I can give the problem another twist, which seems to make it much harder. This is something that has bothered me for a long time. In general relativity, there are coordinate systems, in which the formation of the event horizon (to be distinguished from the Schwarzschild radius, which is a purely mathematical construct; the event horizon also has a physical meaning -- nothing can escape from it) takes infinite time. This is fine as long as a black hole can live infinitely long. However, if we take quantum mechanics into account, then a black hole should decay due to Hawking radiation. The decay takes very long but a finite time for the infinitely far observer. So for that observer, the black hole should evaporate *before* an event horizon forms!

What about an infalling observer? If I try to describe things from outside (and in Schwarzschild coordinates) then he should never be able to cross the horizon. That is, if he were not torn apart by tidal forces even before reaching the horizon, he might survive. On the other hand, for this observer falling across the horizon takes only a finite proper time. Moreover, he will not see any Hawking radiation. One might suppose that his fate is the one that is usually described for observers falling into a black hole.

But then we have two predictions that cannot be true "at the same time". I have some ideas about this but not a definite answer.

In the meantime (2018), I do. Read my publication "Radially falling test particle approaching an evaporating black hole", at this moment available at arXiv:1801.00272, later hopefully in Canadian Journal of Physics.

Okay, so I did not read this paper by Roger Penrose yet: “Golden Oldie”: Gravitational Collapse: The Role of General Relativity, http://dx.doi.org/10.1023%2FA%3A1016578408204 , but it seems that in there the following is described (from the Wikipedia article about Black Holes): An outside observer does not actually see the end of a gravitational collapse. Even though the collapse takes a finite amount of time from the reference frame of infalling matter, a distant observer sees the infalling material slow and halt just above the event horizon, due to gravitational time dilation. Light from the collapsing material takes longer and longer to reach the observer, with the light emitted just before the event horizon forms is delayed an infinite amount of time. Thus the external observer never sees the formation of the event horizon; instead, the collapsing material seems to become dimmer and increasingly red-shifted, eventually fading away.

So, in other words: there had not enough time passed yet in our universe for matter to have fallen through the event horizon, leave alone continue inwards to form a singularity. Or do I interpret this wrongly? ... Perhaps singularities are not a problem then, because they require an infinite amount of time to form?! ... Looking forward to hear your thoughts on this.

May I highly recommend "The Edge of Infinity" by Paul Davies which deals with this subject at non expert yet sufficient level.

Alright. Now I was just reading this article from 1965 http://prl.aps.org/abstract/PRL/v14/i3/p57_1 by Roger Penrose in Physical Review Letters where he writes about gravitational collapse: "To an outside observer the contraction to [the Schwarzschild radius] appears to take an infinite time." ... But then, in the next sentence continues right away with "Nevertheless, the existence of a singularity presents a serious problem for any complete discussion of the physics of the interior region." ... I am sorry, I just don't get this! Why do we need to consider ourselves with something that takes an infinite time to form? Our universe is (probably) around 14 billion years old, in any case, a *finite* amount of time, so no complete gravitational collapse to a singularity (or even below the Schwarzschild radius could have occurred yet. If the universe should end up having a finite lifetime and collapse some day, then yes, perhaps in the last dying moments, singularities could form (as the whole universe itself contracts into a singularity!), but if it instead continues to expand forever (and recent data seems to suggest that), then at any given time in the future, still the matter around any "black hole" would only linger around the Schwarzschild radius / event horizon and not drop any further below, since that would take infinite time which still would not have passed. ... So, again, my question: do we really need to be concerned with (as scientists) with a phenomenon (i.e., singularities) which according to my understanding have never formed and will never form (in finite time) in the future of this universe? Does nature quasi "prevent" the formation of singularities by requiring their formation to take infinite time? - Please: discuss!

Just came across an exchange on LinkedIn from about a month ago where this topic was discussed at length http://www.linkedin.com/groupAnswers?viewQuestionAndAnswers=&discussionID=175477793&gid=3091009&commentID=100079472&trk=view_disc&ut=1hUeCZBThExRs1 and some publication by Zahid Zakir, the initiator of that thread: http://tpac.theor-phys.org/4100-024/#.UKTDCaAQd-A

Just a brief note that new singularities form every time a supernova explodes anywhere in the universe - a rather routine event across the universe.

Most chemicals heavier than Helium (alongside traces of slightly heavier elements like Lithium) have been forged in Supernova explosions, so we would not exist if singularities did not exist as well.

One of the reasons why the subject may appear confusing is because dimensionality intervenes. Amos Ori of Technion for instance, and others, have published models whereby expanding chunks of spacetime look infinite from the inside but finite to an observer outside their light cones. Both time, and surprisingly space, can appear to dilute or stretch infinitely or not - dependent on the observer's vantage point.

In a supernova explosion the star's outer material is expelled into space (yes, including the stuff, elements, that we are made off). Whether or not the remaining mass suffices to lead to a gravitational collapse that would be expected to lead to the formation of a black hole depends on the details of the situation. ... The core question remains however: with GR predicting that time freezes (as observed from the outside, i.e., the rest of the universe), no accumulation of matter should ever be able to cross its own Schwarzschild radius in a finite amount of time.

Ralph, sorry it does not. if the mass is sufficient to lead to a supernova explosion, it is also sufficient to recollapse remainders onto a black hole - please do read up on the calculations. Time does not freeze on the outside - this is why we do observe supernova explosions and we then can deduce from its gravitational effects the size of the resultant black hole.

There is exhaustive literature on the subject out there.

I do not argue that we observe supernova explosions (and for the record: the classifications are such that for star masses below the Chandrasekhar limit we end up with white dwarfs, while above that limit, we obtain neutron stars; if the mass is even higher, exceeding the so-called Tolman–Oppenheimer–Volkoff limit, *then* the formation of a black hole is predicted). So far so good. But: please, read up the above cited and linked papers by Roger Penrose or any other on that matter: for an outside observer, the gravitational collapse below the Schwarzschild radius should indeed take infinite time! Something not moving anymore and taking infinite time to complete a process is, in other words, frozen in time. - The collapse is therefore (as seen from the outside) never completed and no singularity is formed; only in the asymptotic limit the formation of an infinitely dimmed and red-shifted event horizon.

A similar question troubled me for a long time. Finally, I imagined a plausible and simple answer: the radius of the horizon is a function of the total mass of the black hole. If new mass accumulates near the horizon, the mass of the whole "object" (the initial BH plus the incoming mass) increases, giving rise to a larger radius for its horizon, so that, eventually, the incoming mass will be inside this enlarged horizon.

It could be said that it's not the mass that crosses the horizon, but the horizon that grows to swallow the incoming mass.

For sure, the precise description using GR will not be so simple, but I think that the general idea provides the right intuition of what is going on.

Thank you for your thoughts on this Enric. I certainly agree with you that the radius of the horizon is a function of the total mass (it clearly is). But I still cannot quite see the rest of your argument: for the incoming new mass to raise the radius of the existing horizon, it needs to fall below this horizon, for otherwise (even if it's "near", but beyond, further outside), its gravitational pull would be in the opposite direction, away from the center of mass of the existing event horizon. But, again (and we are back to my original problem), for any mass to drop below the radius of the existing event horizon, an infinite amount of time would need to pass (as seen from the outside, like always).

This problem mainly arises due to three-dimensional thinking and the underlying idea (somehow hard-wired in our subconscious) that time is universal. First, the event horizon is not a two-dimensional structure that appears at one moment and did not exist the moment before. It is a three-dimensional object embedded into a four-dimensional space-time. Just when it appears depends on the time coordinate you use in describing that space-time and defining simultaneity. Then the correct statement is that in Schwarzschild coordinates, crossing the event horizon takes an infinite time. Schwarzschild coordinates agree with simple Minkowski coordinates far from the black hole and are a way to continue them to the event horizon, but they are not the only way. If you describe things in terms of the proper time of an infalling observer and his local coordinates -- he will cross the horizon in finite time, so it certainly is present before infinite time has passed. (For the observer using Schwarzschild time, time dilation of the infalling observer goes to infinity, so only finite time passes for that observer throughout the lifetime of the universe.) Moreover, you can define an arbitrary number of different time coordinates which all define distant simultaneity differently (the only condition being that simultaneous events lie on space-like sheets of space-time; their detailed shape is arbitrary). Some of these coordinates share the property with Schwarzschild time to become Minkowski time infinitely far from the black hole. But near the black hole they may advance more slowly than Schwarzschild time, and you can adjust this so that the event horizon forms in finite time.

So the true general relativistic answer to your question is: Whether the event horizon forms in finite time or not depends or your particular choice of time coordinates, and there is nothing in physics that makes one of these choices preferable over the other. It is just a matter of taste, which one you prefer.

Thank you for your explanations Professor Kassner. I do understand that time is not universal and that for an observer following the gravitational collapse at a very intimate distance, the process of crossing the horizon may take only finite time. But while that would be happening, an infinite amount of time would pass "outside" in the nearly "flat" space-time where, e.g., Earth is essentially residing. What that means for the collapse itself is not quite clear to me. For example, if the universe were such that it would at some future time collapse onto itself again (Big Crunch scenario), rather than forever expanding, then couldn't one talk about a finite lifetime of the universe, which therefore does not allow "enough" time (i.e., infinite time) to pass before the process of gravitational collapse has completed? Would it be sensible to talk about singularities in such a universe, when even the formation of an event horizon could not be completed in such a scenario? ... Now, our reality might be different, and the universe may continue to expand forever. But even then, from our perspective, from the flat space-time viewing point, no matter where we look at, all we should see (though extremely red-shifted and thus virtually no longer visible) are gravitational collapses frozen in time, asymptotically approaching their event horizon, but not quite getting there (since, at any point in time on our clocks, only a finite amount of time will have passed since the black hole formation process began, or the birth of the universe for that matter). In other words: from our point of view (and that of the majority of the flat space-time?), nowhere in the universe should a singularity yet have formed (except, perhaps, arguably at the very beginning, in the Big Bang). Could it be a "protection" mechanism of nature to prevent singularities from occurring by requiring a precursor to their generation (i.e., gravitational collapse to below the event horizon) to take infinite time from the viewpoint of the universe at large?

