Undefined: thanks for your contribution. I agree that the clock/local observer "stops timing". But as for the motion only being inward.... sucks teeth. There's a problem. Have you ever heard of Friedwardt Winterberg's firewall? See http://www.znaturforsch.com/aa/v56a/56a0889.pdf
If the spacetime interval between two points is timelike or lightlike then they are causally related. One event can absolutely be considered to precede the other, for all frames of reference. This is not true for spacelike intervals. This is close, but you have it backwards. You're correct that we cannot causally link spacetime points within the event horizon to us, but we can certainly link ourselves to points within an event horizon! This is what everyone means when they say "go jump in a black hole and try telling me they don't exist!" Black holes don't exist in anyone's causal past, as you point out...but they exist in everyone's causal future, therefore they are most certainly causally linked with us. I'm trying to show that they don't exist in anyone's "concurrent existence" which would require points in spacetime within an event horizon which we are unable to reach, touch or influence in any way.
I'm not saying that; I'll deal with other observers in another step. For now, I just want both of us to agree that a self-referencing observer using the Kruskal diagram would declare that all points within an event horizon are timelike separated from him because he would making such a declaration from the perspective of "here and now" which is located at the graph's origin.
Depends. I don't know what you're calling a "self-referencing observer". If you simply mean an observer who happens to be at the origin of the event horizon (i.e. the origin of the Kruskal diagram), then yes, that particular observer would say that the black hole is entirely in their causal future and none of it is in their causal present. That was just point 4) in your previous post. If, instead, you mean an observer anywhere in spacetime putting themself at the origin of their own coordinate system, then no, because the coordinates on the Kruskal diagram are not "self-referencing" for most observers. If you mean something different, you're going to have to explain what you mean by a "self-referencing observer". I can try to guess, but I can't read your mind.
Fair enough: we can never see them in our past: they are always in our future. So you are saying that because we can't , from the outside, ever see an object inside the black hole, we can't claim the inside exists. I'll get back to the specifics of that, but in general, do you think it is or should be required that you witness something happening before you can conclude that it happened?
No, but if the mathematics of GR show explicitly that the something you're talking about only exists in our causal future then we should not conclude that 'it happened'...yet.
Point of clarification: when you say "Kruskal graph", you really mean a Kruskal spacetime diagram, right? Page 4: http://www2.warwick.ac.uk/fac/sci/physics/current/teach/module_home/px436/notes/lecture19.pdf It made it very confusing when I googled "Kruskal graph" last night and found nothing having anything to do with black holes. Anwyay... I wrote a lot of thought experiments and descriptions of my objections, but ultimately it all comes down to this: Your logic works well as a logical proof that an object can never be observed to travel to, much less even observed to exist behind the event horizon of a black hole in our present or future. But, that doesn't address the question of the existence of the black hole itself(1) or the existence of said event horizon(sort of the same thing), which your logic has to presuppose exists(2). And even then, it may still be wrong(3): 1. The mass that makes up the black hole is observed to exist in our present via its gravitational pull and was observed to exist in the past by the light of the star that came before the black hole. All that happened in between, essentially, is a sort of spacetime wall(2) was built between us and it that somehow blocks the light without blocking the gravitational pull. The matter that makes up a black hole at its formation never crosses the event horizon. But it is detectable in our past via the light it gives off as a star and is detectable in our present and future via its gravitational pull. 2. Your logic is a little like saying that a fort doesn't exist because we can't see past its walls, which are the defining feature of what makes it a fort: In order for the event horizon to serve as an impenetrable barrier, it has to exist. Here's my definition and logic for existence: 1. An object exists in the present if it has presently detectable properties. 2. Black holes have the following presently detectable properties (at least in theory): -Mass -Radius -Black-body absorption spectrum Thus, black holes exist because they are observed to exist. (3) This is a largely unnecessary aside, but your logic is based on a strict GR interpretation that is unproeven at best and probably wrong at worst. Whether or not matter or energy can cross the event horizon is an active area of study and not essential to the question of whether black holes exist - that is, of course, the subject of your OP citation. As with #2, the question presupposes the existence of the event horizon/black hole.
