Black Holes - not (yet) possible?

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Black Holes - not (yet) possible?

Postby thefreiburger » Sun Oct 07, 2012 12:30 am UTC

The closer an object gets to a black hole, the slower its time passes. At the event horizon, its time would stand still.
If I throw an object into a black hole and watch it from a certain distance, I will see it become slower and slower, coming asymptotically closer to the event horizon, which it will never touch in any finite time (from my point of view).
Therefore we can say that, seen from the outside, no particle of matter has ever crossed the event horizon of any black hole, because it has yet not had infinitely long time to do so.

The black hole itself is completely frozen in time. If I could watch it from the outside (which I cannot, I know), it would stand completely still.

Now what happens, if I watch a star collapsing to become a black hole? I would expect its time to go slower and slower, so that it would never reach the point when it really becomes a black hole, because then its time would already stand still.
This leads me to the conclusion, that there are no black holes in the universe (from our point of view), because they have yet not had infinitely long time to collapse. All there is are almost-finished black holes, matter that is still in the process of collapsing.

Am I getting something wrong here? Because physicists write and talk about black holes all the time, seeming quite sure that they exist. How can they already have formed in "only" 13 billon years, if their should need infinitely long time for that?
Can one of you solve this mystery for me? :D I would really like to understand this matter properly!

If I'm right and there are no black holes (yet), that would solve all the problems we have with singularities, laws of physics failing, loss of information in the universe etc., because almost-black-holes don't cause that kind of problems.
What do you think?

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Re: Black Holes - not (yet) possible?

Postby Thesh » Sun Oct 07, 2012 2:35 am UTC

Isn't there already matter inside the event horizon when a black hole forms? As the black hole consumes large amounts of matter, wouldn't the mass from the matter at the event horizon push the event horizon out, making the matter that was frozen at the event horizon now inside the new event horizon?
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Re: Black Holes - not (yet) possible?

Postby WanderingLinguist » Sun Oct 07, 2012 2:45 am UTC

thefreiburger wrote:The closer an object gets to a black hole, the slower its time passes. At the event horizon, its time would stand still.

I think this is where you've got it wrong. The object's clock (time as perceived by the object) is unaffected as it approaches the event horizon. So it falls in. No problem.

To an outside observer, the object's clock would appear to slow down as it approached the event horizon. But if I understand correctly, you can't observe the object "frozen in time" at the event horizon because there's no way for light from it to get back to you. So basically, as the objects clock slows (from the perspective of a distant outside observer) the object would become fainter and fainter. It would disappear (no more light from it would come back).

So as an external observer, what you would see is the object fall towards the black hole, the objects clock (as you observe it) would slow and the object would fade away. Meanwhile, the object's mass would have been added to the black hole.

So, yes, there are black holes. The best evidence for them is that the effects of them (x-ray emissions, etc.) can be mathematically predicted, and we can make measurements to confirm those predictions.

(But I am not an expert on this; I am sure others on the forum who are more knowledgeable will correct me where I'm wrong... )

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Re: Black Holes - not (yet) possible?

Postby snow5379 » Sun Oct 07, 2012 3:03 am UTC

I don't really understand the concept of an event horizon. A star has the same gravitational pull before and after it becomes a black hole right? I'm sure at some extreme angles you can get really close to any center of gravity.

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Re: Black Holes - not (yet) possible?

Postby starslayer » Sun Oct 07, 2012 3:52 am UTC

snow5379 wrote:I don't really understand the concept of an event horizon. A star has the same gravitational pull before and after it becomes a black hole right? I'm sure at some extreme angles you can get really close to any center of gravity.
Yes, it does, at equivalent distance (provided it hasn't lost any mass, which it's probably lost a lot of). The thing with a black hole is that you can get much, much closer to the center of gravity while still seeing the full mass of the former star. So close, in fact, that it's possible to get close enough to the point where you can't escape by any means short of traveling back in time. The event horizon is the distance from the singularity where this break point between being able to escape and not occurs. It is linear with the black hole's mass, and is about 10 km for a solar mass black hole. If the Earth suddenly became a black hole, it would end up the size of a ping pong ball.

