Originally posted by twhiteheadAnd this is the main point: Equations are man-made, the reality is not.
I only brought up the unstable possibility of two black holes colliding when adam made the ridiculous assertion that an event horizon can only contain one singularity because the equations dictate that it is so.
Honestly, I'm curious about this too. In any static situation it seems obvious that a singularity would be surrounded by a spherical event horizon, however in a dynamic situation intuition suggests that two merging singularities could have sufficient strength to warp the shape of each others' event horizon. As stated before, intuition is not always right, but it does give you insight into how the brain perceives the problem.
One model that I'm sure many people draw on when conceptualizing these events is the classic demonstration of a marble on a warped tabletop used to illustrate the principles of relativity. When a marble is rolled across the table it rolls in a straight line on the flat sections, but when traveling near a "massive body" represented by a smooth dip in the tabletop, the marble changes direction. Marbles rolling too close to the massive body, or rolling without sufficient momentum, get sucked into the dip. A black hole would be an extreme dip in the table, akin to pinching a piece of stretched nylon and pulling as hard as you can. The circular cross-section of this cone where no marble could escape from would represent the event horizon. This model is a great intuitive aid, as it creates a physical analogy between something mostly inconceivable (i.e. warping of 3-dimensional space) and something easily visualized (i.e. warping of a 2-dimensional surface in 3-dimensional space).
How does this relate to black hole mergers? Well, once might draw on this model again to depict two singularities as deep cones moving towards each other on the tabletop. The event horizon circular cross-sections would definitely remain circular at sufficient distance from each other. However, this intuitive model predicts that as the cones approach each other, certain regions of the tabletop would experience strong tugs in two directions (one from each singularity), not just one. This tug-of-war would produce saddle-points in the regions between the singularities, distorting the cross-sections into shapes most likely resembling eyeballs looking at each other. If the two cones got close enough, the cross-sections would merge into a figure-8 type figure, eventually merging into a single cone with a normal circular cross-section again. This may or may not happen in reality, however I think this is basis from which twhitehead's (and others'😉 questions stem.
All analogies trade accuracy for simplicity. Successful analogies retain the essence of the relationship while discarding the distractions. The question is whether the tabletop analogy retains the essence of the dynamic relationship between two merging black holes or not. The only tool that can really answer that question is the equations governing this situation. Palynka, is there an aspect of these equations that explicitly precludes the use of this analogy in discussing a black hole merger? Or is the answer more subtle?
Originally posted by twhiteheadI'll give this one more chance, but you have an annoying habit of totally misrepresenting what I write. Do you even read what I write? Do you read the links I post?
You just cant seem to keep a straight claim. If your equations specifically deal with a single singularity, it is nonsensical to claim that the equations rule out multiple singularities.
[b]It doesn't need an infinite amount of time to settle. The time period may be big but it always is finite.
I think your biggest problem is you cant admit when y er than light in any of those scenarios? If not, then what does travel faster than light?[/b]
If your equations specifically deal with a single singularity, it is nonsensical to claim that the equations rule out multiple singularities.
When I made the first comment about one singularity for a single BH I was referring to the case were you have a non interacting BH. Your original quote is this: "I also see no reason why two singularities cannot orbit one another (as binary stars do) and thus have a more exotic shaped event horizon." Since you didn't provide your scenario I assumed the simplest one (no interactions) and in that scenario you can only have one singularity. Then you said "Even if I am wrong, if two black holes are orbiting each other, event horizons and all (that certainly is possible), and the event horizons touch, they surely won't instantaneously combine into one singularity - therefore the equations cant possibly rule out my scenario." The word surely makes it a categorical affirmation. And this what I objected too. You certainly (this a categorical affirmation too) don't have the knowledge, nor the technique, nor the intuition to make such a claim. I'm sorry if it bruises your ego, but the same is applied to me and it doesn't bruise my ego.
This sentence of yours is just hilarious "I didn't realize that I made a categorical claim, I merely suggested it as a possibility." Of course you made a categorical claim. That's what the word surely is: categorical.
"It is you that claimed that the equations prove it is impossible"
Either you are misrepresenting me, or you didn't read anything of what I wrote. Here it goes again. A BH that doesn't have a translational motion can only have one singularity. When two BHs collide (a future scenario that you proposed and wasn't in my first analysis) I don't know what happens. I've said so numerous times during our argument and I challenge to find any quote of me that substantiates your claim.
