Graphical example of BH formation by PAllen

[zonde]

I mentioned the Nordtvedt effect because if it held, which is pretty unlikely, such that the gravitational self-energy contributed to its total gravitational mass, then you can't get a relativistic reduction of gravitational mass for an external observer, since even if the inertial mass is reduced its gravitational mass would remain. That's why it would violate the strong equivalence principle. I don't take this effect seriously, but it would render the scenario I described as moot.

So are you saying that I misunderstood you? You was presenting kind of possible (not very strong) argumentation against mass reduction by binding energy?

 

[my_wan]

I was asking if that was the kind of argument you had in mind back in the opening post, where you also characterized "Assume that BH exists" as begging the question. Limiting the creation of black holes through mass reduction by binding energy would be ruled out by the Nordtvedt effect. I only mentioned it to be inclusive of possibilities that contradicted the mechanism I described. Since I don't take the Nordtvedt effect very seriously it actually strengthens the argument. Apparently the answer is no, given your responses.

Consider the apparent relative mass increase of a planet like Mercury, as defined by GR, at its aphelion compared to its perihelion. Conversely a mass minimum at its perihelion. Hence the total relative mass apparently decreases as the mass density increases. For a far removed observer, wouldn't this then indicate that the total relative mass of the system varies inversely with density? This then implies that for a given constant volume of space, as defined by some external observer, the addition of masses to this volume would then add up in a manner similar to the relativistic addition of velocities, as seen by the external observer.

This wouldn't necessarily invalidate an event horizon, for the same reason that an apparent horizon can be present in a particle's accelerating reference, beyond which events are unobservable. This actually makes it possible to accelerate fast enough to prevent a photon from ever catching you.

Anyway, I started thinking about this in response to your apparent objection to assuming black holes exist. Because if your going to object to that assumption some mechanism for avoiding them is required. "We don't know", however valid in general, is not sufficient when specific mechanism are required to avoid black holes.

 

[zonde]

I'm not sure how degenerate matter can be exploited to prevent BH formation. In PAllen's scenario the matter density never even observably got especially dense in any local sense. Even in the event it did, you still have to presume the Fermi-pressure would grow indefinitely as the total gravitational pressure increased. Possible I suppose, but fails completely in PAllen's scenario.

This is rather complicated topic and I would like to discuss it only if we can dedicate some time for that topic alone.

Consider the apparent relative mass increase of a planet like Mercury, as defined by GR, at its aphelion compared to its perihelion. Conversely a mass minimum at its perihelion. Hence the total relative mass apparently decreases as the mass density increases. For a far removed observer, wouldn't this then indicate that the total relative mass of the system varies inversely with density? This then implies that for a given constant volume of space, as defined by some external observer, the addition of masses to this volume would then add up in a manner similar to the relativistic addition of velocities, as seen by the external observer.

I can't consider this scenario. I don't know how to model it.
And I am not sure about the term "relative mass". I imagined it as something like proper mass minus binding energy, is this in the right direction? But then I don't know how it can be represented in GR as I don't know how (or if) binding energy is represented in GR.

Anyways I know we can speak about binding energy as we compare one equilibrium state with another equilibrium state. But I'm not sure how to model dynamics between equilibrium states in respect of binding energy. And certainly aphelion and perihelion of Mercury are not equilibriums states for the whole system.

 

[zonde]

I'm not sure how degenerate matter can be exploited to prevent BH formation. In PAllen's scenario the matter density never even observably got especially dense in any local sense. Even in the event it did, you still have to presume the Fermi-pressure would grow indefinitely as the total gravitational pressure increased. Possible I suppose, but fails completely in PAllen's scenario.

Okay one question is what happens when matter is degenerate but you try to contain it within some volume. I think that degenerate matter can not be contained by other particles i.e. it does not participate in elastic collisions. I am not sure if I can propose solid arguments why it should be so from perspective of QM. The problem is with interpretation of "quantum state" in case of free particles. Anyways we can speculate that this is the case with neutrinos - they are very degenerate and after encounter with other particles they fall back on the same trajectory (the same momentum/position state) as before collision with very high probability.

