These aren't different interpretations. I've pointed this out before. General relativity is simply both a geometric and a field theory (trivially, since the metric, which describes the geometry, is a tensor field). These are not mutually exclusive. In particular, pointing out that GR is a field theory doesn't negate that it still has the same coordinate-system independence ("gauge freedom") built into it. Since Kevin Brown doesn't provide a source, there's no indication where he got the idea these are different interpretations from. This is also somewhat true of gauge field theories like quantum electrodynamics, in that they can also (in a sense you'd find very abstract) incorporate geometric ideas closely analogous to those used in general relativity. For instance, the electromagnetic field (Faraday) tensor plays an analogous role in QED as the Riemann curvature tensor does in GR. So, arguably, it's really gauge field theories that are more patterned after general relativity than the reverse. Then you and anyone else who says this were proved wrong many decades ago. We can identify frames and coordinate systems near and inside the event horizon that are perfectly valid by GR's internal logic. You've never been able to point out anything wrong with them (like why they shouldn't be considered valid, or why the metric expressed in, say, Kruskal coordinates shouldn't be considered a valid metric or solution to the Einstein field equation). The way I see it, the only way you can get something even close to your frozen star interpretation is to take a black hole geometry manifold (such as the Schwarzschild geometry), work out where the event horizon is, and arbitrarily cut the manifold off there and say everything beyond it "doesn't exist". In that case, you'd still have a manifold that was compatible with the Einstein field equation, but most physicists and mathematicians would tell you it was incomplete, and you'd have the odd implication that matter and astronauts could literally disappear off the edge of spacetime in finite proper time.
The point I wanted to get across is that what you think GR is, is not necessarily what Einstein thought it is. Have a look at the Robert Loughlin quote on the Wikipedia aether theories page, look at the arXiv, and see this where Einstein refers to a field as "a state of space". I prefer to refer to space myself.
If that is your point, then you really need to get to know me better. Because I think that in total Einstein and myself are in perfect agreement of about what GR is. It's become fuller and more robust since Einstein first published his 1915 papers. He and others have fine tuned it over the years. But there is no conflict in what Einstein thought GR is and what I think it is. You do realize that Einstein wrote many papers on GR, presented several ideas and interpretations that he later discarded, right? You can not pick any one paper and say "Einstein says,,,, " and be sure of being correct. Each individual paper or interpretation has to considered in the context of the entire canon, because ALL scientists are like ALL other people, they form, present, retract and tweak their ideas all the time.
Noted. His article originally referred to Wheeler and Weinberg. When I queried it with Weinberg, he obviously got onto Kevin Brown who changed the article. No problem. You will have heard me talking about electromagnetism and curved space as opposed to curved spacetime. I haven't been proved wrong, and I have pointed out why they shouldn't be considered valid. Putting a stopped observer in front of a stopped clock doesn't do anything. He doesn't see it ticking normally. He doesn't see anything. As regards a valid metric, the metric is what you measure. And when your clock doesn't tick and light doesn't move, you don't measure anything. Then there is no metric. See this picture. The metric has a hole in it, and it is black. OK, space and time and matter as we know it "doesn't exist" beyond it. But something does. The black hole is massive, and it has a dreadful gravitational field. Then we work to complete it and understand that "odd" implication.
It's not a spatial curvature. You can think of the electromagnetic field as a "curvature", but it's associated with an abstract phase coordinate space (related to an arbitrary phase convention you can use for the charged matter field in QED). Roughly, the Faraday tensor tests for the presence of a nontrivial electromagnetic vector potential (i.e. one that can't be eliminated by changing the field phase convention) in the same way that the Riemann curvature tensor tests for the presence of a nontrivial gravitational field (i.e. one that you can't completely eliminate by changing the coordinate system). But switching coordinates isn't "putting a stopped observer in front of a stopped clock", so you haven't at all criticised what these derivations actually did. Also, you're presuming your own conclusion. It's true that if everything were really stopped at a black hole event horizon, then it would be meaningless to try to identify locally inertial reference frames there, and any attempt to do it would fail. But you've never shown that, and when we try it, it doesn't fail. No. Formally, at the level of how the theory is mathematically defined, the metric defines a scalar product between vectors. It also provides a distance measure (specifically the spacetime interval in GR) simply because, in geometry, a vector's length is the same thing as the square root of its scalar product with itself. When you express the spacetime line element \(\mathrm{d}s\) in terms of infinitesimal coordinate changes \(\mathrm{d}x^{\mu}\), the metric components \(g_{\mu\nu}\) give you a measure of how locally stretched or twisted etc. the coordinate system you are using is. I've only ever seen that picture in popular science-level expositions of general relativity. I've never seen it actually derived from GR, and as far as I know there isn't any sense in which it is an accurate depiction of the Schwarzschild geometry. But generally not at the event horizon. That's the point. Calculate invariant curvature measures from the Schwarzschild metric and you'll find they're generally finite and can be arbitrarily small for a large enough black hole. If you had an inertial astronaut as close as you like to the event horizon of a large enough black hole, they wouldn't experience anything special or uncomfortable there. They generally wouldn't be torn apart by tidal forces, for instance.