And there are no "extreme angles" with most very massive bodies, including black holes, thanks to spherical symmetry.

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Re: Black Holes - not (yet) possible?

Postby thefreiburger » Sun Oct 07, 2012 7:05 am UTC

WanderingLinguist wrote:So as an external observer, what you would see is the object fall towards the black hole, the objects clock (as you observe it) would slow and the object would fade away. Meanwhile, the object's mass would have been added to the black hole.

How much time would it take the object to "fade away" completely, from my point of view? Finitely long?

WanderingLinguist wrote: The object's clock (time as perceived by the object) is unaffected as it approaches the event horizon. So it falls in. No problem.

That's what I mean. I know that the object itself falls in quite fast without even noticing the event horizon. But that doesn't mean that I will observe the same from the outside, right?

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Re: Black Holes - not (yet) possible?

Postby tesseraktik » Sun Oct 07, 2012 11:21 am UTC

I remember once asking my relativity professor if you couldn't extract information about objects beyond their event horizon by measuring their gravitational pull; I figured that if you throw a massive object into a black hole at one end, you experience that the gravitational pull was ever-so-slightly stronger on that end than at the other one.
The way he put it to me was that when an object reached the event horizon, its position would become an unknowable property to an outside observer; it contributes to the black hole's total momentum, charge and angular momentum, but all of its other properties are mangled beyond recognition.
I don't quite understand why, but I believe the key to understanding it is the no-hair theorem.

[I'm not sure, but I believe that every point on the event horizon is connected by a light-like geodesic, making it almost as though it were a single point, which would help explain why position became unmeasurable at this point. That's just me speculating, though.]

Anyhow, with that in mind, I figure that the answer to your question might be that it doesn't matter if the object stops at the event horizon; a shell of 1000 solar masses (with its radius at the corresponding Schwarzschild radius) would have the same gravitational pull as a singularity with the same mass. If you could determine the position of the energy from the outside, that would constitute "hair", which is not allowed.
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Re: Black Holes - not (yet) possible?

Postby Diadem » Mon Oct 08, 2012 2:49 am UTC

thefreiburger wrote:Am I getting something wrong here? Because physicists write and talk about black holes all the time, seeming quite sure that they exist. How can they already have formed in "only" 13 billon years, if their should need infinitely long time for that?
Can one of you solve this mystery for me? :D I would really like to understand this matter properly!

Ok, let me try to answer this.

First off, yes, time slows down (as seen from the outside) for something falling into a black hole. But it still doesn't take infinitely long for something to fall into a black hole. The reason is that whatever is falling into the black hole causes the black hole to increase in size. So the object falling into the black hole doesn't have to reach the old event horizon, just the new one, for it to be swallowed. This takes a finite time.

But there is a more fundamental error in your thinking here.

Imagine a light-source falling into a black hole. Since time for this light source (as seen by you) slows down, the light gets redder, since the photons are stretched, so to speak. But it also gets dimmer. The object sends out a fixed number of photons per second, but as seen from you, its seconds get longer and longer, so it takes more and more time to send out the same number of photons. So objects falling into a black hole get dimmer and redder.

So far so good. But all matter is, fundamentally, waves (the famous wave-particle duality of quantum mechanics). So it's not just the light from the object that gets redder and dimmer. The object itself gets dimmer. It slowly loses its energy. Where does this energy go? Well, there's only one place it can go. That's into the black hole.

So the picture 'the object takes infinitely long to fall into the black hole' is fundamentally wrong. Yes, we see it take infinitely long (well, not really inifite, because of my first point). But all this time, the object is already transferring its energy to the black hole. The object slowly gets phased out of existence, its energy disappearing into the black hole. So most of the object's energy ends up inside the black hole quite fast.
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Re: Black Holes - not (yet) possible?

Postby Dopefish » Mon Oct 08, 2012 3:53 am UTC

My GR-less understanding of stuff going "into" a black hole is more along the lines of the stuff getting smeared all over the surface of the black hole, such that you can't tell where the stuff came from (taking care of the issue of throwing in a massive object), as well as increasing the black holes size.

I don't know if thats a flawed view at things having no formal knowledge of GR/Black holes, but it seems roughly consistant with most of the stuff I've heard about them and doesn't produce any obvious (to me) paradoxes.

