Black Hole Paradox?

[Slinkey]

I wonder what people's thoughts are on this:

 

Imagine we are watching someone fall towards a black hole (BH) from a given distance above the event horizon (EH).

 

According to every book I have read, for observers outside the EH it will take an infinite amount of time for the person to reach the EH due to gravitational time dilation. ie. we will never see them cross the EH. (I'm ignoring redshifting here so please no arguments about not being able to see it due to the light coming from the person being redshifted towards infinity).

 

For the person falling towards the BH they will cross the EH and be destroyed.

 

According Hawking-Bekenstein Radiation, a BH does not exist for an infinite amount of time because it will eventually evaporate and we can calculate a finite time for its existence.

 

As it takes an infinite amount of time to watch someone reach and cross the EH for all reference frames outside the EH, and the BH will evaporate in a finite time, can we ever see anyone reach and cross the EH if we are outside the EH?

 

If we cannot see someone reach and cross the event horizon from one reference frame, then how can they fall in and be destroyed from their reference frame?

 

Would there not be two distinct histories?

[CraigD]

Welcome to hypography, Slinkey! :) You come bearing thought on one of my favorite subjects.

 

I wonder what people's thoughts are on this:

 

Imagine we are watching someone fall towards a black hole (BH) from a given distance above the event horizon (EH).

 

According to every book I have read, for observers outside the EH it will take an infinite amount of time for the person to reach the EH due to gravitational time dilation. ie. we will never see them cross the EH. (I'm ignoring redshifting here so please no arguments about not being able to see it due to the light coming from the person being redshifted towards infinity).

...

Would there not be two distinct histories?

I’ve flirted with this question, and approached it in a couple of previous threads, such as Flash-fried Spaghettification and A mass dilation "paradox" though experiment, but you’ve put it as a straightforward question that I’d love to really work out and get some consensus on.

 

Here, in short, is my take on resolving the paradox of crossing the event horizon of a black hole, which an observer in free fall across the horizon measures as taking a fairly short time, while a distant observer measures it as taking an infinite time.

 

The Schwarzschild radius of a black hole is calculated using the mass of within it, but the assumption behind this has a small “domain of self-reference”, because if one includes mass from bodies slightly outside of it, the radius increases so that those bodies are inside it. Thus, as observed by a distant observer, rather than an infalling body traversing the final distance to reach the event horizon, the Schwarzschild radius increases, moving the event horizon toward the body, to it never traverses the distance that General Relativity calculates would require an infinite duration.

 

Although, after long reflection, I believe this resolution is correct, I’ve not encountered it in any professional science literature, nor worked it out in enough detail to considering attempting to publish it in a peer-reviewed journal. Fortunately, hypography is just the forum for discussing it, and maybe, with some help and inspiration, working out the details (after first learning enough physics to do so).

 

PS:

For the person falling towards the BH they will cross the EH and be destroyed.

An object crossing the event horizon of a black will not necessarily experience such great “spaghettification” forces that it’s destroyed. As I discussed here, and later here, these forces become tolerable small as the mass of the black hole becomes large. For example, for a black hole such as our galaxy’s central one, the spaghettification force experienced by 2 50 kg masses separated by 1 m at its event horizon is about 0.064 N, about that supporting a 6.4 gram object against Earth’s surface gravity.

[Fluxus]

Keeping in mind that my grasp of paradoxes is good and of physics somewhat poor... :D

 

"Falling into a black hole" is highly counter-intuitive, but not really paradoxical. What's happening is that there is one event that is perceived in two different ways.

 

The object that crosses the event horizon is passing through such a tremendous distortion in spacetime that it affects how the external observer perceives the event. E.g. if the object is firing a laser directly at the observer, the photons emitted by the laser will become progressively more and more distorted by the gravity of the black hole. I assume that due to the distortion, what is fired by the laser at a high rate would exit at an increasingly slower rate, until finally it cannot escape and the laser "goes dark."

