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Thread: Length Contraction in the Muon Experiment

  1. #341
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    Quote Originally Posted by Pete
    Apparently we were wrong.
    I'm not completely sure how this pans out as far as length contraction goes... length contraction is hard to follow without objects with length to track.
    Now wait a minute, it can't be both ways. Either the length is contracted for the muon or it isn't. We've only considered the Earth frame and Muon frame - no other frames as far as I know. So does the muon see length contracted or not? Now as for the light reaching the muon, at the instant the muon smacks into the Earth, from the edge of the known universe from the Earth frame: Can the muon see distances further in any of the directions and not as far in some other directions depending on when it would see the universe "created"?

  2. #342
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    Quote Originally Posted by Pete
    Are you sure?
    Am I sure that it's nonsense or am I sure that I wouldn't be dissappointed? The answer to both questions is probably in truth - I am not sure

  3. #343
    I think this means that assuming a universal instant (the beginning of time) defines a universally observable reference frame.
    It defines a reference frame. Whether it is a "universally observable" one is another matter.

    An observer on Earth can tell that they are at rest in the Universe's "creation rest frame", while an observer with the muon can tell that they are moving at 0.98c relative to that frame.
    What do you mean by "creation rest frame"? Are you thinking of some kind of averaged CMBR frame?

    This sounds kind of like the CMBR rest frame - we can tell by looking at the CMBR that we're moving at 600km/s relative to some Universally observable reference frame.
    I don't think so. I think we only know we are travelling at 600 km/s relative to the CMBR (average) that we see in our local vicinity.

  4. #344
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    Quote Originally Posted by James R
    I don't think so. I think we only know we are travelling at 600 km/s relative to the CMBR (average) that we see in our local vicinity.
    You are probably correct in this regard.

  5. #345
    Quote Originally Posted by Aer
    Now wait a minute, it can't be both ways. Either the length is contracted for the muon or it isn't.
    What length?

    We've only considered the Earth frame and Muon frame - no other frames as far as I know. So does the muon see length contracted or not?
    The length of objects at rest in Earth's frame will be contracted in the muon's frame, and vice versa.

    Now as for the light reaching the muon, at instant the muon smacks into the Earth, from the edge of the known universe from the Earth frame: Can the muon see distances further in any of the directions and not as far in some other directions depending on when it would see the universe "created"?
    Yes, but be careful... remember that our model universe is not the same as our real universe.

    Also, bear in mind that the muon is seeing the same things as the Earth is seeing - just giving those things different time and distance coordinates.

  6. #346
    Quote Originally Posted by James R
    It defines a reference frame. Whether it is a "universally observable" one is another matter.

    What do you mean by "creation rest frame"? Are you thinking of some kind of averaged CMBR frame?
    We're not really talking about the real Universe... We're talking about a model Universe which is flat and not expanding or contracting, and in which time began some time ago.
    By "creation rest frame" I mean "the frame in which the beginning of time was simultaneous across the whole Universe".


    I don't think so. I think we only know we are travelling at 600 km/s relative to the CMBR (average) that we see in our local vicinity.
    Isn't the CMBR universal?
    Wouldn't you see the CMBR no matter where you were in the Universe (assuming you're not inside a building, dust cloud, or any other microwave opaque cover)?

  7. #347
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    Quote Originally Posted by Pete
    What length?
    When the muon is created, it sees it's distance as 5000m per the Earth calculation of length contraction that the muon would see. This length contraction only propogates between the muon and the Earth? Distance to all other points are not contracted? So we take the distance to the edge of the known universe from the Earth frame and try to predict that length in the muon frame will give us an erroneous result? Why was the prediction to the muon not erroneous?

    Quote Originally Posted by Pete
    The length of objects at rest in Earth's frame will be contracted in the muon's frame, and vice versa.
    Ahh yes, this beautiful symmetry Why is the length of the known universe not contracted in the muon frame as seen by the Earth? I must have missed something.

    If you can understand anything I just said, I'll be quite surprised. Tiredness has gotten the best of me

  8. #348
    Note that I don't think there's anything particular special about the CMBR frame... the laws of physics are no different in that frame to any other frame.

  9. #349
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    I still think we are looking at nonsense here, something went wrong somewhere.

  10. #350
    Hi Aer,
    The hassle we have here is that "the known universe" isn't some static object with a well-defined length.

    Let's say that at the instant of the muon-Earth collision, a huge stick popped into existence at rest in the muon's frame, with one end at each end of the known universe.
    How long is the stick? 150b ly?
    But hang on... the stick is really beyond the known universe, since it will take some time for light from the ends of the stick to reach us, right?

    Furthermore, in the Earth frame, the stick doesn't pop into existence all at the same time. The -x end popped into existence some time ago and has been approaching at 0.98c since then, and the +x end won't pop for some time yet!

    When it does finish popping into existence, it will be well past Earth and 30b ly long in Earth's frame.


    This is fun!
    Let's consider a stick that popped into existence in Earth's frame at the beginning of time, with one end at each end of the currently known universe.
    That would place its ends at events B and C to begin with, and make it 30b ly long.
    When we transformed events B and C to the muon frame, we found they were 150 b ly apart, so won't that stick be 150b ly long in the muon frame?

    No! Because those events weren't simultaneous! In the muon frame, the +x end of the stick was approaching at 0.98c for 147b yrs before the -x end appeared - so the stick is 150b ly - 0.98x147b ly = 6b ly long!

    Do you see why I think that relative simultaneity and length contraction are really two perspectives of the same thing, and why I prefer to use the Lorentz transform?