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Re: Black Holes - not (yet) possible?

Postby panther991 » Tue Oct 09, 2012 11:02 pm UTC

I mean it's weird... it's not really relevant... but this sounds a bit like Zeno's paradox

You know, the one about running from one point to another... like it'll take you a finite amount of time to get halfway there, and half that to get a quarter of the way there, and ad infinitum until you're actually not moving anywhere at all

And we know that that's only resolved by using mathematics we have today - differentials and integrals - and maybe speculating about the discrete/continuous nature of space... are the same concepts relevant?

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Re: Black Holes - not (yet) possible?

Postby Tchebu » Wed Oct 10, 2012 2:43 am UTC

The scenario the OP describes neglects the gravitational effects of the infalling matter. If you solve the equations of GR for, say, a collapsing spherical shell of matter, the result is that the event horizon forms at the origin even as the shell is larger than its Schwarzschild radius and then expands outwards as the matter is falling in to gobble it up and it all happens in finite time as seen by an observer at infinity.
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Re: Black Holes - not (yet) possible?

Postby thefreiburger » Thu Oct 11, 2012 6:56 pm UTC

Ok, so basically what I understood was, that the falling object does not touch the event horizon by "reaching" it but the event horizon rather expands and reaches the object, while it is still on its way falling. :shock:
Faszinating.

Which, in consequence means that the only thing, that can escape the event horizon, is the event horizon itself. But shouldn't that be impossible? Information cannot leave a Black Hole, and isn't the event horizon carrying the information "at this point the gravitation reaches a certain threshold value"?

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Re: Black Holes - not (yet) possible?

Postby tms » Thu Oct 11, 2012 7:01 pm UTC

How is knowing what happened outside the event horizon yesterday information about what is inside it today?
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Re: Black Holes - not (yet) possible?

Postby Tchebu » Thu Oct 11, 2012 10:10 pm UTC

The horizon isn't "escaping" it's just changing with time. It's not a physical entity (at least classically speaking), but rather a location in the geometry beyond which geodesics (i.e. "straightest paths") end up trapped within a certain region (i.e. "inside the black hole") for the rest of eternity. No one said that the equal time slices of that surface have to be the same, so the fact that your horizon expands is not a problem.
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Re: Black Holes - not (yet) possible?

Postby p1t1o » Wed Oct 24, 2012 1:45 pm UTC

Just a clarification in case it has slipped by anyone:

Time flows *normally* in the space around a black hole.

However, due to the extreme gravity, you are going to be falling at such a rate that your velocity quickly becomes highly relativistic - with all the time dilation effects that that implies.


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Re: Black Holes - not (yet) possible?

Postby Xenomortis » Wed Oct 24, 2012 1:51 pm UTC

There's gravitational time dilation too; it's very real and isn't the same as time dilation from special relativity.
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Re: Black Holes - not (yet) possible?

Postby p1t1o » Wed Oct 24, 2012 2:45 pm UTC

Xenomortis wrote:There's gravitational time dilation too; it's very real and isn't the same as time dilation from special relativity.


Damnit, I had this niggling feeling that there would be some blasted time/space curvature thingummy. I always thought that the velocity-related dilation was the predominant effect.

A 1-line comment and ten minutes on google to discover I'm wrong, I must be slipping, thanks for the heads-up Xeno.

One interesting thing I just found: apparently gravitational time dilation is measurable even on Earth, and people have been able to measure the difference in time even at altitude changes as little as 1 metre!

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Re: Black Holes - not (yet) possible?

Postby some_dude » Wed Oct 24, 2012 7:09 pm UTC

Diadem wrote:So far so good. But all matter is, fundamentally, waves (the famous wave-particle duality of quantum mechanics). So it's not just the light from the object that gets redder and dimmer. The object itself gets dimmer. It slowly loses its energy. Where does this energy go? Well, there's only one place it can go. That's into the black hole.... The object slowly gets phased out of existence, its energy disappearing into the black hole....