 

I'm not sure why you want to try and omit redshifting, because that is basically the relativistic function that is preventing the outside observer from receiving information at the same temporal rate.

 

I.e. it's not so much that there are "two distinct histories," because ultimately it is only one event that is perceived in two different ways, per the theory of relativity.

 

All that being said, I don't think we will have a full explication of black holes until / unless we can harmonize relativity and QM in some fashion.

[RonHughes]

Lets say the person falling is flailing their limbs around as they fall. What the outside observer will see is the fall-ers limbs will almost stop but his velocity will continue to increase and will disappear from our view. That's my take on the events.

[Slinkey]

Thanks for the welcome, Craig. Pleased to meet you, and happy to see that BHs are a topic that intrigues you as well. :)

 

I think I maybe need to elucidate more clearly what I am stating here so that we can focus on that without getting too sidetracked by other effects that may not be pertinent. I'll emphasise certain words to try and clarify what I am pointing at.

 

For observers outside the EH.

 

1. When an object falls towards a BH it will take an infinite time for it to cross the event horizon. ie. anyone outside the EH will never see the object cross the EH.

 

2. According to Hawking-Bekenstein, black holes evaporate and given a finite time they will eventually disappear completely.

 

Conclusion: BHs evaporate before we can see anyone cross the EH because a finite time is far shorter than an infinite time.

 

For the falling observer

 

This observer crosses the EH and falls to the center of the BH in pretty short order.

 

Conclusion: This contradicts the observations outside the EH.

 

I hope that clarifies the problem better.

 

 

Craig, I followed the two links you posted and they took me to completely different threads! Not sure why that happened. Can you check the links are correct?

 

re: Schwarzchild Radius (SR). My understanding is that the SR is defined by a given mass and the volume of space it would need to be confined within to become a BH. Once the mass has become a BH the SR is the same point at which the EH would be. Although I can understand your conjecture that the SR "moves" to encapsulate mass that is just outside the EH I can't actually see why it would unless the mass has been smeared across the entire "surface" (in quotes because the EH is not an actual surface) of the EH, and even then you could argue that the mass is still not inside the EH and thus cannot be added to its mass although you could define the totality of the BH and the mass at the EH to be a system and take that as a whole. This system would be a BH and an external mass.

 

Re: Spaghettification. This is the other effect I want to ignore so that we can concentrate of the time aspect. I accept and agree that tidal forces reduce at the EH as the mass of a BH increases, however once you have crossed the EH these tidal forces would increase substantially the nearer you get to the singularity.

 

 

Fluxus, pleased to meet you and thanks for the reply. :)

"Falling into a black hole" is highly counter-intuitive, but not really paradoxical. What's happening is that there is one event that is perceived in two different ways.

 

I totally agree. The question I am examining here is which of these two histories is the actual event and if something else is happening to the falling observer than what we assume from our calculations because it is an assumption (albeit a very mathematical assumption) that an object actually crosses the EH.

 

I'm looking at it from the other angle: if what the outside observers see is the event then something entirely different happens when you are falling towards an EH than crossing it and being squished by the singularity.

 

As I understand it, there is no preferred reference frame in relativity (hence its name). Thus to say that someone falls through the EH is to assume an event rather than actually know it occurs.

 

re: redshifting of light. I totally agree with your statement here. As the laser beam falls towards the EH the observer of the light will see its frequency decrease (wavelength increase) until it is eventually shifted so far into the infra-red that it is, to all intents and purposes, undetectable. This is what I did not want to include in the thought experiment so that we can concentrate solely on the time dilation aspect. I hope that clarifies what I meant when I said I want to ignore the redshifting. I don't want to remove why the redshifting happens (as that is pertinent to my question) only how it would affect light.

 

Ron, thanks for your reply and pleased to meet you. Your point seems to contradict every book I have read on the subject. I agree that their arm-waving would appear to slow down and that their velocity should increase but due to the extreme time dilation their apparent velocity would actually start to decrease at a given distance above the EH and hence they will never be seen to cross the EH.