Sorry if I have not been clear enough. By the way, the horizon is not an object, nor something that gets "formed" at some time. It is just a theoretical distance computed as a function of mass, and as such it will depend on the reference system you choose.

But let us stay with our familiar reference frame here in Earth.

Take a BH of mass M with a horizon with radius R. Let nearby matter with total mass m approach the BH from all directions and wait for some million years. Let R+r be the radius of the horizon of a BH with mass M+m. As soon as all the mass m reaches a distance d < r from the initial horizon, which should happen in finite time, all of it is inside the sphere of radius R+r, and therefore it is beyond the horizon of a black hole of mass M+m.

Another possible way to see it: As you said, if a new mass approaches the horizon, its gravitational pull would be in the opposite direction. This gravitational pull will attract the BH in the direction of the incoming mass, so that, eventually, the horizon will cross the position at which the mass is frozen.

Let me puzzle you with a tricky question: Can black holes move at all? A BH that moves is space could "collide" with objects in its path, but if we say that, as seen from a distant outside, nothing can cross the horizon in finite time, either the BH must stop, or the object must flee away to avoid crossing the horizon. Both possibilities are absurd, so that a moving BH would be a non-sense.

Thanks for the clarifications Enric! First, I think that the process of the additional mass m reaching a distance d < r from the initial horizon, should also take infinite time, because effectively we are now just forming a (partially preformed) black hole of event horizon R+r and mass M+m, so that gravitational collapse should again grind to a halt as the extra mass m approaches R+r (the new event horizon). - Anyway, regarding your puzzle/tricky question: I see no problem with moving black holes. Objects in its path would be swept up and approach the event horizon distance R in front of it, but only asymptotically in infinite time; they would then travel along with the black hole (same velocity, same direction) keeping a distance R from its center (really, R + dr, where dr is a small distance that goes to zero as time goes to infinity).

Your views are correct within a particular coordinate system (closely related to Schwarzschild's). What would happen in the case of a big crunch cannot be deduced from the Schwarzschild solution alone; you'd have to solve the cosmological equations plus the equations describing black hole formation in that curved background together, and I do not know the answer to that coupled mathematical problem. The Schwarzschild solution is the solution of a one-body problem, i.e., it does not take into account gravitational effects of other bodies.

There are two points in your post, where I would say you'd have to be careful about formulations.Firsrt: "while that would be happening, an infinite amount of time would pass "outside" in the nearly "flat" space-time where, e.g., Earth is essentially residing" What do you mean by "while" here? How do you compare time near the black hole and time at a distance? What you are doing is essentially using the time coordinate of the Schwarzschild metric. (Incidentally, in that time coordinate, also for an observer slightly above the Schwarzschild radius, the time of formation of the latter will be infinite, so you do not have to go *far* outside.) What I said in my last post is that you can find other time coordinates, where *simultaneous* with the time of formation of the event horizon is a finite time at infinity (and at any finite distance, too). The point is that distant simultaneity is not a matter of physics, it is a matter of choice. (Even in special relativity. You can find articles on this by searching for "conventionality of simultaneity" or "conventionality of synchronization".)

The second point, where your formulation is debatable is "nowhere in the universe should a singularity yet have formed". It is a point of view of general relativity, that there is no universal "now". So the statement of something not have happened "yet" at a distant position or even "nowhere" is meaningless. You can make the statement that something happened already at a distant place, if light has had time to get from "there" to "here". If this is not the case, you can always choose a synchroniziation that puts the event in question into your personal future, so it has not happened "yet". You may choose a different time coordinate (for the space-time patch covering the space between "here" and "there") that puts the event (which you may be able to anticipate by calculation before detecting it) into the far past.

What I said in my previous post is that by choosing an appropriate time coordinate *interpolating* between the time of an infalling observer and that of an external observer, you can make the event formation appear at finite time *for the external observer* (without changing his local time coordinate, i.e., it would be the time on his own clock). This is a purely theoretical statement. He cannot detect it at finite time, because no light can get to him from the formed horizon. But he can say that according to his coordinization of space time, the event horizon has formed at some definite time t_0. Of course, he may still observe light from the frozen-looking horizon afterwards. But that light has simply started its journey before t_0.

Thank you again Professor Kassner for further explanations. I agree with you that I should be very careful indeed when using everyday common language with words such as "while" and "now" in a setting which is very remote from our everyday experiences. So, I guess my thinking boils down to what you wrote in the end:

"He cannot detect it at finite time, because no light can get to him from the formed horizon. But he can say that according to his coordinization of space time, the event horizon has formed at some definite time t_0. Of course, he may still observe light from the frozen-looking horizon afterwards. But that light has simply started its journey before t_0."

It seems correct then, to say that, observing (from Earth) gravitational collapses via telescopes anywhere in the universe through the (more and more red-shifted) light that reaches us, will never show us a contraction of the mass below an event horizon. The gravitational collapse as seen for an outside observer takes infinite time, as Roger Penrose already wrote about half a century ago. I understand that from this it does NOT directly (or naively) follow that singularities "never" form "anywhere" in the universe. This is just "our" observational viewpoint (shared, possibly, by other observers or clocks elsewhere residing far away from any gravitational collapses).

Thank you again, to all contributors of this discussion thread, for enlightening a difficult topic! I appreciate your time (and patience).

I can give the problem another twist, which seems to make it much harder. This is something that has bothered me for a long time. In general relativity, there are coordinate systems, in which the formation of the event horizon (to be distinguished from the Schwarzschild radius, which is a purely mathematical construct; the event horizon also has a physical meaning -- nothing can escape from it) takes infinite time. This is fine as long as a black hole can live infinitely long. However, if we take quantum mechanics into account, then a black hole should decay due to Hawking radiation. The decay takes very long but a finite time for the infinitely far observer. So for that observer, the black hole should evaporate *before* an event horizon forms!

What about an infalling observer? If I try to describe things from outside (and in Schwarzschild coordinates) then he should never be able to cross the horizon. That is, if he were not torn apart by tidal forces even before reaching the horizon, he might survive. On the other hand, for this observer falling across the horizon takes only a finite proper time. Moreover, he will not see any Hawking radiation. One might suppose that his fate is the one that is usually described for observers falling into a black hole.

But then we have two predictions that cannot be true "at the same time". I have some ideas about this but not a definite answer.

In the meantime (2018), I do. Read my publication "Radially falling test particle approaching an evaporating black hole", at this moment available at arXiv:1801.00272, later hopefully in Canadian Journal of Physics.

Could we think there are black holes in the center of the galaxies?

Hi, Eder,

Today, it is a well-known fact that each galaxy has its own black hole. The same exist for the black hole at the center of Milky Way. However, I am unfamiliar about a name of this black hole. Has it a name? For example our star is called Sun.

Dear Ralph,

Of course, it "must" be no problem with moving black holes, but I think you didn't catch the "paradox" I posed to you. You said that:

"Objects in its path would be swept up and approach the event horizon distance R in front of it, but only asymptotically in infinite time; they would then travel along with the black hole (same velocity, same direction)..."

Perhaps you have not thought enough about this. Do you mean that a free falling object approaching a black hole that moves towards it, will at some point invert its movement direction just to avoid crossing the events horizon? What physical force or effect would cause this?

I think you must find the response to my paradox by relaxing the idea that nothing can cross the horizon in finite time: it is not an absolute truth. It is only valid for a specific reference frame.

Dear Enric: All I can say is that near the event horizon, dynamic processes should come to a stand-still because of the time dilation due to the extremely strong gravitational field. In my understanding therefore, the object falling towards the black hole would therefore indeed "slow down" and effectively "stop" before the event horizon, in the sense that an increasingly larger amount of time (from out viewpoint) is needed to cross a finite amount of distance. Could we not travel along parallel to the black hole with the same velocity (which is, after all, never absolute) and then have the regular case of an in-falling object? - But, I might be wrong in my understanding. Do you have an answer that you would like to provide as to what will happen in the scenario described by you?

Hi, Ralph:

I can agree with you in that a time dilation will be observed in our coordinate system, probably causing an effective "stop" of the falling object near the horizon. What I do not agree with is that the object will turn back and travel at the fringe of the BH, as if it were pushed away by some hard thing forming the horizon.

Why not accept that the object stops (as seen from our reference frame) when it reaches the horizon, and stays there while it is "traversed" by the horizon that advances with the moving black hole?

This simply would mean that the fact that no object can traverse the horizon in finite time is only valid for an observer for which the BH is not moving. In fact, as you must know, for an observer moving with the falling object, the horizon will be traversed without any delay, without even noticing that something special has been traversed. Therefore, it should not surprise you that, for different observers, the time taken to cross the horizon is different, and becomes infinite only for a particular observer.

Dear Professor Kassner, indeed, the consequence of Hawking radiation adds a very interesting aspect to this problem. I am not sure either what the correct resolution could be, but in practical terms, for "our" universe, it seems that most black holes would not shrink, but rather grow, by absorbing more cosmic microwave background radiation (at around 2.7 K) than emitting Hawking radiation (which corresponds to black body radiation of a temperature that goes inversely with the mass of the black hole, and would, e.g., for one solar mass amount to a T of only 60 nanoK; heaver black holes are therefore correspondingly "cooler"). - The principal paradox remains however: what would happen in the scenario you described were there no "feeding" of the black hole by CMBR. Perhaps we also still lack a full understanding of how Hawking radiation would truly affect the evolution of a black hole.

