Black Holes, for Eta Carinae

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Originally posted by Mike Holland:
Yes, Percy, it gets confusing, because we have Special Relativity and General Relativity effects combining here.

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If we didn't have General Relativity sticking its oar in, then the falling object would reach the speed of light at the event horizon (assuming it fell from infinity), and we would see normal Special Relativity time dilatation (dilation?) effects for both reference frames before this moment.

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But the gravitational field adds a non-relative GR effect. Contrary to Eta's post, atomic clocks in orbit HAVE been observed to run FASTER than those on the ground - after the effects of orbital motion have been eliminated. If an observer was suspended just above the event horizon by a very powerful rocket motor, and we were suspended in a similar manner, but a million kilometres away, then there would be no relative motion to bother about, and he would see us (and the rest of the universe) running fast.

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But if he is falling at high velocity, then SR adds its effects, and I don't know how they add up, but I am certain the GR time dilatation will slow him up just before he reaches the event horizon or speed of light.

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NB. Imagine an object falling through an event horizon. Just as it reaches there it reaches the velocity of light, acquires infinite mass, and sucks the whole universe in with infinite acceleration. Sorry, I don't buy it.

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I am working on a reply to Eta to cover this. Some research needed.

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Mike.

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The issue of falling into a black hole is reasonably well discussed by a number of physicists on the web. There is no particular problem with falling past the event horizon. You just can't see things past the event horizon, because light does not get out.I understand you can express this as an object taking infinite time to fall through the event horizon from the perspective of an observer at rest and an infinite distance away. However, this is not the same as saying that it does not fall through the event horizon, and it is not as simple as the SR case of an observer's frame. In GR you don't speak of a frame so much as as a metric.The perception that things can't fall past the horizon is an error about what the metrics mean. A common metric (the Schwartzschild metric) diverges at the Schwartzchild radius. There are other metrics which are better suited for tracking what happens to an infalling object, such as the Kruskal-Szekeres metric, obtained by a suitable co-ordinate transformation, which also removes the divergence. In any case, a falling object itself certainly passes through the event horizon without dramas, and reaches the central singularity within a finite time. At that point, we don't really have a good grasp of what happens. But conventional physics handles falling past the event horizon fine.The singularity at the event horizon is more an artifact of the chosen co-ordinates or metric; not an indication that anything actually fails to get through. Check out
More about the Schwarzschild Geometry

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Originally posted by Mike Holland:
Thanks for your time and effort, Eta. I am not serious about the falling observer actually seeing the universe fade and die, because it happens in the last billionth of a second (by his clock) before he passes the event horizon.
But please have a look at the diagram on the website referred to by cjhs. It shows the paths of light rays curve up and approach the event horizon asymptotically. This is exactly the point I am making. Light rays never reach the event horizon (in our universe), and neither do falling objects A falling object would be moving slower than light, so its world-line would be more vertical than those of the light rays. As it approaches the event horizon light rays will keep intersecting its worldline, and it 'sees' light approaching it from the outside universe for the rest of (our) time, but all in an instant in its time.

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If you look at the page I cited, there are several diagrams. Not all of them have the discontinuity of the Schwartzchild metric.When you say "our universe", you are using terms in a rather unusual way... which is a nice way of saying "incorrectly".The schwartzchild radius is not the boundary of a "universe"; it is a horizon of visibility. That's all.Rather than saying "light rays never reach the boundary (in our universe)" you should be saying "the schwartzchild metric cannot be used to show the event of light rays crossing the schwartzchild radius (so use a different metric)".The point you are making is not the same point being made by the diagrams. You are making a point that the point of no return from the black hold marks a boundary of the universe. That's not what the term "universe" means.Cheers -- cjhs

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Originally posted by Mike Holland:
The point is, using these metrics, our clocks still read infinity when the object reaches the event horizon. The metrics do not change this fact. They simply distort the picture.