This is incorrect, the de Broglie wavelength of a particle only depends on its kinetic energy so while a particle on its way to the event horizon will appear to redshift infinitely it will only lose its kinetic energy in this process, not its rest-mass energy. And I think the "stolen" energy ends up in the gravitational field just outside the event horizon where the redshifting occurs, anyway. I think the first reason you gave, namely that the event horizon expands, is the correct answer. Another thing to keep in mind is that even if the event horizon didn't expand the infalling matter would in practice still reach the event horizon in finite time as seen from the outside, since it only takes infinite time for an observer who is infinitely far away, which no actual observer ever is obviously.

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Re: Black Holes - not (yet) possible?

Postby Yakk » Wed Oct 24, 2012 7:23 pm UTC

A finitely far away observer falls into the black hole in non-infinite time.

A finitely far away observer who is accelerating has an acceleration event horizon at a finite distance away from it. I believe the particle crosses this first?

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Re: Black Holes - not (yet) possible?

Postby Goemon » Thu Oct 25, 2012 5:32 am UTC

some_dude wrote:it only takes infinite time for an observer who is infinitely far away, which no actual observer ever is obviously.


An infalling particle reaches the Event Horizon when t = infinity as measured by an observer infinitely far away. For a stationary observer at say, (4/3)R_s, where time passes half as fast as the observer at infinity, the particle crosses the Horizon at t = infinty/2. Which is, or so they tell me, still infinity. It takes infintely long from the point of view of any stationary outside observer.

Yakk wrote:A finitely far away observer falls into the black hole in non-infinite time.


Per the same logic as above... even a spaceship that begins near the Horizion, thrusting hell bent downward, still takes an infinite time to actually reach the Horizon from the viewpoint of stationary observers. Silly infinities. They ruin everything.

Yakk wrote:A finitely far away observer who is accelerating has an acceleration event horizon at a finite distance away from it. I believe the particle crosses this first?


The 'acceleration event horizon' for 1g is almost exactly one light year behind you in flat spacetime; the Event Horizon for the Earth - if all its matter were compressed into a Black Hole (but which would still be exerting 1g acceleration on you right now) would only be a few thousand km below. The acceleration horizon is generally a lot farther away. It gets closer as you approach the EH, and they meet as you cross it (I think - not sure how the 'acceleration horizon' gets distorted by the curvature).

p1t1o wrote:However, due to the extreme gravity, you are going to be falling at such a rate that your velocity quickly becomes highly relativistic - with all the time dilation effects that that implies.


Though you crossed this out, I think this bit is actually true. In fact, it's the 'infinite' SR time dilation and length contraction experienced by the infalling observer which cancel out the 'infinities' above. Infinity/2 is still infinity, but infinity/infinity becomes finite: the infalling observer reaches the EH in finite proper time.
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Re: Black Holes - not (yet) possible?

Postby Xenomortis » Thu Oct 25, 2012 8:17 am UTC

Goemon wrote:Though you crossed this out, I think this bit is actually true. In fact, it's the 'infinite' SR time dilation and length contraction experienced by the infalling observer which cancel out the 'infinities' above. Infinity/2 is still infinity, but infinity/infinity becomes finite: the infalling observer reaches the EH in finite proper time.


infinity/infinity isn't necessarily finite, even if defined in the context by some limit.
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Re: Black Holes - not (yet) possible?

Postby Rotherian » Thu Oct 25, 2012 9:24 pm UTC

Xenomortis wrote:
Goemon wrote:Though you crossed this out, I think this bit is actually true. In fact, it's the 'infinite' SR time dilation and length contraction experienced by the infalling observer which cancel out the 'infinities' above. Infinity/2 is still infinity, but infinity/infinity becomes finite: the infalling observer reaches the EH in finite proper time.


infinity/infinity isn't necessarily finite, even if defined in the context by some limit.


I'm no Mathematician, but I believe that any number divided by itself = 1. Unless I'm mistaken, even imaginary numbers follow this rule (as well as infinities). Math majors are free to correct me if my assumption is wrong.
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Re: Black Holes - not (yet) possible?

Postby starslayer » Thu Oct 25, 2012 9:39 pm UTC

Take two limits as x goes to infinity: x/(x+1) and x/(x2+1). The first is one, but the second is zero. Infinity/infinity is not necessarily one, or even finite. Also consider the case of 0/0, which is not one, or necessarily any other number.