A gravitational singularity or space-time singularity is a location where the quantities that are used to measure the gravitational field become infinite in a way that does not depend on the coordinate system. These quantities are the scalar invariant curvatures of space-time, which includes a measure of the density of matter. If you consider a conical singularity -then there is a point where the limit of every diffeomorphism ( which is an isomorphism in the category of smooth manifolds--an invertible function that maps one differentiable manifold to another, such that both the function and its inverse are smooth) invariant quantity is finite, in which case space-time is not smooth at the point of the limit itself, and thus, space-time looks like a cone around this point, where the singularity is located at the tip of the cone. The metric can be finite everywhere if a suitable coordinate system is used. An example of such a conical singularity is a cosmic string.The formation of cosmic strings is somewhat analogous to the imperfections that form between crystal grains in solidifying liquids, or the cracks that form when water freezes into ice. The phase transitions leading to the production of cosmic strings are likely to have occurred during the earliest moments of the universe's evolution, just after cosmological inflation, and are a fairly generic prediction in both Quantum field theory and String theory models of the Early universe. Gravitational lensing offers support evidence for cosmic strings and continued investigation of superstring theory.

Hallo, Judith,

thank You very much for the information.

I can write my address where I leave:

Sagittarius A black hole, Soller System, Earth planet, Eurasian continent, Russia, ....

I have attended a black hole conference in Pohang, South Korea and I have spoken with Professor T. Harko from Hong Kong (Romania). I have sent him one theoretical paper about the light speed that can be from zero to infinity. However, I cannot fond this paper in my e-library. Could anybody say to me about some theoretical works where the speed of light is infinity.

Have a nice day!

Hello Aleksey, how are you?

I think i am your neighbor...

Could we see an "unbroken" singularity?

Of course, most black holes do not shrink at this time, because more energy falls in than comes out. But that postpones things only... If our universe really continues to expand in an accelerating fashion, then the energy density of the cosmological background radiation is bound to fall below that of Hawking radiaton from solar size black holes. So these will start to emit more radiation than they suck in. Clearly, we are talking really huge times here, something like 10^(10^100) years. But infinite time dilation could bridge such a gap, couldn't it?

Dear All,

thank You.

Also, I would like to state that the speed of light can be higher than 3*10^8 m/s near a massive black hole. As a result, a photon can be accelerated by gravitational forces and because there are a lot of photons orbiting the black hole, collisions among photons can exist resulting in possible situation when some photons can even leave the black hole. For this purpose, such photons have to have speeds much higher than 3*10^8 m/s. However, such photons can be slowed down to 3*10^8 m/s when they are around earth anew.

What do You think about that?

Have a nice day!

Aleksey

@K.Kassner: Sounds like the decription of the black hole evaporation before horizon formation as proposed by Gerlach http://prd.aps.org/abstract/PRD/v14/i6/p1479_1

The infalling observer behaves in no way different form the collapsing star which forms the black hole. So he also evaporates before reaching the horizon. I see no contradiction here.

Of course, for quantum effects of gravity it is necessary to give up the equivalence principle.

@Ilja Schmelzer: Hi, Ilja. Nice to hear of you again and thanks for the reference. I'll have to read that paper.

Concerning: "The infalling observer behaves in no way different form the collapsing star which forms the black hole. So he also evaporates before reaching the horizon. I see no contradiction here. "

What would make him evaporate? I was not thinking of an observer falling in with all the matter at the same time but of one that starts his journey much later, when the black hole has really become "black" for all practical purposes for the outside observer, i.e., after the time of "emission of the last photon" as defined, e.g., by Misner, Thorne, and Wheeler. Let it be a supermassive black hole. Then we should agree about the fact that an infalling observer does not note anything particular near the horizon, because the horizon is only a coordinate singularity. We also probably agree that he will not see any Hawking radiation, because that seems to be commonly accepted. Now, how can it be explained that he will not see any Hawking radiation? Should he not be hit by Hawking radiation from the point of view of the outside observer? Not necessarily. My own rationalization of this is that not only does the infalling observer suffer infinite time dilation at the horizon but also infinite length contraction. But Hawking radiation is not emitted from the horizon itself, since it would not be able to escape. It must originate slightly outside. So from the point of view of the outside observer, the infalling one does not see any Hawking radiation because he is too flat. The radiation is created farther away from the horizon than his location. This way he wll never see any Hawking radiation except possibly while he is still far from the horizon, but then the radiation is still very weak. So in a sense, the black hole evaporates from under the infalling observer without him noticing. It should evaporate sufficiently fast so he can never reach the horizon. But then there is nothing to destroy him, so there is no reason for him to get evaporated.

As to: "Of course, for quantum effects of gravity it is necessary to give up the equivalence principle." This is a non-sequitur. It may be that we have to give up the equvalence principle, but the "of course" is by no means clear. An accelerating observer will observe Unruh radiation instead of Hawking radiation. Now there are several papers mentioned above claiming that Unruh radiation and Hawking radiation are described by slightly different formulas and hence the equivalence principle does not hold. Interestingly, these papers agree on the fact that for an observer *at* the horizon, it holds again. Now, the equivalence principle holds only locally, if the gravitational field is not uniform (i.e. virtually always). But the statement that it holds *at* the respective horizons is just the statement of locality. Only for an observer at the horizon itself are Unruh or Hawking radiation locally created. For all observers away from the horizon, measurement of the radiation is not a local experiment, because the radiation comes from close to the horizon, i.e. from a distance. Since the event horizon of a black hole and the horizon present for an accelerating observer have different shapes, it is not surprising that the radiation emitted by both is not exactly the same. But this does not contradict the equivalence principle, which refers to local experiments only.

It is, of course, only my personal position that to give up the equivalence principle is a necessity for quantum gravity. But I think I have a rather strong argument given in arXiv:0909.1408 - an impossibility theorem for a background-independent quantum gravity theory. Of course, it has (as every theorem) some assumptions, but these assumptions seem to be rather weak.

From point of view of my impossibility theorem, your observation that there seems to be a contradiction - which is based on the assumption that the EEP holds - is only independent additional support. ;-)

The point is that in my opinion not all systems of coordinates are equal. (The harmonic ones are more equal than others ;-)) So which is the preferred one? It is one similar to the original Schwarzschild, where at the time when outside the first Hawking radiation arrives, so that the BH has already lost some of its mass, the horizon is not yet formed. And the infalling observer has also not yet reached the not yet formed horizon. But global energy conservation in these coordinates tells us that some of the mass of the BH has been already radiated away by Hawking radiation.

Maybe you remember me as proposing a preferred frame interpretation of GR? I have already changed this and propose now an alternative theory of gravity, with an ether interpretation and an additional term which enforces the harmonic coordinate condition. gr-qc/0205035, and have succeeded in publishing it. Together with a quite simple ether model for the standard model of particle physics, which predicts all fermions and gauge fields of the SM, arXiv:0908.0591, also published, Foundations of Physics seems sufficiently serious for an ether theory ;-) So I have not lost my time.

So it affects us continuously outside the event horison

A mathematical effect without potential physical consequences...sounds to me like a mathematical manipulation...there is a difference

Ralph,

"... everything slows down more and more as the event horizon is approached, because time is stretched. So, how can something in our finite-lifetime universe ever cross the event horizon?"

Certainly, I can offer only inexpert conjecture, but I also understand that unstable muons, produced by high velocity cosmic ray collisions with particles in the upper atmosphere, do not soon decay as they would had they not been affected by relativistic time dilation, but can be detected on the Earth's surface. In this case, the muons' 'experience' of time is retarded, yet they continue at high velocity.

I can't effectively evaluate in the context of relativity, but in the local time frame of a mass collapsing at relativistic speeds, might matter accelerated to relativistic velocities experience the retardation of time progression without slowing its momentum?

I also understand that it's thought that relativistic jets expel energy and matter from a collapsing black hole - similar to feeding supermassive black holes of active galactic nuclei (AGN). Might infalling material, accelerated to relativistic velocities and compressed, disintegrate at the boundary of a growing event horizon - somewhat similarly to LHC collisions - but in this case its enormous amounts of previously bound mass-energy is locally retained while its dimensional particle residue is ejected at relativistic velocities? In this way, perhaps a dimensionless singularity could arise as the focal point of geometrically curved spacetime - without requiring the unphysical retention of any dimensional matter.

As I understand, hard X-ray emission at the inner radii of AGN accretion disks seem to indicate that some high energy processes are occurring near the event horizons of supermassive black holes, perhaps supporting this conception...

Sanjay,

Good question, but from my own perspective, doesn't computing the stellar core collapse (less than 100,000 km , I think) to even a dimensional space of ~1 mm ignore the physical implications for the compression of matter to unphysical scales?

As I understand, there is no even hypothetical form of matter that could achieve the necessary material densities. While conversion of atomic matter to mostly neutrons by a neutron star collapse achieves an enormous increase in mass density through the elimination of high spatial occupancy electrons, there seems to be no increases in density of similar magnitude possible for the further conversion of neutron star material...

Sanjay,

I'm just treading water here, but isn't Hawking radiation thought to be a rather small effect imparted by the manifestation of virtual particles in external spacetime?

I also don't follow how "more and more energy density" can be packed into a "smaller and smaller volume"... isn't this conception simply ignoring all of quantum theory?

Please see my initial post here (2nd prior, today) - isn't a process that extracts mass-energy from unbound matter at the event horizon more consistent with both quantum theory and observations of energetic material being ejected via relativistic jets? I think this would make quantum mechanics a critical component of black hole processes, not just a casual participant as in Hawking radiation. But, I am just speculating, of course.