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What you call "facts" are relative to your chosen co-ordinate system; not absolute statements about spacetime. Your terms are not defined. What do you mean by "when" the object reaches the event horizon? For this statement to make sense, you need to have some kind of relationship between times in different locations in space. But there is no absolute relationship of this kind; and metrics emphatically do not distort the picture. What could that even mean?The distortion is the claim that there is some kind of absolute which the metrics are distorting. That appears to be your error in a nutshull. There is no one correct metric; and you can pick your metric and do appropriate transforms from one set of co-ordinates to another. It is all still the same spacetime.The Schwartzchild metric has a singularity at the event horizon. However, there is no special privileged status for that metric; and the distcontinuity is a property of the metric; not a break down in relativistic physics. For a sufficiently large black hole, a spacecraft flying though the event horizon would not notice any special discontinuity or sudden effect as they fly past the point of no return.For an outside observer, there are various ways (metrics) they might choose to apply co-ordinates to the space. With a suitable transform to more appropriate metrics (more appropriate for discussing what happens as an object falls through the event horizon) there is no singularity or discontinuity. And there is most certainly no absolute basis for matching up events in different locations as being "simultaneous".The singularity which appears at the center of the black hole is another thing entirely. That singularity appears in all the metrics, and it indicates that our current relativistic physics breaks down at the central singularity. We will need a better physical model (a mix of quantum mechanics and relativity) to describe that point in space.But the event horizon presents no such problem. It is described just fine with classical relativistic physics, and there is no reason to think anything special is going on at the event horizon which breaks existing physics.Cheers

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Originally posted by Mike Holland:
Cjhs, you seem to have a conviction that all my concerns can be resolved by considering alternative metrics. You seem to think that event horizons have no real existence, and are theoretical constructs of particular metrics. This is wrong. Matter does not escape from a black hole, in any metric.

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I don't expect all your concerns to be resolved quickly and easily. This is a difficult subject; and I am right at the limits of my ability to explain. No personal criticisms are intended. I do think it would help for you to consider alternative metrics, and why some diverge in some places and others do not.What I think about event horizons is given previously. They are a horizon of visibility. They are a point of no return. Once anything, even light, is inside the event horizon, it will inevitably reach the central singularity within a small finite time. This is even stronger than saying it can't get out. It will proceed to the centre; and at that central point current physics does not have a good description of things.Physics has a good description of things on either side of the event horizon, but not at the central singularity. The major problem of modern physics concerns reconciling quantum mechanics and classical relativity; and the point at which this becomes significant is the centre.I have been quite clear that what is different between the metrics is the divergence of co-ordinates. The event horizon is a point of no return, and metrics make no difference to that. But the horizon is not a singularity in all metrics. That is, comments about "can't get through" the event horizon and being frozen in time are relative to the metric, and not reflecting any absolute reality.Here are some very simple points, which need to be reconciled in any consistent perspective on this matter.

• In some metrics, time diverges as you approach the event horizon, and in other metrics it does not. This divergence is simply about how you choose allocate time co-ordinates to events.
• From the perspective of an infalling object, nothing special happens as you fall past the event horizon; but it does mark a point of no return. You cannot send signals back past the event horizon once you have passed in. You can, however, continue to see the rest of the universe.
• Once you reach the event horizon, you are destined to end up in the central singularity within a small finite time, no matter how powerful your spacecraft. There is no easy way to identify exactly when you pass this point of no return. In that sense, the event horizon is an abstraction.

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Let me try and handle your points one at a time:

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What you call "facts" are relative to your chosen co-ordinate system; not absolute statements about spacetime. Your terms are not defined. What do you mean by "when" the object reaches the event horizon? For this statement to make sense, you need to have some kind of relationship between times in different locations in space. But there is no absolute relationship of this kind; and metrics emphatically do not distort the picture. What could that even mean?

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So when we look at a Schwarzschild spacetime diagram, it is a ‘fact’ that light approaches the event horizon asymptotically, but when we look at an Eddington-Finkelstein diagram we see the ‘fact’ that light goes up the diagram at 45 degrees and crosses the event horizon. Fine. I have no problem with this. It is like the old conundrum ’Do parallel lines never meet, or do they meet at infinity?’.

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Your facts refer to the diagrams and to co-ordinate systems. The diagrams look different, but they describe the same physical situation. Here is a quote from right next to the diagram. Does light go through the event horizon? Yes, it does. You can continue to see the rest of the universe from inside the event horizon. That one of the metrics happens to diverge at the point of crossing the horizon is a statement about the metric; not about whether light gets through or not.

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I see that Finkelstein time is given by F = t + ln(r-1), so at the event horizon r =1, and F = t + ln(0) = t - infinity! So the point where Finkelstein time shows a falling object crossing the event horizon is the point where our clocks read infinity. So we agree. A change of metric does not change the facts; it only changes the figures you use to describe them.

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But I have a problem with that metric because my wristwatch it not calibrated for Finkelstein time.