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Re: Black Holes - not (yet) possible?

Postby speising » Thu Oct 25, 2012 9:55 pm UTC

2*inf is still inf.
So (2*inf)/inf=inf/inf=2

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Re: Black Holes - not (yet) possible?

Postby Xenomortis » Thu Oct 25, 2012 10:17 pm UTC

Rotherian wrote:I'm no Mathematician, but I believe that any number divided by itself = 1. Unless I'm mistaken, even imaginary numbers follow this rule (as well as infinities). Math majors are free to correct me if my assumption is wrong.


Infinity isn't a 'number', rather it is the concept of "having no limit" or (and this is technically wrong*) "never running out".

Consider the following function:
f(x) = x^2 / x
What occurs when x is arbitrarily large? x^2 grows much faster than x, so even if x is as large as you want, x^2 will be so much bigger that dividing by x will never cancel it out (it leaves x; which is exactly as large as you wanted x to be in the first place :D ).
A more extreme example that doesn't have obvious canceling:
g(x) = exp(x) / log(x)
Both exp(x) and log(x) tend to infinity as x does, but the limit is still infinite.

So when you say infinity/infinity is finite, you first must prove that, not only does a limit exist, but that the two functions that give you your "infinity" as a limit, head to it at close to the same rate.
I was skeptical because the maths involved in general relativity is not simple and I wasn't in a time nor place suitable for checking myself.


*
Spoiler:
This is something that comes up when comparing sizes of sets; you may have heard that there are more real numbers than integers, even though there are the same amount of integers as even numbers. No matter how you try to pair up real numbers to integers, I can always find a real number you missed; you "run out" of integers.
However, this is beyond the scope of my argument.
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Re: Black Holes - not (yet) possible?

Postby Rotherian » Fri Oct 26, 2012 8:47 pm UTC

Xenomortis wrote:
Rotherian wrote:I'm no Mathematician, but I believe that any number divided by itself = 1. Unless I'm mistaken, even imaginary numbers follow this rule (as well as infinities). Math majors are free to correct me if my assumption is wrong.


Infinity isn't a 'number', rather it is the concept of "having no limit" or (and this is technically wrong*) "never running out".

Consider the following function:
f(x) = x^2 / x
What occurs when x is arbitrarily large? x^2 grows much faster than x, so even if x is as large as you want, x^2 will be so much bigger that dividing by x will never cancel it out (it leaves x; which is exactly as large as you wanted x to be in the first place :D ).
A more extreme example that doesn't have obvious canceling:
g(x) = exp(x) / log(x)
Both exp(x) and log(x) tend to infinity as x does, but the limit is still infinite.

So when you say infinity/infinity is finite, you first must prove that, not only does a limit exist, but that the two functions that give you your "infinity" as a limit, head to it at close to the same rate.
I was skeptical because the maths involved in general relativity is not simple and I wasn't in a time nor place suitable for checking myself.


*
Spoiler:
This is something that comes up when comparing sizes of sets; you may have heard that there are more real numbers than integers, even though there are the same amount of integers as even numbers. No matter how you try to pair up real numbers to integers, I can always find a real number you missed; you "run out" of integers.
However, this is beyond the scope of my argument.


Rotherian wrote:I'm no Mathematician, but I believe that any number divided by itself = 1. Unless I'm mistaken, even imaginary numbers follow this rule (as well as infinities). Math majors are free to correct me if my assumption is wrong.


Relevant portions of my post emphasized.
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Re: Black Holes - not (yet) possible?

Postby Copper Bezel » Fri Oct 26, 2012 9:09 pm UTC

Numberphile just had a neat video on the weirdnesses of 0 and ∞. Check it out.
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Re: Black Holes - not (yet) possible?

Postby Xenomortis » Fri Oct 26, 2012 10:19 pm UTC

Rotherian wrote:Relevant portions of my post emphasized.


Consider yourself corrected; I only hope you have some understanding on why you were so wrong.
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Re: Black Holes - not (yet) possible?

