Causal mechanism for gravity

Discussion in 'Alternative Theories' started by RJBeery, Apr 5, 2020.

  1. RJBeery Natural Philosopher Valued Senior Member

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    My contention is that "they" (meaning Gibbs, Baez, James R, Halc, et al) say that black holes are not created under those conditions to simply side-step the inherent logical contradiction. Claiming that such-and-such cannot happen because it would cause a logical contradiction is fine...unless your theory otherwise predicts it. No explanation is given on why kinetic energy must be accounted for everywhere in general relativity except in the formation of black holes. Remember, kinetic energy is a real thing with real consequences, as I mentioned earlier: https://authors.library.caltech.edu/1544/
     
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  3. exchemist Valued Senior Member

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    I'm no expert on relativity but my understanding is that, uniquely, kinetic energy is frame-dependent. So it seems to me that it cannot be treated by relativity like other kinds of energy. It must be treated differently. Is this right, do you know?

    If so, then it seems likely to me that it will turn out that kinetic energy will not crop up as a factor in determining whether or not a black hole forms, due to the different way it is treated.
     
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  5. James R Just this guy, you know? Staff Member

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    Have you done the maths?

    Is it your claim that GR is wrong because you think it makes logically contradictory predictions?

    You haven't actually shown anything that is logically contradictory, so far.

    No explanation has been given by you as to why kinetic energy wouldn't be accounted for by GR.

    Your complaints are baseless unless you can show they are based on something concrete in the theory. I don't think you've done the maths,
     
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  7. RJBeery Natural Philosopher Valued Senior Member

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    No, I believe general relativity is completely fine; the interpretation that it predicts black holes has problems - including a logical contradiction.
    This is false. A logical contradiction supersedes any "deep dives" into the mathematics of a theory. Making a proclamation that the problem doesn't exist is not addressing the problem.

    By the way, I'm not even demanding that this problem exists - I'm asking for an explanation. I can identify a bullshit explanation when I see one, and Gibbs' was bullshit. I, apparently unlike yourself, will not accept on blind faith that the truth is buried in the math but is apparently too complex to be explained using words.
     
  8. exchemist Valued Senior Member

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    It seems to me that for the type of answer that will satisfy you, you need to talk to someone who is adept at the mathematics of GR. Unless I'm much mistaken, there is nobody on this forum in that category.

    Tell me, do you know Markus Hanke? You can find him on scienceforum.net - assuming you have not already been banned from there as a crank (only kidding

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    ).

    He I think is the sort of person who will able to take you through it.

    But I am sure that GR will have not only the maths to show why black holes are predicted, but also the maths to show that kinetic energy cannot give rise to one. This seems to me obvious from the qualitative arguments so far, combined with the fact that GR has not collapsed from lack of self-consistency.
     
  9. RJBeery Natural Philosopher Valued Senior Member

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    I'll check it out, thanks for this.
     
  10. przyk squishy Valued Senior Member

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    There is no contradiction in GR. Rather, you seem to be mixing GR with your own assumptions that contradict it. Specifically, you seem to be under the impression that there is some simple relation in GR that always applies along the lines "if the energy density is higher than some threshold then you will always have a black hole". That is wrong.

    First, the gravitational field in GR does not depend on the "energy" or "energy density" but on the stress-energy tensor, which is more general. Like the name implies, the stress-energy tensor is a tensor. If you don't know what that is, you can think of it as a kind of generalised vector. Like a vector in Euclidean geometry, it is an invariant object. It has components and those individually depend on the reference frame, much like the \(x\), \(y\), and \(z\) components of a vector depend on the axes you choose, but the tensor as a whole is a geometrical object defined on the spacetime manifold and can be understood as such independently of any choice of coordinate system.

    The stress-energy tensor has ten components in any given coordinate system. In an inertial reference frame, one of those components is the local energy density. The other nine consist of the \(x\). \(y\), and \(z\) components of the momentum density and six momentum fluxes.

    Another thing about the stress-energy tensor is that it is a field, which means it is a function of position in spacetime. So if you were comparing a moving mass to a stationary one then not only are the momentum components now nonzero but also the tensor and its components will now be changing over time, since the place where the energy and momentum are concentrated is moving, and you would need to take all of that into account if you were attempting to calculate what gravitational field a moving mass will produce. It is not like the "energy" of a moving mass is a bigger number and everything else is the same.

    Second, the relation between the stress-energy tensor and the gravitational field itself is not simple. If there were a simple rule that always tells you when you would have a black hole, it would be pretty amazing given that nobody even knows how to accurately predict the gravitational field in general in GR. Unlike in Newtonian gravity, GR does not have a simple rule that directly tells you if the stress-energy tensor is such-and-such then the gravitational field will be such-and-such. GR instead only says that the gravitational field and the stress-energy tensor must be related in such a way that they satisfy the Einstein field equation. So predicting the gravitational field (including whether there is a black hole or not) in general requires solving the Einstein field equation for a given stress-energy tensor or integrating it starting from some known initial conditions. The problem here is that the Einstein field equation is a complicated nonlinear differential tensor equation. Solving it is very hard. Nobody knows how to do it accurately in general.

