The Paradoxical Nature of Black Holes

[Slinkey]

I havent read through the thread but to make it clear - if the background temp is higher than the temp of the black hole the blackhole not only doesnt evaporate, it increases in mass; this increase in mass causes its temperature to DROP, which in turn causes it to gain even more mass (ie slight positive feedback). The same applies when the blackhole temperature goes above background, it loses mass which causes it to gain temperature, which in turn increases the rate of evaporation. ie it will not reach an equilibrium, it will either get bigger or smaller.

 

The original premise was that black holes cannot be entered; specifically, that nothing can be seen to cross the event horizon (for the purposes of this thought experiment we were ignoring gravitational redshifting and tidal forces) by an outside observer due to the time dilation when an infalling object nears the event horizon.

 

So, in order to do this thought experiment correctly you have to take that into account when talking about the CMBR. As the premise was that nothing can be seen to enter a black hole this would include the CMBR. ie. a black hole does not absorb the CMBR as it defies the postulate being put forward. Thus black holes cannot gain mass they can only "evaporate".

 

As to the evaporation itself. I haven't read up on it for a long time but from what I remember the mass loss of a black hole is due to the creation of particle-antiparticle pairs at the event horizon allowing one of the pair to fly off to infinity and the other to fall back into the black hole(!) (whereas normally they would annihilate in short order) creating a mass deficit for the black hole and thus reducing its mass (correct me if I am wrong here. I always welcome correction as the purpose of this discussion was/is to learn more). However, this view of Hawking radiation would defy the postulate of the thought experiment also. Thus when there is particle-antiparticle creation at the event horizon, according to the thought experiment, they must both escape to infinity.

 

Conclusion: the time it takes for a black hole to "evaporate" is less than that postulated by Bekenstein and Hawking.

 

This also means that evaporation of black holes is not subject to the temperature of the CMBR (which is after all just photons at a specific wavelength) and would seemingly be in contradiction to the laws of thermodynamics. This leads to another interesting question: as photons do not fill every point in spacetime what is the actual temperature of spacetime when there is no CMBR photon present? The temperature we measure is not spacetime itself but photons that are whizzing about within it.

 

Further, we call a photon a massless particle and one of the laws of physics is that massless particles must travel at the speed of light. You would therefore assume that if you "pointed" photons in the direction of a black hole they would cross the EH in pretty short order. However, as I reiterated above the premise was that nothing can cross the EH, and a photon is something. So, I postulate that something is happening to spacetime at the EH that allows a photon to continue moving at light speed but to never cross the EH.

 

My idea is that from an outside observers point of view time would appear to slow down for an object as it approaches the EH but not only that but spacetime is being "compressed" as well. ie. as an object falls towards an EH it finds there is an infinite distance to be crossed before it can get there, and in that time the BH will have evaporated before it can actually cross the EH.

 

Call me crazy if you like, but I find BHs to be so bizarre as to be impossible and what we call a BH is actually something that was approaching infinite density but evaporates before it can get there. It's the whole reason I have embarked on a physics degree because this question needs to be answered. I'm not saying that I will ever have a recognised contribution to this question, only that it has intrigued me so much that I intend to get educated enough to try and answer my own questions.

[imatfaal]

I will read back the thread if I can find time for 6 pages - and from your summary its tough stuff

 

I must admit I find myself at odds with your very opening; nothing can enter =/= nothing can be seen to enter

 

The original premise was that black holes cannot be entered; specifically, that nothing can be seen to cross the event horizon (for the purposes of this thought experiment we were ignoring gravitational redshifting and tidal forces) by an outside observer due to the time dilation when an infalling object nears the event horizon.

 

The fact that Bob in an accelerated exterior reference frame sees nothing cross the event horizon does not mean that nothing can enter a black; all it means is that nothing can be seen from that frame to enter a black hole. Alice in freefall enters the blackhole from her reference frame; Bob sees this in slower and slower motion, dimmer and redder due to the gravity of the blackhole. In the classical two diamond space time diagram of a simple blackhole whilst Bob follows a hyperbolic fixed radius line Alice follows a straight line; Bob never sees Alice cross not because she doesn't but because he is in a different reference frame and no 45deg light-like signal from Alice can ever intersect with Bobs space time line that is asymptotic to the 45deg light-like line.

 

But I will read the thread to see how you have dealt/argued with this. I will also dig out a diagram to better explain the above paragraph.

[MigL]

I will try this again.

 

Let's not consider an infalling astronaut, into a black hole. Let's consider a photon of visible light, with a given amount of energy, approaching the event horizon. Now we all agree that as it approaches the event horizon, it approaches a deep gravity well, and so time slows down. Time will eventually slow to zero at the event horizon so some members assume that since time is at a standstill, the photon cannot actually cross the event horizon.