Postby Velexia » Sun Nov 11, 2012 5:00 pm UTC

thefreiburger wrote:The closer an object gets to a black hole, the slower its time passes. At the event horizon, its time would stand still.
If I throw an object into a black hole and watch it from a certain distance, I will see it become slower and slower, coming asymptotically closer to the event horizon, which it will never touch in any finite time (from my point of view).
Therefore we can say that, seen from the outside, no particle of matter has ever crossed the event horizon of any black hole, because it has yet not had infinitely long time to do so.

The black hole itself is completely frozen in time. If I could watch it from the outside (which I cannot, I know), it would stand completely still.

Now what happens, if I watch a star collapsing to become a black hole? I would expect its time to go slower and slower, so that it would never reach the point when it really becomes a black hole, because then its time would already stand still.
This leads me to the conclusion, that there are no black holes in the universe (from our point of view), because they have yet not had infinitely long time to collapse. All there is are almost-finished black holes, matter that is still in the process of collapsing.

Am I getting something wrong here? Because physicists write and talk about black holes all the time, seeming quite sure that they exist. How can they already have formed in "only" 13 billon years, if their should need infinitely long time for that?
Can one of you solve this mystery for me? :D I would really like to understand this matter properly!

If I'm right and there are no black holes (yet), that would solve all the problems we have with singularities, laws of physics failing, loss of information in the universe etc., because almost-black-holes don't cause that kind of problems.
What do you think?


I disagree that the singularity itself is frozen in time. The event horizon phenomena is caused by the immense force of gravity relative to the distance from the center of mass. What happens after the critical point at which time stops at the event horizon? I would postulate that time is no longer 'stopped' past the horizon. Mathematically this seems to be true, and that's the best we can get for what happens beyond the event horizon.

I am of the belief/opinion that black holes actually create universes. The inverse of a black hole is a white hole, and the only thing that would fit that is possibly, the big bang. If this is true, then it fits quite nicely... The universe(s) self perpetuates fractally through lower and lower dimensions. Our 6th dimension is simply the 3rd dimension in the universe where our universe is nested (as a singularity). Our 0 dimension is the 3rd dimension one fractal layer below us. These universes are completely cut off at the moment of creation. Nothing enters, nothing leaves.
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Re: Black Holes - not (yet) possible?

Postby Diadem » Sun Nov 11, 2012 5:08 pm UTC

some_dude wrote:
Diadem wrote:So far so good. But all matter is, fundamentally, waves (the famous wave-particle duality of quantum mechanics). So it's not just the light from the object that gets redder and dimmer. The object itself gets dimmer. It slowly loses its energy. Where does this energy go? Well, there's only one place it can go. That's into the black hole.... The object slowly gets phased out of existence, its energy disappearing into the black hole....


This is incorrect, the de Broglie wavelength of a particle only depends on its kinetic energy so while a particle on its way to the event horizon will appear to redshift infinitely it will only lose its kinetic energy in this process, not its rest-mass energy. And I think the "stolen" energy ends up in the gravitational field just outside the event horizon where the redshifting occurs, anyway. I think the first reason you gave, namely that the event horizon expands, is the correct answer. Another thing to keep in mind is that even if the event horizon didn't expand the infalling matter would in practice still reach the event horizon in finite time as seen from the outside, since it only takes infinite time for an observer who is infinitely far away, which no actual observer ever is obviously.

Really? Are you sure?

That would be .. embarrassing.
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Re: Black Holes - not (yet) possible?

Postby gmalivuk » Sun Nov 11, 2012 5:41 pm UTC

Velexia wrote:What happens after the critical point at which time stops at the event horizon?
It's not stopped at the event horizon, though. It merely appears to slow down indefinitely to someone infinitely far away. Which no one actually is anyway. But to folks falling in, nothing special happens at the event horizon.
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Re: Black Holes - not (yet) possible?

Postby Velexia » Sun Nov 11, 2012 10:15 pm UTC

gmalivuk wrote:
Velexia wrote:What happens after the critical point at which time stops at the event horizon?
It's not stopped at the event horizon, though. It merely appears to slow down indefinitely to someone infinitely far away. Which no one actually is anyway. But to folks falling in, nothing special happens at the event horizon.


You are incorrect in regards to needing to be infinitely far away. Welcome to my field, by the way. Time does in fact not exist at the event horizon... nothing will ever reach it.