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Since you are not at the event horizon, you can't speak sensibly about what your clock reads "when" something else crosses the event horizon without using some co-ordinate system relating times at your location to times somewhere else. That was the major important question in my extract above, which you have quoted, but not answered. Indeed, you continue to make the same mistake by speaking of "the point when our clocks read infinity".Metrics are not ways to calibrate wrist watches. They are ways of giving time and space co-ordinates to events which are not next to you. What your wristwatch reads is time at your location (in any metric). It is a nonsense to speak of calibrating your watch to a spacetime metric.

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The distortion is the claim that there is some kind of absolute which the metrics are distorting. That appears to be your error in a nutshull. There is no one correct metric; and you can pick your metric and do appropriate transforms from one set of co-ordinates to another. It is all still the same spacetime.

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As I pointed out above, a change of metric does not change the facts. But you are the one proposing to solve the problems by a change of metric. This is your error in a nutshell. Refer to your own first post on this topic:

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The perception that things can't fall past the horizon is an error about what the metrics mean. A common metric (the Schwartzschild metric) diverges at the Schwartzchild radius. There are other metrics which are better suited for tracking what happens to an infalling object, such as the Kruskal-Szekeres metric, obtained by a suitable co-ordinate transformation, which also removes the divergence. In any case, a falling object itself certainly passes through the event horizon without dramas, and reaches the central singularity within a finite time.

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So you propose to resolve the problem by choosing a more suitable metric!

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Sheesh... Yes, I do resolve the "problem" of infinite time at the event horizon by choosing a metric where time is not infinite at the event horizon. So does anyone else who knows physics. If you don't even recognize that, I can't help you. Be careful not to read more in to that more than what I have said explicitly.

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The Schwartzchild metric has a singularity at the event horizon. However, there is no special privileged status for that metric; and the discontinuity is a property of the metric; not a break down in relativistic physics. For a sufficiently large black hole, a spacecraft flying though the event horizon would not notice any special discontinuity or sudden effect as they fly past the point of no return.

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Yes and no! I have always accepted that the infalling observer would not see any space or time deformities, but the Schwarzschild diagram agrees with me that he would see a sudden effect if he looks back at the outside universe, because of the relative time dilatation. I have not analysed the other metrics in this regards, but if they disagree then we have a problem.

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To the best of my knowledge, the Schwarzchild metric and time dilation does not imply any sudden effects at all for what is seen of the outside universe by an infalling observer. You are still mixing up divergence of lines in one particular metric with an inability for light to pass the horizon. That’s wrong. An observer who is actually inside the event horizon can continue to see light from the outside universe.Here is another page you may find of interest. Falling to the Singularity of the Black Hole. It includes movies of what can be seen as someone falls into the black hole. The associated text describes what is going on at different stages, in fractions of the Schwarzchild radius. Those fractions are 1.5, 1.0, 0.95, 0.68, 0.35, 0.01, 0.000000001, 0. Four of these views and descriptions refer to observations being made from well inside the event horizon, and the last refers to the singularity where current physics can't help us.

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Have another look at the Schwarzschild diagram. All those outside light rays curve upwards, but as the observer would be falling more slowly than light, his worldline would be more vertical, and all approaching light rays would intersect his worldline, for the rest of forever up the diagram. If you disagree with this reading of the diagram, please explain why. And if any of the other metrics give a different result, we have a problem.

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Of course other metrics give different co-ordinates. The Eddington-Finkelstein diagram, for example, has incoming light paths being nice straight lines which don't diverge at all. There's nothing wrong with that. It is just a different allocation of co-ordinates to events. The "problem" is just one of learning the physics of relativity; not a problem with physics itself which is troubling to cosmologists. Humbling as it may be, you badly need to see the problem as one of understanding physics for a student. I'm in the same position, by the way.

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For an outside observer, there are various ways (metrics) they might choose to apply co-ordinates to the space. With a suitable transform to more appropriate metrics (more appropriate for discussing what happens as an object falls through the event horizon) there is no singularity or discontinuity. And there is most certainly no absolute basis for matching up events in different locations as being "simultaneous".

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Did I say ‘simultaneous’? Well, I suppose I implied it by talking about the clock of an outside observer when something happens at the event horizon.

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Yes, that is all I mean. Using your watch to time events somewhere else requires a notion of simultaneity. I'm not trying to trick you with any of this.