 

This logic is flawed.

 

We don't actually 'see' the photon slow down, what we see is a lengthening of the photon's wavelength, which tends to infinity at the event horizon. Now one important property of a photon with infinite wavelength is zero energy, ie the photon ceases to exist, since the photon, before it began its journey towards the black hole had an energy inversely proportional to its wavelength. According to the law of conservation of mass/energy, the energy of the photon cannot simply disappear. It has to go somewhere, so the black hole gains the equivalent mass of the photon's energy. In effect THE PHOTON HAS CROSSED THE EVENT HORIZON INTO THE BLACK HOLE.

 

I don't know how some people got the idea that things falling into a black hole stop at the event horizon, but that is not the case. If it were true, it would be impossible for a black hole to form ( think about it ) and this whole argument would be moot.

 

To recap. Things do fall into black holes. Primordial microscopic black holes ( left-overs from the big bang ) do evaporate and probably did so a long time ago or else we would see extreme flashes of gamma rays when their mass becomes less than critical and they explode. Massive black holes, formed from collapsing stars do evaporate, but they continuously ingest more mass than the evaporated amount and so gain mass, not loose it, so in effect they will never evaporate enough to explode and re-enter our space/time ( that may even violate the second law of thermodynamics as entropy would decrease on a very large scale ).

[csmyth3025]

Thanks Imatfaal for the black hole calculator link you provided in post #99. It's very instructive (and handy) for someone like me who doesn't have the math knowledge to make these calculations from scratch. (This is just one example of why the Internet is so great!)

 

I have to agree with MigL's comment:

 

I don't know how some people got the idea that things falling into a black hole stop at the event horizon, but that is not the case. If it were true, it would be impossible for a black hole to form ( think about it ) and this whole argument would be moot.

 

To Slinkey I would offer this bit of logic: If nothing can get past the event horizon of a black hole then all the "stuff" that gets stuck on this imaginary surface will just pile up. As more and more stuff piles up it will increase the gravity of this surface layer until the gravitational acceleration that defines an event horizon moves outward - thus enclosing the stuff that you feel is stuck on the outside of the original event horizon.

 

Whether stuff falls through the event horizon (the mainstream view) or stuff is stuck at the event horizon (your view) and the event horizon moves outward to gobble it up (thus forming a new event horizon onto which more stuff can get stuck) - the net effect is the same. The mass of the black hole increases and the Schwarzschild radius increases in a finite time.

 

Chris

[Slinkey]

I will read back the thread if I can find time for 6 pages - and from your summary its tough stuff

 

I must admit I find myself at odds with your very opening; nothing can enter =/= nothing can be seen to enter

 

 

No problem. I'm at odds with it too but I'm finding it very hard to come to a definite conclusion because of the presumed nature of black holes, and the logic that is entailed from the presumed nature of them.

 

The fact that Bob in an accelerated exterior reference frame sees nothing cross the event horizon does not mean that nothing can enter a black; all it means is that nothing can be seen from that frame to enter a black hole.

 

Indeed. But here's the point - science is about observation. Thus if we do not see something enter a BH then nothing has entered the BH. When science leaves the realm of observation we enter a grey area of postulates that we cannot prove in any way shape or form except maybe in mathematics which (according to Godel) cannot be self-consistent.

 

Alice in freefall enters the blackhole from her reference frame; Bob sees this in slower and slower motion, dimmer and redder due to the gravity of the blackhole. In the classical two diamond space time diagram of a simple blackhole whilst Bob follows a hyperbolic fixed radius line Alice follows a straight line; Bob never sees Alice cross not because she doesn't but because he is in a different reference frame and no 45deg light-like signal from Alice can ever intersect with Bobs space time line that is asymptotic to the 45deg light-like line.

 

Yep, that's the assumption.

 

But I will read the thread to see how you have dealt/argued with this. I will also dig out a diagram to better explain the above paragraph.

 

There's a pretty good diagram in Kip Thorne's "Black Holes and Time Warps".

 

I will try this again.

 

Let's not consider an infalling astronaut, into a black hole. Let's consider a photon of visible light, with a given amount of energy, approaching the event horizon. Now we all agree that as it approaches the event horizon, it approaches a deep gravity well, and so time slows down. Time will eventually slow to zero at the event horizon so some members assume that since time is at a standstill, the photon cannot actually cross the event horizon.

 

This logic is flawed.

 

Actually, no it's not and you explain why it's not below (which I hadn't considered because I was ignoring redshifting for the purposes of the thought experiment).