From the reference frame of a person falling into a black hole, approaching the horizon of a significantly large enough black hole (to avoid the "spaghetti effect") the rest of the universe outside is accelerating in time as you accelerate toward the horizon. As it takes an infinite amount of time from an outside reference frame for you to reach the horizon, in your frame the entirety of time will pass as you reach it. Of course the light will also be moving in a non linear fashion, yet your brain will interpret it as being linear, so you will see the horizon moving up and around you as everything that you once saw all around you quickly becomes a single point of light, which one can only assume will be swallowed entirely should you ever reach the horizon... But for you to reach the horizon, even in your reference frame, time would have to end. My advice? Don't fall into a black hole. The entirety of the universe, it's structure, and time will end, for you, if you do. You probably won't survive the trip to the horizon, but if you do... you definitely won't survive everything ceasing to be (I'm sure it would stop ceasing to be at some point as well, but you'd be done.). Despite all that, all you have managed to do is reach the horizon. There is another infinite expanse of time just to get from the horizon to the singularity. I would say that sounds pretty special...

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Re: Black Holes - not (yet) possible?

Postby gmalivuk » Sun Nov 11, 2012 10:29 pm UTC

Velexia wrote:You are incorrect in regards to needing to be infinitely far away. Welcome to my field, by the way. Time does in fact not exist at the event horizon... nothing will ever reach it.
This is only true in the frame of someone unaffected by the black hole's gravity (i.e. in flat space, infinitely far away).

From the reference frame of a person falling into a black hole, approaching the horizon of a significantly large enough black hole (to avoid the "spaghetti effect") the rest of the universe outside is accelerating in time as you accelerate toward the horizon. As it takes an infinite amount of time from an outside reference frame for you to reach the horizon, in your frame the entirety of time will pass as you reach it.
This is not at all true, because you're meanwhile speeding up and experiencing time dilation as a result, and the light from significantly later on in the universe's history won't have time to reach you before you hit the singularity.

An infalling observer in the Schwarzschild metric hits the singularity in finite proper time.
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Re: Black Holes - not (yet) possible?

Postby p1t1o » Sun Nov 11, 2012 10:37 pm UTC

But stuff DOES actually fall into black holes, right? So some of these infinities flying around here must not extrapolate all the way to the horizon. I'm struggling to think of a way for that not to be true.

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Re: Black Holes - not (yet) possible?

Postby gmalivuk » Sun Nov 11, 2012 10:50 pm UTC

None of the infinities actually happen at the horizon, as that's just a coordinate singularity in the original metric. It's the singularity where stuff blows up to infinity regardless of the coordinate transform we use, so it's only there that General Relativity doesn't have an answer for what should happen.
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Re: Black Holes - not (yet) possible?

Postby Velexia » Mon Nov 12, 2012 3:05 am UTC

p1t1o wrote:But stuff DOES actually fall into black holes, right? So some of these infinities flying around here must not extrapolate all the way to the horizon. I'm struggling to think of a way for that not to be true.


Once the singularity has formed, nothing ever passes the event horizon, or even reaches it. So nothing ever truly falls into a black hole, just toward it. Black holes grow in size by adding mass around the outside of the horizon like a shell, which relative to the outside observer creates a proportionately larger horizon.
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Re: Black Holes - not (yet) possible?

Postby gmalivuk » Mon Nov 12, 2012 3:06 am UTC

Where are you getting this information?

Because that's not at all what the GR equations actually say happens from the perspective of the stuff falling in.
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Re: Black Holes - not (yet) possible?

Postby Velexia » Mon Nov 12, 2012 3:22 am UTC

gmalivuk wrote:This is only true in the frame of someone unaffected by the black hole's gravity (i.e. in flat space, infinitely far away).


This is simply not correct. Yes, gravity, and therefore mass distorts time... what you are seeming to imply is that time dilation is not real, but it is.

