How to test length contraction by experiment?

Discussion in 'Physics & Math' started by PengKuan, Jun 17, 2019.

  1. PengKuan Registered Senior Member

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    136
    Suppose the higher counting station has a clock synchronized with that on the ground. When the muon passes the counting station, the clock shows zero. When the muon passes the ground , the clock shows 1.36 micro second. This is correct with Lorentz transformation in the frame of the muon.

    But in the frame of the ground, the clock shows 34 micro second. Then, is it 1.36 or 34? Both are legitimate for Lorentz transformation. There is contradiction.

    I'm not questioning the knowledge of SR of anyone, but questioning the consistency of SR itself.
     
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  3. Halc Registered Senior Member

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    Your question just got me to wonder what my max velocity change over one second has ever been. No, I've never done drag racing.

    Meanwhile, I had no idea that the question was muon related. That seems to be something you're discussing with PengKuan.
     
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  5. billvon Valued Senior Member

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    I know what mine has been - 110mph.
     
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  7. Confused2 Registered Senior Member

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    I spent many years applying SR equations without understanding why and then wondering what the result actually meant. For years it looked (to me) like a clock sychronisation issue but this made no sense because SR isn't a clock sync issue it is the result of the laws of physics being the same in every frame*. Given a free hand for PenKuan I would prescribe a derivation of time dilation from nothing more than than the laws of physics being the same in every frame - in particular the speed of light is the same in every frame. Having established time dilation as a natural consequence of the way the universe is constructed then length contraction follows naturally. The difference is comparable to the effect of looking at a picture of a fire and setting fire to your hair.

    *the frames here are inertial and in locally flat space.

    There is a fairly good light clock derivation of time dilation here

    https://en.wikipedia.org/wiki/Time_dilation#Simple_inference_of_velocity_time_dilation

    I went through several light clocks and was still left wondering what I just did there so I looked for more derivations of time dilation. The best came from David Waite which is now lost to us. I also made up my own which worked for me and might be worth trying if all else fails.

    Without first addressing the origin of a result that appears counter-intuitive I predict any meaningful answer about length contraction will get lost in the muddle of clock sychronisation.
     
  8. Neddy Bate Valued Senior Member

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    2,548
    You should be able to work this out yourself from this table:
    http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/muon.html#c4

    Please Register or Log in to view the hidden image!


    IN THE EARTH REFERENCE FRAME:
    Event: Muon passes HIGHER earth clock:
    Higher Clock Time: 0.0 micro seconds
    (Lower Clock Time: 0.0 micro seconds)
    Muon Clock Time: 0.0 micro seconds
    Event: Muon passes LOWER earth clock:
    (Higher Clock Time: 34.0 micro seconds)
    Lower Clock Time: 34.0 micro seconds
    Muon Clock Time: 6.8 micro seconds

    IN THE MUON REFERENCE FRAME:
    Event: Muon passes HIGHER earth clock:
    Higher Clock Time: 0.0 micro seconds
    (Lower Clock Time: 32.6 micro seconds)
    Muon Clock Time: 0.0 micro seconds
    Event: Muon passes LOWER earth clock:
    (Higher Clock Time: 1.4 micro seconds)
    Lower Clock Time: 34.0 micro seconds
    Muon Clock Time: 6.8 micro seconds

    Notice that the earth clocks which are synchornised in the earth frame, are not synchronised in the muon frame. Notice also that in the earth frame, the RATE of the muon clock is 1/5 the RATE of the earth clock. And notice also that in the muon frame, the RATE of the earth clocks is 1/5 the RATE of the muon clock, yet there is NO CONTRADICTION. Everyone agrees the coordinates of the second event are"Lower Clock Time: 34.0 micro seconds" and "Muon Clock Time: 6.8 micro seconds".
     
    Last edited: Mar 13, 2020
  9. Neddy Bate Valued Senior Member

    Messages:
    2,548
    And, in case anyone wants to see the actual Lorentz transformations for the above muon experiment, here they are:

    First, the table shown in post #185 (above) mixes units of microseconds and kilometers, so we want to fix that so we are using microseconds and light-micro-seconds. (A light-micro-second is the distance light travels in one micro-second, in a vacuum.)

    Since the speed of light is about 300000 km/sec it follows that 300000 km is about the distance light travels in one second, and so 1/1000000th of that is the distance it travels in one micro-second, which is 0.3 kilometers. So, taking our given distances (from above) of 2km and 10km, we just have to divide each of them by 0.3 km to convert them to light-micro-seconds:
    2km = 2/0.3 = 6.7 light-micro-seconds
    10km = 2/0.3 = 33.3 light-micro-seconds

    EARTH FRAME:
    v = 0.9798c
    gamma = γ = 1 / √(1 - (v²/c²)) = 5.0
    t = 34.0
    x = 33.3

    t' = γ(t - (vx / c²))
    t' = 5.0*(34.0 - (0.9798*33.3)) = 6.8 micro-seconds

    MUON FRAME:
    v = 0.9798c
    gamma = γ = 1 / √(1 - (v²/c²)) = 5.0
    t' = 0.0
    x' = 6.7

    t = γ(t' + (vx' / c²))
    t = 5.0*(0.0 + (0.9798*6.7)) = 32.8 micro-seconds LOWER CLOCK time when muon passes UPPER CLOCK.

