Special relativity question

Discussion in 'Physics & Math' started by Dinosaur, Feb 24, 2011.

  1. QuarkHead Remedial Math Student Valued Senior Member

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    Hmm, I find this a curious and confusing comment. It seems to imply that the universe (whatever you mean by that) "has its own reality" irrespective of observers moving relative to it, which in turn implies the existence of an absolute reference frame.

    Is that what you mean? Surely this anti-SR, or have I got hold of the wrong end of the stick?
     
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  3. RJBeery Natural Philosopher Valued Senior Member

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    I agree with your take that, basically, length contraction is an illusion but you must be mistaken on the point above. Your "net and pole" paradox is virtually identical to the bar and ring paradox already discussed in this thread, accept you've added a net (and I don't believe that simply adding a net changes Physics). I'll give it a shot to explain what would happen...

    Presuming the bars are held in the direction of travel, as are the net faces such that all are parallel, then a downward motion is necessary for capture. The bar and ring paradox shows that this would translate to holding the net at an angle from the "at rest" point of view, which would normally allow the bar to pass right through the net face with ease. Your introduction of the net itself simply means that the bar being captured would be accelerated with the passer-by such that the length would no longer fit in the net regardless, as the net holder would see it lengthen very quickly.

    Edit: Actually, Farsight, after talking it out I realized that you're right that the nets would be unable to capture the poles, but the ultimate reason is that "capturing" involves accelerating the poles such that their length contraction is removed RATHER than what I interpreted your implication to be, which is that length contraction would not allow the poles to fit through the net faces.
     
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  5. Farsight

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    It certainly does. There is nothing more real than the universe. When an observer changes his motion through it he observes it differently, but the universe hasn't changed. His motion has changed, and this affects him rather than the star he's approaching. The best way to appreciate this is to think of two observers moving towards a star from orthogonal directions. Each will assert that the star is "really" flattened in the direction of his motion, but when they compare notes they appreciate that their perceptions of reality are contradictory. They conclude that they have different perceptions of reality rather than that two contradictory realities coexist.

    It isn't anti-SR, it's just acknowledging modern cosmology and the CMBR dipole anisotropy. If you're way out in space with no nearby stars of galaxies you can gauge your motion through the universe with respect to the CMBR rest frame. Search google to see how this is sometimes described as an "absolute" reference frame because the universe is as absolute as you can get. But if you're inside a non-accelerating box, you can't tell whether you're moving. You cannot detect an absolute reference frame, just like SR says.
     
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  7. Farsight

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    I meant it to be the same, the addition of the net forces us to look more closely at length contraction.

    The point I was trying to make did away with acceleration. Can you and I sweep our nets down over one another as we pass? No. Even though you might measure my pole to be length contracted to only 1m, you cannot sweep your net over it like so: |_| . And nor can I do the same to you.

    The acceleration is causing confusion here. Forget about it and imagine the pole keeps on going. If you could sweep your net down over the whole length of my pole it would leaves a hole in the rear face of your net. But you can't sweep your net down over the whole length of my pole to do this, and I can't do the same to you.
     
  8. Tach Banned Banned

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    LOL, you don't understand what you are reading. Again. And you twist what you don't understand to fit your misconceptions.
     
  9. przyk squishy Valued Senior Member

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    More correctly, it's because you've accelerated and your notions of distance, time, and simultaneity have changed.

    Actually, the answer is "yes", just not for long. If we caught each other's poles this way and didn't immediately release them, our nets would fit over the poles just fine but then break as the poles were slowed down and stretched back to their rest lengths.

    No he doesn't. He sees it contracted and vertical. The smeared out /\ shape isn't something anyone sees, you get it by drawing where a single light pulse was at different times all on the same diagram. But at any given time, one mirror is always directly below the other and a light beam reflecting between the two would just appear as a vertical line, thinner than its rest width.

    Even with stars and a CMBR, we can only say who's moving relative to the stars and/or CMBR. There's nothing unique or "absolute" about the CMBR frame: physics is the same in that frame as in any other (locally) inertial frame.

