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Special relativity implies very odd results

  1. Dec 11, 2011 #1
    Do you want to interpret this as a fallacy in relativity? I posted part of this example before. Which is: what if you had 2 rocket ships a and b traveling from planet X to planet Y and they were both going 0.9999 times (or very close to) the speed of light, let d be the distance from X to Y, and the ships are 7/8d distance apart and a was only 10mi or so from Y and b was only 10mi or so from X. Then observers on both crafts would observe that the distance from X to Y would only be about 20mi or so (Ʃ of all the distances) because of the very well known length contraction formula. And what if rocket ship 'a' suddenly took a right angle turn? Then the distance from b to Y would suddenly seem to increase to many thousands of miles!

    I didn't go as far with this the last time I said there appears to be a contradiction here and one of you very intelligent physicist wannabees told me this is physics, not math. But, Einstein's conclusions were all based on these very same sort of math calculations. It was because many of his results were verified by experimental observation that they became accepted. What say you to the above?
     
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  3. Dec 11, 2011 #2

    DaveC426913

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    The error is in your understanding of relativistic contraction.

    This is ambiguously worded. In particular, the word 'suddenly'.

    At .9999c, rocket a has a transverse (sideways) velocity relative to all other observers of zero. When it "turns" sideways, it still has transverse v of zero. It is simply pointing its nose to the side. Absolutely nothing else has changed. Rocket a could happily set itself spinning on its axis and it would have no effect on any aspect of the experiment.

    Rocket a continues to have a transverse v of zero so until and unless it begins to accelerate transversely - which it does so at normal accelerative rate.

    Do you acknowledge this?
     
    Last edited: Dec 11, 2011
  4. Dec 11, 2011 #3
    I shouldn't have said only 10mi+10mi=20mi or so because this would be 1/8th the distance from X to Y which would make the planets awfully close.
     
  5. Dec 11, 2011 #4

    ghwellsjr

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    Special Relativity is all about describing and analyzing everything from a single inertial Frame of Reference. If you do that, there will be no odd results, no fallacies, and no contradictions.
     
  6. Dec 11, 2011 #5

    DaveC426913

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    It doesn't matter. Yes, at extremely high relativistic velocities, the planets could get awfully close. Not a problem.

    What you're failing to recognize is that the rocket cannot 'suddenly' make a 90 degree turn. It must accelerate from zero in the new direction. As it does so it will eventually reach relativistic velocities in this new direction. As it does this, length contraction in the new direction will become apparent.
     
  7. Dec 11, 2011 #6
    I'm thinking rocket 'a' is still going at the speed of near c, but at right angle to the path from X to Y. But, this doesn't matter. Its now that its velocity on the path from X to Y is now zero. Thinking of rocket ships should be analogous to 2 point charges moving in a wire. Since a current in a wire would have thousands of charges moving it would be hard to observe anything like this. If one ship was moving at near c velocity the distance from X to Y would be very slightly less for people on the ship. I think you see what I'm saying in my previous post.
     
  8. Dec 11, 2011 #7

    DaveC426913

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    No it isn't.
    No it isn't.


    Ignoring circuitry analogy...

    This is not a problem. Let it go.

    Distance from X to Y can be much much less. At extremely high v, distance from X to Y could, in fact, be reduced arbitrarily small. Again, no problem here.


    The only problem here is in your mistaken concept that a rocket ship can suddenly turn from going "North" at .9999c to going "West" at .9999c. It simply can't. That is the crux of your misunderstanding. Embrace this. Let everything else go.

    In order to go from .9999c "North" to .9999c "West" the spaceship must do two unrelated course changes:
    1] It must begin to accelerate in a Westerly direction starting from 0 to .9999c
    2] It must decelerate in its Northerly direction of travel from .9999c to 0.
    Until it does at least one of these things, nothing in the experiment will change.

