Is this an Ill-posed Question?

[Phrak]

Is the query "Do black holes exist?" an ill-posed question?

 

[russ_watters]

Not at all - as long as we are clear on what a black hole is!

 

[Phrak]

Not at all - as long as we are clear on what a black hole is!

Sure enough, you can't get away with anything around here, where every word and phrase is put under the microscope. I think that's why physics is so attractive. Anyway, I have given this some small amount of thought before posting, and have come up with only a half-baked notions of what defines a black hole.

However, the word that disturbs me is 'exist'--and not in any philosophical sense.

For instance, the round trip time to the event horizon and back according to an external observer is infinite, while an infalling observer will measure the time to the (external observer's defined) event horizon to be finite.

There is a distinction to be made between finite and infinite temporal intervals that may require categorizing various meanings of 'exist' when talking about the formation of black holes from collapsing matter.

 

[russ_watters]

However, the word that disturbs me is 'exist'--and not in any philosophical sense.

For instance, the round trip time to the event horizon and back according to an external observer is infinite, while an infalling observer will measure the time to the (external observer's defined) event horizon to be finite.

There is a distinction to be made between finite and infinite temporal intervals that may require categorizing various meanings of 'exist' when talking about the formation of black holes from collapsing matter.

What you have described there is just two different and contradictory mathematical implications/formulations of the theory. It doesn't really have anything to do with whether black holes exist except to describe why/why not. Since they contradict, at least one must be flawed.

The question of whether black holes exist is not a theoretical question, it is an observational question: do we observe objects that fit the description (to whatever precision we require) attached to the word "black hole".

Asking 'Is this theory explaining black hole formation correct' is completely different than asking "Do black holes exist".

 

[Phrak]

Russ, I'm afraid that this question raises such subtle points that those here, who seem to be acquainted with these matters, such as Dale, and DrGreg, might hold themselves in reserve--or it's not really an interesting question.

I should have left things much simpler and asked instead, is the question "can Scharzchild black holes exist" an ill posed question in the framework of relativity.

 

[russ_watters]

Or perhaps they don't see anything useful to discuss in this thread (not quite the same as "interesting"...). Maybe it would help if you explained more why one might consider such questions to be "ill posed".

 

[Dale]

Russ, I'm afraid that this question raises such subtle points that those here, who seem to be acquainted with these matters, such as Dale, and DrGreg, might hold themselves in reserve--or it's not really an interesting question.

For my part I just don't like questions about whether or not something exists. They almost always seem to bog down into a purely semantic argument about the definition of "exist".

 

[jim mcnamara]

This is not my discipline, but DaleSpam is correct - this is totally Ontology. The study of existence and being.

My understanding is that there are numerous repeatable observations to support the claim that black holes exist.

Because you can't see something - literally not see it because no light reflects off it - does not mean you cannot establish existence criteria for it. Geological processes and
particles like neutrinos have this in common. I have not personally seen Pangea. No human has. Also there is an incredibly remote probability of a neutrino interacting with pigment molecules in my eye, today. Or any day. So humans cannot see them either.

Your question is not ill-posed, just not germane to this forum. Try posting this in the Philosophy forum where it belongs. IMO.

 

[atyy]

It may be ill-posed.

http://relativity.livingreviews.org/Articles/lrr-2004-10/
Isolated and Dynamical Horizons and Their Applications
Abhay Ashtekar and Badri Krishnan
"The future event horizon is defined as the future boundary of the causal past of future null infinity. While this definition neatly encodes the idea that an outside observer can not ‘look into’ a black hole, it is too global for many applications. First, since it refers to null infinity, it can not be used in spatially compact space-times. Surely, one should be able to analyze black hole dynamics also in these space-times. More importantly, the notion is teleological; it let's us speak of a black hole only after we have constructed the entire space-time. Thus, for example, an event horizon may well be developing in the room you are now sitting in anticipation of a gravitational collapse that may occur in this region of our galaxy a million years from now. When astrophysicists say that they have discovered a black hole in the center of our galaxy, they are referring to something much more concrete and quasi-local than an event horizon. Is there a satisfactory notion that captures what they are referring to? "

 

[pervect]

We know that there's a very massive object at the center of the galaxy. We don't know that it has any sort of event horizon, we just know it's too big to be anything else but a black hole according to GR, there's a limit on the possible mass that a star could have, and its well over that limit. We also know that it's not emitting a lot of radiation (IR, I belive, is needed to see in that region) so that it appears black to us, as well as being very massive.

