Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Length contraction in Lorentzian relativity

  1. Feb 14, 2009 #1
    Hi,

    I'm trying to understand Lorentzian relativity (Lorentz ether theory, whatever) which is empirically equivalent to the Einsteinian STR. I have, however, a problem in comprehending length contraction.

    In the Lorentz theory we have a preferred frame and length contraction is a real physical effect. It has a causal explanation in terms of motion of the body with respect to this absolute space which causes distortions in the electromagnetic field and hence in the intermolecular forces holding rods and clocks together.

    Of course no experiment has ever been performed which checks length contraction directly, as there is no known way to accelerate a macroscopic object to relativistic speeds.

    However, why doesn't the following imply a difference between Einsteinian STR and Lorentz?

    Imagine we can build a spaceship which will travel at 0.995c. In the frame of a stationary observer, everyone agrees that the spaceship looks squished as it flies past (because of a perspective effect in Minkowski spacetime for STR, or because it actually is squished for Lorentz).

    However, if I am actually on the ship then other things inside either should look squished (because they are - Lorentz) or they do not look squished (because all inertial frames are equivalent - Einstein). Now whenever I have seen this discussed one just reads that in Lorentz theory measuring rods are distorted too so I can't measure the effect. But surely if I'm going at 0.995c then things will just look distorted (spheres not being spherical etc) and I can tell the damned measuring rod is a lot shorter than it used to be (because it's now square, rather than a long rectangular metre rule).

    So maybe it's because my eyes are distorted, or whatever - but isn't this dangerous? Being compressed to the thickness of a piece of cardboard can't be good for the human body surely..

    What's the flaw here? All opinions gratefully received.

    Cheers,
    Zenith
     
  2. jcsd
  3. Feb 14, 2009 #2

    atyy

    User Avatar
    Science Advisor

    As long as everything in your body is equally compressed (including the chemical bonds), you would be ok.
     
  4. Feb 14, 2009 #3

    Dale

    Staff: Mentor

    The part in bold is incorrect. What makes you think that?
     
  5. Feb 14, 2009 #4

    atyy

    User Avatar
    Science Advisor

    High uniform velocity won't kill you. High accelerations even to relatively low velocities will.
     
  6. Feb 14, 2009 #5
    I know it's incorrect in Einsteinian STR where every inertial frame is equivalent, but I'm trying to understand the Lorentzian viewpoint. There is a real physical length contraction, because I am going at 0.995c with respect to the fixed absolute space. Why can I not see the distortion if I am on board a ship going that fast with respect to the 'aether'?
     
  7. Feb 14, 2009 #6
    Why would I be OK? I'm only physically compressed in the direction of travel - that distorts my shape - and if I'm only an inch across in 1 dimension that is going to block some blood vessels.. There's go to be health issues.

    Thus high speed space travel is dangerous in the Lorentzian case and not so in Einsteinian STR?
     
  8. Feb 14, 2009 #7

    Dale

    Staff: Mentor

    I understand that you are talking about Lorentzian aether theory. My question is why, using that theory, you would think there would be any visible distortion when you acknowledge that there is no measurable distortion. It seems like a strange assumption, particularly since so many of our measuring instruments use optics.

    How so? Your blood cells and platelets would also be contracted so they would not block the vessel.

    You are just making some rather strange assumptions that I don't understand.
     
  9. Feb 14, 2009 #8
    How do you know that? Have you tried it? We can't accelerate macroscopic objects to anywhere near a speed where the contraction would even be noticeable.

    And again, you're right in a spacetime where all inertial reference frames are equivalent. But in the Lorentzian theory where we have a privileged frame and a real physical contraction if we travel at high speeds with respect to that frame, I don't see why it is true.

    Apologies if I'm being slow, but everyone seems to be answering my question using the Einsteinian formulation, not the Lorentz one.
     
  10. Feb 14, 2009 #9

    Dale

    Staff: Mentor

    No, we are not. It is just that the things that you are saying are not predictions of the Lorentz formulation.
     
  11. Feb 14, 2009 #10
    I didn't acknowledge that there is no measurable distortion. What I'm saying is roughly as follows:

    In the Lorentz theory a physical object (a ball 1 metre across in absolute space, say) is contracted in the direction of travel. It is true that - as all the books say - a metre rule pointing along that direction will also be contracted. So if you use the metre rule to measure the diameter of the ball then it will still read '1m' because both objects have contracted.

    But surely the ball will have distorted so that it is no longer spherical, and if I go to high enough speeds the length of the metre rule will be equal to its transverse width. These are distortions that I ought to be able to see with my eyes, no?
     
  12. Feb 14, 2009 #11

    Dale

    Staff: Mentor

    Ahh, there is the problem. You either don't understand the motivation or the implication of Lorentz's aether theory (LAT). Allow me a brief historical digression that will hopefully clear things up.