It is like a Bow and arrow....it is all in the string.There is the initial tension, but as we pull back on the string the energy density increases more and more packing it into the back of the arrow---The Schwarzschild radius of an object is proportional to the mass.Assuming constant density, the Schwarzschild radius of a body is proportional to its mass, but the radius is proportional to the cube root of the volume and hence the mass. Therefore, as one accumulates matter at normal density (103 kg/m3, for example, the density of water), its Schwarzschild radius increases more quickly than its radius. At around 150 million(1.5 x 108) times the mass of the Sun, such an accumulation will fall inside its own Schwarzschild radius and thus it would be a supermassive black hole of 150 million solar masses--->However, due to extremely large or extremely small constants, it is generally impossible to verify more than two or three properties for any object. The Schwarzschild radius represents the ability of mass to cause curvature in space and time. Any mass can become a black hole if it collapses down to the Schwarzschild radius - but if a mass is over some critical value between 2 and 3 solar masses and has no fusion process to keep it from collapsing, then gravitational forces alone make the collapse to a black hole inevitable. Down past electron degeneracy, on past neutron degeneracy and then on past the Schwarzchild radius to collapse toward zero spatial extent - the singularity. The Schwarzschild radius ( or event horizon) just marks the radius of a sphere past which we can get no particles, no light, no information.However--->there is an important difference between the black hole radiation as computed by Hawking and thermal radiation emitted from a black body --it is that the latter is statistical in nature, and only its average satisfies what is known as Planck's law of black body radiation, while the former fits the data better. Thus---> thermal radiation contains information about the body that emitted it, while Hawking radiation seems to contain no such information, and depends only on the mass, angular momentum, and charge of the black hole (the no-hair theorem). This leads to the black hole information paradox.

However, --->according to the conjectured gauge-gravity duality (also known as the AdS/CFT correspondence), black holes in certain cases are equivalent to solutions of quantum field theory at a non-zero temperature. This means that no information loss is expected in black holes (since no such loss exists in the quantum field theory), and the radiation emitted by a black hole is probably the usual thermal radiation. If this is correct, then Hawking's original calculation should be corrected, though it is not known how !

Regarding Evaporation energy---->However, since the universe contains the cosmic microwave background radiation, in order for the black hole to dissipate, it must have a temperature greater than that of the present-day black-body radiation of the universe of 2.7 K = 2.3 × 10−4 eV. This implies that M must be less than 0.8% of the mass of the Earth[22] - approximately the mass of the Moon. So the Cosmic microwave background radiation universe temperature is 2.725 K---> this shows that black holes can interact thermally with the rest of the Universe...

Susana,

"... if a mass is over some critical value between 2 and 3 solar masses and has no fusion process to keep it from collapsing, then gravitational forces alone make the collapse to a black hole inevitable. Down past electron degeneracy, on past neutron degeneracy and then on past the Schwarzchild radius to collapse toward zero spatial extent - the singularity."

I understand that all you've said is generally consistent with general relativity and black hole theory. However, there seems to be no theory of matter that supports collapse to anything approaching a zero spatial extent. That's understandable since GR was conceived well before quantum theory.

The objective of my conjecture is to conceive of a general process by which black holes can be produced in accordance with GR but where the collapsing matter is subject to the specifications of quantum physics - and is not required to go to a place 'where the laws of physics break down' and unknown processes are required.

and what specifications of Quantum Physics are you thinking about?

Susana,

As a layperson I'm certainly not qualified to specify, but I think there are effects that would be imparted to matter accelerated to extreme velocities and geometrically condensed. Some references are included in http://www.nature.com/news/astrophysics-fire-in-the-hole-1.12726

James, Sanjay, and Susana: thanks for your recent contributions to this discussion board. I think what James might be referring to is the uncertainty principle, which gives particles confined to smaller and smaller volumes inverse-proportionally higher and higher momentum. The problem here is really, as I understand it, that no theory of quantum-gravity exists yet (i.e., a theory that can simultaneously describe quantum effects in the presence of a strong gravitational field). - Indeed, to come back to the original question, if time essentially "freezes" (as seen from the outside at least) as the collapse to the Schwarzschild radius is approached, then we do not have to worry about packing matter to extremely high densities, or?

Dear Mr. Dwyer.....from the reference you gave..."The team’s verdict, published in July 2012, shocked the physics community. Such firewalls would violate a foundational tenet of physics that was first articulated almost a century ago by Albert Einstein, who used it as the basis of general relativity, his theory of gravity. Known as the equivalence principle, it states in part that an observer falling in a gravitational field — even the powerful one inside a black hole — will see exactly the same phenomena as an observer floating in empty space. Without this principle, Einstein’s framework crumbles.

Well aware of the implications of their claim, Polchinski and his co-authors offered an alternative plot ending in which a firewall does not form. But this solution came with a huge price. Physicists would have to sacrifice the other great pillar of their science: quantum mechanics, the theory governing the interactions between subatomic particles."....The Equivalence principle is at the art of the debate.....and how could or would a singularity form in finite time....to get around it by projection---holagraphically speaking..."the deadlock was broken by a discovery made by Juan Maldacena, a physicist then at Harvard University in Cambridge. Maldacena’s insight built on an earlier proposal that any three-dimensional (3D) region of our Universe can be described by information encoded on its two-dimensional (2D) boundary3–5, in much the same way that laser light can encode a 3D scene on a 2D hologram. “We used the word ‘hologram’ as a metaphor,” says Leonard Susskind, a string theorist at Stanford University in California, and one of those who came up with the proposal4. “But after doing more mathematics, it seemed to make literal sense that the Universe is a projection of information on the boundary.”...so mathematically you could experience the singularity by projection from 3D to 2D....is it possible physically in 3D....you need to measure that energy or the temperature (same thing)...Maldacena's mathematical formulation allows an envisioning of the potential phenomena....if these ultraweak energies are measurable by some device or by proxy we could get closer to understanding the true physical impact and effect of these stellar phenomena on Earth. To tie in with Dr. Scheicher's comment, you might enjoy reading this recent reference http://arxiv.org/abs/1307.1202 :"Expanded limits on violations of the equivalence principle from solar-system observations"..by James M. Overduin, Jack Mitcham, Zoey Warecki (Submitted on 4 Jul 2013). on violations of the Equivalence principle.Measuring Non-local phenomena has been done in biological systems. The Japanese are far along in this regards. You may wan to google these terms and research it yourself ..you may fing very interesting correlations to this topic and your acute comments...kindest regards and good hunting!

Here is a little help:http://www.tcm.phy.cam.ac.uk/~bdj10/papers/bell.html; http://cdn.intechopen.com/pdfs/13844/InTech-The_holographic_principle_and_emergence_phenomenon.pdf; https://www.math.ucdavis.edu/~mogilner/Lee.pdf :-)

Thanks for all your kind help!

I think at the heart of the question is the example of muons, produced by high velocity cosmic ray collisions with particles in the upper atmosphere, that do not soon decay as they would had they not been affected by relativistic time dilation, but can be detected on the Earth's surface. In this case, the muons' 'experience' of time is retarded, yet they continue at extreme velocity.

While, in accordance with GR, it might be expected that relativistic matter nearing a BH event horizon might appear to a distant observer to halt and, following the example of the relativistic muon, its decay is halted - but it moves right along. In fact, if its momentum was halted - would it still be subject to relativistic effects?

In the (simpler case of ingested matter) scenario I describe, relativistic matter at the event horizon boundary disintegrates from friction with other compressed particles, much like occurs in particle collider experiments. Here, however, its bound mass-energy, now released, is absorbed by the curved spacetime of the BH. Meanwhile, disintegrated high energy fundamental particles are generally redirected to the polar jets by EM fields... As a result, no matter crosses the event horizon boundary.

Again, this is merely a suggested scenario that might incorporate quantum particle interactions and effects in conditions produced by relativistic gravitation, that could also explain how material mass (in the form of naked curved spacetime) could be seemingly condensed to produce a singularity - a singular focal point of spacetime curvature.

Dear Susana Curatolo,

Thanks for your considerable help!

Regarding the concern about the equivalence principle - I don't see any conflict with the idea of a 'firewall'. I think that "an observer falling into a" black hole _would_ have seen "exactly the same phenomena as an observer floating in empty space" - IF they had not been disintegrated! Perhaps somewhat like jumping into the LHC tunnel during an experiment, I guess...

Re.: "... any three-dimensional (3D) region of our Universe can be described by information encoded on its two-dimensional (2D) boundary3–5, in much the same way that laser light can encode a 3D scene on a 2D hologram." I'm merely a retired 'information systems analyst', but I cannot comprehend the view that information about the configuration of all matter and/or spacetime in the universe, etc., is somehow encoded and presumedly physically stored - anywhere. I also haven't heard of any theory explaining how process(es) reference any stored information in processing matter, etc.; no projection beam transcribing any physical boundary encoding of information to reconfigure or transform matter, etc.... As a consequence, I can only ignore such discussions. Thanks very much for your interesting references, though!

@Sanjay Sood: Not "bringing in the time of formation" looks like head-in-the-sand policy to solve the problem. Once the BH evaporates, the radiation is seen far away, thus, has to be originated before horizon formation. So how the BH horizon can be formed before evaporation?

The problem behind this is energy conservation, which is not well-defined in GR because of covariance. Hawking radiation is a way to transform energy of the gravitational field into radiation. Or you give up energy conservation (a bad idea without any empirical support) or covariance.

@James Dwyer, thanks for pointing me to the http://www.nature.com/news/astrophysics-fire-in-the-hole-1.12726 article. The firewall seem to be something similar to the Gerlach scenario http://prd.aps.org/abstract/PRD/v14/i6/p1479_1 where the BH evaporates before the horizon is formed.

Yet another contradiction between covariance and common sense in the quantum domain. The most popular is the violation of Bell's inequality (contradiction with realism). My personal contribution is arXiv:0909.1408, where I argue that a covariant quantum theory would be unable to predict the outcome of a trivial double slit experiment (is a gravitational interaction with a test particle sufficient to destroy a superposition) which could be trivially predicted in a Newtonian version of quantum gravity.