    The one you're really stuck on is 1]. It must begin accelerating Westerly starting from zero. Only when it has been accelerating so long that it's reached relativistic velocity in a Westerly direction, will it begin to experience any contraction along that axis.
     
    Last edited: Dec 11, 2011
  9. Dec 12, 2011 #8
    So, what if ship 'a' crashed into the surface of planet Y instead of making the right angle turn-oops, major screwup? You say with its relativistic mass and extremely high velocity it would transfer a huge amount of kinetic energy to Y. Maybe even enough to give Y some new velocity. And it might even travel over a mile deep before it completely stopped, but in 2 or 3 seconds observers on ship 'b' would see planet Y suddenly shoot off into the distance.

    What if there were no rocket ship 'a' and in its place there were a piece of dirt of arbitrarily small size moving with the same velocity vector as 'a' had and it hit the surface of Y? Then Y would barely know it. And, in this case those on ship 'b' would originally think they could almost reach out and touch Y. So then, if a ship is moving at near c and other objects were moving in front of it in the same direction at the same speed the ship's destination would be far closer.
     
  10. Dec 12, 2011 #9
    I think I might have answered my own question. What if no actually particle is considered at all, but just a point in space is considered to be moving this velocity and these points would always exist. So, If you could get up to near the speed of light distant planets etc would only be a stone's throw away.
     
  11. Dec 12, 2011 #10

    Dale

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    Your scenario describes a non-inertial reference frame. Why shouldn't distances suddenly increase a thousand-fold in a non-inertial reference frame?

    As ghwellsjr mentioned, if you avoid non-inertial reference frames then you would never get such a situation, and if you don't avoid non-inertial reference frames then you expect such situations. (btw, the standard formulas, such as length contraction, don't apply in non-inertial frames)
     
  12. Dec 12, 2011 #11

    Fredrik

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    I think you should consider a simpler scenario instead. What if there's just one rocket and its pilot slams the breaks and comes to a quick stop (relative to X and Y)? Will the distance between that rocket and the destination planet increase?

    Short answer: It won't increase in any inertial frame.

    Longer answer: Suppose that we compare the following two distances:

    a) the distance between the rocket that has just "stopped" and the destination planet, in an inertial coordinate system in which the rocket was stationary before it "stopped",

    b) the distance between the rocket that has just "stopped" and the destination planet, in an inertial coordinate system in which the rocket was stationary after it "stopped".

    Then yes, the distances will be very different, but there's no reason to think that this is a contradiction, since we're talking about coordinate assignments made by two different coordinate systems.
     
  13. Dec 12, 2011 #12

    Fredrik

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    I don't have a problem with this. I just think it's an unnecessary complication, because now we'd have to do velocity addition in 2+1 dimensions.

    It's of course impossible to do it with an actual rocket engine, but no matter how small a region of spacetime you would choose for me, I'd still say that it's possible in principle to make that velocity change inside of that region, because there's nothing in SR that says that it's impossible.
     
  14. Dec 12, 2011 #13

    DaveC426913

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    The OP is having trouble seeing a sharp turn as an acceleration like any other. The OP thinks that going to .9999c North to .9999c West is merely turning a corner. The OP is envisioning a dramatic change in length contraction along the north axis to along the West axis because of this and thinks this is paradoxical.
     
  15. Dec 12, 2011 #14

    DaveC426913

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    None of this has to do with your original question. This is causing you, and everyone else, confusion and consternation. Can we stay on track? Can you ask one specific question and we'll try to answer it, then move on?
     
  16. Dec 12, 2011 #15

    D H

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    That is what an observer in this magical spaceship will see. As per the title of the thread, "Special relativity implies very odd results."

    There is no true paradox here. As is the case with all of the paradoxes of relativity, it is just an apparent paradox. The paradoxes of special relativity result from our first-hand experience making us think that space is Euclidean and time is that universal (all observers agree on how clocks tick). The resolution is that our first-hand experience is limited; it does not give a true picture of how the universe as a whole works.
     
