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Do atmospheric muons accelerate?

  1. Dec 6, 2014 #1
    <<Moderator note: This discussion was originally posted in another thread. It has been moved as it did not concern the OP of that thread.>>

    The muons never accelerate from A->B?
     
    Last edited by a moderator: Dec 7, 2014
  2. jcsd
  3. Dec 6, 2014 #2

    Nugatory

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    For all practical purposes they are moving relative to the earth's surface and atmosphere when they are created, and they continue to travel at that speed for their entire (short) lifetime.
     
  4. Dec 7, 2014 #3
    What's "practical"? I was commenting on Orodruin's reply "The distance they travel in their own rest frame is zero." Which implicitly says the muon also doesn't proper accelerate. Since it claims the muon determines it had zero displacement. In either case you and Orodruin refer only to the observer dependent....which has what "practical" physical importance? none, it's relative. Either way your point or Orodruin's; it's moot. The proper acceleration part is of "practical" physical importance

    The muon would be wrong to think that maybe the Earth moved to it during any part of it's observation, due to the first part
     
  5. Dec 7, 2014 #4

    Orodruin

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    No, the muon is perfectly valid in thinking the Earth is moving towards it. The muon essentially never accelerates, it is born with a velocity relative to the Earth and it decays with essentially the same velocity. The muon does have zero displacement in its rest frame by definition of the rest frame. In the muon rest frame, the Earth is moving.
     
  6. Dec 7, 2014 #5

    What does "essentially" mean? Doesn't that mean non-zero?

    I presumed that the muon accelerates after it's "put" into existance. I'll trust what you're saying (the muon is put into existence while simultaneously having a velocity) if the muon is massless. in which case the "frame" (and in turn the "observations") of the muon are not physically valid anyways.



    I interpret it as the muon would be correct in saying the length to Earth contracted. Which is physically valid & compatible to "our" frame of "the muon's clock ticked slower" & how Russ_watters described the two frames. What is not physically valid & compatible amongst all observations is "the Earth moved." Which makes it wrong...practically, and was your amendment.

    Yes due to relative motion "In the muon rest frame, the Earth is moving." But that's not the whole story, just a physically symmetric however moot point of view between two frames of an asymmetric scenario/reality.

    [moderator's note - edited to remove off-topic personal theory]
     
    Last edited: Dec 7, 2014
  7. Dec 7, 2014 #6

    Dale

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    The muon has initial velocity even given that it is massive. It is created with some velocity and being a fundamental particle it has a characteristic fixed mass.

    The "essentially" and "practically" caveats that you are worried about are simply there because a muon is charged and there may be some small EM fields present around the earth. Ideally those are 0 and then the muon does not accelerate at all. If they are practically or essentially 0 then it practically and essentially doesn't accelerate. Also we are ignoring g which is essentially and practically OK.
     
    Last edited: Dec 7, 2014
  8. Dec 7, 2014 #7

    Nugatory

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    Why can the particle only be created with motion if it is massless?
    Suppose I create a particle that is at rest relative to me in my lab (possible in principle, although it would be a fair amount of work in practice). How would you describe the motion of the particle if:
    A) my mobile lab just happened to be aboard a truck driving past at 100 km/hr while you are standing alongside the road?
    B) my mobile lab is still in the truck, but now it's parked by the side of the road?
     
  9. Dec 7, 2014 #8

    It seems curious to me that a massive particle can have a velocity upon it's creation from the rest frame of it's creation. Which you tell me is "in Motion" relative to the source of it's creation, yet had experienced no acceleration. Yes it's idealized there are no "surprise" variables accelerating the muon.
     
  10. Dec 7, 2014 #9

    Not so simple, this is a creation of a particle We have a very good reason to use that event as "at rest", and the destination is idealized to be "at rest" to the source of the muon creation. It's not the same as a muon is created while on a truck going 100 kph past me so I measure the velocity to be x +100kph
     
  11. Dec 7, 2014 #10

    Dale

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    what frame are you referring to here. Its creation is an event and an event doesn't have a rest frame.

    Muons are created having velocity in the rest frame of the earth. Muons typically come from the decay of a pion into a muon and a neutrino. Because the neutrino carries a small amount of momentum the muon rest frame is not the same as the pions rest frame.
     
    Last edited: Dec 7, 2014
  12. Dec 7, 2014 #11

    I was suggesting the point where the muon comes into existence be used as 0,0 and that from it we see the muon has accelerated.

    So the momentum of the energy was Already in motion compared to earth, it broke up into a neutrino and muon, so those two are created in motion from Earths frame. Wow, I see how it can really be that the Earth is moving towards the muon from start to finish. It actually never experiences proper acceleration.