I do realize the Schwarzchild solution is a BH in its most simplest form. What I'm not sure about is whether they do not represent any real BH. I have asked this question in the Kerr BH thread I started. Spin and a magnetic field if any can be [and probably are] negated over time. The relevant part to your claim that the Schwarzchild BH does not exist, is how long any negation will take. But anyway, other then that little anomaly, the Schwarzchild limit still applies to all BH's, representing the escape velocity of light. Therein lies my claim. That is once that Schwarzchild limit is reached, further collapse is compulsory. So in effect GR predicts its own downfall at the Singularity or Quantum/Planck region of space/time OK, that seems to answer my question. In part anyhow. The compulsory collapse is predicted. I'm not sure I understand the bit about, "some mathematical solutions" Can you elaborate on that? I'm not sure of the source....It may have been Thorne's book, "Black Holes and Time Warps"not sure. Method? I found this...... "First, the average density of a supermassive black hole (defined as the mass of the black hole divided by the volume within its Schwarzschild radius) can be less than the density of water in the case of some supermassive black holes.[5] This is because the Schwarzschild radius is directly proportional to mass, while density is inversely proportional to the volume. Since the volume of a spherical object (such as the event horizon of a non-rotating black hole) is directly proportional to the cube of the radius, the density of a black hole is inversely proportional to the square of the mass, and thus higher mass black holes have lower average density." at.... http://en.wikipedia.org/wiki/Supermassive_black_hole Reality is another question I agree. Suffice to say, I have a broad outlook as to what is real or what isn't. Just because we cannot see, touch, smell something, does not mean it is not real. Do you see space/time as real? If you answer no to that, then tell me what GP-B was measuring to incredible precision.
Actually, they'd instantly die. They'd be 'sucked in' by the huge gravitational well, and then be beyond the EH (or 'frozen' at the EH if you accept Farsight's interpretation). If you are 'arbitrarily close' to an EH, without any kinetic energy moving you away from the BH's EH, you are then going to be falling into the BH. Whether you 'cross' the EH or are 'frozen' at the EH is irrelevant. You are dead. This is true even if it is a pre-blackhole such as a neutron star that is still sucking in matter, just before it collapses into a BH. If you fall to the 'surface' of a neutron star you are squashed flatter than a pancake, and your atoms are all turned into neutrons (one huge nucleus of neutrons). It's even worse for you if the neutron star takes in more matter and collapses into a BH.
I have long since considered this MAINSTREAM 'realistic possibility' to be one of the main arguments I would use to support the generic hypothesis that all the observable universal energy-space extent is a mere insignificant region in some SINGULAR Universal Complete black hole, where the EH is so far away from the interior source of any extremal effects whatsoever, so that the dynamics and processes we observe have their own 'local universal process' characteristics/evolutions that are essentially independent of anything other than the local energy-space conditions/contents/distributions etc. Are we part of a universal black hole FAR EVENT HORIZON's GENTLE (ie, effectively/practically non-existent tidal forces) upper-local-layer dynamics essentially 'causally separated' from the lower more EXTREMAL 'layers/core' conditions/regions? That's what I get hypothetically IF I extrapolate your stated (my bolding) perspective above, przyk. Please Register or Log in to view the hidden image! Any scientifically based comments on that extrapolation scenario would be welcome. Please Register or Log in to view the hidden image!
That's the way I see it also. To put it as simplistically as possible, it is the gradient or criticality of the space/time curvature which contributes to the tidal effects of gravity....which can be interpreted as the differences in gravity between one's head and one's feet. Naturally then a SMBH has less pronounced gradient, so less tidal effects. Again from Thorne's book "Black Holes and Time warps" this is the accepted scenario.
Hi paddo. Since you concur with przyk there, what is your scientifically considered view on the logical/physical extrapolation from that, as outlined in my post #728 above? Thanks.
My own reaction long ago (and still current) to the initial hypothetical of pair-separation near event horizon etc, was: How the heck can a background ZERO energy that DOES separate into TWO opposite energy states WHICH STILL EQUAL ZERO energy taken together, and which cannot, as far as the GRAVITY will drag them BOTH downwards into the EH, be imagined to affect the BH energy content EITHER WAY? They fall in, they equal ZERO energy, and the quantum states of the BH are unaffected one way or the other, surely? Else if the energy-pair can increase the BH mass/effect/extent, then every black hole that was ever created by implosion of spent star cores would eat up surrounding 'virtual quanta pairs' and grow in no time to universal size! There is definitely something left to be sorted out in HAWKING RADIATION and like hypotheses before anyone can take them seriously, in my opinion based on the above observation. Still, it IS fun conjectures, and fodder for 'all those betting types', hey? Please Register or Log in to view the hidden image!
