either A and B agree on. At the moment the two pions meet A is dead and B is alive. This fact has gotta be the same for every observer. And it is.

But the situation is totally symmetric, right?

Actually it's not. The key is back at the beginning when the two pions were created at the same time according to the observer on the earth. In fact, according to the observer attached to pion B the two are not created at the same time. This is the relativity of simultaneity. According to the observer traveling with pion B, pion A is created long before pion B is. And even though observer B sees pion A take longer than 1 unit to decay (time dilation), pion A was created so much earlier than pion B that by the time the two pions meet pion A has decayed but B hasn't. So the two observers really do agree on the observation AND, crucially, both see the other's clock ticking slow!

• Thanks sums up well with one correction until your restating the question: "But the situation..." Let's assume the particle created artificially and at the same time, same as in Dr Lincoln's experimetn, and then one is accelerated but not the other. Then we should have full symmetry, right? Aug 18 '20 at 4:08
• I don't know what Dr. Lincoln's experiment is, but what you describe does not have full symmetry. I think you're saying that in the Earth frame both particles are created at rest and at the same time and afterward pion B is accelerated toward the ground. But then in this case an observer attached to pion B is not an inertial observer, while an observer attached to A is inertial. So we shouldn't expect exact symmetry in what they think happens.
– Alex
Aug 18 '20 at 18:46
• I know this isn't a complete explanation because it doesn't tell the story from B's perspective but the non-inertial frame will be the key in breaking the symmetry.
– Alex
Aug 18 '20 at 18:54