So its time to give up covariance as being something fundamental.

Ilja Schmelzer,

You're most welcome - I'm glad to help in some small way. Again, I'm really not capable of evaluating the Gerlach scenario, but from what I could gather black body radiation is a phenomenon produced by objects that are at thermodynamic equilibrium with their environment - this does not seem to fit collapsing or feeding black holes. Likely I misunderstood something - or many things...

I was confused by your statement that GR gravity was a background free theory. The best I can do is envision spacetime as the dimensional coordinates of the background vacuum, whose kinetic energy density and perhaps virtual particle manifestations are reconfigured by boundary interactions with potential mass-energy. This reconfiguration of background energy density physically corresponds to the distortion of dimensional spacetime employed by GR to describe gravitational effects. In this conceptual scenario gravitation is not strictly a quantum particle force interaction - perhaps this could account for its apparent relative weakness when compared to the particle-particle force interactions. Sorry I can't better comprehend...

Isn't Hawking radiation thought to evaporate black holes because 'ingested' antimatter virtual particles are thought to have negative energy. Has this been confirmed? Wouldn't this require that antimatter have negative mass?

Not necessarily. I always interpreted the creation of a particle-antiparticle-pair as "borrowing" energy for a short amount of time (as per delta E times delta t less than Planck's constant) and if the pair cannot be annihilated then (because one of the partners falling disappearing out of reach behind the black hole's horizon) then someone has to "pay the bill" and since the escaping partner (independent of whether it is a antiparticle or "regular" particle) carries away positive energy, the black hole will have its energy reduced by the corresponding amount. - Too naive a picture, or basically correct?

Ralph,

Thanks - that helps, and I think is generally agrees with what I can find and comprehend regarding Hawking Radiation.

However, I have to wonder - shouldn't it be considered that all virtual particle pair manifestations - anywhere - are condensations of vacuum energy, and that their energy when annihilated is returned to the vacuum? In that case, it seems that the accounting for their energy is either as particles or as vacuum energy. Certainly there should be no issue with any energy 'ingested' by a black hole - it's still considered to exist within the universe, correct? In that case, it seems that any virtual particles that persist should be 'borrowed' from the vacuum and that any Hawking Radiation propagated from an event horizon would also simply indicate an identical mass absorbed by the black hole - just like any other matter it ingests. Perhaps this is not consistent with some other established interpretations, but Occam's razor states that one should proceed to simpler theories until simplicity can be traded for greater explanatory power. In the absence of supporting evidence...

I find that much of the entry http://en.wikipedia.org/wiki/Hawking_radiation is lifted verbatim from:

K.N. Prasanna Kumar, B.S. Kiranagi, C.S. Bagewadi (2012). "Hawking Radiation - An Augmentation Attrition Model." Advances in Natural Science, 5 (2), 14-33. DOI:10.3968/j.ans.1715787020120502.1817. http://cscanada.net/index.php/ans/article/view/j.ans.1715787020120502.1817/2663

From its introduction:

"... The electromagnetic radiation is as if it were emitted by a black body with a temperature that is inversely proportional to the black hole’s mass. Physical insight into the process may be gained by imagining that particle-antiparticle radiation is emitted from just beyond the event horizon. This radiation does not come directly from the black hole itself, but rather is a result of virtual particles being “boosted” by the black hole’s gravitation into becoming real particles.

"A slightly more precise, but still much simplified, view of the process is that vacuum fluctuations cause a particle-antiparticle pair to appear close to the event horizon of a black hole. One of the pair falls into the black hole whilst the other escapes. In order to preserve total energy, the particle that fell into the black hole must have had a negative energy (with respect to an observer far away from the black hole). By this process, the black hole loses mass, and, to an outside observer, it would appear that the black hole has just emitted a particle..."

The introduction concludes:

"A black hole of one solar mass has a temperature of only 60 nanokelvins; in fact, such a black hole would absorb far more cosmic microwave background radiation than it emits. A black hole of 4.5 × 1022 kg (about the mass of the Moon) would be in equilibrium at 2.7 Kelvin, absorbing as much radiation as it emits. Yet smaller primordial black holes would emit more than they absorb, and thereby lose mass."

The concluding statement, seems to indicate that only black holes whose equivalent mass is less than the moon's should actually lose mass from evaporation - then only if no new mass is accreted... Moreover, I can't comprehend what any near or far observer has to do with these processes - certainly they must occur even in the absence of any observers!

Dear Ralph,

your question about the NATURE of black hole is very important and is debated since the formulation of General Relativity by Einstein in 1915 – 1918.

By the way there is a paper by Einstein, "On a stationary system with spherical symmetry consisting of many gravitating masses", Ann. Math. (USA), 40, 922 - 936, 1939 where he wrote: "The essential result of this investigation is a clear understanding as to why 'Schwarzschild singularities' do not exist in physical reality". Actually Einstein demonstrated that at Schwarzschild radius the special relativity is violated and GR should be modified to exclude such matter behavior.

Also there is a photo of Einstein and Oppenheimer (Princeton 1949), where he explains to Oppenheimer why there is no black holes in physics! It was presented by J.Bernstein in Scientific American, vol. 274, N 6 (June 1996), 66 - 72, 1996, in the paper "The reluctant father of black holes". Bernstein considered this as Einstein’s mistake, but now it is well-known that there are a lot of physical paradoxes related to event horizon, including also your question.

However there is a natural approach to gravity which is free from black holes.

In modern physics ALL fundamental forces (strong, weak, electromagnetic) are explained by the exchange of virtual and real bosons (integer spin particles) between fermions (half-integer spin particles – matter). As Richard Feynman emphasized in his book devoted to field approach to gravitation (Richard Phillips Feynman, Fernando B. Morinigo, William G. Wagner, Brian Hatfield, "Feynman Lectures on Gravitation (Frontiers in Physics)" , 2002 | ISBN: 0813340381 | 232 pages ) “the geometrical approach is not necessary for gravity physics.”

Field gravity approach is based on Lagrangian formalism of the modern relativistic quantum theory and describe gravitational potential as the second rank symmetric tensor field in Minkowski space-time, which guaranty the conservation of the energy-momentum tensor of the gravitational field (which is absent in general relativity). Intriguingly .all classic relativistic gravity effects, which really tested by experiments/observations has the same values in both geometrical and field approaches. Moreover there are several crucial experiments which can distinguish between these approaches. For detailed discussion of such possibilities see

the book http://link.springer.com/book/10.1007/978-94-007-2379-5/page/1

and papers http://arxiv.org/abs/0809.2323 and http://arxiv.org/abs/0809.2328 .

Dear Yurij,

While gravitational theories may have been constructed that are "free from black holes," more recent observational evidence strongly indicate that they exist in the universe. Please see http://en.wikipedia.org/wiki/Black_hole#Observational_evidence for a discussion that includes many references. Among the most compelling evidence is the observed orbital characteristic of stars within the area Sagittarius A*...

Yurij, I have taken a look at your theory from point of view of my own theory of gravity in http://arxiv.org/abs/gr-qc/0205035 which is, if one restricts himself to the equations of motion, equivalent to Logunov's massive RTG but with very different metaphysics and other subtle differences.

I agree about the importance of having a reasonable energy-momentum conservation. My theory has one. But I fail to understand why you thing that for the gravitational part taken alone there should be T^00 > 0. This should be valid for the whole EMT, the subdivision is IMHO arbitrary and irrelevant. I also fail to understand why the trace should be zero.

It would be helpful for the presentation of your theory if it would have been given in terms of the effective metric, if there is one. This would make it much easier to understand the differences between your theory and GR.

James, there are theories without black holes which have, nonetheless, stable "frozen stars" or "gravastars" which are only slightly greater than their Schwarzschild radius. The evidence about the existence of black holes does not contradict these theories. See http://arxiv.org/abs/1003.1446 where I have discussed this for my own theory.

Ilja,

Thanks. Please also see http://en.wikipedia.org/wiki/Black_hole#Alternatives

Also see http://en.wikipedia.org/wiki/Black_hole#Galactic_nuclei

"From the orbital data they were able to place better constraints on the mass and size of the object causing the orbital motion of stars in the Sagittarius A* region, finding that there is a spherical mass of 4.3 million solar masses contained within a radius of less than 0.002 lightyears. While this is more than 3000 times the Schwarzschild radius corresponding to that mass, it is at least consistent with the central object being a supermassive black hole, and no "realistic cluster [of stars] is physically tenable""

Also see http://arxiv.org/abs/0810.4674 and http://arxiv.org/abs/astro-ph/9807210

I can't evaluate whether even quark degeneracy pressure could prevent the complete gravitational collapse of such a compact massive object, but I suspect not...

Dear James,

to discuss the nature of black holes one should know original papers about measuring parameters of black hole candidates (to see how they were derived) together with the theoretical problems with the physical meaning and definitions of the singularity and event horizon.

In the reference you mention there is now such analysis – it is wiped out under the carpet.

I have a doubt that you read papers on theoretical problems with general relativistic ignorance of the energy-momentum of the gravity field which is the true source of all paradoxes of the black hole physics, including origin of horizon from real objects which has finite binding energy and gravitational field energy around them.

As for observations of the sizes of BH candidates by x-ray spectroscopy K_alfa line and 1.3mm VLBI, they both CLOSED the Schwarzschild black holes because the emitted light region has sizes less than 6 R_sch (the size of last stable orbit) and actually as small as 0.6 R_Sch. This was interpreted as the existence of the EXTREEMLY rotating (with velocity close to c) Kerr BH, but again it is not prediction but explanation after observations. Actually field gravity theory predict minimal radius for relativistic compact objects as small as 0.5 R_Sch.