[RonHughes]

When an object approaches an EH is it gaining velocity? It most assuredly is. Your saying that it doesn't gain velocity but is slowing, an absurdity that would defy explanation. Yes if your watching a person approach an EH his clock is slowing but his velocity is increasing.

[Fluxus]

I don't think you can separate the redshift from the distortion in spacetime, because it's the same thing. Any subatomic particle that makes contact with the event horizon will be unable to escape (except as Hawking radiation) and will be distorted for the same reason as it happens to a photon.

 

By the way, I'm not 100% sure this is correct, but my belief is that two aspects resolve the dilemma. One is that Hawking radiation actually escapes the event horizon, and as the particle moves away from the event horizon the effects of the gravitational distortion is reduced. I.e. Hawking radiation still works in this scenario.

 

The other is the Holographic Principle, which (to be very brief and if I have it right) asserts that the interior of the black hole is actually a projection of what's happening on the event horizon. So in a sense, we might say the particle isn't exactly crossing the event horizon, more becoming a part of it.

[Slinkey]

When an object approaches an EH is it gaining velocity? It most assuredly is. Your saying that it doesn't gain velocity but is slowing, an absurdity that would defy explanation. Yes if your watching a person approach an EH his clock is slowing but his velocity is increasing.

 

You seem to have misread what I said and missed out a crucial word. I agreed that you would indeed still be accelerating but that your apparent velocity would seem to decrease. Let me explain in more detail just so you know we are on the same page:

 

Let's say we are hovering above an EH at say 1million km. A finite distance. We drop a clock and let it fall toward a BH, of say 10 solar masses, under the influence of gravity alone. We can calculate how quickly the clock will reach the EH. However, what we see is quite different. What we see is the clock race off and then as it approaches the EH it slows down. Not only do the hands of the clock slow down but the progress towards the horizon appears to slow down too as we can see the clock for far longer (an infinite amount of time according to every book I have read) than it would take to fall to the EH according to our calculation.

 

Conclusion: from our frame of reference the clock must accelerate first and then at a given point will appear to deccelerate. This must be what we see if the clock is visible for an infinite amount of time to cover a finite distance.

 

I hope that clarifies what I said.

[Slinkey]

I don't think you can separate the redshift from the distortion in spacetime, because it's the same thing. Any subatomic particle that makes contact with the event horizon will be unable to escape (except as Hawking radiation) and will be distorted for the same reason as it happens to a photon.

 

I'm not trying to separate the redshift from the distortion. I'm just ignoring the effect on light so that we don't go down the road of saying "the light from the object will be redshifted to infinity and thus will become unobservable". I accept this and it is a given, but it is not what I am discussing here. The thought experiment requires that you can see the object for an infinite amount of time which you could in principle observe. Let's say we have a clock that sends out a time pulse every 1 billionth of a second. At some point above the horizon this pulse will reduce to 1 pulse per second, then every 2 seconds... then every year, then every two years.... then every decade... then every century.... etc. The pulses will get farther and farther apart but they will not stop as the clock will never be seen to cross the EH.

 

By the way, I'm not 100% sure this is correct, but my belief is that two aspects resolve the dilemma. One is that Hawking radiation actually escapes the event horizon, and as the particle moves away from the event horizon the effects of the gravitational distortion is reduced. I.e. Hawking radiation still works in this scenario.

 

I don't quite see the relevance of this. Perhaps you can elucidate?

 

The other is the Holographic Principle, which (to be very brief and if I have it right) asserts that the interior of the black hole is actually a projection of what's happening on the event horizon. So in a sense, we might say the particle isn't exactly crossing the event horizon, more becoming a part of it.