 

[atyy]

http://www.perimeterinstitute.ca/Outreach/Black_Hole_Bistro/Black_Hole_Bistro_Overview/

 

[Phrak]

This is not my discipline, but DaleSpam is correct - this is totally Ontology. The study of existence and being.

My understanding is that there are numerous repeatable observations to support the claim that black holes exist.

Because you can't see something - literally not see it because no light reflects off it - does not mean you cannot establish existence criteria for it. Geological processes and
particles like neutrinos have this in common. I have not personally seen Pangea. No human has. Also there is an incredibly remote probability of a neutrino interacting with pigment molecules in my eye, today. Or any day. So humans cannot see them either.

Your question is not ill-posed, just not germane to this forum. Try posting this in the Philosophy forum where it belongs. IMO.

Philosophy is the love of never-ending debate where the flavor of every word spurs differences of opinion to no end. The intent is to perpetuate never-ending debate. Physics is about ending the debate and moving forward; to establish concrete foundations established on physical evidence. I thought I made this intention clear.

Can you make any?

 

[DrGreg]

Russ, I'm afraid that this question raises such subtle points that those here, who seem to be acquainted with these matters, such as Dale, and DrGreg, might hold themselves in reserve--or it's not really an interesting question.

I should have left things much simpler and asked instead, is the question "can Scharzchild black holes exist" an ill posed question in the framework of relativity.

The mention of my name woke me up, eventually...

I should start by saying that by no means am I a black hole expert. I paddle in the shallow waters only; there are others in this forum who are more competent to move to the deep end.

Are you really asking about when a black hole exists, given that a hovering observer can wait an infinite time and still not be able to say "there's a black hole over there right now, according to my time coordinate"?

We have a problem with the English language. We have verb tenses for past, present and future, but nothing to express the concept of something occurring outside our spacetime coordinate system. If we can't assign a time coordinate to an event, and we can't see the event with our eyes (or radio receivers or whatever), does that mean the event doesn't happen?

I don't know if you are familiar with Rindler coordinates and the Rindler horizon. If you are in deep space, where gravity can be assumed to be zero, and you are in a constantly accelerating rocket, you will experience "pseudogravity" due to your acceleration a and an "apparent horizon" will form at a distance of c²/a behind you, as measured by yourself. This horizon behaves remarkably similarly to the event horizon of a black hole. Nothing, not even light, can pass through the horizon towards you. If you "drop" something out of your spaceship, it falls towards the horizon but never actually quite gets there. You see it slow down as it approaches the horizon and its image is red-shifted. Even if you calculate its position after allowing for propagation delays, it still never reaches the horizon. But of course from the perspective of the dropped object, it reaches, and passes through the "horizon" in a finite time -- in fact, a horizon cannot be detected at all.

Take a look at the spacetime diagram attached to this post. Look at the left-hand diagram only, in which the horizontal and vertical grid is just standard inertial Minkowski coordinates. The black line is an accelerating observer. Each red line is a constant distance from the observer in his own frame. Each green line is a line of simultaneity in his own frame. So the red and green gridlines are the observer's coordinate system i.e. Rindler coordinates. Any event that occurs in the blue region will never be seen by the observer -- the light from that event, traveling in a "northeast" direction on the diagram, never reaches the black line of the observer. An object "dropped" from the spaceship at time t=0 follows a vertical line (x=0) on the graph, passing into the blue zone when t=10. But the observer never sees this. The event (t=10, x=0) in inertial coordinates becomes (T=∞, X=−10) in the observer's Rindler coordinates, and beyond that point the events have no Rindler coordinates at all.

Does it make sense to say the events in the blue zone "do not exist" because the observer never sees them and is incapable of assigning time coordinates to them?