Speaking about degeneracy and density dependence. To claim that the two are varying proportionally we have to assume that there is some cut-off distance for quantum level occupancy, meaning that particles don't compete for quantum state given sufficient distance. However we can assume that this "quantum level occupancy" effect drops as inverse square law. And in this case density factor does not exactly determine degeneracy level and it is more related to number of particles and distance to them.
And assuming this PAllen's scenario is still subject to questions about degeneracy levels as number of particles is much higher even so the distances are bigger as well.

 

[PAllen]

Okay one question is what happens when matter is degenerate but you try to contain it within some volume. I think that degenerate matter can not be contained by other particles i.e. it does not participate in elastic collisions. I am not sure if I can propose solid arguments why it should be so from perspective of QM. The problem is with interpretation of "quantum state" in case of free particles. Anyways we can speculate that this is the case with neutrinos - they are very degenerate and after encounter with other particles they fall back on the same trajectory (the same momentum/position state) as before collision with very high probability.

Speaking about degeneracy and density dependence. To claim that the two are varying proportionally we have to assume that there is some cut-off distance for quantum level occupancy, meaning that particles don't compete for quantum state given sufficient distance. However we can assume that this "quantum level occupancy" effect drops as inverse square law. And in this case density factor does not exactly determine degeneracy level and it is more related to number of particles and distance to them.
And assuming this PAllen's scenario is still subject to questions about degeneracy levels as number of particles is much higher even so the distances are bigger as well.

So, you propose two stars 10 million miles apart are fine, but add more, further away, there is a problem of quantum occupancay? It would be a wild theory, different from any currently known, to have such an effect. Which all gets back to: you can say BH don't form if and only if you admit you say GR is seriously wrong. Which is fine, but be willing to say it.

 

[zonde]

you can say BH don't form if and only if you admit you say GR is seriously wrong.

It would be nice to be as confident as you are ... but I am not.

Say I have heard that particles without any forces applied to them follow geodesics. But as I look more into details it turns out it is an approximation. You have to assume that particle has zero (negligible) mass.
So maybe you can tell me (if you know) - when we take into account particle's own gravity in what (space-time) direction it deviates from original geodesic (if we speak about particle falling radially toward gravitating mass)?

 

[PAllen]

It would be nice to be as confident as you are ... but I am not.

Say I have heard that particles without any forces applied to them follow geodesics. But as I look more into details it turns out it is an approximation. You have to assume that particle has zero (negligible) mass.
So maybe you can tell me (if you know) - when we take into account particle's own gravity in what (space-time) direction it deviates from original geodesic (if we speak about particle falling radially toward gravitating mass)?

It won't change direction. It will emit some amount of gravitational radiation and slow down (assuming the initial configuration had exactly zero angular momentum).

Let's turn it around: on what basis are your doubts about what GR predicts (as opposed to any beliefs about reality)? Note that we have the following:

- artificially perfect exact solutions showing formation of black holes
- theorems with very weak assumptions showing black hole formation is inevitable under general, realistic conditions
- ever more precise numeric simulations of black hole formation
- no theoretical counter arguments I've seen that don't actually modify GR (e.g. incorporating some model of quantum correction).

Note, even your argument about quantum occupancy is an argument that GR is incorrect, since such cannot be represented in a stress energy tensor, and cannot be described classically. If your actual argument is that there exist approaches to apply quantum arguments to GR that avoid singularities and event horizons, this is a no brainer. I can link dozens of such arguments, some may be close to how the world works, but none are statements about what GR predicts as a classical theory; all are modifications of GR in the same spirit as QED is to Maxwell EM.

 

[zonde]

It won't change direction. It will emit some amount of gravitational radiation and slow down (assuming the initial configuration had exactly zero angular momentum).

Let's turn it around: on what basis are your doubts about what GR predicts (as opposed to any beliefs about reality)?

I have doubts about exactness of GR predictions. It's too open for interpretation.

Note that we have the following:

- artificially perfect exact solutions showing formation of black holes

Are there any exact solution for runaway gravitational collapse? No? Then you can't claim that.
Obviously you need such a solution to claim that massive body undergoing runaway gravitational collapse and not emitting gravitational waves is a valid solution to EFE.

EFE take as arguments continuous 4D tensor fields. I simply do not get why I should believe it's something calculable without radical approximations.