So before taking information about ultimate detection of a black hole please check how this claims was derived.

Ilja,

I have read through your paper http://arxiv.org/abs/1003.1446 - although as I said, as a layperson my ability to comprehend theoretical arguments is very limited, I found your reasoning quite accessible. However, I was not able to comprehend why it is considered that the gravitational collapse of an object of several million solar masses would be halted before reaching superluminal velocities. In the case of a (relatively minute) neutron star, for example, it seems that the mechanical formation of dense neutron matter provides sufficient degeneracy pressure (along with local neutron-neutron strong interactions) to oppose further collapse. However, I don't understand what physical opposition to the continued collapse of a larger body (a star of more than several dozen solar masses, for example - much less than millions of solar masses).

Not comprehending the mathematics of collapse, if, for example, quark-gluon plasma in the early universe condensed (never producing nuclear fusion) to form a supermassive black hole of perhaps a million solar masses, what might have halted its gravitational collapse? It seems that similar condensations of hydrogen gas and dust produces stars in the more recent universe, but their collapse is halted by the pressure of nuclear fusion.

Certainly, even relatively small supermassive black holes could not have been formed by the collapse of a single star, but if they represent a compact physical object of millions of solar masses, it seems that some unknown form of hyperdense matter is necessary to oppose complete gravitational collapse, preventing the formation of a black hole of some sort...

Thanks for your consideration!

I think it would be interesting to look at this question from the other side. Say someone who was expecting to receive an answer to this question arrived to the horizon (and for this observer it did form in finite time). Now he realized that waiting for the answer from a fellow college from Earth will take an infinite amount of time (and clearly being at horizon he could not go back to Earth). So he begins to ponder if the question itself is still a matter to him...

Dear Cyrill,

your thought experiment is too cheap to be interesting for understanding physical reality. In real physics one needs to operate with experimental/observational data and basic theoretical assumptions and concepts together.

James, in my theory there appears a new actor, namely absolute space and time. These are different from observable distances and clock time. We cannot measure them directly - what we measure is measured with distorted rulers and clocks. And the reason why we cannot measure them is relativistic symmetry. A symmetry which, in my theory, is derived as a consequence of the action equals reaction symmetry.

Nonetheless, even if unobservable, by direct clock or length measurements, the distortions have in my theory an influence on the equations of motion of the gravitational field. A very small influence, but it becomes important and decisive in a situation where otherwise the distortion of lenght and distance measurements would become infinite.

And this is what happens near the horizon region. My theory has an equation for absolute time as well as the absolute Euclidean coordinates. So, in my theory we can compute where time dilation is small or large, and where it would become infinite without the additional terms. And, however small the importance in everyday life, these additional terms would become infinite if time dilation becomes infinite. So, a short time before this happens, these new terms become the leading terms and prevent a further collapse.

Dear Yuirij,

On the contrary, I believe that my experiment would be rather expensive!

Ilja,

Thanks for explaining! Perhaps I'm simply naive, but in my lay opinion there would have to be some physical cause for the collapse of a hypermassive object to be halted, such as neutron degeneracy pressure that halts the collapse of much less massive objects.

Cyrill,

feasible experiments should be based on an achievable technologies and has detailed proof of the possibility of its performance. Such experiments cost a lot. Your suggestion costs zero because nobody will do it.

Dear, Yurij,

I believe now I have to explain myself. My experiment was of completely different nature. It was designed to check if a development of the sense of humor has to be part of the training of the scientist. Now I think that the answer for this question is affirmative (I new it for a long time about mathematicians, but I was not sure about physicists yet).

Ilja,

One who suggest a new theory of gravity should demonstrate that his theory can explain all existing really tested experimental/observational facts. And what is even more important, it should predict new experiments that can distinguish between GR and the new theory.

Has your theory such predictions?

Ok, long time it was too much humor in papers about black holes and cosmology that now is time to discuss seriously the bases of gravity physics.

For see the humor please see:

http://www.amazon.com/Alexander-Unzicker/e/B00DQCRYYY

Sanjay - Thanks!

As I understand, the collapse of a progenitor star larger than 4-8 Solar masses is generally thought to produce sufficient momentum to overcome even neutron degeneracy pressure - allowing complete collapse of its mass to produce a gravitational singularity. As I understand, compressing neutrons beyond that point would require their disintegration into some component particles, logically a quark-gluon plasma. Any unbinding of neutrons would release their binding energy, obtained through the confinement of quark kinetic propagation energy. My intent is to suggest a mechanism by which complete gravitational collapse, producing a singular focal point for gravitationally contracted spacetime, can be achieved without requiring unphysical densities of matter.

It seems quite reasonable that highly energetic interactions among collapsing particles could, much like the collisions of protons during LHC experiments, produce the disintegration of matter, producing fundamental particles and releasing binding mass-energy, which represents the majority of all atomic mass. The dimensional matter might then be expelled from the event horizon, while most of the material's atomic mass-energy could be imparted to the localized gravitational contraction of spacetime - focused on an abstract singularity.

Please see http://en.wikipedia.org/wiki/Gamma-ray_burst_progenitors#Collapsar_model.

It and its references seem to suggest that smaller or more metal-rich progenitor stars' jets may not be able to penetrate the collapsing star's hydrogen envelope...

My statements re. Hawking radiation were not really intended to relate to relativistic jets. They were based primarily on http://cscanada.net/index.php/ans/article/view/j.ans.1715787020120502.1817/266, whose introduction concludes by stating:

"A black hole of one solar mass has a temperature of only 60 nanokelvins; in fact, such a black hole would absorb far more cosmic microwave background radiation than it emits. A black hole of 4.5 × 1022 kg (about the mass of the Moon) would be in equilibrium at 2.7 Kelvin, absorbing as much radiation as it emits. Yet smaller primordial black holes would emit more than they absorb, and thereby lose mass."

Sanjay, once you claim without evidence that I have not understood even elementary special relativity, given that I have been able to publish arXiv:gr-qc/0205035 in a peer-reviewed journal, with an alternative theory of gravity with the Einstein equations of GR as a limit, I can only tell you that you have not understood my theory. arXiv:1003.1446 is also a peer-reviewed book chapter, and discusses the black hole collapse and the comparison with observation in more detail.

Yurij, I have, the additional term in the equations of the theory lead, in a technical sense (a''(tau)>0 in the very early universe) to inflation. Then, the predicted stable frozen stars slightly greater than their black hole horizons would be observable in principle, even if for the limit Y->0 they become indistinguishable from GR black holes.

But I think the more important argument is that the theory can be easily quantized. See arXiv:0909.1408 for an argument why a theory of quantum gravity needs a background. The experiment considered there is, of course, only a thought experiment. But GR, and every background free quantum theory of gravity, is even unable to predict a result, while the result itself is quite simple already in canonically quantized Newtonian gravity.

James, the cause is, in my theory, a physical one. Of course, physical in terms of my theory. If the ether density becomes close to infinite, its of course a physical cause in an ether theory.

Ilja,

There's certainly no doubt that I can't fully appreciate your theory - thanks very much for your helpful explanations!

Sanjay, as if in a scientific conversation the ego would matter. What counts are arguments. Unfortunately, if in modern science theories are too far away from the mainstream (string theory), simple ignorance counts as an argument. So I don't even hope that it will be accepted by the mainstream. Right or wrong does not matter if ignorance counts as an argument.

Unfortunatly the acceptance or rejection of an idea by the mainstream is not a measure of its being true or wrong.

In the meantime, I have done some reading.

As to the Gerlach paper, most of which I have read, I have not yet formed a final opinion. My impression so far is that the author does not really give a mechanism for Hawking radiation. He concludes to parametric resonance from the fact that the WKB approximation fails in the vicinity of the surface of the star. That is a very strange conclusion of a kind I have not seen elsewhere. Failure of the WKB approximation near turning points is a well-known phenomenon and what it means normally is that you need a better approximation at turning points, which you then have to match with the WKB solution at a distance. It does not constitute a physical effect but just the breakdown of a mathematical approach. Moreover, the author argues that this breakdown is not a mere coordinate effect. He considers Schwarzschild time and tortoise radial coordinate to be preferred coordinates in a physical sense on the basis of two statements, namely that the wave equations acquire constant coefficients and that these coordinates become equal to the ordinary time and radial coordinates of Minkowski spacetime at infinity. But the latter condition does not uniquely determine these coordinates (there are other time coordinates which remain nonsingular at the horizon and become equal to Minkowski time at infinity) and the first is not a physical criterion. On the contrary, in a curved spacetime, I would expect the wave equation *not* to have constant coefficients.

I have also read the Einstein paper from 1939 mentioned by Yurij Baryshev. Since Einstein has a pretty clear style, this one is much easier to assess. In fact, this is the first time I see a major flaw in one of Einstein's papers. (Of course, I am not the first person to notice this.) What he does is to consider a spherically symmetrical dust of particles that move in circular orbits around the center. He then shows that there is a lower limit to the radius on which such a circular orbit is possible, which is correct. (The limit is 1.5 r_s, r_s being the Schwarzschild radius corresponding to the total mass; for stable orbits it is 3 r_s.) From this, he concludes that dynamical equilibrium below this radius is impossible, which is also correct. But when discussing the question of collapse, you should look at instabilities of the equilibrium state; looking at equilibrium alone is insufficient. The collapsing state is an unstable dynamical state, not an equilibrium one. A particle injected into the gravitational field of the dust at a radius below 1.5 r_s will simply spiral inward, it cannot stay in a circular orbit. So the consideration of dynamical equilibrium situations is a conceptual error. However, Einstein gives another argument, only in passing, that reveals his beliefs in that matter and clarifies where he went wrong. He states that smaller radii than the limiting one cannot be achieved because particle speeds would have to exceed the speed of light.

