Relativistic parallel rods

Discussion in 'Physics & Math' started by Pete, Apr 30, 2013.

  1. Undefined Banned Banned

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    In my naive way, I can't understand all this fuss over the term "apparent". The term "relative" means much the same thing in the scientific context. But nobody makes a fuss over that being used in the name for relativity theory. Neither term has any kind of "absolute reality-ness" attached to its meaning. Both mean "dependent" on some perspective or other information to give it any meaning in the sense of "invariance" or "absoluteness" or some such "reasoned result" making sense in a logical or mathematical model of the situation irrespective of any particular point of view or "measurements"? I naively think we should be homing in on and pinning down the more serious "physical versus unphysical" usages and meanings, which have been too loosely and confusingly implied by some people here, before we get overexcited about "relativity versus apparency", yes?
     
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  3. Fednis48 Registered Senior Member

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    I think brucep just doesn't like the term "apparent" because, unlike "relative", it doesn't have a super-precise definition in the context of physics. I agree that, as far as people are using the term here, "apparent" can be replaced with "according to some but not all observers" with no loss of meaning.
     
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  5. Pete It's not rocket surgery Registered Senior Member

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    I prefer "measured" over "apparent", because 'apparent' has connotations of visual appearance.
    This can be confusing because it's then not obvious whether an effect described as "apparent" is an effect related to the actual time of events, or related to the time that light from events arrives at an observer.
     
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  7. Undefined Banned Banned

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    As long as it is specifically explained what the "measurement" process involves and what it does not involve there is no preference to my naive understanding. It is when people just use the plain word measurement, when they actually should be saying something like "measurement dependent on certain information between frames or from theoretical manipulation of that information", then it confuses me and makes the rest of that person's "explanations" or arguments "muddy". At least if one starts from the "apparent" stage, then further clarification is required and expected to follow without people getting all emotional about it beforehand because of the mixup with what is meant when saying measurement or "measurement". In my earlier posts with brucep I explained how that was confusing me because people weren't clarifying what exactly they meant regarding the status of a measurement or "measurement" in different frames?
     
  8. OnlyMe Valued Senior Member

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    Even "measured" involves time of light delays, but there is a connotation associated with apparent that suggests some question or uncertainty.

    Pete, did you think about my comment concerning the ridged rod in the diagonal, in the OP of this thread?
     
  9. Pete It's not rocket surgery Registered Senior Member

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    From [post=3068331]a post in another thread[/post]:
    Hi OnlyMe
    I'm assuming you mean "rigid", not "ridged".
    I'm not sure why it would be easier without rods in the boxes, or what the issue with the rod is.
    Are you thinking that the rods should be length contracted differently to what is shown in the animations?
     
    Last edited: May 11, 2013
  10. ash64449 Registered Senior Member

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    but you need to remember that length contraction takes place in the direction of motion pete...
     
  11. OnlyMe Valued Senior Member

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    Yes rigid.

    Pete, what has been bothering me is described below. I am pretty sure it has been addressed by someone and I am just missing it or not remembering...

    In the frame that is length contracted, as the box becomes length contracted the orientation of the diagonal line relative to the velocity of the box changes. That is what you were demonstrating and that is obvious in the case of the diagonal line and "apparent" for a rigid rod. (I use that word here because of the following.) The changing orientation of the diagonal the diagonal line between the corners, changes the "rods" orientation relative to the velocity.., toward in the extreme case right angles. If you just calculate the Lorentz contraction of the rod from it resting orientation it returns different results than the same transformation applied as it moves toward a right angle to the velocity.

    I have to assume that this has been looked at by someone in the past, I just don't remember running across it. The closer the velocity is to c, the more the Lorentz contraction of the rod would affect its cross section and less it would affect its length. In the extreme the rod would be close to its resting length while the diagonal of the box would be approaching the length of its resting sides.

    I think somewhere I mentioned that there was a flavor of Bell's spaceship paradox in this, but I really don't remember if I said that or just thought it.
     
  12. Trooper Secular Sanity Valued Senior Member

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    That's why I thought it was similar to the bar and ring paradox.

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  13. OnlyMe Valued Senior Member

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    Except in the bar and pole paradox the rod and hole do not share a common velocity. The box and diagonal line do. When I mentioned the Bell's spaceship paradox above, I think I mentioned that in reference to the other thread, but the intent was.., whether the Lorentz transformation should be applied to the frame as a whole or to individual components, within that frame.

    For the OP here it might resolve the issue I raised, if the transform were applied to the box and diagonal as a frame, but that would suggest that in the other thread the transform should also be applied to the falling rod as a frame, rather than independently to each end.

    Actually I referenced Bell's spaceship paradox from passive recall and should probably go back and look at it again. I have only ever explored these paradoxes as anstract puzzles. So for the most part each time I encounter one it is like working through the puzzle from scratch, or nearly so.
     
  14. Trooper Secular Sanity Valued Senior Member

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    Oh, I see. It’s similar to problem 12 then, right?

    http://oyc.yale.edu/sites/default/files/problem_set_7_solutions_6.pdf
     
  15. Beer w/Straw Transcendental Ignorance! Valued Senior Member

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    Couldn't there be a formal debate...