 

We don't actually 'see' the photon slow down, what we see is a lengthening of the photon's wavelength, which tends to infinity at the event horizon. Now one important property of a photon with infinite wavelength is zero energy, ie the photon ceases to exist, since the photon, before it began its journey towards the black hole had an energy inversely proportional to its wavelength.

 

Ok, I'll now pull the observation card on you here. You cannot see a photon enter a black hole you can only see photons that enter your eye or your equipment thus you are arguing an assumption. You are actually arguing the "trans-plancking problem" in reverse. ie. a photon emanating from a black hole (Hawking radiation) that we measure to have a finite wavelength must've had an infinitely small wavelength at the EH. What you could be doing here is questioning the nature of photons and what we think they are (no one knows what they are - we just measure an effect).

 

According to the law of conservation of mass/energy, the energy of the photon cannot simply disappear. It has to go somewhere, so the black hole gains the equivalent mass of the photon's energy. In effect THE PHOTON HAS CROSSED THE EVENT HORIZON INTO THE BLACK HOLE.

 

You're contradicting yourself. If according to physics a photon reaches an infinitely long wavelength then can it be said to actually exist? What you're actually saying is that black holes exist and they logically create a scenario where they defy conservation of energy - they are redshifted to infinity ie. a wavelength longer than the "width" of the universe - but in order to sidestep it you demand that the photon must've entered the BH (crossed the EH) without actually showing how it can exist at the EH.

 

I don't know how some people got the idea that things falling into a black hole stop at the event horizon, but that is not the case. If it were true, it would be impossible for a black hole to form ( think about it ) and this whole argument would be moot.

 

Which is what Lawrence Krauss argues. If you check above in this thread you'll find the link to his article.

 

To recap. Things do fall into black holes.

 

With respect, that's what we're discussing and you are now assuming the conclusion as part of the premise. ie. begging the question.

 

Primordial microscopic black holes ( left-overs from the big bang ) do evaporate and probably did so a long time ago or else we would see extreme flashes of gamma rays when their mass becomes less than critical and they explode. Massive black holes, formed from collapsing stars do evaporate, but they continuously ingest more mass than the evaporated amount and so gain mass, not loose it, so in effect they will never evaporate enough to explode and re-enter our space/time ( that may even violate the second law of thermodynamics as entropy would decrease on a very large scale ).

 

It might also violate the conservation of information law as outlined in Leonard Susskind's "The Black Hole War", which I highly recommend. His answer to this paradox, to my mind, is also highly unsatisfactory. He calls it "black hole complementarity" in a similar vein to particle-wave complementarity. ie. something falling toward a black hole both enters and does not enter the BH. Edit: Literally, a black hole creates two histories for anything that falls towards it.

Edited May 14, 2011 by Slinkey

[MigL]

Don't understand your objection to the fact that an infinitely red shifted photon has zero energy, and since energy cannot be destroyed it must end up as added energy ( mass ) to the black hole. Maybe I wasn't too clear in my explanation, or maybe you mis-read.

 

Don't follow your reasoning that

 

"a photon reaches an infinitely long wavelength then can it be said to actually exist?"

 

What does that mean?

 

An existing photon is red-shifted to infinity and CEASES to exist, so the energy/mass must go to the black hole!

Also I only used a photon to make the argument more manageable, but feel free to use an astronaut or a spaceship, they will both 'loose' their mass/energy at the event horizon, and it will have to go to the black hole since a black hole is the ultimate information shredder.

 

Incidentally thesame but reverse argument is responsible for evaporation ( Hawking radiation ). If mass/energy 'appears' next to an event horizon due to virtual particles, then even though the black hole absorbs one of the pair, it must repay the debt to the universe and LOOSES mass/energy ( instead of gaining ).

[alan2here]

For matter it takes an infinite time to reach the black hole from the point of view of an outside observer, or infinite time would have passed after a finite time from the point of view of the matter before it reaches the black hole, either way when the mass gets there the black hole dosn't exist anymore. For a photon is this no longer the case? maybe not, photons are not like other matter. If it is still the case with a photon then the photon won't become infinitly redshifted untill after the black hole has evaporated.

Edited May 15, 2011 by alan2here

[imatfaal]

Slinkey - quite apart from Migl's arguments that I need to think over - this section of your argument I think has a lot of problems

 

Indeed. But here's the point - science is about observation. Thus if we do not see something enter a BH then nothing has entered the BH. When science leaves the realm of observation we enter a grey area of postulates that we cannot prove in any way shape or form except maybe in mathematics which (according to Godel) cannot be self-consistent.