 

With all due respect to Lenny Susskind, I think this is completely wrong. Sure, I accept that all the information within a 3D object can be recorded on a 2D surface (as he went to great pains to clarify and explain in "The Black Hole War"). That does not mean this is actually the case. The problem I have with his idea (and it is only an idea) is why would the formation of a BH turn it into a 2D surface? Not only that but he has extrapolated this to the entire Universe and conjectured that everything we see in the Universe is actually a projection of the 2D surface at the limit of the Universe, like the Universe is a hollow bubble with all the information on the surface of the bubble. This would mean the 2D surface of a BH would also be encoded on that "Universe bubble surface" and it is actually just a hologram too. For me, this explains nothing and seems a massive conjecture to explain away the paradox that I have outlined above.

[Little Bang]

A hypothetical spaceship that can accelerate at a thousand gee's. It also has a powerful light that can be seen from about half a light year away. It starts accelerating away from an observer and about 165 to 168 hours later the light becomes so red shifted that it is no long visible to the observer. This is basically the same scenario as an astronaut falling into a black hole. Long before he reaches the event horizon he would become invisible to any observer far away. The black hole paradox isn't really a paradox. Your trying to show a relationship between two events that have different clock rates and there isn't any way to do that. From the in falling astronaut's perspective he simply sees the Universe go into hyper velocity and the far away observer can't see anything about the astronaut.

[Slinkey]

Thanks for your reply, Little Bang.

 

You have stated precisely what I said we need to ignore in this thought experiment ie. an object becoming invisible due to redshifting. I've already stated that I accept this happens. In this thought experiment however, we are ignoring this and concentrating on what we would see if we could see it.

 

If we could see the astronaut approach the EH he would appear to slow down to a virtual stop and would be visible at just above the EH until the BH evaporates. ie. he would be visible for the entirety of the BH's existence. Our current theory therefore creates a situation whereby the astronaut is visible for the entire time the BH exists (to all reference frames outside the EH), and yet, he has also crossed the EH and been crushed to non-existence at the singularity (from the astronauts reference frame). So either the astronaut is visible for the entire existence of the BH or he will be seen to cross at some time before the BH evaporates. He cannot do both.

 

If he crosses the EH before the BH evaporates then that violates the claim that he will never be seen to cross the EH by any observer outside the EH and time is not infinitely dilated at the EH.

 

If he does not cross the EH before the BH evaporates then that violates the claim that he will cross the EH and be crushed by the singularity.

 

If you want me to expound on my conjecture of what happens then I'll be happy to do so.

[Little Bang]

Scientists say the laws of physics break down at the event horizon. In truth the laws probably start breaking down someplace just outside of it. We both know the paradox that we speak of is not possible just as the grandfather paradox is not possible in our Universe. How could something stop the greatest force that we know of second only to the force that created the BB? My guess as to what's going on is a proton or an electron approaching an event horizon will get spaghettified into a wave whose wavelength is equal to the energy of the particle at that time. Our paradox is really an argument in semantics.

[JMJones0424]

Slinkey- it appears to me that you are committing an error in visualizing the problem. You slide back and forth between two VASTLY different inertial frames of reference and make claims that rely on time measurements. The paradox you describe only exists as a paradox because you are failing to consider the fact that the outside observer and the infalling observer are in two different perspectives that diverge dramatically as the infalling observer approaches the black hole.

 

Inertial frame 1)

Observer sees an infalling astronaut "smear" into the event horizon, forever freezing at that moment for the rest of the existence of the black hole.

 

Inertial frame 2)

Infalling observer passes through the event horizon and (if the black hole is large enough), experiences nothing out of the ordinary at all until he gets closer and closer to the black hole and gets ripped apart due to gravitational forces.

 

Please show the math you used to transform temporal measurements from inertial frame 1 and inertial frame 2. I think if you attempt to do this, you will see why your paradox isn't a paradox at all, but simply a misunderstanding.

[Little Bang]

I could have sworn I said that in #10 and #12.

[Qfwfq]

I could have sworn I said that in #10 and #12.