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The singularity which appears at the center of the black hole is another thing entirely. That singularity appears in all the metrics, and it indicates that our current relativistic physics breaks down at the central singularity. We will need a better physical model (a mix of quantum mechanics and relativity) to describe that point in space.

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But the event horizon presents no such problem. It is described just fine with classical relativistic physics, and there is no reason to think anything special is going on at the event horizon which breaks existing physics.

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But these are exactly the problems that my view resolves. I do not believe anything special is going on at the event horizon - I do not believe that objects falling from infinity would reach the speed of light there and acquire infinite mass; I do not believe in a total time dilatation where time comes to a complete stop (in any metric or reference frame); I do not believe in a singularity at the centre where the laws of physics break down. It is you guys who believe in all these weird things.

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Modern physics is weird, yes. You will never ever understand it if you insist on making it not weird. Note that infalling objects do not acquire infinite mass in any metric, and that divergence of time co-ordinates is an artefact of one allocation of time co-ordinates to events.

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Have another look at my original post. My position is that the slowing of time as gravity increases means that these situations are never quite reached, however close conditions may approximate to them. I propose a universe with no such absolutes or singularities or breakdowns of physics. And I hold that this is the universe implied by Einstein’s theories.

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If you approach this under the impression that you have a new theory of physics which resolves all the various breakdowns which are spoken of in the pages cited, then you are doomed to be yet another crank. The relativity groups are full of them.If you approach this with the recognition that you are student grappling to understand a difficult subject, then you can make progress. I won’t be able to help very much at all; since I am not an expert in relativity. Reading though the tutorials supplied by Professor Hamilton would be a good start. He is an expert.Best wishes -- Chris[This message has been edited by cjhs, 02-01-2004]

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Originally posted by RingoKid:
...is this singularity the same singularity of the pre big bang and if so where is it and if not where is it and how can you have two of them ???

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Here are three kinds of singularity.

• The big bang singularity.
• The singularity in the Schwarzchild metric at the event horizon of a black hole.
• The singularity at the center of a black hole.

They are not all the same; they are all very different.The term singularity is mathematical. It means that a mathematical function becomes badly behaved or diverges. For example, the function y = 1/x has a singularity at x=0.The mathematical solutions for classical relativity have singularities in the conditions indicated.For the big bang and the center of a black hole, the singularity indicates a point at which physics breaks down, and fails to give a good description of what is happening. A new physics will be required to handle those conditions; involving an combination of quantum mechanics and relativity. We don't have a theory able to handle those cases just yet.For the event horizon of a black hole, the singularity is not a consequence of physics failing to work properly, but of one particular metric which could be applied. With a suitable transformation to another metric, there is no singularity.That is, the singularity at the event horizon is a property of a description; the singularity at the big bang or center of a black hole is a consequence of extreme conditions that modern physics cannot presently model.Every black hole is a singularity; and includes a region where physics breaks down. There seems to be a large black hole in the center of most galaxies; which indicates that there are many billions of them. There are also many smaller black holes within the galaxy, though these are hard to detect.The Hubble space telescope has been very useful at finding and studying black holes. Here is a selection of stories about these observations:
NEWS RELEASES