You need coordinate system to express continuous tensor field. And this coordinate system is supposedly defined using this same tensor field. To me it seems like circular definition.

Hyperbolic coordinates is a dirty cheat unless you can provide a very serious arguments why they should be considered physically meaningful. So I do not believe argument about coordinate singularity in SC coordinates is valid (as I see "frozen star" is equivalent to "exterior of black hole").

Not to mention that I still don't know how binding energy can be represented in GR. And I consider it important in order to understand GR.




So make your pick.

 

[PAllen]

I have doubts about exactness of GR predictions. It's too open for interpretation.

You could say this about quantum mechanics, QFT, etc. It is a vacuous statement without specific arguments.

Are there any exact solution for runaway gravitational collapse? No? Then you can't claim that.

Sure there are. It's just that the exact ones are implausibly symmetric. How is this different from many other theories where approximation is required for realistic cases?

Obviously you need such a solution to claim that massive body undergoing runaway gravitational collapse and not emitting gravitational waves is a valid solution to EFE.

.
GW emission is expected for any collapse in the real world. Not sure why you thought otherwise. It is only known (mathematically) not to occur for perfect spherical symmetry, which will never exist in the real world. For realistic scenarios, we have (at least) 4 strong reasons to say GR predicts black holes, and you have still not provided a single reason for believing GR does not:

(1) simple, exact solutions (considered as indicative of general features of more realistic cases)
(2) general singularity theorems
(3) absence of any process with GR + classical matter models + reasonable quantum models that could prevent super massive BH formation (that is, matter coalescing within the horizon radius; any type of horizon you like).
(4) numeric models of ever growing sophistication (these, for example, model the precise GW emission spectrum expected from realistic collapses).

EFE take as arguments continuous 4D tensor fields. I simply do not get why I should believe it's something calculable without radical approximations.

see above

You need coordinate system to express continuous tensor field. And this coordinate system is supposedly defined using this same tensor field. To me it seems like circular definition.

This makes no sense to me. You need coordinate charts to define manifold topology. You do not define a coordinate system from a tensor field. This circularity is your invention or misunderstanding.

Hyperbolic coordinates is a dirty cheat unless you can provide a very serious arguments why they should be considered physically meaningful. So I do not believe argument about coordinate singularity in SC coordinates is valid (as I see "frozen star" is equivalent to "exterior of black hole").

1) So you reject 'general covariance' or diffeomorphism invariance: a definitional principle of GR. This is completely equal to the statement that you reject GR, which for some reason you are unwilling to admit.
2) Are you aware that you can derive the Kruskal metric directly from the EFE without ever introducing the SC coordinates? (I'm guessing that by hyperbolic coordinates you mean Kruskal).
3) Lemaitre coordinates are not hyperbolic and have no horizon singularity, and can also be derived directly from the EFE.

Not to mention that I still don't know how binding energy can be represented in GR. And I consider it important in order to understand GR.

1) To the extent this argument is valid, it is an argument against the validity of GR, which for some reason you remain resistant to admit.

2) In any case, GR says plenty about binding energy, but there are loose ends and open issues. First, in any asymptotically flat spacetime, there is globally conserved energy. Binding energy for non-catastrophic collapse is modeled by emission of ordinary radiation + GW. It is true that without an asymptotic geometry assumption, GR cannot account for total energy conservation, and that none of quasi-local approaches is fully satisfactory. However, for practical purposes, you can take a sufficiently isolated region, and model it as if it were embedded in asymptotically flat spacetime. To the extent this is a cheat (and it is, technically), your issue is with GR itself. Another anomaly of GR itself is that catastrophic collapse is predicted to be irreversible to an extent beyond what can be explained with binding energy (e.g. the Oppenheimer-Snyder collapse emits no radiation at all (GW or regular), yet is irreversible in the sense that you can't continue the forward time solution from after the horizon forms to a re-expansion without violating the EFE. Note, within the Lemaitre-Tolman generalization of Oppenheimer-Snyder, you can have WH->BH solutions but not BH->WH solutions. Time reverse WH->BH and you still have WH->BH.)