"and has even got you starting a new thread trying to prove the superiority of those equations."
You totally missed the point of the new thread. Totally. First it was way more general than those equations, as you put it, and it was never to show the superiority of any equation. What I meant was to show that for one to have a serious discussion related to physics one can't only rely on equations, nor on common sense. What is needed is a lot of mathematical tools, but what's more important one needs to interpret the equations and their solutions. And that's pretty explicit there for anyone that reads what I wrote. Once again I challenge you to provide a quote of me in that thread that substantiates your claim.
"I am curious, does matter actually travel faster than light in any of those scenarios? If not, then what does travel faster than light?"
Read the articles.
Originally posted by PBE6Just a few remarks on what you said:
Honestly, I'm curious about this too. In any static situation it seems obvious that a singularity would be surrounded by a spherical event horizon, however in a dynamic situation intuition suggests that two merging singularities could have sufficient strength to warp the shape of each others' event horizon. As stated before, intuition is not always right, but ...[text shortened]... the use of this analogy in discussing a black hole merger? Or is the answer more subtle?
"One model that I'm sure many people draw on when conceptualizing these events is the classic demonstration of a marble on a warped tabletop used to illustrate the principles of relativity."
These analogy has two big problems: the first is that it uses gravity to explain gravity. The second is that the 2D curvature is a lot different than a 4D curvature.
Another aspect that I'd like to point is that in that analogy we need a 3D space were a 2D surface is embedded to have a 2D curved surface. Our space-time is a 4D space that in the context of GR needs no higher dimensional space in order to have curvature.
"Honestly, I'm curious about this too. In any static situation it seems obvious that a singularity would be surrounded by a spherical event horizon, however in a dynamic situation intuition suggests that two merging singularities could have sufficient strength to warp the shape of each others' event horizon."
For rotating BHs the event horizon isn't spherical and to tell you the truth I don't if a non-rotating (and non colliding with another BH) but moving BH still has a spherical event horizon.
"This model is a great intuitive aid, as it creates a physical analogy between something mostly inconceivable (i.e. warping of 3-dimensional space) and something easily visualized (i.e. warping of a 2-dimensional surface in 3-dimensional space). "
It's even more inconceivable than that. It's the warping of a 4-dimensional space that doesn't need to be in higher dimensional space to warp.
"once might draw on this model again to depict two singularities as deep cones "
In this model you propose the singularities aren't the cones. The singularities are the tips of the cones. In GR (and all of physics)a singularity is a point (or more generally a region) where you can't calculate a derivative. In the case of the cone the only such place is at its tip.
"The question is whether the tabletop analogy retains the essence of the dynamic relationship between two merging black holes or not."
What makes me distrust these kinds of analogies is their extreme simplicity. The situation you just describe is very simple an I think that even could write a computer program (given enough time and patience) put it to run on my home pc and get a solution. What happens in reality is that modeling collisions between BHs (even in simplified scenarios) causes supercomputers to crash.
And have you read the wikipedia link I posted on the Fermi-Pasta Ulam problem? This is a much simpler non-linear problem that had Fermi and Ulam utterly wrong. Not somewhat wrong, not so-so wrong, but totally wrong. and the problem wasn't that non-linear, the equations weren't that hard, and those two guys sure knew a lot about physics (by all accounts Fermi was a monster). Still they got all wrong. And this is troubles me more in this situation. The scenario we are discussing is a lot more extreme and yet a certain degree of frivolity is being applied to its analysis. And this is what I've been opposing in this thread. I'm not saying that after two BHs collide it is impossible for the two singularities to coexist. I'm just saying that it isn't certain. I'm also saying that even if the singularities combine instantaneously (or just with a speed greater than c) with what I know it doesn't necessarily mean that SR is violated (if this process doesn't carry information SR certainly isn't violated). And even if SR is violated? So what?! SR isn't a dogma. It is a man made physical theory. Of course it will break down some day. Not to mention the conditions in which SR is valid may be violated inside a BH where a collision is taking place with another BH.
And I'm not saying let's stop discussing this issue. What I'm saying let's just have the notion of how tough this issue is and let us apply some self-criticism to our analysis, arguments, and conclusions.
Originally posted by PalynkaI'm asking you because you said this:
Are you asking the guy who knows nothing of physics? 😀
All I'm saying is that in your analogy, it's still two bloody cones!