    There are some predictions in GR that do give relations between matter/energy density and getting a black hole, but you need to keep in mind that they are not general and it is not justified to assume whatever relation they predict will apply outside of the specific conditions they are derived for. For example, the Schwarzschild geometry tells us that you can't compress a sphere of mass smaller than a certain radius without getting a black hole, but that relation only necessarily applies under the conditions and assumptions that the Schwarzschild geometry is derived for as a solution to the Einstein field equation. Importantly, one of those assumptions is that the gravitational field is static and the source producing it is at rest, so you can't just take the result and assume it will be the same for a moving mass.

    Or to summarise all of the above: things are not as simple as you are assuming.
     
    Last edited: Apr 29, 2020
  11. RJBeery Natural Philosopher Valued Senior Member

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    Thanks przyk, this is good stuff. I've also posted at ScienceForums.net per exchemist's suggestion. I'll digest things and get back.
     
  12. exchemist Valued Senior Member

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    Very illuminating, if only to show what a swamp we are potentially getting into with this topic.

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  13. Derek.H. Registered Member

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    In regards to the speeding car versus the speeding houses issue ; I postulate that only one of the two will experience relativistic time-dilation , if both are measured objectively (not by lightwaves) .
     
  14. exchemist Valued Senior Member

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    There is no "objective" measurement that is independent of a frame of reference. And different frames of reference will measure length and duration differently. There is no frame of reference that is any more fundamental than any other.
     
  15. Derek.H. Registered Member

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    Then I postulate that no matter what your frame of reference , you will observe time pass more slowly in the relativistic car , than in the non-relativistic houses .
    D.
     
  16. exchemist Valued Senior Member

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    There are no non-relativistic houses. The houses are just as "relativistic" to someone in the car as the car is to someone in the houses. And there is no means of determining one is more right than the other.
     
    Last edited: May 3, 2020
  17. river

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    Highlighted

    Two dimensions , and will different frames of reference measure depth and breadth differently ?
     
  18. Halc Registered Senior Member

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    If I'm sitting at the head of my table, the 2-D surface has length 2M and breadth 1M. If seated at the side, it has length 1M and breadth 2M.
    So it's not so controversial that dimensions of things are frame dependent.

    Yes, the length, width, and breadth of objects are all frame dependent. Likewise, the spatial (and temporal) separation of two specific events is also frame dependent.
     
  19. river

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    And depth . Where is depth here ? No where .

    Without depth there is no table to begin with .
     
  20. James R Just this guy, you know? Staff Member

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    The mathematics shows that black holes are a valid solution of the Einstein equations. There's no logical contradiction in that.

    I don't accept it on blind faith. I understand what przyk is talking about in his post above. Do you?
     
  21. Halc Registered Senior Member

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    No, but it being a valid solution to equations does not preclude logical contradictions. Tachyons are also a valid solution to those field equations, and yet their existence would allow me to own a picture of my nonexistent grandchildren, a logical violation of the premise that information cannot be sent to the past.
    Hence the existence of black holes (in particular, matter crossing the event horizon) is not necessarily the case just because the mathematical description of one is a valid solution to the field equations. There may be logical contradictions still, even if RJBeery is unable to identify one.

    His argument seems to work on the grounds of: "I don't understand it, therefore it is contradictory", which of course is fallacious. I personally would love to understand it enough to have posted what przyk did, but I defer to the experts for things beyond my current level of understanding rather than declaring said experts all to be wrong.
     
  22. RJBeery Natural Philosopher Valued Senior Member

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    Yes, black holes, wormholes, negative mass, time travel, etc. That isn't the logical contradiction, anyway. The contradiction, as I've understood the explanations given, is that angular momentum is treated differently from linear momentum when calculating the threshold needed for black hole creation.

    For example, it's well known that the energy from a rotating mass contributes to the energy threshold required for black hole creation...fine. But rotation is basically spatially-constrained linear motion (by gravity, for example). Take two massive bodies, A and B, and put them in a very tight two-body orbit which we claim would collapse into a black hole. At what point do we consider the A-B system a "singular system", susceptible to black hole creation? What if we trace the A and B bodies' trajectories backwards, prior to them entering orbit? The Misner, Thorne and Wheeler explanation in Gravitation is a bit vague on this issue, claiming that momentum energy doesn't exist locally. On its own, that kind of makes sense, but now I need to understand how that applies to angular momentum because that doesn't exist locally either. If angular momentum only exists "in a system" then linear momentum also exists "in a system".
     
  23. przyk squishy Valued Senior Member

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    No. You're once again making assumptions. Angular momentum is handled via the stress-energy tensor just like everything else energy/matter/momentum-related that is coupled to the gravitational field. That is, if you have something like a rotating mass then its local momentum will vary (have different magnitudes and be pointing in different directions) depending on position and distance relative to the axis of rotation, which makes the stress-energy tensor for a rotating system different than for a non-rotating one.
     

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