I too do not believe in black-holes.
RJBeery said:3) Any reasonable definition of concurrent existence between two points in spacetime must have a spacelike interval
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.Please justify this definition.
When a space-like interval separates two events, not enough time passes between their occurrences for there to exist a causal relationship crossing the spatial distance between the two events at the speed of light or slower. Generally, the events are considered not to occur in each other's future or past. There exists a reference frame such that the two events are observed to occur at the same time, but there is no reference frame in which the two events can occur in the same spatial location.
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.Russ_Watters said:How do you define "event horizon"? Consider the following:
If one defines the event horizon as (or simply lists as one of its features) the line that separates events that cannot be causally linked to us from those that can, then the definition of "event horizon" includes #4 and your logic proves that black holes exist, not that they don't. In other words; yes, as an outside observer, we can never see an object pierce the event horizon or see what is going on behind it. That's a feature of black holes, and proof that they do exist, not proof that they do not exist.
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.The origin of the Kruskal diagram is conventionally located at the junction between all of regions I, II, III, and IV. It's a very specific location in space and time. You can certainly consider the point of view of an observer there, but you can't pretend all observers are there.
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.
Fair enough: we can never see them in our past: they are always in our future.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.
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'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.
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.in general, do you think it is or should be required that you witness something happening before you can conclude that it happened?
And that "something" is witnessing an object cross the event horizon?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.
Thus, black holes exist because they are observed to exist.
I've referred to The Formation and Growth of Black Holes by Kevin Brown.
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
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
I just glanced at the Preface and realized I like his writing style. Thanks for the link.
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.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?
Me too.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.
I'm not one for religion, Beer w/Straw.
Have a read of the history of the Schwarzschild metric.
See where it says major players in the field including Einstein believed the singularity at the Schwarzschild radius was physical. I'm with Einstein. See this:
"In 1939 Howard Robertson showed that a free falling observer descending in the Schwarzschild metric would cross the r = r[sub]s[/sub] singularity in a finite amount of proper time even though this would take an infinite amount of time in terms of coordinate time t".
Imagine a free-falling observer started falling a billion years ago. He hasn't crossed the r[sub]s[/sub] singularity yet.
Ironically, considering that black holes have become one of the signature predictions of general relativity, the theory’s creator published arguments purporting to show that gravitational collapse of an object to within its Schwarzschild radius could not occur in nature. In a paper published in 1939, Einstein argued that if we consider progressively smaller and smaller stationary systems of particles revolving around each other under their mutual gravitational attraction, the particles would need to be moving at the speed of light before reaching the critical density.