  11. #351
    Pete:

    The CMBR is found everywhere, but it participates in the expansion of the universe. Therefore, the part of the CMBR in a distant galaxy will have an average motion with respect to the part in our Milky Way.

    Since everybody everywhere sees other galaxies moving away from them, the averaged CMBR frame is still local - it doesn't give us some kind of absolute universal frame.

    I think.

    Aer:

    Why is the length of the known universe not contracted in the muon frame as seen by the Earth?
    I don't understand the question. The Earth doesn't see the muon frame - only the muon does. The words "as seen by the earth" in your question seem to be redundant.

  12. #352
    Quote Originally Posted by James R
    Pete:

    The CMBR is found everywhere, but it participates in the expansion of the universe. Therefore, the part of the CMBR in a distant galaxy will have an average motion with respect to the part in our Milky Way.

    Since everybody everywhere sees other galaxies moving away from them, the averaged CMBR frame is still local - it doesn't give us some kind of absolute universal frame.

    I think.
    Oh, OK. Yes, I think you're right.

  13. #353
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    OK, first of all, I am going to bed - but I'll make one comment first regarding your first statement:

    Quote Originally Posted by Pete
    The hassle we have here is that "the known universe" isn't some static object with a well-defined length.

    Let's say that at the instant of the muon-Earth collision, a huge stick popped into existence at rest in the muon's frame, with one end at each end of the known universe.
    How long is the stick? 150b ly?
    But hang on... the stick is really beyond the known universe, since it will take some time for light from the ends of the stick to reach us, right?
    If we can't see light from beyond 15b ly away, how can the muon see light from further away? Of course we would say, well, it can't.... But that is not what these numbers seem to indicate.

  14. #354
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    Quote Originally Posted by James R
    I don't understand the question. The Earth doesn't see the muon frame - only the muon does. The words "as seen by the earth" in your question seem to be redundant.
    As calculated by us in the Earth frame.

  15. #355
    The muon isn't seeing beyond what Earth is seeing.

    The event 148.5b ly away and 148.5b y ago in the Muon frame is the same event as the one 15b ly away and 15b y ago in the Earth frame.

    Earth and the muon are seeing the same thing. (except for blueshift/redshift, of course )

    Goodnight!

  16. #356
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    I think it is safe to assume your statement:
    Quote Originally Posted by Pete
    Earth and the muon are seeing the same thing. (except for blueshift/redshift, of course )
    Is true.

    Now:
    Quote Originally Posted by Pete
    The muon isn't seeing beyond what Earth is seeing.
    Ok, I'll entertain your assertion - especially given the above.

    Quote Originally Posted by Pete
    The event 148.5b ly away and 148.5b y ago in the Muon frame is the same event as the one 15b ly away and 15b y ago in the Earth frame.
    So the muon can see 148.5b yrs ago? This is accordig to the time on the muon clock of course. Also, in the other direction, I thought you concluded the muon could only see 1.5b yrs ago - IF we only assume 3b yrs have passed since the universe was created in the muon frame, then we have the muon seeing further than the Earth, do we not? Or is there some special type of barrier past 1.5b ly in that direction?

  17. #357
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    Quote Originally Posted by Pete
    We're not really talking about the real Universe
    Now lets qualify our model universe and see if there is anything drastically wrong.

    We assumed the big bang event to be true. This is noted as the "creation of the universe".

    In our real universe, there is accelerated expansion. So when we "see" light that is 15b ly away (took 15b yrs to arrive), that distance is in actuality more like 75b ly away.

    To compensate for the lack of expansion in our model and to keep the calculations simple, we assumed the "creation of the universe" happened everywhere and stars (ignoring time for formation, etc) started emitting light immediately and remained stationary.

    I think that about sums it up? It seems like our reduced model would be acceptable, but maybe not.

  18. #358
    Quote Originally Posted by Aer
    So the muon can see 148.5b yrs ago? This is accordig to the time on the muon clock of course. Also, in the other direction, I thought you concluded the muon could only see 1.5b yrs ago - IF we only assume 3b yrs have passed since the universe was created in the muon frame, then we have the muon seeing further than the Earth, do we not? Or is there some special type of barrier past 1.5b ly in that direction?
    There is indeed a "special type of barrier", which you introduced!

    Consider this diagram, which shows the history of events in the muon's frame.
    It's a space-time diagram. It shows the Universe left-to right, with historical events below the line, and future events above the line.

    The muon's path lies on the vertical axis (this is the muon's frame, so the muon is stationary).
    The Earth's path is the green line.
    The blue lines are light from the beginning of time arriving at the muon and Earth.

    The Red line is the "special type of barrier" - it's the beginning of time. Before time began, there wasn't anything to see, right?



    Well bugger...
    I get a php error uploading files, so my lovely diagrams have gone to waste.
    I don't know if this post is any use, but I've worked on it for a while, so I'm leaving it upanyway.

  19. #359
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    Quote Originally Posted by Pete
    I don't know if this post is any use, but I've worked on it for a while, so I'm leaving it upanyway.


    Whatever you think of my barrier, the light that is reaching the Earth is going to reach the muon upon impact with the Earth as well and the fact that it concludes the light traveled since before the begining of time... well, hum-tee-dum. I guess that's just how it'll have to be.

  20. #360
    Of course.

    In the hypothetically-wonderful-diagrams, the beginning of time barrier is as you'd expect - a horizontal line drawn at t = -15b yr in the Earth frame. But in the muon frame, the beginning of time barrier is not horizontal - it indicates that in the muon frame, the Universe has a different age at different places. In fact, the line crosses the x axis at about x = -3b ly... meaning that in the Muon frame, there is nothing beyond 3b ly years behind it. Time hasn't yet begun past that point.

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