    Because it isn't. Or at least, to the extent you're right, you're not explaining yourself very well. You seem to have the right basic idea, that the measuring instruments of an observer are affected after they've accelerated to a different inertial velocity, but you've got the details wrong. The moving observer isn't "smeared out", they're length contracted. It might sound paradoxical that a length-contracted observer could see the one "at rest" as length contracted. In relativity, this is made possible by the fact that the "moving" and "rest" observers disagree on their notions of simultaneity.

    This isn't a very good explanation of relativity. The author has a number of misconceptions, and where he's right, he tends to have stumbled on "insights" that are already well known. For example, on page 2, after recalling that the wave equation is Lorentz invariant, he says:
    Lorentz invariance is a property of equations that are Lorentz invariant. This is not restricted to waves. For example the relativistic version of Newton's second law, \(f^{\mu} \,=\, \frac{\mathrm{d}p^{\mu}}{\mathrm{d}\tau}\), is Lorentz invariant and yet it applies to point-like particles. It has nothing to do with waves. On the same page:
    I'll get into this later, but for now I'll just point out that he doesn't seem to realise that relativity already answers this question, making his essay rather poorly motivated.

    After showing that we can rederive the relativistic relations just by defining length in terms of wave propagation time, and recalling the SI definition of length (page 5):
    he reaches the conclusion on page 7 that:
    First of all, I have no idea what the first sentence is supposed to mean, since the only things we can say about space and time are what we can measure about them using our measuring instruments. As to the second, it's true that we can render all the relativistic relations regarding distance and time "true by definition", eg. just by enforcing the SI definition quoted above, but this misses the whole point of relativity. In relativity, the principle of relativity - that the laws of physics are the same in all reference frames - implies that all possible operational definitions of distance and time would transform the same way from one frame to another. If one set of definitions of length and time Lorentz-transforms, then according to relativity, they all do.

    After considering waves in elastic solids, he reaches the conclusion on page 13 that (emphasis added):
    I'd sum up my reaction here as: No shit, Sherlock!. This idea is so old that it arguably even predates relativity. For example, you might know that Lorentz and Fitzgerald proposed length contraction as a possible explanation for the null result of the Michelson-Morley experiment. This idea didn't just drop out of the sky: it was inspired by Heaviside's discovery that, according to Maxwell's equations, the electromagnetic field around a moving point charge would be length contracted compared to the electrostatic Coulomb field around a charge at rest. The idea was that if the intermolecular forces in matter had the same sort of character as electromagnetic forces, this would naturally imply the length contraction of moving material objects.

    This was about fifteen years before Einstein published his 1905 paper. The whole point of Einstein's theory of relativity was to make this idea precise, in postulating that all the laws of physics had the same symmetry property (Lorentz invariance) as electrodynamics does. This has been one of the central guiding principles of theoretical physics ever since. If I put the Standard Model lagrangian in front of Close, he might "discover" that the whole theory, and not just the electrodynamic sector, was Lorentz invariant. This isn't just some happy accident: the Standard Model was deliberately constructed that way.

    So, to recap, Robert Close has "discovered" something about relativity that Einstein explicitly included as a postulate in his theory and which has been a cornerstone of theoretical physics ever since. Where's he been the last hundred years?

    Of course, his next statement:
    doesn't follow. Relativity only requires that matter is governed by Lorentz invariant laws, which aren't restricted to just the wave equation. If he thinks Lorentz invariance implies "everything is composed of waves propagating at c", then basically most of modern physics consists of numerous counter-examples to this conclusion.
     
    Last edited: Feb 27, 2011
  10. Pete It's not rocket surgery Registered Senior Member

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    But you can't tell whether the entire universe is moving or not, which is the essence of SR. You might like to assume it's at rest (because it's the universe, man!), but that's just a convenient assumption, no more absolute than your convenient assumption that the ground is at rest when you go for a walk.

    I sympathize with this point of view, but I think it's not correct.

