michel123456

Well understood. The muon is stationary in its own frame. Here below: On the left side, the muon is at rest and the atmosphere goes from down to up. L0=2km The contraction of the path L & the muon M is shown. Do you have any problem with that? -------------- oops the labeling does not correspond to previous posts. Working on it. Done

Yes, I agree it is well understood. In my posts, L0 is the length of the path in muon's frame (2km) and M0 is the proper length of the muon. These are distinct values. ----------------- But they are tied together: when the path is contracted, so is the muon. The same γ factor apply to both values.

10 km corresponds to M1 muon length as observed in S 2km correspond to M0 muon length as observed in S' The value 2km is the path as seen from the muon's frame and is the value contracted by a value of γ=5 wrt the 10 km atmosphere. The value 2km is the path contracted. Whatever corresponds to the 2km value is the result of the equations of Relativity. It is accepted physics. This value of 2km corresponds to M0 which is the length of the muon in its own rest frame. This value M0 is the value already contracted. It is the proper length of the muon. What you are proposing is the contraction of an already contracted value. What you should propose is that the value M1, as measured in S from Earth, divided by γ=5 gives you the value M0 contracted. Unfortunately the accurate value of M1 is null which doesn't help much, but you have the path and can make the calculation 10km/5=2km which gives you the contracted value of the path.

You are wrong.

No I meant that abstract thought is tied to evolution. I don't think we are especially gifted for doing maths. Sometimes a simple multiplication is a challenge. If we were so brilliant we wouldn't need computers that much.

I am not sure. I'd better say that we are using or skills to whatever. In-between this whatever there are mathematics. As an abstract thought.

You are saying that L1=1/5 of L0

Mathematics is only a field of human thinking. I suppose the human kind would have feel very early the need for counting. Maybe even before being a human. IIRC it is argued that some animals have this ability.

He is not. I agree +1

Again The muon, in its own frame, measures its own proper length L0 and is at rest while 2km of atmosphere comes through it. As seen from Earth, the atmosphere is 10km thick at rest and the muon of length L1 travels through it. You are saying that L1 is less than L0 I say that L0 is the contracted value of L1

That's the point of divergence. If the muon, in its own frame, travels 2km, then what we call the contracted muon in our frame is the muon's proper length. If we cannot agree on this, then there is no hope.

Here wonderful hand drawings http://www.mymodernmet.com/profiles/blogs/colouring-book-rafael-araujo-golden-ratio

With all my respect maybe you should start to think by yourself instead of repeating other's thoughts. Fact 1: The atmosphere is at rest and 10 km thick. You are observing the muon going through 10km. Fact 2: A contracted muon goes through a 2km atmosphere, not through a 10 km atmosphere. Fact 3: what we call a "contracted muon" is the muon's proper length. Is anything wrong in the above? Because if nothing is wrong, it comes out that a contracted muon does not go through a 10 km atmosphere, IOW that this observation is impossible. ----------------- edited. Strikethrough useless comment

So you believe that from frame S (Earth) the muon's proper length is observed?

Marcel died. -------------------- (edit) Music please I need to change my mind.

Ok. So it is the distance traveled by the atmosphere as seen from the muon frame at rest. ------------------------------- But the diagram does not depict what one sees. The diagram is a graph of the algebraic equations, showing that it is all geometry. What I say is very simple: The earthling sees a muon traveling a 10 km path through atmosphere. The earthling knows that for the muon, this same path represents only 2 km. That means the path is contracted, and the muon is contracted also. But the earthling doesn't see 2km, he sees 10 km. As such, the earthling does not see the muon contracted. Because the muon contracted corresponds to 2 km. And the earthling does not see 2 km. Is that so complicated?

I have to admit that is not so easy to grasp Question below: I don't get this last one because it is stated at the beginning that: So, if the muon is at rest in S', what distance did it travel in S'? The distance AC in S' is the distance traveled by the muon at rest?

Here I have made a slight change to the diagram, so that the contraction on the left side (the muon's frame) is more evident.

You are correct, it is the same atmosphere. Wrong wording from me. If the atmosphere was a solid wood, the one is measuring it 10km, the other 2km. OK that is your post #151. The bold part is important. The entire post is important. I don't understand especially the bold part. To me: 1. the muon sees the atmosphere as 2km thick. It goes through it in 6.8 μs, at velocity S. 2. the earthling sees the atmosphere as 10km thick. He observes the muon going through it in 34μs, at velocity S. Both observe the same velocity. They are no crossing observations, for example 3. the earthling does not observe the atmosphere 2km thick and the muon at 34μs. It is wrong. 4. And as another example, the earthling does not observe the atmosphere 10 km and the muon at 6.8 μs. It is also wrong. The observations are as stated in points 1 & 2 above. They are no crossing observations.

Yes. You can't have one speed be different than the other. That's not even some feature for just special relativity. It's true in Newtonian physics as well. So we have on the left side a muon traveling at speed S through 2km. As seen from Earth, the SAME distance is not 2km but 10km. As a result the earthling concludes that time must be different for the frame of the muon, because it is obliged that S is the same for both observers. The time of the muon is dilated as seen from Earth. But also what one must do is compare 10km and 2 km, by scaling the 2km distance onto the 10 km. Because it is the SAME distance (as viewed by the 2 different frames) The value of the scaling is 5 = γ One must stretch the 2 km by a factor of 5. Because the distance as seen from Earth is 10km, not 2 km. Are you following till here?

Yes.

Thank you. So we have to do with 2 different frames, one for the muon, one for the Earth. In both frames, the velocity is the same. 10 km/34μs = 2km/6.8 μs Is that correct?

Is that correct?

From the link you provided it appears that 1. As seen from Earth, the muon traveled 10 km in 34μs 2. As seen from the muon, the muon traveled 2km in 6.8 μs That is the situation as given by the equations. In the diagram the muon is represented as a black dot. It has been overscaled for the sake of understanding. Here below, on the left side the situation as observed by the muon, on the right side as observed by the Earth. In the middle is the scaling of the muon, as observed by the Earth. If you take as granted that the muon (the object) is an ellipsoid, then on the left side it is contracted (it is a circle). From this, if I am correct, the observer on Earth does not directly observe a contracted object. The contracted object is given by the equations and describe what the muon observes. More something like a scaling, since length & time work together.

Swansont wrote: I showed it would be elongated. Exactly the contrary of what Swansont posted. Please explain where I get it wrong.