This deserves a closer discussion, because it shows how easily fallacious arguments may arise. Indeed, it is known that an observer traversing the event horizon will approach the speed of light from the point of view of a local observer at rest near the horizon. As seen by an observer at rest *at* the horizon, the speed of light would in fact be reached by the infalling observer, in clear contradiction with special relativity. But there *is* no observer at rest at the horizon. There cannot be one. Superluminal speeds can and do arise in general relativity, as ample examples from cosmology show. There are galaxies that receded from our position at superluminal coordinate speed when emitting the light we receive from them now [1]. Superluminal motion of objects at a distance is not a problem at all. The law that has to be obeyed is that a particle cannot move faster than light in any local inertial system. Local is the important word here. To put it into a more geometrical language: the world line of any particle must, at any of its points, always be directed towards the inside (including, in the case of photons, its boundary) of the future light cone of that event. Now you can construct at any point of the Schwarzschild metric with r>r_s, a local inertial system that is instantaneously at rest with respect to the coordinates. But this is impossible for points inside r_s. All inertial systems there must be falling towards smaller r (*all* the time). Moving at a speed smaller than the speed of light with respect to one of these does not imply the coordinate speed in Schwarzschild coordinates to be smaller than c. Einsteins mistake was to assume (or to just have the intuition, without checking it) that you can have local inertial systems that are instantaneously at rest everywhere in the Schwarzschild spacetime. If that were true, his argument of the impossibility of an infalling object to acquire a speed that reaches or exceeds the speed of light, would indeed imply the impossibility of the formation of a horizon. But his basic intuition was wrong in this case. Alternatively, one could say that his mistake was to confuse the Schwarzschild time coordinate with "real" time (even though it does not coincide with the proper time of any local stationary observer). Since the collapse takes infinite Schwarzschild time, his second argument remains correct within the part of spacetime described by all finite Schwarzschild times.

In fact, the same year 1939, a seminal paper by Oppenheimer and Snyder [2] appeared, which gives an explicit solution for a collapsing star. There is a nice discussion in [3], how the influential authority of Einstein, whose paper (wrongly) contradicted the (correct) results from [2], prevented Oppenheimer and Snyder's paper to be discussed as it deserved it for a long time, so that it took until the sixties that black holes became accepted.

As to the general discussion of the basic question of this thread, I think this discussion should be lead within the framework of the currently accepted theory of gravitation, which is general relativity. To discuss the topic within Ilja's theory or that of any theory interpreting the metric as just a field on a background with trivial topology, is moot. Within these theories, interpreting the Schwarzschild time as the "real" one, the answer is trivial: no horizon can form within finite time and hence there are no black holes, only apparently frozen stars. But these theories deprive general relativity of its fundamental interpretation that had a lot to do with its success, viz. that gravity is just the geometry of spacetime. Of course, quantization is easier in theories with a background and therefore, for a restricted class of problems, such an approach may be useful. But it is not impossible in theories not having such a background, as I am told by string theorists.

In my opinion, the original question is interesting only within general relativity (and other theories enabling nontrivial topologies), where the answer seems less clear, if quantum mechanics is provided for. In the quest for an answer it might be useful to note that it is possible to construct, via resynchronization, a new time coordinate for the Schwarzschild metric that remains finite at the instant an infalling observer crosses the horizon *and* that reduces to the Minkowski time at large r. In this respect, it is different from other nonsingular time coordinates such as the ones appearing in Kruskal-Szekeres coordinates or Eddington-Finkelstein coordinates. This time coordinate is not orthogonal to the Schwarzschild spatial coordinates, but that does not prevent its use. In the description of relativistic physics on a rotating disk, such a time coordinate is the most practical one [4]. A brief discussion of Einstein synchronization (which is used in the Schwarzschild metric) versus other synchronization procedures may be found in [5].

[1] Davis, Tamara M., and Charles H. Lineweaver. "Expanding confusion: common misconceptions of cosmological horizons and the superluminal expansion of the Universe." Publications of the Astronomical Society of Australia 21.1 (2004): 97-109.

[2] Oppenheimer, J. Robert, and Hartland Snyder. "On continued gravitational contraction." Physical Review 56.5 (1939): 455.

[3] Zakharov, A. F. "Black holes: the concept birth and modern status (theory and observations)." Proceedings of the XXIII Workshop on High Energy Physics and Field Theory, IHEP, Protvino. 2000.

[4] Kassner, K. "Spatial geometry of the rotating disk and its non-rotating counterpart." American Journal of Physics 80 (2012): 772.

[5] Kassner, K. "Ways to resolve Selleri's paradox", American Journal of Physics 80 (2012): 1061.

Nice post, but I do not see how the spacetime interpretation has been important for the success of GR, except leading to mystical popular representations (which, of course, appear attractive to a lot of romantic children who may later become physicists).

Instead, the spacetime interpretation has prevented the IMHO most successful approach to quantum gravity as an effective field theory. Because the spacetime interpretation suggests a fundamental insight, which, therefore, should be true for all distances, while in effective field theories relativistic symmetry is not necessarily fundamental but can appear as a symmetry of the approximate theory.

And, then, "told by string theorists" is not really helpful. I have an argument in arXiv:0909.1408 that quantum gravity without background is not possible.

To remember in this context about alternative theories is important also because otherwise people tend to think that existing evidence for observing things which look like GR black holes is a proof that black holes exist.

K. Kassner,

"Superluminal speeds can and do arise in general relativity, as ample examples from cosmology show. There are galaxies that receded from our position at superluminal coordinate speed when emitting the light we receive from them now."

As I understand, the cosmological redshift of ancient light is not an indicator of velocity between the emitting galaxy and the detector resulting from the application of any kinetic energy to either, but of the historical metric expansion of spacetime traversed. The redshift accumulates solely as a function of distance traversed and historical spacetime expansion.

Just outside the event horizon of a black hole, the required escape velocity for any object would be a significant fraction of the speed of light. Since the effects of gravitation nearer the singularity would be much greater, the required escape velocity would exceed the speed of light. Simply following this reasoning, it seems that the local velocity of freefalling objects within the event horizon should exceed the speed of light.

IMO, these conditions can only exist if matter disintegrates prior to entering the event horizon, with its unbound mass-energy being converted into gravitational energy (dilated spacetime) while its residual charged particles are expelled via polar jets.

J. Dwyer,

I was not talking about the red shift. I was talking about the recession speed of galaxies as calculated in cosmological models. You are right that the cosmological red shift can be seen as a measure of the ratio of the current expansion scale of the universe to that of the time when the light was emitted, so no velocity enters its calculation (on the other hand one can also calculate it via parallel transport of the four velocity of the receding galaxy to the detector, which gives the same result).

But the expansion of the universe has the consequence that galaxies are receding from us, and if one calculates their velocities, one finds that if they are sufficiently far away, their recession velocity (time derivative ot the scale factor times coordinate distance) may exceed the speed of light. Nevertheless, light from those of them not outside our cosmological event horizon (which exists due to the acceleration of the expansion) will reach us, and the event horizon does not necessarily correspond to a recession velocity of c, it can be at a higher velocity. I suggest you have a look at the very nice paper by Davis and Lineweaver cited in my last post, in which all of this is explained in some detail.

I once gave an exercise to the students in my cosmology course to solve the equation of motion of a photon emitted from a far-away galaxy in a universe expanding with a scale factor proportional to t^n. If n is smaller than one, the light will always manage to get to our place; if n is bigger than one, there is an event horizon, from beyond which it will not arrive anymore. But there are some galaxies receding faster than light, from which photons can get to us. Their motion is quite funny then: first they move away from us (because they were emitted from a galaxy moving away faster than light), but this recession of a light front slows down until it turns around and finally manages to acchieve a positive velocity component towards us. Afterwards, it will of course reach us.

By the way, how far do you think, was the source of the microwave background that reaches us today, when the light was emitted? The light took roughly 13.7 billion years, so one might think, it comes from a distance of that order of magnitude, right? But it doesn't. The initial distance was about 26 million light years. The expansion of the universe first carried this light away from us, but finally, it overtook this drift effect and moved towards us, taking 13.7 billion years for the whole trip. Calculations allow one to explain counterintuitive facts :-)

Ilja,

The geometrical interpretation was all the motivation for Einstein, so it has of course a lot to do with the success of general relativity. There would be no general relativity without this interpretation. This does not mean that we have to stick to it all the time and it also does not mean that the success of the predictions of the theory, which in the long run determine its fate, needs that interpretation. (Althoug I believe you underestimate the importance of that interpretation.) In my opinion, the interpretation of a theory is rarely a decisive factor regarding its eventual success, although it may be crucial at the moment when the theory produces a new paradigm. Look at quantum mechanics. So many interpretations, but its success which is undeniable, is not a consequence of its interpretaions, but rather of the precision of its predictions.

Presumably, any classical theory will in the end have to be regarded as an effective theory only, simply because of the existence of quantum mechanics. But this may hold for our concepts of space and time as well. They may be considered classical fields. There is a branch of quantum theorists who think that space and time have to emerge from the operator algebra (which should be the basic structure on which to found a theory) and be derivable from it. In this kind of approach, there is no quantization problem, everything is quantized from the start, and if the classical theory emerges as a limit, then we know its quantized version, too. I am not saying that these guys have advanced very far yet in their research programme, but I believe that your argument against quantization without a background will not hold in such an approach.

As to what string theorists told me: This was some years ago, when we wanted to hire a new professor with the specialisation elementary particle physics. The circle of our most promising candidates consisted of four string theorists, who gave their talks. There was consensus among them that general relativity is already contained in string theory. (We, the commission, were baffled, because they were effectively saying that the unification between quantum theory and general relativity had already been achieved.) The problem is not that it is not there, the problem is to get rid of all the additional stuff contained in string theory that you do not want to appear in the classical limit. So quantization of general relativity is not a problem of principle in string theory, all that remains are huge technical problems.

