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A Flaw of General Relativity?

  1. Mar 24, 2006 #1
    Numbered for reference:

    1. The equivalence principle tells us that the crew of a rocket, traveling in flat spacetime and where the crew feels a constant acceleration, experiences a uniform gravitational field identical to that experienced locally by an observer on a planet.

    2. Special relativity tells us that in principle the crew can traverse between any two points A and B in flat spacetime in an arbitrarily short proper time, where the two points are at rest with respect to each other and the rocket accelerates from rest at point A to the halfway point and then decelerates from the halfway point to rest at point B.

    3. Then the crew can observe free-rising objects (such as an object floating stationary at the halfway point) to recede apparently arbitrarily fast—a million c is not out of the question—while causal contact is maintained since the actual velocity is always less than c.

    Example: Let the rocket travel from Earth to Andromeda, two million light years away as we measure. (Assume that Earth and Andromeda are at rest with respect to each other and the spacetime between them is flat.) Let a buoy float stationary at the halfway point. Let the half of the trip from the buoy take ten proper years as the crew measures. Then during this half the buoy recedes by one million proper light years in ten proper years, an apparent (not actual) velocity of one hundred thousand c. From the crew's perspective the buoy free-rises in a uniform gravitational field.

    4. Then why does general relativity not predict the same possible observation for the observer on the planet?
     
    Last edited: Mar 25, 2006
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  3. Mar 24, 2006 #2

    Doc Al

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    I assume you are referring to the fact that two objects a distance [itex]L_0[/itex] apart in their own frame can be passed by a rocket within an arbitrarily short time (according to the rocket) if the rocket moves fast enough with respect to the objects. But this is entirely due to the rocket's speed, not its acceleration.
     
  4. Mar 24, 2006 #3
    Which numbered point are you objecting to? How does what you're saying refute the point?
     
  5. Mar 24, 2006 #4

    Doc Al

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    I fail to see any argument for your point (#4). #1 has to do with acceleration, while #2 & #3 have to do with speed. Your conclusion (#4) does not follow.
     
  6. Mar 24, 2006 #5
    You must disagree with #1, 2, or 3 for #4 to not follow. (I added some clarification. Take another look.) Free-rising objects have speed for either the crew or the observer on the planet.
     
  7. Mar 24, 2006 #6

    Doc Al

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    #1 has nothing to do with #2 or #3. (Note that #2 & #3 apply regardless of acceleration.) #4 is a non sequitur.
     
  8. Mar 24, 2006 #7

    selfAdjoint

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    No he doesn't. He just has to show that #4 doesn't FOLLOW from #1, #2, and #3. He did that, by pointing out that the acceleration mentioned in #1, and which you invoke in the gravity of #4, has nothing to do with the speed statements in #2 and #3. Three true statements that have nothing to do with one another do not lead to a conclusion, other than their union.
     
  9. Mar 24, 2006 #8
    #1 shows that whatever the crew can experience, the observer on the planet can also experience locally. #3 shows what the crew can experience, based on #2. Then if you agree with #3, #4 is a valid question.
     
  10. Mar 24, 2006 #9
    See my reply to him above. If he agrees with #1, 2, and 3, then #4 is a valid question--it follows.
     
  11. Mar 24, 2006 #10

    ZapperZ

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    You seem to think that "acceleration" implies "velocity". I think there's more a flaw in your understanding of kinematics rather than there's a flaw in GR.

    I can show you something with zero velocity, yet it has an acceleration. Therefore, #2 and #3 that DEPENDS on velocity doesn't apply to #1, they are not automatically related. That is why you are being told that #4 makes no sense.

    Zz.
     
  12. Mar 24, 2006 #11

    Doc Al

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    #1 states that the effect of the rocket's acceleration is equivalent to the planet's gravity.

    #3 and #2 discuss effects due to the rocket's speed not its acceleration. So #1 is irrelevent.

    If the planet moves at the same speed with respect to those objects as does the rocket, then the planet observer will see the same speed-dependent effects. (Nothing to do with the equivalence principle.)
     
  13. Mar 24, 2006 #12
    Regardless of what #3 depends on, the observer on the planet should be able to experience the same observation as described in #3, according to #1. A free-rising object in the local frame of the observer on the planet has velocity relative to the observer.

    Let's try this:

    A. #1 shows that whatever the crew can experience, the observer on the planet can also experience locally.

    B. #3 shows what the crew can experience, based on #2.

    C. Then if you agree with #3, #4 is a valid question.

    Which of these statements do you object to?
     
  14. Mar 24, 2006 #13
    Given that, whatever the crew can experience, the observer on the planet can also experience locally.

    #3 is based on #2. Neither are based on #1. According to #1, #3 is an effect that applies equally well to a free-rising object in the local frame of an observer on a planet. A free-rising object has speed relative to either the crew or the planetary observer.

    Then #4 is a valid question, since the free-rising objects in either case can move at the same speed.
     
  15. Mar 24, 2006 #14

    ZapperZ

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    No, you can't sweep this under the carpet. It DOES depends on velocity. This is not negotiable because if you ignore this, you are ignoring SR. So then why are we even discussing this if you wish to make up your own laws?

    Acceleration is not velocity.

    Zz.
     
  16. Mar 24, 2006 #15

    George Jones

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    This is roughly true.


    I agree completely.


    Here, I'm a little lost.

    What does "recede apparently arbitrarily fast—a million c is not out of the question" mean?

    Regards,
    George
     
  17. Mar 24, 2006 #16
    I'm not disagreeing with you on what #3 depends on. If you object by saying that #3 depends on velocity, then I say that velocity applies as well to the observer on the planet, because a free-rising object in the local frame of the observer on the planet has velocity relative to the observer. Whatever the crew can observe (velocity, acceleration, whatever), so can the observer on the planet in a local frame, according to #1.

    Then what is your objection?
     
  18. Mar 24, 2006 #17

    ZapperZ

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    Show me an example of a "free-rising" object on a "planet" and show me how another inertial frame would observe this very same object in the idential way.

    Zz.
     
  19. Mar 24, 2006 #18

    Doc Al

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    If all you are saying is that an observer on a planet moving with the same speed as the rocket with respect to those objects will see the same speed-dependent effects as an observer on the rocket, then why all the mumbo jumbo with the equivalence principle? It's your argument that doesn't make sense, not that last statement (if that's what you were trying to say).

    And what does this have to do with some supposed "flaw" in GR? What flaw?
     
  20. Mar 24, 2006 #19
    An example: Suppose the rocket travels from Earth to Andromeda, 2 million light years away as we measure, in 20 proper years. (Assume spacetime between is flat.) Then in the crew's frame a buoy floating stationary at the halfway point, between passing the buoy and arriving at Andromeda, recedes one million proper light years in ten proper years, an apparent (not actual) velocity of one hundred thousand c. From the crew's perspective the buoy free-rises in a uniform gravitational field.
     
  21. Mar 24, 2006 #20
    An apple thrown upwards.

    Why? The two frames discussed here, in which an object is free-rising, are non-inertial frames.
     
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