 

[TrickyDicky]

1) So you reject 'general covariance' or diffeomorphism invariance: a definitional principle of GR. This is completely equal to the statement that you reject GR, which for some reason you are unwilling to admit.

Then many relativists "reject GR", because there is an unsolved controversy (mostly from the LQG people) about what exactly is "general covariance" for dynamical theories.

 

[PAllen]

Then many relativists "reject GR", because there is an unsolved controversy (mostly from the LQG people) about what exactly is "general covariance" for dynamical theories.

LQG is a successor to GR. It definitely assumes GR is true only in a limited domain. This is also what I believe is true of the universe, but that is not relevant to a discussion of what GR predicts.

 

[TrickyDicky]

LQG is a successor to GR. It definitely assumes GR is true only in a limited domain. This is also what I believe is true of the universe, but that is not relevant to a discussion of what GR predicts.

Hmmm.. this is a tricky position...in a limited domain? how limited and who decides where the limit is? Just asking so I know what predictions of GR should I take seriously.

 

[PAllen]

Hmmm.. this is a tricky position...in a limited domain? how limited and who decides where the limit is? Just asking so I know what predictions of GR should I take seriously.

My personal opinion? Somewhere near the singularity - e.g. when the mass/energy is near Planck temperature; and also that the event horizon is not really a horizon at the microscopic quantum level, but macroscopically is very close in behavior to GR predictions.

 

[TrickyDicky]

My personal opinion? Somewhere near the singularity - e.g. when the mass/energy is near Planck temperature; and also that the event horizon is not really a horizon at the microscopic quantum level, but macroscopically is very close in behavior to GR predictions.

I see, it's just your opinion but I consider it an informed one.

 

[zonde]

You could say this about quantum mechanics, QFT, etc. It is a vacuous statement without specific arguments.

Fair. So let me give something more substantial. We can model curvature as deformation of surface in higher dimensional space (Gaussian curvature) or we can model curvature as rescaling of coordinate units (Einstein's marble table analogy). Which one I should pick and why?
And of course any approximation/assumption is subject to interpretation (is it ok to do it or not).

Sure there are. It's just that the exact ones are implausibly symmetric. How is this different from many other theories where approximation is required for realistic cases?

Give some idea about what solution you are talking.
Idea about approximations is fine as long as it is balanced by extensive experimental testing.

This makes no sense to me. You need coordinate charts to define manifold topology. You do not define a coordinate system from a tensor field. This circularity is your invention or misunderstanding.

Never mind. I found what I was looking for. It's Gaussian curvature and Theorema egregium.
I will let it seep in before any further discussion.

1) So you reject 'general covariance' or diffeomorphism invariance: a definitional principle of GR. This is completely equal to the statement that you reject GR, which for some reason you are unwilling to admit.

Yes, I reject general covariance. So I can say that I reject GR and exactly why.

This sentence from wikipedia is in essence what is unacceptable for me:
General covariance: "The essential idea is that coordinates do not exist a priori in nature, but are only artifices used in describing nature, and hence should play no role in the formulation of fundamental physical laws."
Essential idea is that physical laws do not exist a priori in nature. "Map is not the territory."
What bridges theory (or coordinate system) with nature is coordinate unit.

 

[my_wan]

Speaking about degeneracy and density dependence. To claim that the two are varying proportionally we have to assume that there is some cut-off distance for quantum level occupancy, meaning that particles don't compete for quantum state given sufficient distance. However we can assume that this "quantum level occupancy" effect drops as inverse square law. And in this case density factor does not exactly determine degeneracy level and it is more related to number of particles and distance to them.
And assuming this PAllen's scenario is still subject to questions about degeneracy levels as number of particles is much higher even so the distances are bigger as well.

I was hoping to see a more complete response to PAllen's response to this. You apparently assume a cut-off distance, but then assume it still applies if the density falls short of forcing the particles within this cut-off distance, per PAllen's description. In fact, it seems to me that, PAllen's description is tailor made to reject this very kind of argument, and your last sentence merely hand waves it away. It's as if when you said degeneracy and density dependence that density was a globally defined property such that local densities, particle separations, within it need not be effected. I can't wrap my head around that without adding some extra unspoken conditions.