  17. Dec 12, 2011 #16

    DaveC426913

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    Yes, they would - if they could "turn a corner" while moving at .9999c. The OP thinks that a turn like that is like doing it in a car. He is not seeing that going from .9999c North to .9999c West in a time frame he calls "suddenly" would constitute an acceleration of billions of gs.

    If the OP were to realize that the rocket ship would have accelerate from 0 to .9999c but could do so no faster than its initial blast off from Earth, then he would see why there's no paradox.
     
  18. Dec 12, 2011 #17

    D H

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    Ignore that. Pretend that the singularity has come, that we can download our minds onto a tiny, tiny chip that can withstand thousands of gs of acceleration or more. Pretend that we can build a very tiny but very sturdy spaceship that can hold this tiny, tiny version of ourselves. Pretend that this tiny spaceship can unleash the energy of multiple H-bombs over a very brief span of time. Pretend that it can more or less turn on a dime at relativistic speeds.

    The problem with the original post isn't the physical impossibility of making such a turn. The problem is that this sharp turn adds unnecessary complexity to what is already something that is very hard to grasp. Some people who don't grasp relativity try to look at it from the perspective of some "Rube Goldberg paradox" (google "Rube Goldberg device" if you don't know that term). There are apparent paradoxes galore that can be expressed simply. The key to understanding relativity is to understand these simple paradoxes. There is no need to invent yet another Rube Goldberg paradox.

    Suppose our tiny spaceship is en route to the Andromeda galaxy (M31), moving at 0.999999999992 c with respect to that galaxy. There's no need to make a right hand turn to illustrate this apparent paradox. All our tiny spaceship needs to do is to come to a stop with respect to M31. The apparent distance to M31 will grow from about 10 light years to 2.5 million light years. There's nothing wrong with that. That is what relativity says our little spaceship will see. Just grok the weirdness.


    To the OP: You won't find mathematical inconsistencies in special relativity. The Poincare transformation forms a mathematical group.
     
  19. Dec 12, 2011 #18

    DaveC426913

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    You and I see the source of the OP's confusion differently, and have different ways of highlighting it.

    You and I know that but I'm trying to answer the question he asked with as little change to it as possible. In my experience, when someone is struggling with a problem, it sometimes does more harm than good to show them a different experiment and have them miss the parallels between them.

    Not that I am saying yours isn't a good explanation; I hope one of us gets through. :wink:


    It is my belief that the OP already understands the basics of length contraction; he states it right in his opening post.

    What he is having difficulty with is that he thinks this length contraction will spectacularly switch axes by "merely" turning his ship.
     
  20. Dec 12, 2011 #19

    Fredrik

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    Would he? When you emphasize how enormous the acceleration would be, it sounds like you're saying that the resolution of the imagined paradox is that "your rocket's engines are too weak", or "if you would try this, your rocket would be instantly vaporized". At least, that's what I think it must sound like to him.

    The imagined paradox is not resolved by any practical issues, but is resolved by the observation that in order to claim things like "the rocket will experience a dramatic change in length contraction", we must first define what we mean by "the rocket's experiences" in a way that makes the claim true. We can do this for example by choosing to always call the coordinate assignments made by the momentarily comoving inertial coordinate system "the rocket's experiences".

    The key to understanding most, if not all, of the imagined paradoxes in SR, is that experiences are defined by coordinate systems. Things only look paradoxal if you compare the coordinate assignments made by two different coordinate systems, and forget that you're looking at assignments made by two different coordinate systems.
     
    Last edited: Dec 12, 2011
  21. Dec 12, 2011 #20

    DaveC426913

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    Well, I'm simply framing his (correct) understanding that the length contraction would change directions if the rocket's direction of travel changed, but that it would not happen "suddenly". The contraction would happen just like he knew it happened when the ship first blasted off from Earth and began accelerating from zero.

    Anyway, not sure it matters. The OP has moved on several times now since that first fleeting thought.
     
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