"LOL, whatever man. If you don't see how ridiculous it is to say that event horizons may not be spherical because of another body interacting with it (the second singularity) then I'll just move on."
I'm curious as to why this is set in stone.
Some clarification is needed here.
I never said that the tabletop example was MY analogy, or the RIGHT analogy, just that it is THE analogy used to describe relativity to the layman. I also said that this is where the layman will begin his thought process in conceptualizing the interactions between merging black holes. The only question is whether, in making the trade-off between accuracy and simplicity, the analogy retains the essence of the problem and therefore whether it has any predictive power. If it does NOT retain the essence, then it does NOT have any predictive power. However, if you wish to convince a layman as to why their conception of the problem is wrong, I guarantee you will have to address the applicability of this analogy. If you wish to dissuade intuition, you must understand the intuition in question.
One interesting thing you mentioned is that "what happens in reality is that modeling collisions between BHs (even in simplified scenarios) causes supercomputers to crash." I think this may be overstating the case, considering the article I posted earlier in this thread about the seemingly strange momentum of a singularity resulting from the collision of two others. No matter, it may be a special case. But if supercomputers are crashing left and right while pondering these things, how are people here drawing such strong conclusions?
There seems to be two main questions in this thread that are getting lost in the muck. I think we can simplify this discussion immensely by answering the following questions:
1. Consider two black holes approaching each other in space.
(a) (i) Under what circumstances would the event horizons remain spherical? (ii) Why?
(b) (i) Under what circumstances would the event horizons change shape? (ii) Why?
2. Consider two black holes approaching each other closely.
(a) (i) Under what circumstances would these black holes merge? (ii) Why?
(b) (i) Under what circumstances would these black holes enter into mutual orbit with each other? (ii) Why?
I think that once we have definitive answers (possibly including the definitive answers "yes", "no" and "science cannot answer that question yet", in addition to more explanatory answers), we will be much further along.
Originally posted by adam warlockWho made reality? It's not a trick question, is it? It's not Spiritual Forum, is it? 😉
Who made reality then? And what is reality?
And if reality and what we say of reality isn't identical how do we surpass that obstacle? And is it really an obstacle?
I say that the reality is not made, it's just there, as the result of the laws of nature.
Yes, I think it's really an obstacle. And what we have to do is to refine the equations further. But we cannot ever refine it to obay the reality. We have to make simplifications. Newton did, and noone complains. Einstein refined them, the future will tell if it's enough for our purposes.
Originally posted by PBE6"I never said that the tabletop example was MY analogy, or the RIGHT analogy, just that it is THE analogy used to describe relativity to the layman. "
Some clarification is needed here.
I never said that the tabletop example was MY analogy, or the RIGHT analogy, just that it is THE analogy used to describe relativity to the layman. I also said that this is where the layman will begin his thought process in conceptualizing the interactions between merging black holes. The only question is whether, in maki ...[text shortened]... question yet", in addition to more explanatory answers), we will be much further along.
What I did was to point out the problems with that analogy. And I did that because people sometimes takes analogies too far and the GR analogy is a very good example of that happening.
I didn't mean to attack you or anything I just wanted to tell the problems with that analogy so that people don't get too carried away with it.
" However, if you wish to convince a layman as to why their conception of the problem is wrong, I guarantee you will have to address the applicability of this analogy."
In my view this analogy is great for a very small number of cases. If one is dealing with a static body interacting with a moving one, than it certainly is a great analogy. But unfortunately most of the cases in the Universe aren't like that. And once again I'll talk about the fact that this analogy only works because we have a 3D space were to embed the 2D surface that will curve. For space-time we don't need to embed it in a nD (where n is a number greater than 4) dimensional space for it to be curved. And this is highly problematic if one tries to analyze problems in the real 4D universe that we live in using that analogy. There are a lot of effect that have no analogue in the 2D analogy, and some effects that exist in the 2D analogy don't get mapped into the real world.
" I think this may be overstating the case, considering the article I posted earlier in this thread about the seemingly strange momentum of a singularity resulting from the collision of two others."
I also posted a few links on that but I'll post here again:
I also made a google search and this is what came up:
As two galaxies merge, their supermassive black holes have to eventually interact. Either through a direct collision, or by spiraling inward until they eventually merge as well.
And that's when things get interesting.