If you did, you said it in a totally different way. Whether or not you said the same thing, there's nothing wrong with JM saying it, in his own way... :shrug:

[Slinkey]

Scientists say the laws of physics break down at the event horizon. In truth the laws probably start breaking down someplace just outside of it. We both know the paradox that we speak of is not possible just as the grandfather paradox is not possible in our Universe. How could something stop the greatest force that we know of second only to the force that created the BB? My guess as to what's going on is a proton or an electron approaching an event horizon will get spaghettified into a wave whose wavelength is equal to the energy of the particle at that time. Our paradox is really an argument in semantics.

 

I think it is more than a semantic argument personally. I agree that the paradox is impossible hence my questioning of the two viewpoints that do not lead to a mutual singular event. As I understand relativity we consider a singular event and how that event is viewed dependent on reference frame. There is no argument about the event itself only a disagreement on how the event is witnessed from different reference frames.

 

In the example I have given we have contradicting events. ie. one person views the astronaut failling towards the EH but never sees the astronaut cross the EH (ignoring redshift in line with the thought experiment) whereas the astronaut himself experiences destruction at the singularity. These are two distinct events and not a singular mutual event.

[Slinkey]

Thanks for your reply, JMJones. Pleased to meet you.

 

Slinkey- it appears to me that you are committing an error in visualizing the problem. You slide back and forth between two VASTLY different inertial frames of reference and make claims that rely on time measurements. The paradox you describe only exists as a paradox because you are failing to consider the fact that the outside observer and the infalling observer are in two different perspectives that diverge dramatically as the infalling observer approaches the black hole.

 

I don't think this is what I am doing rather the contrary, in fact. You yourself agree that we never see the infalling astronaut cross the EH in your next statement:

 

Inertial frame 1)

Observer sees an infalling astronaut "smear" into the event horizon, forever freezing at that moment for the rest of the existence of the black hole.

 

ie. we never see the astronaut cross the EH for the remaining lifetime of the BH itself. Thus he will always be seen outside the EH until the BH evaporates at which point he would still be outside the BH.

 

Inertial frame 2)

Infalling observer passes through the event horizon and (if the black hole is large enough), experiences nothing out of the ordinary at all until he gets closer and closer to the black hole and gets ripped apart due to gravitational forces.

 

Indeed. Which contradicts the above reference frame.

 

Please show the math you used to transform temporal measurements from inertial frame 1 and inertial frame 2. I think if you attempt to do this, you will see why your paradox isn't a paradox at all, but simply a misunderstanding.

 

I don't have the mathematical capability of doing this at this time as I am in my first year of my Natural Science (Physics) degree course with the Open University, however, consider this:

 

First, let's assume we have a BH with a mass of 1.5 trillion solar masses (extraordinarily massive sure, but this is a thought experiment so permissible). The acceleration at the EH (approx. 10.1 m/s^2) would be almost the same as at the surface of the Earth and the tidal forces would be negligible.

 

1) No matter what height I am above the EH, if I was to drop a clock and allow it to free fall towards the EH it would always reach a point where it appears to have slowed to a standstill. This is true whether I drop the clock from 10 billion metres or from 1 meter. I would never see it cross the EH for the entire remaining existence of the BH.

 

Do we agree that the clock would take an infinite amount of time to "tick"? ie. it would, for all intents and purposes, have stopped for any reference frame (observer) outside the EH?

 

2) Now imagine we are at the EH and hovering there (again, this is a thought experiment so bear with me). We look at our clock and it is ticking just fine. When we look at any clock above the EH it will be ticking infinitely fast. It could be a metre away or ten billion metres away. It would not matter. Any clock would appear to be ticking infinitely fast apart from our clock which would be ticking along normally.

 

Do you agree that any clock that is not at the EH and located above it would appear to tick infinitely fast compared to the clock at the EH?

 

I will continue with my point depending on your agreement or disagreement with my two points above.