I can possibly see some kind of argument against the presumed singularity at the center of a BH based on something similar. However, the event horizon would persist. Hence, even if so, it is still technically a BH.

Yes, I reject general covariance. So I can say that I reject GR and exactly why.

This sentence from wikipedia is in essence what is unacceptable for me:
General covariance: "The essential idea is that coordinates do not exist a priori in nature, but are only artifices used in describing nature, and hence should play no role in the formulation of fundamental physical laws."
Essential idea is that physical laws do not exist a priori in nature. "Map is not the territory."
What bridges theory (or coordinate system) with nature is coordinate unit.

This harks back to the original issue of coordinates and observer frames. When it says "do not exist a priori in nature" it is not the same as saying "do not exist". Now mathematically general covariance takes on a form to deal with accelerated motion. Which is observer independent much like the spacetime interval. To illustrate why general covariance is required I'll skip the mathematics and describe one of the things I did in kindergarten with rocks in the back seat of the car. Then repeat the above justification given that scenario. It Galilean character doesn't change its essential character.

If, sitting in a car, you toss a rock straight up it comes straight back down into your hand. Now you look out at the fence post along the road and notice the rock arcs up at one fence post and over till it lands at the next fence post. This arc, I now know, is of course a parabola. You can also consider Earth's motion and view the trajectory as one that angled off to the left or right. The question is, is this straight up and down trajectory "really" the exact same path as the parabola? Well of course it is, the rock didn't take a quantum superposition of paths. General covariance, at its fundamental core, is nothing more than an axiomatization of this sameness, with the added provisions that simultaneity and global geometry vary per perspective in exactly the same manner as the path of our rock.

The conceptual difficulties arise because our description does not specify a path as such, per the stated condition that nature doesn't uniquely specify it. Yet any observer is by definition stuck with observing reality from a certain perspective. Rejecting general covariance is tantamount to claiming the rock either took multiple paths, or that all but one of the possible observable paths is an illusion, such that only one real path remains. This is exactly the error of reasoning that lead to the failures of the classical ether theory. It doesn't even mean something resembling an ether doesn't exist. It just means not only that any such ether model cannot be used to uniquely specify a coordinate choice, but also that any coordinate choice we do make must covary with any relative variances of the supposed ether.

When you say the "map is not the territory" is valid but often misleading. In effect, by rejecting general covariance, you are attempting to force fit all coordinate choices single coordinate choice, while failing to recognize that general covariance is fully justified on the foundational grounds that all these coordinate choices are describing the exact same "set of paths" (states) to begin with. This rejection, in turn, falsely implies the "real" territory (like ether theory) is a singular coordinate choice, as if the choice between using metric or English had some real physical meaning.

Anyway, that seems to me to be the logical consequences of your issues with coordinates and observer perspectives. Just remember that general covariance simply entails that all the different paths observers might describe your rock to take in the car is the exact same path, plus time and geometry.

 

[Mike Holland]

Very nicely and logically explained. There is just a rock, but we impose time and geometry on it by choosing our coordinate systems, all of which are equally valid. Except that MY coordinate system is special because it is MINE!

"The map is not the territory" goes back to Count Alfred Korszybski's General Semantics, in his book "Science and Sanity". But maybe he stole it from somewhere else. Takes me back to my "Ics" period in the 1950's, when I was reading physics, electronics, genetics, semantics, logics, dianetics, mathematics!

Sorry about the interruption.

Mike

 

[zonde]

I came up with simple argument why perfect spherical symmetry forbids gravitational collapse.
Assume we have two different entities - mass and non-mass (field). Mass and field are separated by border (surface) between them.
Now if we require perfect spherical symmetry for some mass and field configuration then all the surfaces between mass and field have to be sphericaly symmetric too. But in that case mass and field can not exchange places and that is exactly the thing required for gravitational collapse.
And to check from other side we can ask if this described symmetry is the one required for Birkhoff's theorem? And yes it is because any deviation from such symmetry will allow propagation of transverse waves.

