# Length Contraction in the Muon Experiment

Discussion in 'Physics & Math' started by Aer, Jul 26, 2005.

1. ### AerRegistered Senior Member

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Concerning the Muon Experiment:

The muon doesn't see time dilation in it's own frame nor does the Earth. So both their clocks are ticking along at the same rate in their respective frames but they see the other's clock tick slower. The muon is explained by saying the Earth sees the muon's clock slower and the muon, with a normal tick rate in it's own frame, sees the Earth move over a smaller distance. This argument seems inadequate to me because isn't the reverse true if neither frame is preffered. That is, the muon sees the Earth's clock slower while the Earth sees the muon move a smaller distance. Can anyone point out where this thinking is flawed? I have not been able to resolve this issue and would like to!

Consider time for the muon, in order for no light to reach it beyond the edge of the known universe as defined in the earth frame (156b ly) and the muon frame (9.6b ly), then the time accumulated on the muons clock (if it could exist forever, consider the time accumulated by an observer in the muons frame) would have to be less than that accumulated on the Earth clock. That statement does not agree with the statement that each clock ticks normally in their own frame and each sees the other clock as running slower.

3. ### LucasRegistered Senior Member

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I don't see any problem, the observers on Earth will also observe the muon to move a shorter distance. If you consider the muon to be embedded in a fictional crystal, then the size of the crystal as observed from Earth will be shorter if the Earth is moving towards the muon (i.e. the muon is moving towards the Earth), so you can say that the muon has moved a shorter distance

5. ### AerRegistered Senior Member

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Impossible and Nonsensical. If the Earth observer saw the muon move over a shorter distance, how does the muon reach the Earth's surface? I am not sure you are completely familiar with the Muon Experiment. See here

In who's frame? I already think I mentioned that the Earth moves a shorter distance from the muon's perspective.

Last edited: Jul 26, 2005

7. ### kevinalmRegistered Senior Member

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The resolution of your difficulty is that in both frames the determining factor is the perceived thickness of the Earth's atmosphere. In order to get the symmetric situation you are looking for you would have to collide two Earths.

8. ### AerRegistered Senior Member

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I stated this. I already know know how the muon experiment is explained. Read my post carefully. The difficulty arrises from this explaination, NOT, this explaination resolves the difficulty.

I am not looking for such a symmetric situation. I merely posed the question, why does the symmetry not exist if neither frame is preferred. Nothing more nothing less.

9. ### kevinalmRegistered Senior Member

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You may have missed my point. Let me restate it this way. The muon is created in the Earth's upper atmosphere, traversed it, and then decayed. The Earth wasn't created in the muon's "upper atmosphere", didn't traverse it, and didn't decay.

The factor that controls both frames is soley in the Earth's frame.

Or perhap's I'm not understanding your question?

10. ### AerRegistered Senior Member

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The Earth created the muon so the Earth's viewpoint superceeds the muon's viewpoint. Thanks! That is tremendously helpful.

11. ### LucasRegistered Senior Member

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Anyway, the muon is a point, how do you want to contract a point?

12. ### geistkieselValued Senior Member

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Aer, Kevinalam, Lucas et al you miss the point of science,

The muons are created not at one altitude, not at two altitudes, but a spectrum of altitudes. At each measured point then, of the number created there, 1/2 were created 600 meters higher up and so on.

Prove to us, you who believe, but are not experimentally saavy, that 1/2 of the muons counted on the surface of the earth weren't created 600 meters up, and 1/4 created 1200 meters op, and 1/8 created 1800 meters up and 1/16 created 2400 meters up on ad infinitum.

I don't recall seeing any reference to "1/2 life" in this thread, or 1/2 life significance. I only see three brainless ones discussing special realtivity idiocy.

Prove the source of atoms detected on the surface originated higher than 600 meters for instance. I bet a clever fellows like you can find us an Einstein quote to solve this ticklish problem can't you? or something devilishly clever to resolve the "where created" problem can't you?

The three of you ought to combined your brain power and come close to unity, on this I am sure.

Why not analyze the problem from first principles {if you aware of these things, that is], instead of assuming you singularly know the answer? As to this points I am only able to determine collective stupidity, as well meaning as it is projected in this thread, that is.

Geistkiesel

13. ### funkstarratsknufValued Senior Member

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Right.
Come again? What do you mean the "Earth move over a smaller distance"? In the muon frame the Earth (and it's atmosphere) are length contracted, and since the muon originates somewhere in the atmosphere the surface reaches it before it (the muon) decayes.
I think your problem might originate in the "smaller distance" thing. I'm not sure what you are referring too, but I assume that you're thinking of length contraction. An important invariant is that both the muon and the Earth will observe the other to be moving at the same speed, relative to the observer's rest frame.