It's very elementary: An event horizon is the area surrounding a black hole where light cannot escape (if moving tangentially, it circles the black hole infinitely, there is also a point where even if the light vector is moving perpendicularly away from the singularity it cannot escape, and this is the classical horizon.) Objects falling toward the horizon are accelerating toward it, and as they accelerate toward the horizon their relative mass is increased (F = ma). As this happens the time dilation increases. Because they have mass, the maximum velocity will always be less than c. They will never reach the horizon, they can only approach closer and closer while moving through time slower and slower. This is regardless of which framed of reference you are in. How it is perceived is what is changed when the reference frame is changed.

This is not at all true, because you're meanwhile speeding up and experiencing time dilation as a result, and the light from significantly later on in the universe's history won't have time to reach you before you hit the singularity.

An infalling observer in the Schwarzschild metric hits the singularity in finite proper time.


The light is traveling faster than you ever will, so it will in fact, reach you. You are fundamentally misunderstanding the last thing you said.

gmalivuk wrote:Where are you getting this information?

Because that's not at all what the GR equations actually say happens from the perspective of the stuff falling in.


What you need to ask yourself is where you are getting your information. You have a misunderstanding of what you have read or heard.

My information comes from a lifetime of interest, research, and pursuit of my degree. So I cannot break it down to a single article, book, class, or video for you.
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Re: Black Holes - not (yet) possible?

Postby gmalivuk » Mon Nov 12, 2012 3:31 am UTC

Velexia wrote:
gmalivuk wrote:This is only true in the frame of someone unaffected by the black hole's gravity (i.e. in flat space, infinitely far away).
An event horizon is the area surrounding a black hole where light cannot escape (if moving tangentially, it circles the black hole infinitely, there is also a point where even if the light vector is moving perpendicularly away from the singularity it cannot escape, and this is the classical horizon.)
These are actually at different places. Photons at 3/2 the Schwarzschild radius can circle around indefinitely. Between 1 and 3/2 times that radius, they will either escape to infinity or fall into the singularity. Below 1, which is the event horizon, they will fall into the singularity.

This is not at all true, because you're meanwhile speeding up and experiencing time dilation as a result, and the light from significantly later on in the universe's history won't have time to reach you before you hit the singularity.

An infalling observer in the Schwarzschild metric hits the singularity in finite proper time.
The light is traveling faster than you ever will, so it will in fact, reach you. You are fundamentally misunderstanding the last thing you said.
Light is traveling faster than you, but it's still traveling at a finite speed. Which means that it will not all reach you in the finite proper time you perceive as passing before you hit the singularity (or, more practically speaking, before you get spaghettified by the tidal forces).

We don't even need curved spacetime or General Relativity to have this sort of thing happen. In a perfectly flat universe, if you left home accelerating at a constant proper 1g, then from your perspective looking back at your house you'd see things getting slower and slower, and you'd never see anything that happens more than 1 year after you leave. Even though its light is traveling toward you at c, which is faster than you'll ever go.

This isn't quite the same thing as an infalling observer sees, of course, because there the important thing is that you simply won't have time to see the whole future happen.

Velexia wrote:What you need to ask yourself is where you are getting your information. You have a misunderstanding of what you have read or heard.

My information comes from a lifetime of interest, research, and pursuit of my degree. So I cannot break it down to a single article, book, class, or video for you.
Do your professors know the extent of your misunderstanding?

The notion that an infalling observer hits the singularity in finite proper time is not controversial nor is it obscure.
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Re: Black Holes - not (yet) possible?

Postby Yakk » Mon Nov 12, 2012 3:47 am UTC

Velexia...

Have you considered the possibility that you actually don't know much about relativity?

Have you considered the possibility that you in fact know far less about most things you think you know about than you do?

Have you heard of Mr Dunning and Mr Kruger?

Do you have a PhD in physics? A masters in relativistic physics? An undergrad with final year relativistic maths courses from a reputable university? With that kind of credentials, you might have a valid reason to presume that your knowledge is going to be more on the correct than the incorrect side. If you lack that kind of credentials, and you think you understand relativity, Dunning-Kruger indicates you probably are actually incompetent at understanding relativity (because non-experts systematically overestimate their knowledge of subject areas they aren't experts in).

You need to calibrate your ignorance. It is bigger than you think it is.
One of the painful things about our time is that those who feel certainty are stupid, and those with any imagination and understanding are filled with doubt and indecision - BR

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