 

[zonde]

You apparently assume a cut-off distance

No

This harks back to the original issue of coordinates and observer frames. When it says "do not exist a priori in nature" it is not the same as saying "do not exist". Now mathematically general covariance takes on a form to deal with accelerated motion. Which is observer independent much like the spacetime interval. To illustrate why general covariance is required I'll skip the mathematics and describe one of the things I did in kindergarten with rocks in the back seat of the car. Then repeat the above justification given that scenario. It Galilean character doesn't change its essential character.

If, sitting in a car, you toss a rock straight up it comes straight back down into your hand. Now you look out at the fence post along the road and notice the rock arcs up at one fence post and over till it lands at the next fence post. This arc, I now know, is of course a parabola. You can also consider Earth's motion and view the trajectory as one that angled off to the left or right. The question is, is this straight up and down trajectory "really" the exact same path as the parabola? Well of course it is, the rock didn't take a quantum superposition of paths. General covariance, at its fundamental core, is nothing more than an axiomatization of this sameness, with the added provisions that simultaneity and global geometry vary per perspective in exactly the same manner as the path of our rock.

The conceptual difficulties arise because our description does not specify a path as such, per the stated condition that nature doesn't uniquely specify it. Yet any observer is by definition stuck with observing reality from a certain perspective. Rejecting general covariance is tantamount to claiming the rock either took multiple paths, or that all but one of the possible observable paths is an illusion, such that only one real path remains. This is exactly the error of reasoning that lead to the failures of the classical ether theory. It doesn't even mean something resembling an ether doesn't exist. It just means not only that any such ether model cannot be used to uniquely specify a coordinate choice, but also that any coordinate choice we do make must covary with any relative variances of the supposed ether.

When you say the "map is not the territory" is valid but often misleading. In effect, by rejecting general covariance, you are attempting to force fit all coordinate choices single coordinate choice, while failing to recognize that general covariance is fully justified on the foundational grounds that all these coordinate choices are describing the exact same "set of paths" (states) to begin with. This rejection, in turn, falsely implies the "real" territory (like ether theory) is a singular coordinate choice, as if the choice between using metric or English had some real physical meaning.

Anyway, that seems to me to be the logical consequences of your issues with coordinates and observer perspectives. Just remember that general covariance simply entails that all the different paths observers might describe your rock to take in the car is the exact same path, plus time and geometry.

You have provided nice argument defending relativity principle (even if you call it "general covariance"). But I'm not rejecting relativity principle.

Please pay attention (apart from sorting out what is "general covariance" and what is "relativity principle"). When I say I reject "general covariance" I am not giving any arguments about coordinate systems but instead I am saying that physical laws are just as artificial as coordinate systems if not even more. That's the essence.

"General covariance" on the other hand claims that physical laws are more "natural" than coordinate systems.

 

[PAllen]

I came up with simple argument why perfect spherical symmetry forbids gravitational collapse.
Assume we have two different entities - mass and non-mass (field). Mass and field are separated by border (surface) between them.
Now if we require perfect spherical symmetry for some mass and field configuration then all the surfaces between mass and field have to be sphericaly symmetric too. But in that case mass and field can not exchange places and that is exactly the thing required for gravitational collapse.
And to check from other side we can ask if this described symmetry is the one required for Birkhoff's theorem? And yes it is because any deviation from such symmetry will allow propagation of transverse waves.

I don't see any logic here at all. If the layering is vacuum(outside), matter, field (in the center), the matter and field collapse together, no need to change places. This is just a spherical shell collapse with field inside instead of vacuum. Alternatively, if it vacuum, field, matter, then the matter collapses, possibly taking some field with it.

The purported need to change places is your illogical straw man. There is no such need at all.

 

[PAllen]

Generally, I think all that is useful has been said. Your newest arguments are getting less and less sensible or even comprehensible. I'll check occasionally if something worth discussing pops up.

 

[PAllen]

No


You have provided nice argument defending relativity principle (even if you call it "general covariance"). But I'm not rejecting relativity principle.

Please pay attention (apart from sorting out what is "general covariance" and what is "relativity principle"). When I say I reject "general covariance" I am not giving any arguments about coordinate systems but instead I am saying that physical laws are just as artificial as coordinate systems if not even more. That's the essence.

"General covariance" on the other hand claims that physical laws are more "natural" than coordinate systems.

This makes no sense at all so there is nothing to respond to.

 

[berkeman]

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