I did not accuse you of being a crank. You might be; I'm not yet sure. We don't flog cranks; or punish them in any way. Here is what I actually said: It would be a good idea for you to clarify in your own mind what it is you are trying to do. If you do think that the mismatches between your ideas and those of Andrew Hamilton are because he lacks your insight; then you are likely to end up as a crank. If you think the mismatches indicate that there is something lacking in your own understanding, then you are right; and you have a chance to learn something. I can help, if you let me.You do understand some of this material; I endorse your attempts to explain the Big Bang expansion to Ringokid. The movies show that someone continues to see light from the rest of the universe even from within the event horizon. That means that the light, and the observer, is all crossing the event horizon. The situations are reached just fine.The quiz question 2 of Professor Hamilton is actually this: The correct answer is "false".The plain prediction of conventional relativistic physics is that an observer who falls into a black hole, will continue to see the rest of the universe as they fall. They fall very quickly, reaching the center in a very short time. Light from the far future does not somehow catch up with them along the way.As for blue shift, you need to read the pages again. Hamilton says that there is a substantial gravitational blue shift of the rest of the universe as seen by someone falling into the black hole. See his description of Gravitational redshift. He also gives a redshift map which corresponds to a view of the falling observer from about 0.68 Schwarzchild radii; that is, from inside the event horizon. Some parts of the sky are redshifted, and some are blueshifted. The effects are calculated from a combination of gravitational blueshifts, and velocity based red or blue shift. Eta Carina is correct; and Andrew Hamilton has done the calculations and presented them in a pictorial form. The simplest case for velocity is to use the velocity of a free fall from rest at infinite distance. But whatever velocity you use, all the way to the singularity there will be parts of the sky that are blue shifted, and parts that are red shifted. At no point do gravitational blueshifts dominate over the entire sky.You are incorrect in thinking that you can go in slowly. No matter how good your retro rockets might be, once past the event horizon you will go in very quickly indeed; and it is possible to calculate an upper bound on the time it will take to hit the center singularity. An outside observer will not be able to observe anything from you after you have crossed the event horizon, and from that point you are doomed to hit the central singularity within a tiny fraction of a millisecond, no matter what you do with retrorockets. You mean "Eddington-Finkelstein", not "Finkelstein-Einstein".It is an error to speak of "our" time. This sneaks in the implicit assumption of a privileged absolute time scale. It is a common mistake. I've tried to point this out several times already. There are many metrics which might be used to give time and space co-ordinates to events which we observe at a distance. In some metrics, the time co-ordinate of events on the event horizon are infinite. In others, it is not infinite. That is what I mean by metrics where time at the horizon is not infinite.One useful notion of time is the time experienced by a falling observer. In this case, the time metric for an event in spacetime corresponds to that experienced by the falling observer. The corresponding spacetime diagram is displayed at the pages cited previously. You can see clearly that the observer experiences finite time to hit the center; and that the observer crosses a finite number of photon world lines.The relationship between "Eddington-Finkelstein time" and "Schwarzchild time" is "tF = tS + log|r-1|" (in appropriate units). "r" is distance, which is the same in both metrics.I cannot make any sense of your last comment about an observer passing through the event horizon before they start falling. If you think you can just do what you like with relativistic metric transformations, then that is another error. This is a simple and unambiguous mathematical error on your part. If you do the math, you can see it is false.The world-line of a free falling observer will only cross a finite number of world-lines of in-falling light rays. Furthermore, it will cross the exact same finite number of light rays, no matter what metric is used for plotting world lines.Take a Schwarzchild diagram. Plot world-lines of light rays, and as you say they all diverge upwards at the event horizon. Take a free falling observer, who is falling more slowly than the light. It also will diverge upwards, but not sloping as much as the light rays. But it still only crosses a finite number of the light rays. That is just a mathematical fact. This is backwards. Only a small number of photons hit the world line of the falling observer, and you can't make them hit the world line of the infalling observer by any transformation. The events don't happen, in any diagram.Eta Carina is probably better able to manage the maths than I am. I do not know off hand the formulae for the world line of a free falling observer. But we can approximate it.The diagrams have "r" as the horizontal axis, representing spatial distance from the black hole, and "t" as the vertical axis, representing time. Let "N" be a parameter indicating different photons. The world line for an in-falling photon in the Schwarzchild metric is the line defined by: Different values of "N" give different photons.An infalling observer might have a world line defined by: This is not really a free fall; but some kind of powered descent. It falls more slowly than the photons. You will find that this line diverges upwards to infinity at the event horizon (r = 1); and that it "slopes less" than the photon world lines.The observer will cross the world line of photons for which "N < -1". Inside the event horizon, this observer crosses the world line of a few more photons, those with "-1 < N < 0". Photons for which "N > 0" will never ever hit the world line of the observer. Those are the photons that hit the central singularity strictly after the observer hits the central singularity.The observer also crosses the world line of one photon; the "N = -1" photon, right on the event horizon; but of course we can't show that event on the Schwarzchild diagram due to the singularity. We can show it just fine on the Eddington-Finkelstein diagram.The statement that an infinite number of photons cross a free-fall line which "slopes less" is just false. You would need a line that corresponds to an observer who uses infinitely powerful retro rockets to hold themselves above the event horizon indefinitely, in their own time frame. Shrug. You have a lot to learn before your opinions of maverick cosmologists are meaningful. Halton Arp is a maverick of considerable real ability, but handicapped by a massive blind spot and a bad chip on his shoulder. His observations of peculiar galaxies are interesting, but he does not actually have a good interpretation. He thinks something else must be causing high red shifts for quasars, but does not know what. The rest of the astronomical community considers his claims for the close association of quasars with galaxies of less red shifts to be adequately refuted. The evidence for association he presents is very thin. Be careful also; he has made some serious basic errors in statistical analysis of some of his evidence; which he has since recognized (grudgingly). Alas, many enthusiasts will continue to cite the flawed analysis as if it means something.But in any case, I am quite sure that Halton Arp would not make the kinds of elementary errors in relativistic analysis seen above. No worries, mate. They are fascinating.Try to take this in good humour. You may not accept this yet; but you are still making really really basic errors; and I am not going to hide that or pretend that we are discussing this as equals. I'm not an expert, but I know enough to see where you are going wrong, and to point you in roughly the right direction. If you can recognize that you are still learning, there is no reason you can't make progress.Perhaps I am a bad teacher for not being sufficiently respectful of your ideas; or perhaps you have been handicapped by lack of a teacher who is willing to tell you frankly when you are making silly mistakes. But I am trying to help.My advice is to focus on your claims about world lines of falling observers and photons in the Schwarzchild spacetime diagram, until you have resolved it. Use some actual maths. See if you can find a mathematical description of the world line for an free fall from infinite distance. I don't know it; if you can figure it out let me know! Seriously. But the fact that it crosses a finite number of photon world lines is definite.Cheers -- cjhs[This message has been edited by cjhs, 02-04-2004]