    Too much junk in threads to hold a serious interest. They only serve to argue.


    Or was Tach's reasons as simple as this:

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  16. OnlyMe Valued Senior Member

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    I took a brief look at problem 12, and I don't see the same issue. The question I was raising involves only one velocity, as it would affect two physical objects, which at least superficially do not "appear" that they would be equally affected by that common velocity.

    Again, it is clear that as the rigid box transforms to a rectangle the diagonal line between two corners, will both deviate from parallel relative to, the same diagonal line in a stationary box. The problem I see is that at the same time the distance between the corners of the Lorentz transformed rectanglular box, relative to the square stationary box, does become shorter.., measured from the frame where the Lorentz contraction is observable... As the diagonal line moves away from parallel with its stationary counter part, it also moves closer to a right angle with the velocity of the box. As the rod moves from a 45 degree angle relative to its velocity toward a right angle to its velocity, the Lorentz contraction would apply more to its diameter (assuming a round rod) than to its length. Carried to a theoretical extreme, when the diagonal line of the transformed rectangle approaches the lenth of the sides (v = c) there would be no length contraction of the rod end to end and its length would be equal to the length of the diagonal in the rest frame of the box... All from the frame where the Lorentz contraction is observable.

    The only possible solution I can see conceptually, is if the transform were required to be applied to the box frame as a whole, instead of to the box and rigid rod diagonal individually... But that introduces problems for the hypothetical involving the falling rod. The rules for how the transform is applied have to remain constant.

    I will have to take a closer look at problem 12 later, unless someone posts the solution or corrects my misguided conceptualization... I will be mulling it over but will also be out of town most of the day...
     
    Last edited: May 11, 2013
  17. OnlyMe Valued Senior Member

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    I have some passive recall of both the ion bunching and the ion pancaking, but any real discussion would require better references that Tach offered. There is no real description of "measurement" data, methods or controls in the two articles he linked.

    If I remember correctly, the conclusions presented in those articles are debatable. Generally the data did seem, to me to suggest that length contraction is real, but it also suggests possible mechanisms that complicate some of the hypothetical applications we are use to.

    Without better reference a debate would be of no real value. Even if someone wanted to endure, the pain of a debate with Tach.
     
  18. Beer w/Straw Transcendental Ignorance! Valued Senior Member

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    Isn't also length contraction a prerequisite of GR?
     
  19. eram Sciengineer Valued Senior Member

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    Just curious, why did you suddenly bring up GR?
     
  20. brucep Valued Senior Member

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    It's really one big theory that models the physics of curved spacetime using a Riemannian manifold and using a Minkowski manifold to model the physics in an approximate flat manifold where the effects of gravity, on empirical measurements, can be ignored. Think of it this way. The Minkowsk manifold is tangent to every point on the Riemann manifold. This means 'nearly all' local proper frame measurements are conducted in a spacetime that is approximately flat. Physicists sometimes refer to this as the 'tangent space'. All the tests for GR are conducted in the Riemann spacetime. So all the mathematics we use in SR and GR are part of Einstein's Theory of Relativity. For example the GPS requires that frame tick rates of dt_shell=4.4453E-10s be accounted for. If such a 'micro' delta between frame tick rates [or any other measurement] isn't required then you conduct you experiment in the 'tangent space'. Such a place might be particle experiments conducted at CERN. In the 'tangent space' [SR] we account for Length contraction. In the Riemann spacetime the 2nd component of the metric refers to another relativistic effect sometimes called 'gravitational stretching'.

    For the Schwarzschild metric it's

    dt_shell = dr/(1-2M/r)^1/2
     
    Last edited: May 12, 2013
  21. Pete It's not rocket surgery Registered Senior Member

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    It sounds like you're trying to apply length contraction twice. Once from rest to one velocity, then again from that velocity to a greater velocity. Don't do that, it doesn't work that way.
     
  22. Undefined Banned Banned

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    How can the CERN accelerator tube environment during a high-energy run be considered as "flat" or "tangent space" experimental scenario when the particles and the space around them is within a flux region of immensely high electromagnetic energy pumping through that space and into the particles?
     
  23. mikelizzi Registered Senior Member

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    I’d like to try to reconcile the apparently contradictory positions of some very knowledgeable and respected members here.

    First, with regard to the position that parallel vectors in one reference frame transform parallel, I would like to suggest clarifying an assumption built into that conclusion.
    It should read
    “Parallel vectors constructed from pairs of events in one reference frame transform parallel”.

    Second, with regard to Pete’s and my apparently contradictory position that parallelism is not invariant, it should be clarified by saying that
    “Parallel vectors constructed from pairs of points on bodies in one reference frame may not transform parallel”.

    Those two clarified statements are not contradictory as far as I am concerned. And I am prepared to show why. The second clarified statement allows for the behavior that Pete showed in his animation (in a different thread). I, for one, am certain that animation is correct.

    If we can get past the subject of this thread, then we can move on to the really challenging work of explaining how a rod falling and hitting the floor at an angle may not experience shear or axial stresses.
     

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