According to simulations made by G.A. Shields from the University of Texas, Austin, and E.W. Bonning, from Yale University, the result is often a powerful recoil. Instead of coming together nicely, the forces are so extreme that one black holes is kicked away at a tremendous velocity.
http://www.universetoday.com/2008/02/29/what-happens-when-supermassive-black-holes-collide/
And this link also provide some information: http://news.cnet.com/Supercomputer-simulates-black-hole-collision/2100-11397_3-6062605.html
Just let me point out this: Earlier trials failed since the equations based on Einstein's general relativity theory were so complicated that they made supercomputers crash. So back in the day even super computers crashed while trying to tackle this difficult problem.
I also found this. http://www.sciencedaily.com/releases/2006/04/060411080753.htm
But I can't seem to find no definite proposition to what happens to the two different singularities.
"But if supercomputers are crashing left and right while pondering these things, how are people here drawing such strong conclusions?"
Exactly. That's what I've saying all along.
As for your questions:
1.
a) Non rotating BHs have nonspherical event horizons. Moving BHs, even if not rotating, I don't know, but I suspect that their event horizons isn't spherical. If this issue gets more pressing we can always google search.
a) If a non rotating BH acquired angular momentum it would cause a change in the form its event horizon.
Another possibility is through some kind of interaction. But this is just a possibility and I don't know enough to tell you anything remotely concrete.
2.
a) I don't know but it seems a very pertinent question.
b) In this one I think it just I need a little bit of clarification: do you mean mutual orbiting without the two event horizons overlapping?
But anyway my answer is a very powerful "I don't know".
Originally posted by FabianFnas"I say that the reality is not made, it's just there, as the result of the laws of nature."
Who made reality? It's not a trick question, is it? It's not Spiritual Forum, is it? 😉
I say that the reality is not made, it's just there, as the result of the laws of nature.
Yes, I think it's really an obstacle. And what we have to do is to refine the equations further. But we cannot ever refine it to obay the reality. We have to make simplificati ...[text shortened]... one complains. Einstein refined them, the future will tell if it's enough for our purposes.
A clear demonstration of a circular argument.
"Who made reality? It's not a trick question, is it? It's not Spiritual Forum, is it? 😉"
We can discuss this question scientifically.
"Yes, I think it's really an obstacle. And what we have to do is to refine the equations further. But we cannot ever refine it to obay the reality. We have to make simplifications. Newton did, and noone complains. Einstein refined them, the future will tell if it's enough for our purposes."
Are you using the terms refinement and simplification as equivalents? In maths and physics a refinement is achieved by the opposite of simplification.
And what simplifications did Newton made? Newton theories had a lot of detractors so a lot of people did complain. Newton was one of them by the way.
And do you refine equation? With verbal arguments? With arguments that relied on analogies. That was tried in the middle ages and people concluded that it doesn't work (apparently).
Originally posted by PBE6What is set in stone? Do you think the cone is a bad description because you could have two cones? To say that an event horizon is not necessarily spherical because you can have two event horizons interacting sounds silly to me.
I'm asking you because you said this:
"LOL, whatever man. If you don't see how ridiculous it is to say that event horizons may not be spherical because of another body interacting with it (the second singularity) then I'll just move on."
I'm curious as to why this is set in stone.
Originally posted by adam warlock"A clear demonstration of a circular argument."
"I say that the reality is not made, it's just there, as the result of the laws of nature."
A clear demonstration of a circular argument.
"Who made reality? It's not a trick question, is it? It's not Spiritual Forum, is it? 😉"
We can discuss this question scientifically.
"Yes, I think it's really an obstacle. And what we have to do is to refi ...[text shortened]... was tried in the middle ages and people concluded that it doesn't work (apparently).
I don't think it's circular. Can you describe the circle?
"We can discuss this question scientifically."
I don't think so, but if you try to convince me, I'm open minded.
No, I don't think Newton simplified any equation. He just stated them as he thought was right. And in his domain he was right. But still, his equation worked only under ideal circumstanses.
Einstein came later and refine the equations in his relativity theories. Refine, meaning more valuable in extreem conditions, like massive gravitational sources and such.
The equations doesn't work for themselves. They have to be explained verbally. Giuseppe Peano tried to formalize mathematics to a strict language. Some of it are used today, but still there are mathematical books written in English, Swedish, or whatever. So a language is actually needed to explain mathematics. Therefore math is not everything.