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Originally posted by RingoKid:
oh, not the balloon again...

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if all of those things were right up next to each other then where was this ???

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The balloon analogy is an attempt to help you answer this question. In the analogy of the balloon, space corresponds to the surface of the balloon, and ONLY the surface of the balloon. Of course, this analogy is not exact, because the surface of a balloon is two dimensional, and the space we experience is three dimensional. But expansion of three dimensional space is not something people find easy to grasp, so we use the ballon analogy to help.In my own experience, however, it often hinders because students mistake the analogy, and think of the universe including points which are not on the skin of the balloon.The balloon expands. There is no point on the balloon which is the center of the expansion. The center is back in the past, when the balloon was tiny, and all points on the skin of the balloon were very close to all other points on the skin of the balloon.Where was the center of expansion for the universe? Right here. And also over there. Every point we see in the universe has equal claim to being a center.A better analogy may be an infinitely large loaf of rising raisin bread. As the loaf rises, all the raisins are expanding from all the other raisins. Galaxies are like raisins; they are all moving away from each other as the universe expands. In the past, they were all infinite close together. But there is no one point in the loaf, or in the universe, which can be seen as the center. The initial singularity is just a point of infinite density and infinite heat, in which every point in space is infinitely close to every other point in space.Don't think of a point in space as being the unique center of expansion. That is a common error.Cheers -- cjhs

Always keep in mind that all of these analogies are just analogies, and break down at some point.The universe does not have a center of mass.In the analogy of the loaf, I tried to express this by speaking of an infinite loaf. An infinite loaf of bread, like the universe, does not have a center of mass.However, we don't really know if the universe is infinite, or finite. For the simplest topologies, the most recent results suggest an infinite universe, since it is "open". However, even in this case the universe might be finite if it has a more complex topology. There was, briefly, a newsreport last year about a twelve sided model for the universe. The model was refuted almost as soon as it was published, and it has been discussed in this forum. That was a case of considering a complex topologicial structure for a finite but open universe.To get an idea of how strange this is, if true it would mean we could see the exact same regions of space by looking in several different directions. It does not mean the universe has a 12 sided edge.Trying to get reasonable analogies for this that will help give a good mental picture is very difficult. We need to get back to the balloon again. The universe may be like the skin of a balloon. It is unbounded (no edges) but (possibly) finite. Or (as recent observations suggest) it is like the skin of a saddle point in the mountains (negative curvature), which is (in the simplest case) infinite. Mix in a funny topology like a torus or doughnut, and it could still have negative curvature and be finite at the same time. The really tough thing in these analogies is to recognize that the universe is analogous to the skin of the structure; without being embedded in a higher dimensional space..A common feature of all the models is that there is no center of mass. That is because, as I tried to explain last time, the nature of the expansion of the Big Bang is that there is no point you can identify in space as the point from which expansion occurs. It is an expansion of all space, with all points having equal claim to being a center of the expansion. If the analogy fails to get that across, it is a defect in the analogy. It is not meanginful to speak of the shape of the singularity. You can speak of the shape of the universe; but that does not mean what you think. In any case, the universe expands or stretches over time, but the overall shape or topology (which is not known) remains the same.The singularity is the break down in description back in the past when all points in space were arbitrarily close to all other points in space; but there was never, at any point, a distinguished central point in space. I do see what you are getting at; it is a very common mistake as we start to try and grasp modern cosmology. The problem is that you are still thinking of the universe as a "thing" in space, which has a center and a boundary. That is incorrect. The universe is not like a particle in space. When cosmologists speak of the "shape" of the universe, it is confusing, because they don't mean that the universe has a boundary they can trace. They are talking of the structure of spacetime and intrinsic curvature, with no presumptions at all of an embedding into a larger space. No, it isn't. The nature of the expansion is that all points in space used to be arbitrarily close together. The ideas of expanding space are really hard to grasp, because expansion of space is not the same as the expansion of a physical object. But that is relativity for you. It's difficult, and it is counter intuitive. But it is not a cop out for avoiding the intuitions you may about a central point.Cheers -- cjhs