    MUON FRAME:
    v = 0.9798c
    gamma = γ = 1 / √(1 - (v²/c²)) = 5.0
    t' = 6.8
    x' = 0.0

    t = γ(t' + (vx' / c²))
    t = 5.0*(6.8 + (0.9798*0.0)) = 34.0 micro-seconds LOWER CLOCK time when muon passes LOWER CLOCK.
     
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  10. PengKuan Registered Senior Member

    Messages:
    136
    I agree with that correct application of The Lorentz transformation. When muon passes Higher Clock, Lower Clock marks 32.6 micro seconds, when muon passes Lower Clock, Lower Clock marks 34 micro seconds. So, for the Lower Clock, the duration of the travel is well 34-32.6 = 1.4 micro seconds. So, for the ground, muon has done the 10 km in 1.4 micro seconds, and its velocity is 10000/1.4 10-6=23.8c.

    What counts in the time of the ground is the duration, not the mark at one given time.

    In fact, this paradox is a disguised twin paradox. The twin on the ground cannot agree with the twin traveling with the muon. Since the twin paradox cannot be solved, this paradox neither can be solved.
     
  11. DaveC426913 Valued Senior Member

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    18,935
    The twin paradox is not an actual paradox. Where did you get that idea? Only misunderstandings of relativity lead to the apparent paradox.

    This might be a good time to read up on it to see how it is resolved correctly.
     
  12. PengKuan Registered Senior Member

    Messages:
    136
    The twin paradox cannot be solved with Lorentz transformation because it gives contradictory result. One has resolved to accept the contradictory result because no one could give a solution.
     
  13. DaveC426913 Valued Senior Member

    Messages:
    18,935
    No and no.

    It has the correct resolution if you apply SR correctly. It is only an apparent paradox if you apply SR incorrectly.

    Read up on it.
     
  14. PengKuan Registered Senior Member

    Messages:
    136
    If the twin on earth uses Lorentz transformation, he will find the time in the spaceship is slower.
    If the twin in the spaceship uses Lorentz transformation, he will find the time on earth is slower. Does he wrongly apply Lorentz transformation?
     
  15. DaveC426913 Valued Senior Member

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    18,935
    You have not studied the twin paradox.

    There's little point in discussing it until you've read up on it. If you have specific questions about it, that would be the time to ask.
     
  16. PengKuan Registered Senior Member

    Messages:
    136
    Hmmm, How do you know that I did not study the twin paradox?

    For giving you a hint, read my « Twin paradox when Earth is the moving frame » the title is clickable.
     
  17. Confused2 Registered Senior Member

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    609
    My impression is that this line owes more to expediency than understanding.
    Edit..Perhaps if you could explain in more detail - all might become clear.
     
  18. Halc Registered Senior Member

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    350
    Please don't try to learn relativity from PengKuan or his linked papers. They all seem not only very wrong, but deliberately so, seemingly for the purpose of discrediting the theory rather than explaining it.
     
  19. phyti Registered Senior Member

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    732
    PengKuan

    #144;

    [(Adding to earlier responses) While moving inertially, the ship is in a state of equilibrium with no forces acting on it. That means the only time it can become length contracted is when it is accelerating. The moving observer cannot detect his own td and lc. He cannot detect his own inertial motion, which is why he can consider himself at rest, per SR. He can only detect a change in velocity. He is affected by motion to the same extent as all objects in his frame, thus his ship will always measure the same.]

    #157;

    [The 1st postulate requires 2 observers with relative motion, to have reciprocal descriptions of events for the other. If the anuat's ship is lc as seen from the moon as it passes, then the anaut should see the moon lc as it passes.]

    [You can perform this experiment in the privacy of your own home. Measure a metal rod. Heat it with a torch. Measure it again. Hoover! It changed length in its own frame!
    Conclusion...there are no rigid rods.
    We are not measuring the changing distance of observer and target. In my example, the anaut concludes, the earth-moon distance has contracted, along with the earth and moon, as they pass by in the opposite direction.]
     
  20. phyti Registered Senior Member

    Messages:
    732
    Halc #156;



    [Maybe anomalies isn't the best word choice.

    Romer's observations of Jupiters moons, which contradicted instantaneous light speed,

    Fizeau experiments with various mediums,

    Lorentz and his electron theory,

    the null results of the MM experiment,

    electromagnetic processes, thus the long title 'OTEOMB'.

    Collectively, these details gave him reason to challenge current thinking, specifically absolute concepts.
     
  21. DaveC426913 Valued Senior Member

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    18,935
    Because, when interpreted correctly, it does not lead to a paradox.
    And yet, you think it does, so you need to study it until you figure out where you went wrong.
     
  22. Confused2 Registered Senior Member

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    609
    Another attempt at this single line.
    Generally (at the heart of the Twin Paradox):-
    "Why does time dilation occur in one frame and not the other?"
    In particular:-
    "Why does a clock carried between two points in a frame behave differently to a clock that remains stationary with respect to those two points?"
     
  23. Confused2 Registered Senior Member

    Messages:
    609
    PengKuan clearly isn't going to take any notice of me.
     

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