    Prior to Lorentz the prevailing aether theory (AT) essentially said that EM radiation propagated through a medium called the luminiferous aether and that Maxwell's equations, which predict a wave velocity of c, were only valid in the aether's frame. If you were moving through the aether then AT predicted that the speed of light would be some other value besides c, and this would lead to detectable optical effects (basically the opposite of what you were describing above, optically things would look stretched out in the direction of travel). Michelson and Morley built a very sensitive interferometer in order to detect precisely these kinds of optical effects. Although they couldn't accelerate a macroscopic object to a significant fraction of c, their interferometer was sensitive enough to detect the expected optical effects at speeds of about 8 km/s through the aether (Earth's speed around the sun is ~30 km/s).

    As you know, they obtained a null result, which dealt a serious blow to AT. Lorentz' then proposed his LAT in order to explain the lack of any optical effect. Basically, he asserted that there was some physical length contraction and time dilation that exactly counteracted the changed speed of light so as to eliminate the optical effect. So, things got physically squished in such a way that, with the changed speed of light, they looked normal. Therefore, in LAT you have length contraction precisely in order to avoid any optical distortions of the type you are describing. That is why your suggestions seemed strange to me and why I mentioned that you were describing things that were not predictions of LAT.
     
  13. Feb 14, 2009 #12
    You're perfectly correct. Along one space dimension. The contraction (along the x-axis, say) is not measurable because the measuring device contracts in the same direction.

    The point I'm trying to make is that I don't understand why the three-dimensional effects are not visible.
    So if a ball that I am watching distorts into a flattened sphere, then the shape of the lens in my eye has to distort in such a precise way that the flattened sphere looks spherical again.

    And there is the problem of physiological effects. Let's say I go to 0.9999999c. My body will be physically flattened to less than the width of a piece of paper. You and the other poster were trying to imply that this has no physical, biochemical effects. I don't see why not. As far as I can see I would die in short order.

    Again, I'm perfectly happy to concede the point - but I haven't yet heard an argument which convinces me.
    Sorry to be obtuse..

    Zenith
     
  14. Feb 14, 2009 #13

    Dale

    Staff: Mentor

    Again, you are describing things that are simply not predicted by LAT. The Lorentz transform includes three spatial dimensions and the Michelson Morely interferometer worked along two spatial dimensions. The optical effects you are thinking of are simply not there, in fact, getting rid of them is the whole point of LAT.
     
  15. Feb 14, 2009 #14
    OK : Standard configuration (coord systems aligned; same origin; v along x-axis - Lorentz transformations are:

    t' = gamma (t-vx/c^2)
    x' = gamma (x-vt)
    y' = y
    z' = z

    with the Lorentz factor gamma = 1 / sqrt{1-v^2/c^2}.

    The three spatial dimensions are all there, as you state, but only one of them is changed. You're squashing a ball along the x-axis - it looks flattened. If you squash my eyeball lens the same way, the equations of geometrical optics don't imply that I see the ball as a perfectly sphere.

    And what about the physiological effects. Is it really true that a body can still live when flattened to the thickness of a piece of paper? If not, then Lorentz and Einstein are not empirically equivalent.

    I'm sorry - it's not obvious to me.
     
  16. Feb 14, 2009 #15
    Hello zenith8.

    Trying to paraphrase DaleSpam i think the point is that due to our relative motion through the aether a length increase was expected. The Lorentz contraction was "designed" to exactly balance out the expected increase. This was needed to explain the null result of MM. So nothing happens.

    Matheinste
     
  17. Feb 14, 2009 #16
    Hello,

    Hmmm.. Are you sure? I thought that due to our relative motion through the aether, no length contraction at all was expected. Hence the Galilean transformations used before MM. Then Lorentz/Fitzgerald came along and said there was actually a 1D length contraction, and that indeed explains the null result of MM.
    I completely understand this point.

    It just seems to me that a distortion of a 3-dimensional object along one space dimension is visible and not compensated through a distortion of the eyeball or anything else. That is *not* what MM was designed to detect.

    And squashing of your body to a significant extent *will* kill you, surely? We are talking about a real physical distortion in Lorentz theory where the atoms actually get closer together. Biochemistry with active sites on enzymes and all that will no longer function in the same way.

    Zenith
     
  18. Feb 14, 2009 #17
    Hello zenith8.

    The MM experiment was designed to measure the speed of the earth through the aether. A null result was not expected. The contraction was proposed to compensate for the expected effects and explain this null result. As nothing happens, even in LAT,due to the expected effect and the compensating Lorentz, contraction, the body has no problem.

    Matheinste.
     
  19. Feb 14, 2009 #18
    Er, really? I did not say that people expected a null result in the MM experiment - of course they didn't! You said, and I quote: "due to our relative motion through the aether a length increase was expected". What I said was that this is absolutey not true. No-one was talking about either length contraction or length increases before Michelson-Morley. People expected lengths to stay the same, hence they would be able to detect the motion of the earth through the ether.

    You seem to be misunderstanding my original question as well as misquoting what I said, no?

    Zenith
     
  20. Feb 14, 2009 #19
    Hello zenith8.

    ""The MM experiment was designed to measure the speed of the earth through the aether. A null result was not expected."" This was meant as a statement of fact and i did not not mean to imply that you said or believed otherwise.

    Matheinste

    I just wanted to clear that up quickly before any further response.
     
  21. Feb 14, 2009 #20
    Ah sorry - my mistake.

    Zenith.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Length contraction in Lorentzian relativity
Loading...