The only problem I see with that conclusive remark, is that it is common sense and logic....Shame on you! Please Register or Log in to view the hidden image! [tic mode on of course]
Hey, there's something dark, doesn't send out light, and its supermassive, at the center of our galaxy. we keep posting links to the stars observed orbiting about it at close proximity, and their orbits allow us to calculate that it is ginormous in mass. For lack of a better term, because it is black, and anything that goes into it turns black and 'goes away' so we never see it again, let's call it a "black hole". Sounds good to me. http://www.zmescience.com/space/closest-star-black-hole-orbit-milky-way-20313/
Farsight, you link mathpages.com and reference Kevin Brown often. Some of what I find "there" is at least interesting, but I don't find any reference to who he, Kevin Brown is. Do you have a link to some background information? Who is Kevin Brown? Maybe I am just missing something obvious, but I don't find any reference to him anywhere but his.., mathpages.com. Maybe it's just that my formal schooling predates him? This is not an attempt to debate what he presents. I just like to know who a person is and where they are coming from. Much of what is being discussed on these forums amounts to opposing conceptualizations of theoretical models. Sometimes the theory itself but mostly just how one or another person interprets, our theoretical understanding of things we cannot observe and measure directly.
Out of curiosity I did a little searching "A complete online course on relativity is available, entitled Reflections on Relativity by Kevin Brown." http://scipp.ucsc.edu/~haber/ph171/index.html#sec9
That was kind of my point. I can find reference to what he writes, but little in the way of who he is.
He's prolific. Check all the books he's written on scientific subjects. I've been referring to Reflections on Relativity for at least 15 years. It's not surprising that you would like his style. http://www.mathpages.com/home/ Where it says 'About Kevin Brown' none is written. Pretty much what I've been able to find out about Kevin Brown. None except he sure knows his physics.
At the risk of distracting from my previous post, I feel it is important to point out in additon that RJBerry's entire approach is flawed, not just the logical proof itself. The idea of demonstrating the reality (or non-reality) of an idea/phenomena through logic alone is Aristotle's failed method of discovering how the natural world works - it is the wrong way to approach the question, as Aristotle himself demonstrated: Aristotle was said to have logically proven that a fly has four legs because that is what is necessary to satisfy bilateral symetry and provide stability. And he never bothered to look at a fly up close to see if he was right. Though he added a lot to mankind's body of knowledge about how the natural world works, a great deal of what he added was wrong and his method so flawed that it stood in the way of advancement. Replacing Aristotle's method with the scientific method, which hinges on observation/experimentation is what brought us out of the Dark Ages.
Black holes Did you see the tv series : curiosity with Stephen Hawkings (episode: Did God Create the Universe) He talks about black holes, i think this is a good theory, i'm not a rocket scientist, but comming from a guy like Hawkings, it makes me think differently about this subject. After all he's one of the most intelligent man on earth!
I'm sorry, I don't have a link to any background information. Kevin S Brown is "elusive". As bruce indicates, he's fairly well respected. I had a google and read "John Baez, Chris Hillman and Dr Kevin Brown were the three main figures from the 1990s on sci.math". I also read Chris Hillman saying he didn't agree with everything in Kevin Brown's Reflections on Relativity. Me too. RJ: see what Russ said too. Sorry mate. Point-singularities don't exist. Hawking radiation doesn't exist. But black holes do.
Farside, can you link to where Einstein agree’s with you that the event horizon has physical significance and it takes forever to get there ? You have been suggesting that nothing reaches the horizon because it takes forever to get there, or if it did get there it would be ‘stopped’ because of infinite time dilation. You make the point of saying Einstein is on your side? Einstein, according to these two sources, thought matter couldn’t collapse down to the required densities to form singularity because of the speed they would acquire in their orbit, not because of your reason of taking forever. Your wiki link, use the reference number 9 to see where that info came from. Your find It comes from ‘The Explanding Worlds of General Relativity‘. This is from that book…. View attachment 6865 Look for the book on google books, page 239. And this is Kevin Brown making the same point… Falling Into and Hovering Near A Black Hole
