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  1. Colleen Hurley-Bates says:

    Great work Aron!

  2. David J. Marcus says:

    Paradox (I think):

    Imagine a star that is just on the verge (a few atoms shy) of imploding into a black hole.

    Imagine two stationary observers (A and B), relative to the star, who are very far away.

    Imagine that observer A starts accelerating towards the star. By relativity, the observer is justified in claiming that the star is accelerating towards him (observer A).

    At some velocity, the star's apparent mass will exceed the threshold of collapsing into a black hole.

    Therefore, observer A can rightly claim that the star is collapsing..

    Observer B, at the original observation point (who remains stationary relative to the star) claims that the star has not reached a mass level that initiates a collapse and therefore the star is not collapsing.

    Given that a collapse to a black hole is not reversible, we have a paradox.

    One observer seeing a collapse, the other does not.

    Worse yet, once the collapse is initiated (for observer A), that same observer A can decelerate to a relative velocity of zero (relative to the star). At this relative velocity of zero, a mass measurement reveals that the start is not massive enough to collapse and, in fact, has not done so.

    This must mean that as observer A is decelerating the collapse to a black hole is somehow reversed.

    ---

    This seeming paradox has been bugging me for years and I have not been able to reverse it.

    Is there any indication that quantum gravity can explain this?

  3. Aron Wall says:

    Welcome, David.

    Your problem can be resolved within the scope of GR, so there's no need to bring in quantum gravity. There are a couple things you are assuming that came from people's attempts to explain GR, but unfortunately they often use some sloppy explanations which can be misunderstood.

    The first issue is with this statement:

    Imagine that observer A starts accelerating towards the star. By relativity, the observer is justified in claiming that the star is accelerating towards him (observer A).

    This is not really a correct statement of the principle of relativity. The correct statement is that the laws of physics are invariant under a change of coordinates. But this change of coordinates will affect the spacetime metric as well as the star and the observer, so you can't account for it in the way you say.

    Given the metric of spacetime, you can determine in an absolute way whether or not an object is accelerating. An accelerating object does not behave in the same way as an unaccelearted object! This is similar to the mistake some people make with the twin paradox, where they think that relativity allows them to symmetrically interchange the life histories of the two twins. It doesn't. One of them is accelerates and the other doesn't. This is an objective physical fact.

    The second issue is with this statement:

    At some velocity, the star's apparent mass will exceed the threshold of collapsing into a black hole.

    You have been told that:
    1) objects that are moving faster have a greater energy relative to the frame of reference of a stationary observer, and
    2) when enough mass/energy is concentrated into a small enough space, a black hole forms.
    so you have deduced that an object moving fast enough must collapse into a black hole. But this interpretation of #2 is false. In order for a star to collapse into a black hole, it needs to have a certain amount of mass as measured in the frame of reference of the star itself. Giving the star a velocity, no matter how large, does not make it collapse into a black hole.

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