Finally, I do not mind considering alternative theories or mentioning them. But since the basic question of this thread has a trivial answer in these alternative theories (as you will agree), it is not interesting to discuss it within them. We know the answer and I have stated it in my last post.. We are not so sure what is the answer of general relativity, which is the prevailing theory of gravity. Therefore, that discussion is interesting -- at least to me.

K. Kassner,

Are not the products of cosmological models typically derived from redshift?

While distant galaxies can be considered to be receding away from us, as the distance between us is increasing, IMO, there is no superluminal velocity between us and them, since, if the contribution of expanded spacetime to cosmological redshift could be precisely determined, remaining peculiar velocities would be relatively trivial.

I'm merely a retired information systems analyst - not a physicist, but not a student, either. As I understand, it must also be considered that it is we who are receding away from the origin of ancient light emissions as much they are from us, since it is actually the expansion of intervening spacetime that is increasing the distances between us as a function of time.

Actually, what is identified in the redshift of distant light is not the proper motion of the emitting galaxy alt all, but the expansion of spacetime between us and the light packet that is effectively propagating towards us - to be eventually detected. The subsequent proper motion of the emitting galaxy is effectively indeterminable.

The distance between us and more distant galaxies may have increased more per unit of time than nearer ones because the rate of spacetime expansion was greatest in the early universe (despite any reacceleration of expansion) and that the effects of expansion on redshift is cumulative.

Ralph,

Back to the original question, essentially, can a black hole form despite time dilation? I think the most straightforward explanation is:

- It is only the core of a massive star that collapses: its outer material is blown away.

- There is effectively no relativistic event horizon until a black hole has formed.

- We can and have observed the evolution of supernovae explosions over finite periods of time - I think weeks. We have also observed neutron star remnants of SN explosions and, I think the absence of such luminous remnants of large SNe, the inferred production of a black hole where otherwise a hot neutron star would be.

While a supernova may produce a neutron star core, neutron degeneracy pressure is not sufficient to halt the complete gravitational collapse of a sufficiently massive stellar core. In that case, it should be considered that the neutrons disintegrate and that their released binding mass-energy is converted to gravitational energy in the form of contracted (dilated) spacetime.

The event horizon is simply the boundary at which no light can escape the local gravitational energy. Once sufficient mass-energy has been converted, an external event horizon forms - it very rapidly expands as additional mass-energy is converted to gravitational energy. Spacetime dilation effects increase only as the localized gravitational energy very rapidly accumulates.

None of this process (however accurate my description) can ever be observed, since the event horizon would quickly envelope the entire black hole proper.

The key is that the collapse and production of a black hole occurs very quickly. Once an event horizon has formed, light from the event horizon may take a very long time to reach us. However, X-rays that must be emitted from very near the event horizon are being observed after having been reflected from the surface of a distorted accretion disk, even exhibiting signal oscillations. Please see http://web.mit.edu/newsoffice/2005/spacetime.html http://www.nature.com/news/spin-rate-of-black-holes-pinned-down-1.13512 and http://arxiv.org/abs/1306.4786v1

We may also learn a great deal from the upcoming very near approach of the large gas cloud G2 to Sagittarius A* in the Milky Way. Please see http://en.wikipedia.org/wiki/Sagittarius_A*#Discovery_of_G2_gas_cloud_on_an_accretion_course

Detailed presentation material from simulations of stellar collapse can be found at http://hipacc.ucsc.edu/Lecture%20Slides/2011ISSAC/Ott.pdf

J. Dwyer

"While distant galaxies can be considered to be receding away from us, as the distance between us is increasing, IMO, there is no superluminal velocity between us and them, since, if the contribution of expanded spacetime to cosmological redshift could be precisely determined, remaining peculiar velocities would be relatively trivial."

The recession velocity is not the peculiar velocity, which in the idealizing models is assmumed to be equal to zero. It is the velocity *due* to the expansion of spacetime. And that *does* become superluminal. Trust me. Or read the indicated paper :-). It is very nicely written and its inclusion into my cosmology course definitely improved the course and made it more interesting for students.

K. Kassner,

Of course I understand that it is the apparent recessional velocity that is produced by spacetime expansion.

Perhaps this can better express to you my objection to your use of the term superluminal to describe apparent velocities resulting from the expansion of spacetime:

http://en.wikipedia.org/wiki/Faster-than-light#Universal_expansion

"The expansion of the universe causes distant galaxies to recede from us faster than the speed of light, if comoving distance and cosmological time are used to calculate the speeds of these galaxies. However, in general relativity, velocity is a local notion, so velocity calculated using comoving coordinates does not have any simple relation to velocity calculated locally[16 ] (see comoving distance for a discussion of different notions of 'velocity' in cosmology). Rules that apply to relative velocities in special relativity, such as the rule that relative velocities cannot increase past the speed of light, do not apply to relative velocities in comoving coordinates, which are often described in terms of the "expansion of space" between galaxies..."

You might like to consider some discussion of this topic in your cosmology course... BTW, I spent >25 years as a Technical Fellow in one of the world's leading multinational companies. I trust no one implicitly in technical matters - not even university professors.

J. Dwyer

Well, then I cannot do more than referring you to the paper again. I am well aware of these different notions of velocity, and I even mentioned one to you. If you use parallel transport of the four velocity of the galaxy to our current position, you will never get a speed faster than light, and if you calculate the red shift from the so-obtained velocity via the *special relativistic* red shift formula, you will get the right result, proving that the cosmological red shift can also be interpreted as a redshift due to motion, an interpretation that is as valid as the standard one, but less well-known.

But: The superluminal recession of some galaxies is *not* "apparent". Wikipedia is not infallible, and I understand various things on general relativity better that Wikipedia. I have even corrected an article and the correction was not removed later. Why is the superluminal velocity, defined as the change of the proper distance of the galaxy (a well-defined concept) not only apparently superluminal, not just a coordinate effect? Because it can be compared with the speed of light. Light emitted by such a galaxy will first recede from us (as the microwave background did in the past). Hence it is clear that the galaxy moved away from us faster than light. If the light later manages to arrive at our position (and I have done the calculations myself verifying that this is possible under certain conditions) then we obviously were/are able to see a galaxy that receded from us faster than the speed of light at the time of emission.

Anyway, I think this is off-topic and I have said enough on it by now. If you do not have access to the journal article, there is also an copy of it on the arxiv server:

http://arxiv.org/abs/astro-ph/0310808

Klaus Kassner, I do not underestimate the role of interpretations, but see them in a different domain - they are the guide to a more fundmental theory. Or, in case of Copenhagen or the spacetime interpretation, not.

So I agree with the success of quantum theory itself, independent of the interpretations - but there was almost no progress toward a more fundamental, subquantum theory. The de Broglie-Bohm interpretation is already a much better guide to something more fundamental. For example, with Valentini's subquantum H theorem and the resulting computation of the Born rule as defining quantum equilibrium.

If the spacetime somehow appears from operators, it does not mean at all that my theorem fails. Anyway it is a theorem about properties of certain approximations of the theory. So it may be that in these approximations the spacetime has already appeared as a background. Anyway, if there is a background-free QG, the approach would have to clarify which of the assumptions I have made fails.

Regarding the successful quantization of gravity in string theory I have my doubts. As far as I understand, string theory is Minkowski-causal in this large 10 or 11D space. So the resulting theory in 4D should be causal too. Is it? GR allows for solutions with closed causal loops.

K. Kassner,

IMO, it is a misconception to believe that the proper motion of any distant object imparts any substantial spectral shift to any sample of its light. The observed redshift of light from distant galaxies exhibits the spectral expansion imposed by the expanding spacetime it traverses over up to billions of years. I suggest that expansion always increases the distance that light traverses and the affect on its spectrum is cumulative - making any motion attributed to it (either the emitter or receiver, or both) appear to be superluminal. Again, it is equally (in)valid to attribute the cosmological redshift to the motion of the detector as it is to attribute it to the motion of the receiver. In fact our own galaxy has inarguably also been receding away from all others - the apparent increases in distances cannot in any case be properly attributed solely to emitting galaxies...

Surely you will allow me to have the last word on the subject, as a courtesy, rather than demanding it for yourself? I remind you again that I am not one of your charges.

J. Dwyer,

Some misconceptions are not a matter of opinion. They can be refuted on the basis of sound mathematical analysis. I suggest you read the paper that I indicated. It may help you understand which of your own ideas are misconceptions and which ones are not. If you are interested, I can point you to additional literature elucidating the origin of spectral shifts (and unifying the three concepts of Doppler shift, gravitational shift and cosmological shift).

I. Schmelzer,

I never thought you underestimated the role of interpretation. Rather, from my point of view, you overestimate it. For me, interpretations are ways to make precise (mathematically founded) results more intelligible and to help grasp the contents of formulas in order to guess or estimate the outcome of an experiment without complicated calculations. This way they may also guide theories sometimes. But interpretations don't have truth values. Different interpretations of the same theory are possible and may be indistinguishable (an example is the idea that the universe is expanding versus the idea that all measuring rules are shrinking -- there is no way to assign a "reality value" to one of the two that would allow to distinguish it from the other by experiment, which *probes* reality, so you can use whichever of these interpretations you favor). One should not confuse interpretations with hypotheses about reality. That is theory.

Of course, I do not agree about the de-Broglie-Bohm interpretation. It does not work for relativitstic physics, not being able to describe particle creation and annihilation.

Locally, general relativity is of course Minkowski-causal and what string theory contains is general relativity in small space-time patches. With the possibility of non-trivial global topologies. The appearance of causal loops in general relativity is believed to be avoided by instabilityof the corresponding solutions. Since in quantum gravity there are always quantum fluctuations, any unstable solution would never appear.