    I think that length is a property of a relationship between an object and a reference frame. Length contraction is what we call the way length changes as the relationship changes. In this paradigm, length contraction is just as real as length, but length is more nebulous than we might intuit.


    But...
    There is a valid intermediate paradigm in which relative length contraction is an illusion and the intuitive physical reality of length is retained, that you might find useful to think about.

    The first paragraph might be uncomfortable, but read on.

    Consider the idea that there is a luminiferous ether with some definite state of motion. In the rest frame of this ether, light always moves at c, measurements of length are real physical lengths, measurements of time are real physical times, and simultaneity is absolute.
    Now, imagine that things moving through this ether undergo physically length contraction and time dilation by the lorentz factor.

    In this paradigm, we find ourselves in a Universe identical to an SR universe. We can't detect the ether wind. It is impossible to absolutely synchronize our clocks. Using any sensible method of synchronization leads to clocks that are absolutely out of synch in such a way that light seems to propogate isotropically at constant speed, and all clocks and rulers moving relative to us seem to be dilated and contracted. In other words, it means that all inertial reference frame look exactly like the absolute ether frame.

    So in that paradigm, length contraction is real in the absolute reference frame (which is undetectable), but illusory in all other reference frames.

    EDIT:
    The Robert Close paper linked by Farsight seems to be founded on exactly that paradigm.

    But as przyk says, the paradigm isn't novel, and is not useful in practice. But I do think it is potentially a useful tool for learning/teaching the concepts of SR, particularly in this online amateur environment. I wish I'd understood it back when MacM was around, because his biggest issue was the notion of mutual length contraction and time dilation. This paradigm shows that mutual contraction and dilation are a natural consequence of absolute contraction and dilation, and also that an absolute reference frame doesn't seem to be measurably different to any inertial reference frame.)
     
    Last edited: Feb 28, 2011
  11. RJBeery Natural Philosopher Valued Senior Member

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    If we ignore acceleration, as you suggested, then the answer is yes. If you examine the bar and ring paradox you will see why: the net face's velocity is approaching the contracted bar at an angle (by necessity if the net face is to remain parallel to the bar from the net's perspective!). The bar fits in the net face with no problem from the net's perspective "because" the bar is much shorter than the net. Conversely, from the bar's perspective, we have a shortened net face approaching us but it ISN'T PARALLEL to us! It's actually tilted such that, again, the bar fits easily through the net face "because" the bar is entering one side before the other...

    Here is the relevant Wiki quote explaining this. This disturbed me at first, but then I realized that when we are discussing two lines or planes remaining parallel (such as the pole and the net face) as they move toward each other we are actually invoking the concept of "now". IOW, both ends of the net face must remain the same minimum distance from the pipe "at the same time", and of course "at the same time" has no absolute meaning in Relativity...therefore parallels do not necessarily remain so if they involve Relativistic movement toward or away from each other!
     
  12. RJBeery Natural Philosopher Valued Senior Member

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    Yep, I've read this before, and I get it. We have no way to preclude the aether and an absolute frame. Frankly, I rather like the idea of an absolute frame but that's neither here nor there. My point about length contraction being an illusion is simply the way I deal with it in my head. I "choose" to assign an object's true length as that which is measured in its rest frame. I don't do this arbitrarily, btw, but to explain in more detail will require some visuals. Maybe I'll start another thread this week...
     
  13. Emil Valued Senior Member

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    We do not take a reference system nor A nor B.
    We take into account a reference system moving with half the relative speed between the two bodies.
    So we have two bodies approaching from opposite sides with the same speed.
    Same speed so there is no problem.

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    Edit.
    I was wrong.The reference system is not moving.It is find midway between the two bodies and is "stationary".
     
    Last edited: Mar 1, 2011
  14. Emil Valued Senior Member

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    2,801
    And a question.
    If the two bodies have a speed equal to 51% the speed of light and opposite directions.
    They arrive, suppose in eight seconds in the middle. So they met in 8 seconds.
    Now we're moving the reference system on body A.
    What was the speed of B into a new reference system?
     
  15. siphra Registered Senior Member

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    .81c
     

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