The muon experiment from the muon's frame of reference

I was considering the muon experiment that is typically used to provide a justification to special relativity.

I understand the experiment from the Earth observer's perspective (with time dilation). However, I have trouble understanding the experiment from the muon's perspective.

I understand that the length should contract, but what I do not understand is why time dilation does not occur. From the muon's perspective, isn't the Earth moving towards it at a very high speed? If so, shouldn't the time it takes the Earth to travel to and meet up with the muon dilate? Therefore, wouldn't the effects of time dilation and length contraction cancel out?

I know I am at fault somewhere, I just do not know where. Any help would be appreciated. Thank you!

• You're completely right, in that from the muon's frame of reference, the lab clocks are running slow, so it looks like the muon's lifetime should be shortened according to them rather than lengthened. The effect that you're missing is called the relativity of simultaneity, you can search that term to see lots of previous questions about this. – knzhou Aug 23 '16 at 23:02
• This might be helpful hyperphysics.phy-astr.gsu.edu/hbase/relativ/muon.html just scroll down the page and also this site nobelprize.org/educational/physics/relativity/… – user108787 Aug 23 '16 at 23:11
• I think the problem here is that your arguments are rather vague. Please show your calculation of what you think happens, applying time dilation and/or length contraction. Then we - and probably you also - can see more clearly where the fault is. – sammy gerbil Aug 24 '16 at 0:27
• @sammygerbil My line of reasoning was the following: From the muon's perspective, the Earth is rushing towards it at 0.99c. Since this speed is constant, the relativistic factor, y, is constant. So, the length between the muon and Earth is L/y. The time it takes for the Earth to travel this distance, though, is t*y (L is the proper length and t is the proper time). Therefore, the speed of the Earth, if it reaches the muon, is about L/y / (t * y) = L/(ty^2). And I think I see my error :). So, the effects would not cancel. However, why do most websites not account for this? – dts Aug 24 '16 at 14:44
• An example of a website that does not account for this is hyperphysics.phy-astr.gsu.edu/hbase/relativ/muon.html#c1 (thank you @count_to_10 for providing this link) – dts Aug 24 '16 at 14:45

I think the thing that you are missing here the lifetime of a muon is a property of the particle. It is defined in terms of the time that passes for the particle.

In essence decay lifetimes are clocks in the particle frame of reference. So the scientist has to correct for time dilation, but a hypothetical muon-fair just uses the time on his fairy-watch.

And they both use the length of the lab as they measure it (which is shorter for the fairy).

In the end they make the same prediction.

If what is seen from Earth frame is correct (effective life time extension due to muons process slowing down) is true, then:

1. The muons once created must have had accelerated to the relative speed to us. You do not expect earth accelerating to a static muons every time they enter atmosphere. You would feel enormous acceleration forgetting all other absurdities involved.
2. The abstract coordinate system associated with muon would still be including Einstein's Clock synchronisation to give the muon frame an illusion that it does not move relatively to light. This would create an apparent reciprocal effect of earth time rate slowing down contrary to reality. It is more elaborate to prove that effective lifetime of muons will be consistently calculated from both points of view.

I am unable to see how anyone can feel that they have done this subject justice without deeply considering clock synchronizations as an integrated part of any working model they accept, and I am just not seeing the integration in other people's thinking. As a mere deeply interested layman, I only get to read about the work of others, which is quite limiting. Nevertheless, the June 16, 2016 activity contained in this link interests me greatly, especially the way it ends, and seems directly relevant to this question: https://www.researchgate.net/post/Is_relative_simultaneity_a_misinterpretation_of_Special_Relativity

Andrew Wutke · Thales Group

Allan

Thanks for the response to this old question. By now this question is now an affirmative statement. The relative simultaneity does not exist. Only relative synchroneity of clocks

I would encourage anyone who harbors doubts about the current prevailing wisdom of relative simultaneity (which is to say anyone who thinks kinetic energy is more than an idle observer of the dynamics of our existence) to read that entire post. While the details are beyond the scope of my own current concerns, the generalities of the conclusions agree with my own thoughts.

Furthermore, I found much of the high level notions presented in this earlier work quite compelling, and at odds with current prevailing wisdom: https://arxiv.org/pdf/physics/0606188.pdf

Finally, I present my own thoughts for consideration or otherwise for anyone that feels that something here just isn't quite right. Alas, I have no professional qualifications to support my thinking, just years of obsessive consideration and a deep intuitive sense that I see things as they are. I wrote this before finding the other two links previously posted, and maybe some day, after my knowledge grown deeper and my thoughts are more evolved, I'll write a more professional and technical piece: https://www.quora.com/The-muon-experiment-shows-that-scientists-record-time-as-moving-more-slowly-for-the-muons-than-for-the-scientists-Would-the-muons-think-that-time-had-passed-more-slowly-for-the-scientists/answer/Craig-Heile

• Welcome on Physics SE :) Could you add short summaries of the links you provided? This way, even once the links are dead, readers can still see the point of your answer. – Sanya Oct 9 '16 at 16:37
• Thanks, I'll keep an eye on doing that. They should be good for a good many years though. (I get really obsessive on this topic and feel I need to pull away for a bit for my own mental health). :) – Craig Heile Oct 9 '16 at 16:41
• Read the article, most of it is just crack-pot babble about the relativity of simultaneity being incorrect because light always travels at the same speed. – CStarAlgebra Oct 9 '16 at 17:50