The ramifications are that a finite universe would have a finite mass, but still no centre.Again; the balloon. The balloon does not have a center. Recall, in the analogy, you may only consider the skin of the balloon; anything else does not belong in the analogy. That is what a finite universe would be like, in the simplest case. All points in the universe are equivalent, like all points on the surface of the balloon. There is a finite mass in the universe, just like the balloon surface has a finite mass. There is no central point in the universe, just like there is no central point on the surface of the balloon.We use the balloon analogy simply because it might help to grasp these hard to understand points. The surface of the balloon is an analogy to explain these aspects of the universe. The ultimate reality is the universe; not the balloon.Of course, science can never be sure about their models. But even if our cosmological models are all fundamentally wrong, this is still not going to restore simple ideas based on particles expanding from a central point in a nice simple flat three dimensional space. If you are thinking of the "nothing/void" as a large empty expanse pretty much like what you can find in an empty box, then indeed it is not possible for the models of the universe we are trying to explain to be embedded in such a space.It is mathematically possible to define higher dimensional spaces in which a curved three dimensional universe might be embedded, in many cases; much like the two dimensional surface of a balloon is embedded in the higher dimensional (three dimensional) space of our normal experience. Nothing is gained by such an exercise. The higher dimensional spaces are far less intuitive than anything you have tried to grasp so far, and they add nothing useful to the models. The higher dimensions are not something we experience, and cannot give you a point in our universe as its center, and do not correspond to anything physical in our universe.It is likely that there are in fact more dimensions than the three we experience normally; but we would need a whole new set of analogies to try and discuss that idea. These models involve tightly curved dimensions, not higher dimensions in which the space of out normal experience is embedded. The models we have for the universe do not involve expansion into a void. Such a notion is in conflict with all the evidence. The evidence we have indicates a Big Bang style expansion -- which is why that is the basis of cosmology.Cheers -- cjhs

The light in the Schwarzchild metric also gets "frozen" before reaching the event horizon; they both take forever. This is an artefact of the metric, which is such that it gives a divergence at points in spacetime which cannot send signals back to the outside observer. An observer hovering outside the event horizon for any length of time would see much more blue shift, because they have all the gravitational blue shifting effect, and none of the velocity red shifting effects.To see the entire future of the universe, an observer has to remain above the event horizon forever, according to their own clock. This requires an enormously powerful retro rocket. There are no stable orbits within 1.5 Schwarzchild radii; to remain somewhere between 1.5 and 1 Schwartzchild radii for any length of time (in the observer's own experience) requires continuous application of other forces to overcome gravity. Inside the event horizon no force can save you at all. I agree with you; good catch. The term "in reality" is not a good one, it sneaks in the idea of a privileged time scale. The phrase "long ago" in reference to events at a distance implies a metric. It cannot be an absolute statement about reality; and I'll bet that on reflection, Eta would agree.There are some absolute statements we can make about events. For example, suppose you are in a parent ship holding steady somewhere outside the event horizon by virtue of retro rockets, and you release a probe which drops into the hole. In principle, at all times into the future you might get a signal back from the probe. If you get a signal, it must have been released by the probe before it crossed the event horizon. However, photons take a long time to climb out of the gravity well. They also get red shifted into invisibility. In fact, the red shift of signals from the probe rapidly (in the frame of the parent ship) reach a point where you can't really tell the difference between Hawking radiation and signals sent by the probe. Bear in mind that the peak wavelength of Hawking relation is around the length of the Schwarzchild radius, I think.On the other hand, by your own clock there is an identifiable time very shortly after release of the probe where you lose contact, in the sense that you can no longer hope to send signals to the probe. Any photons you release after that point will never reach the probe. There is also a short interval of time (by the parent ship's clock), in which signals may be sent that will reach the probe, but no response is possible because the signal reaches the probe inside the event horizon. (This corresponds to the falling probe seeing the stationary observer for a brief interval of time between crossing the event horizon and being crushes in the central singularity.)That is, from the perspective of the outside observer:

