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Thread: How does physics "break down" in a black hole?

  1. #1
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    How does physics "break down" in a black hole?

    Is the common meme that physics (usually Einstein physics) 'breaks down" past a BH event horizon because of conceptual issues (e.g. time slows to zero) or is there something in the maths that literally breaks down (e.g. a division by zero). What is that something?

    And are claims that quantum mechanics is able to continue operating in a black hole environment correct? Why?

    Thanks!

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    It's our models of physics that break down, because you can't get much in terms of predictive or explanatory power out of the singularity that results from the math of GR at the center of a black hole (the event horizon is a coordinate singularity which is easily worked around). It presumably becomes inaccurate somewhere before reaching a singularity, but we have no ability to test such conditions.

    And a quantum theory of gravity may or may not be able to describe what goes on within black holes, it's just thought that working out the differences in the two approaches and coming up with a unified theory would at least be progress toward doing so.

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    Quote Originally Posted by Cheap Astronomy View Post
    Is the common meme that physics (usually Einstein physics) 'breaks down" past a BH event horizon because of conceptual issues (e.g. time slows to zero) or is there something in the maths that literally breaks down (e.g. a division by zero). What is that something?

    And are claims that quantum mechanics is able to continue operating in a black hole environment correct? Why?

    Thanks!
    Good reference here:

    https://en.wikipedia.org/wiki/Gravitational_singularity

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    Quote Originally Posted by Cheap Astronomy View Post
    Is the common meme that physics (usually Einstein physics) 'breaks down" past a BH event horizon because of conceptual issues (e.g. time slows to zero) or is there something in the maths that literally breaks down (e.g. a division by zero). What is that something?

    And are claims that quantum mechanics is able to continue operating in a black hole environment correct? Why?
    The singularity is the issue, so it is essentially more like a divide by zero error. Time dilation at the event horizon is a non-issue as it is co-ordinate dependent, time doesn't 'stop' there and you can happily use GR on both sides and across it if you pick the right co-ordinates.

    QM doesn't include gravity - so in the case where gravity and quantum effects are important (near the centre of a black hole) neither gives the full picture.

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    Quote Originally Posted by Cheap Astronomy View Post
    Is the common meme that physics (usually Einstein physics) 'breaks down" past a BH event horizon because of conceptual issues (e.g. time slows to zero) or is there something in the maths that literally breaks down (e.g. a division by zero). What is that something?

    And are claims that quantum mechanics is able to continue operating in a black hole environment correct? Why?

    Thanks!
    Einstein's GR is based upon differential geometry to describe curved space time. Einstein's field equations have a set of differential equations as their solutions. The solutions to the differential equations that describe the curvature tend to infinity as the singularity is approached.

    There is a slightly more subtle issue that is related to quantum mechanics (QM) and the Heisenberg Uncertainty Principle (HUP). At small scales, the theories of quantum mechanics and general relativity become incompatible. For example, there are treatments of quantum loop gravity (QLG) that demonstrate how HUP can be theoretically violated in closed loop trajectories. However, there are other treatments of QLG that suggest HUP is only an approximation at the scales of QLG, and further uncertainty will be introduced. The up shot of this is that at small scales there needs to be a more complete account of general relativity that incorporates quantum theory. So at small scales Einstein's relativity breaks down, not just from its maths, but from compatibility with another pillar of physics (QM).

    Edited to improve flow of English.
    Last edited by Baron Greenback; 2018-May-01 at 10:18 PM.

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    Random thought I had. If string theory is right in that there is a 'smallest' unit of space time below which nothing exists, does this not mean that the stuff falling into a black hole will eventually reach his limit and start piling up there? Sure it's extremely small, but in theory it's not ininfite density? Come to think of it, this logic would have to apply to the start of the visible universe too. How could all that stuff fit into such a small space?

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    Quote Originally Posted by Inferno returns View Post
    Random thought I had. If string theory is right in that there is a 'smallest' unit of space time below which nothing exists, does this not mean that the stuff falling into a black hole will eventually reach his limit and start piling up there? Sure it's extremely small, but in theory it's not ininfite density? Come to think of it, this logic would have to apply to the start of the visible universe too. How could all that stuff fit into such a small space?
    Good, you've looked at the and-waving stuff presented in popular media, and correctly found one of the answers for the OP: How does Physics break down in a Black Hole.
    As a parable, you can look at the laws of thermodynamics, and those laws are very repeatable when you test them, but they break down when you start looking at individual particles and collisions, but you can reproduce the laws of Thermodynamics from statistical mechanics. It is not known what the story is in very strong gravity situations, but there is hope that it will be possible to make observations that will give clues. This is one of the exciting searches of this Century, and a reason why it might be fun to be a scientist right now.
    Forming opinions as we speak

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    Quote Originally Posted by Inferno returns View Post
    Random thought I had. If string theory is right in that there is a 'smallest' unit of space time below which nothing exists, does this not mean that the stuff falling into a black hole will eventually reach his limit and start piling up there? Sure it's extremely small, but in theory it's not ininfite density? Come to think of it, this logic would have to apply to the start of the visible universe too. How could all that stuff fit into such a small space?
    String theory describes black holes as "fuzzballs": https://en.wikipedia.org/wiki/Fuzzball_(string_theory)

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    Quote Originally Posted by Inferno returns View Post
    Random thought I had. If string theory is right in that there is a 'smallest' unit of space time below which nothing exists, does this not mean that the stuff falling into a black hole will eventually reach his limit and start piling up there? Sure it's extremely small, but in theory it's not ininfite density? Come to think of it, this logic would have to apply to the start of the visible universe too. How could all that stuff fit into such a small space?
    Strictly that isn't what string theory says, I am afraid. It is what people have generalised from a duality and simplified to the point of it almost being wrong. Essentially string theory says that there is a smallest scale we can measure, because below that limit every measurement we take is the same as a measurement at a larger scale but with certain quantum numbers swapped.

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    Another article of string theory and black holes here: https://fqxi.org/community/articles/display/228

    And here: https://www.quantamagazine.org/how-f...radox-20150623

  11. #11
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    Quote Originally Posted by Cheap Astronomy View Post
    Is the common meme that physics (usually Einstein physics) 'breaks down" past a BH event horizon because of conceptual issues (e.g. time slows to zero) or is there something in the maths that literally breaks down (e.g. a division by zero). What is that something?

    And are claims that quantum mechanics is able to continue operating in a black hole environment correct? Why?

    Thanks!
    I don't know if physics breaks down, but usually this has been linked with the equations breaking down at the singularity. There are good reasons though to think singularities do not exist. It may be a matter, of a new physics, or maybe one we have considered properly that will answer these questions more clearly.

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