If both fall in together, the net gain by the BH is zero. If they both fly off together, the universal net is still zero. If the negative of the pair falls in the total in the BH goes down a net 1, but the stuff outside goes up a net 1. The universal total is the same. But the black hole has gone down, the outside stuff has gone up. But the real problem I have with Hawking radiation, is statistical mechanics dictates that just as many of the in-falling of the pair will be positive as there will be negative, so in the end the Hawking radiation puts in just as much as it takes out and makes me want to just forget Hawking's tunneling virtual pairs to keep things simple.
Sure, agreed....except that that (my bolded) hypothetical situation has yet to be fully examined under the real gravity acceleration and other effects near the EH such that both of the pair will be dragged down before either one can escape. Even if one of the pair does negate with some real infalling particle, the only 'addition' will be BY that real infalling particle having made the other virtual pair particle a NET contribution thereby (since its opposite twin virtual particle was negated BY a real particle as it also fell in. See what I was getting at? Only REAL infalling particle energy values (whether electron or positron etc) will determine how and by how much a BH actually increases its net energy-mass state/content, since all particles, virtual or otherwise are dragged in by gravity NEAR the horizon where such HAWKING RADIATION (from pair production/separation speculations) are postulated. Gotta go. See/read you round, Declan. Please Register or Log in to view the hidden image! Cheers.
I'm not sure I understand what it is you are saying? If a neg particle falls in it annihilates with a pos, The BH is reduced by one. While the pos particles goes outside and annihilates with a neg. The outside is increased by one. The net for the universe is zero, the neg plus the pos. It has only shifted a particle's worth from inside the BH to the outside. If the neg and the pos fall in, that is no net change anywhere. If they both fly out into the universe there is still no net change anywhere. It doesn't matter which falls in, the universal net change is zero. If the neg falls in the BH decreases by one. The outside increases by one. So if one falls in and the other doesn't, the net change for the universe is zero. Energy has been conserved, only moved into or out of the BH. My problem is I can't imagine where all or most of the in-falling pairs are of one charge, it seems to me, that over time, just as many neg partners as pos partners will end up falling in. Resulting in no net change over time due to Hawking radiation.
Kevin Brown knows what he' talking about and Farsight is stuck on one set of coordinates being preferred. Kevin does the analysis for the Schwarzschild coordinates concluding the plunger DOES fall into the black hole in finite time 7.2 The Formation and Growth of Black Holes http://www.mathpages.com/rr/s7-02/7-02.htm And this one has a nice graph for the time coordinates dTau and dt-bkkpr in the Schwarzschild geometry. 6.4 Radial Paths in a Spherically Symmetrical Field http://www.mathpages.com/rr/s6-04/6-04.htm The fact that Farsight is referencing Kevin Brown is because it's his newest quote mine and he doesn't understand the way Kevin explains it any more than the rest of us have explained it to him. At least Kevin doesn't know Farsight exists.
I'm utterly amazed how many variations in interpretations we have, other than the accepted mainstream model. sheesh!
Physicists who write research papers, lecture notes and text books on the subject of General Relativity - like me - often receive mails by amateur scientists with remarks and questions. Many of these show a genuine interest in the subject. Their requests for further explanations, as well as their descriptions of deeper thoughts about the subject, are often interesting enough to try to answer them, and sometimes discussions result that are worthwhile. However, there is also a group of people, calling themselves scientists, who claim that our lecture notes, text books and research papers are full of fundamental mistakes, thinking they have made earth shaking discoveries themselves that will upset much of our conventional wisdom. Indeed, it often happens in science that a minority of dissenters try to dispute accepted wisdom. There’s nothing wrong with that; it keeps us sharp, and, very occasionally, accepted wisdom might need modifications. Usually however, the dissenters have it totally wrong, and when the theory in question is Special or General Relativity, this is practically always the case. Fortunately, science needs not defend itself. Wrong papers won’t make it through history, and totally ignoring them suffices. Yet, there are reasons for a sketchy analysis of the mistakes commonly made. They are instructive for students of the subject, and I also want to learn from these mistakes myself, because making errors is only human, and it is important to be able to recognize erroneous thinking from as far away as one can ... http://www.staff.science.uu.nl/~hooft101/gravitating_misconceptions.html
I agree with the options you described. I described the option (more likely, given the extreme gravity so near the EH) that any real particle appearing in the vicinity to negate with either of the virtual pair will be dragged into the EH. So THREE particles (two virtual, one infalling real particle) are involved in my extra option. Basically, NO particle escapes to negate elsewhere 'outside' and away from the EH. So any real particle infalling may negate with either virtual pair particle, BUT since none of the 'three' escape, the universe outside 'loses' the energy-content of the infalling real particle and the BH interior 'gains' that energy. Whether the infalling real particle negates with either virtual particle as it is is being dragged in with them both, the net effect will (in that option I described where none of the three escape at all) be that the BH gains ONLY whatever energy-content equivalent infell as a real particle....the charge of which would determine which particle it may negate with and which other charge/energy is left as the NET contribution to BH charge/energy. The outside universe always LOSES in that EXTRA scenario as I described which differs from all the ones you covered above. That was my point. Please Register or Log in to view the hidden image!