• There is a small finite elapsed time after which you can no longer send signals to a dropped probe.
• There is a slightly smaller finite elapsed time after which you can no longer send signals to a dropped probe and get a response.
• Towards the end of this very small interval in time in which signals can be sent with the hope of a response, there is no limit to the time you might need to wait before the reflected signal returns, and the red shift of signals from the probe increase without bound.
• For any physically realistic photon detector, there is a small finite interval of time beyond which you can no longer detect signals from the probe; it is practically lost to sight even though in theory it should be visible at very long wavelengths.
• The black hole itself is not actually black; it shines with Hawking radiation that will eventually outshine signals from the probe! This gets into quantum effects, and when these are taken into account the probe may indeed end up inside the event horizon within Schwarzchild time, I think. I'm not sure; I've just passed the limits of my competance.

These are absolute times, because they refer to time measured by your own clock of events at your own location. The metric is needed only if we want to speak of the time of an event at some distance.From the perspective of the falling probe:

• There is a small finite time before you get crushed at the central singularity.
• There is a slightly smaller finite time after which you can no longer hope to send signals back to the parent ship. The point at which you can no longer send signals is the event horizon; after that your signals will simply follow you into the hole.
• There is a smaller finite time value which corresponds to the last glimpse you have of the clock on the parent ship.

Science relies on people throwing up new and revolutionary ideas from time to time. Often such ideas are initially rejected. Often this is the right thing to do; the ideas were wrong. Sometimes the ideas are new and useful insights, and they get confirmed in time. Science is basically about trying to tell the difference. But sometimes individuals get attached to bad ideas and never ever let them go; that is part of science also.There is always room for speculation. As time passes, we learn more about the universe. This gives new scope for new matters on which we can speculate, but it also limits the scope for reasonable speculation on specific matters. Uninformed speculation continues, of course; but I don't find that particularly fascinating.I stand by all my comments with respect to Halton Arp. I didn't call him a crank; I called him a maverick. This was deliberate.In Halton Arp's areas of interest, there is a very relevant example of a maverick who prevailed against othodoxy to establish new and better views of reality: Hannes Alfven. Read the link. You'll like it. Alfven had many revolutionary ideas, some of which panned out. He won the physics Nobel in 1970. He was also a critic of Big Bang cosmology. His alternative ideas on cosmology are an example of a case where his ideas did not pan out; he was wrong. People like Eric Lerner continue to try and press his ideas on cosmology, but they can only do so by ignoring and misrepresenting accumulated evidence which bears upon the matter. On the other hand, in my very amateur view it seems there is still scope for Alfven's ideas on plasma physics to play a role in improving our understanding of galaxy formation and development. Time will tell.Although scientific knowledge is never complete or formally proven; we can still get better and better understandings over time. Dark matter is a good case in point. It was first detected (indirectly) in 1933 by Fritz Zwicky. In principle there might be other ways to explain observations; but pretty much everyone in the field is convinced it is dark matter; and the question is "What is it?". That is still the question; but the observations have continued to improve. For example, here is an article from last year showing a Map of Dark Matter developed using observations with Hubble. The method is to observe gravitational bending of light to map the masses which cause this bending.In this image, the pale blue is dark matter. The blue is not actually visible light; it is the inferred map of dark matter superimposed on the image of a galaxy cluster. The link is to associated discussion and more images.
(Image Discussion link)The aquatic ape is a case where speculations moved from maverick to ridiculous. What someone finds fascinating is, of course, subjective. I find human evolution and what we can learn about it to be fascinating. I find the aquatic ape itself irrelevant. That is, of course, a whole other topic for debate. The relevance to creationism is tenuous; but there are some parallels. I think a discussion might be interesting; but not in this thread.Best wishes -- Chris