    Thanks for explaining that Dalespam.
     
    Last edited: Dec 7, 2014
  13. Dec 7, 2014 #12

    Dale

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    Yes, the pion's momentum must be conserved in its decay products, so pion already moving wrt earth -> muon and neutrino created already moving wrt earth, each other, and pion*. Otherwise, momentum would not be conserved.

    *(or rather the inertial frame where the now deceased pion was at rest)
     
  14. Dec 7, 2014 #13

    Orodruin

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    I want to highlight this point made by DaleSpam above: The muon and neutrino are not going to be at rest in the initial pion rest frame. If they were, then energy would not be conserved. In order for energy to be conserved, it is necessary that the muon and neutrino have an initial velocity with respect to the initial pion rest frame.
     
  15. Dec 7, 2014 #14
    Yea that is where I went wrong. I was presuming point "a" and "b" were at rest to each other, and the muon moves from "a" to "b". oddly here the starting point is the muon's creation and has a non-zero momentum compared to point "b". never seen that before and don't like it lol

    I need to think it through until I see it just like Nugatory said. The pion is the lab in motion.
     
  16. Dec 7, 2014 #15

    Dale

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    It is a little odd at first glance, but then if you think about Nugatory's point above it makes sense. When it is created it has some value for momentum, even if that value is 0. And if you look at it from any other reference frame then the momentum will be different. So if it just randomly happens to be 0 in the first frame, then it will definitely be non-zero in the second.

    Since there are an infinite number of frames where it is non-zero and only one frame where it is zero, just randomly you would expect things to usually be created with non-zero momentum.
     
  17. Dec 7, 2014 #16

    PeterDonis

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    This doesn't make sense. "Points" in space (which is what you appear to mean) are frame-dependent to start with; the muon doesn't move from point a to point b in space in any invariant sense, it only does so with respect to some particular frame. Also, points don't have momentum, and, as DaleSpam pointed out, objects don't have momentum in an invariant sense, they only have momentum with respect to some particular frame.

    What you have in this problem are simply three different frames:

    (1) In the frame in which the Earth is at rest, the pion has some velocity, and the muon and neutrino that are created from the pion have different velocities.

    (2) In the frame in which the muon is at rest, the pion has some velocity, the neutrino has some different velocity, and the Earth has another different velocity.

    (3) In the frame in which the pion is at rest, the muon has some velocity, the neutrino has a different velocity, and the Earth has yet another different velocity.
     
  18. Dec 7, 2014 #17

    My "points" "A" and "B" could be thought of as the ends of a very long ruler. A start and finish line is all.
    The starting point of the observation ("A") is the same as the muons creation. Simply put I was wrong by not considering the "running start" of the muon's inherited momentum wrt Earth. I thought, for some unfounded reason, that it was implicit the muon is created & then accelerated; wrong on so many levels opps. But it instead, inherits the properties of the pion's comparative motion (less the neutrino, and some change in velocity wrt the original pion rest frame).
     
    Last edited: Dec 7, 2014
  19. Dec 7, 2014 #18

    PAllen

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    I wonder if the basic misunderstanding here is applying classical intuitions to a quantum process. Classically, if you look at a bomb exploding with high speed photography, pieces of the shell start out at rest and go through all speeds before reaching their terminal speed. However, for radioactive decay, a nucleus at rest emits (say) a beta particle and neutrino at some speeds, and recoils, with none of the particles or nucleus having any 'intermediate' speed.
     
    Last edited: Dec 7, 2014
  20. Dec 7, 2014 #19
    Yes, weak nuclear is how was assuming this "muon being "put" into existence", thanks for identifying the source of "intuition" lol. So much so I scoffed at Nugatory's very accurate and elementary example, suggesting to him it's not so simple....but it is as he said.


    I didn't even consider the whole process is in motion,
     
  21. Dec 7, 2014 #20

    PeterDonis

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    And how is that ruler moving? In which frame is it at rest? You have to pick one.

    If the ruler is at rest in the Earth's rest frame, then the pion has a very large velocity when it hits point A, where it turns into a muon and a neutrino; and the muon has a slightly different but still very large velocity as it leaves point A.

    If the ruler is at rest in the pion's rest frame, then it's not "very long"; it's pretty short. The pion can be viewed as being at rest at point A in this frame; but at some instant it turns into a muon and a neutrino, and the muon has a fairly small velocity from A towards B. It doesn't take long to reach B because the distance from A to B, in this frame, is very short.
     
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