On second thought, I think I know exactly where the flaw lies: I see what you mean with "smaller distance"; the distance from the point in the atmosphere the muon originates to the surface of the Earth is shorter in the muon frame than the Earth frame, so for the Earth's surface to reach the muon it only has to travel a short distance, which is possible within the decay time of the muon (from the muon frame). You want this situation to be equally true from the point of the Earth, but the equivalence (which is real) does not let you conclude that the muon cannot reach the Earth. Why? Because the two frames will not agree on time. Think about it...
I'm not sure what you mean that it does not agree. Near relativistic particles could indeed pass over the observable universe (as viewed from earth) in quite small proper time. I fail to see the inconsistency, because the observable universe of the muon would be quite different. Remember that time doesn't make sense without space, so the fact that the muon and the Earth would disagree about these and other things (such as the age of the universe) doesn't make it inconsistent.

14. ### Janus58Valued Senior Member

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The resolution is based on the conditions of the experiment. How much time passes for both the Muon and Earth clock between two Events? These two events are the creation of the muon in the upper atmosphere, and the muon reaching the surface of the Earth. Both of these events must occur for both frames in order for the experiment to be complete.

Thus in the Earth Frame, the Muon can not be seen as moving a shorter distance because the conditions of the experiment require it to cross the depth of the atmosphere, and the atmosphere is in the same frame as the Earth and thus this distance does not contract in the Earth frame.

That is not to say that you could not devise a different experiment in which the reverse is true, where the Earth measures the muon as traveling the shorter distance, but this would be a different experiment with different conditions. For instance, you could have two muons, one created after the other and compare how much time passes between the first muon striking the Earth and the second striking the striking the Earth as measured by the second muon and an Earth clock.

15. ### superluminalI am MalcomRValued Senior Member

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Geist you fucking asshole. Back to the pseudoscience forum and let people discuss actual science.

If you don't want to read all this, they use balloon lofted instruments and know very well the muon fluxes in the upper atmosphere.

http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/muon.html

http://www.cosmicrays.org/

http://www.lbl.gov/abc/cosmic/SKliewer/Cosmic_Rays/Muons.htm

http://pandora.physics.lsa.umich.edu/schubnel/papers/PhysRevD_70_092005.pdf

http://people.roma2.infn.it/~aldo/A51prl_cap94_mu.pdf

And the explanation for why muons with a HALF-LIFE of 2.2us reach the ground, is that from our frame, the muon lasts much longer. From the muon's frame an earth clock would also appear to run slower. So, as the muon ticks normally, it decays when it reaches the ground (say). It will always have seen the earth clock as much slower. It never changes frames, it just dies. Time and space are different for earth and muon.

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What?

17. ### AerRegistered Senior Member

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Perhaps this is the source of the issue. How is what you are saying any different from what I said?

How is the "smaller distance" not length contraction.

I am not convinced by this explaination - I think the issue is just cloudy for one or the other of us.

I am not talking about the time issue. I made up an entirely different issue which I have not yet come to the conclusion yet as being valid/invalid. That is the light that the muon sees compared to the light the Earth sees.

18. ### AerRegistered Senior Member

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Agreed.

This seems like an ex post facto argument. How might you reach this conclusion using Special Relativity laws only a prior?

Are you sure this predicts what you say it will predict?

19. ### AerRegistered Senior Member

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I do not wish to go into a discussion with you on any topic related to science or otherwise. Not because I think you are an idiot or anything, just personal preference

Last edited: Jul 27, 2005
20. ### LucasRegistered Senior Member

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I don't see any problem with the lack of symmetry in your gedankenexperiment, as long as the experiment agrees with the laws of Special Relativity. Show me what law is violated, and then we can discuss (after all, the theory is called Relativity, that is different observers measure different times, sizes, etc)

With respect to your response in the third post, yes I knew that the distance of the muon as seen from the Earth is the same, but you're assigning extra importance to the fact of the creation of the muon in the athmosphere. You should try to imagine a fictional frame of reference centered in the muon. As observed from earth, this frame of reference would contract if the muon is moving, so in a sense, the movement of the muon between two points of its frame of reference is shorter as seen from Earth than the distance between those points if the muon was stationary (as seen from Earth). This is the same as the case as say, as seen from the muon, in a frame of reference centered in the surface of Earth, you choose the two points to be the surface of Earth and the upper part of the athmosphere

Last edited: Jul 27, 2005
21. ### AerRegistered Senior Member

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This is not a thought experiment. It is an analysis of the explaination given to the Muon Experiment.

You need to read my post. I am analysising the explaination of the laws of Special Relativity, not saying they are violated.

This makes no sense. "distance of the muon as seen from the Earth is the same"? What frames are you talking about? I never put any importance to the creation of the muon in the atmosphere. Would you like to explain this process in detail?

You are just reiterating the analysis I already provided.

22. ### LucasRegistered Senior Member

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i mean,seen from the Earth frame of reference, when the muon is created its distance to the surface of Earth is the same if the muon is created stationary with respect the frame of Earth, or moving with respect to the same frame

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No it's not.