You are making the incorrect assumption that for an observation to be valid it must be able to be made from all frames of reference - the whole concept of SR, lightcones, simultaneity etc showed this to be false. This is a hangover from newtonian physics; the reality of Bob's observations from an accelerated reference frame do not compromise the reality of Alice's observations from the free-falling reference frame. I don't believe you are questioning the nature of blackholes - it is just a lack of engagement with altered frames of reference

[MigL]

Alan2here, your argument/assumptions have more holes than swiss cheese.

 

Slinkey, your argument ultimately reduces to "black holes cannot exist", since they cannot even ingest the original mass/energy that creates them.

If you would like to argue THAT point, I've gotta warn you, I have GR on my side, and helping me with my argument will be Einstein, Swartzchild, Oppenheimer, Wheeler, Kerr, Penrose, Thorne and Hawking.

 

Who's on your side ??

Edited May 15, 2011 by MigL

[alan2here]

I think stars actually tend to colapse into a black hole as a result of a change within them. It's not always mass coming together untill there is enough in one place, for example if a star took on some more mass and as a result had enough gravity to be considered a black hole. It's more that there is already enough mass but the star has structure that holds the star together (or more to the point holds the star appart), this then collapses when the star runs out of some sort of fuell it needs and the star becomes more dense in the process making it dense enough to become a black hole.

 

But if somone is saying that new matter cannot merge with a black hole by reaching its surface then that makes sense, it just adds to the black holes gravity near the black holes surface.

 

It dosn't bode well for my reasoning but the gravitational signals given off by orbiting black holes show a distinct change as they go in a quick step from orbiting to merged.

 

Maybe I'm wrong. I would like to know if I am and to understand why. I can't make it make sence any other way.

 

(the falling observer observes (maybe he can't see it with his eyes but it occurs) infinite time passing out side the black hole before he reaches it's surface, how long the falling observer experances it taking to reach the black holes surface dosn't matter in this case but should be some finite time) and (some or all black holes evaporate to nothing after a finite time) and (the falling observer reaches the black holes surface eventually).

 

A, B and C can all be true on there own. It's (mostly certainly and probably entirely) logically possible in pairs, but certainly paradoxical when all three statements are taken together.

 

Someones reality is going to be way out of whack with somone elses, and it's not just in a relativity thing.

 

It's increasingly hard to get someone away from of a black hole nearer they get to it, so maybe it doesn't matter if there reality becomes out of sync with everyone elses.

Edited May 16, 2011 by alan2here

[MigL]

Alan2here, there are numerous books that describe black hole formation due to stellar collapse. Radiation pressure constantly fights gravitational collapse in large objects like stars. When nuclear reactions no longer supply the outward radiation pressure because the stellar core has become iron, the star, or more specifically the core will collapse.

If the star/core is smallish it will collapse until electron degeneracy ( Pauli exclusion principle for occupation of Quantum States ) starts pushing back and halts the collapse. These are known as white dwarf stars.

Larger stars won't be stopped by electron degeneracy, but will actually force electrons to combine with protons to form neutrons, until the whole core is mostly neutronium and neutron degeneracy stops the collapse. these are known as neutron stars or pulsars.

Even larger stars' cores won't stop at solid neutrons, as a matter of fact we know of no force which can stop the collapse if the core is of a certain size. Even if they blow away most of the mass in a supernova explosion. These are known as black holes.

[Slinkey]

To Slinkey I would offer this bit of logic: If nothing can get past the event horizon of a black hole then all the "stuff" that gets stuck on this imaginary surface will just pile up. As more and more stuff piles up it will increase the gravity of this surface layer until the gravitational acceleration that defines an event horizon moves outward - thus enclosing the stuff that you feel is stuck on the outside of the original event horizon.

 

Assumed black holes we "see" in the Universe have jets associated with them which are obviously firing a great deal of mass away from the black hole at near light speed. These jets clearly cannot emanate from beyond the EH thus a lot of matter is clearly not reaching the EH. This could be enough to halt mass reaching black hole density and extended the EH as you conjecture.

[csmyth3025]

Assumed black holes we "see" in the Universe have jets associated with them which are obviously firing a great deal of mass away from the black hole at near light speed. These jets clearly cannot emanate from beyond the EH thus a lot of matter is clearly not reaching the EH. This could be enough to halt mass reaching black hole density and extended the EH as you conjecture.

From your posts, then, I take it that it's your position that once a black hole initially forms it cannot gain any mass. Is this correct?

 

Chris

[Slinkey]

Don't understand your objection to the fact that an infinitely red shifted photon has zero energy, and since energy cannot be destroyed it must end up as added energy ( mass ) to the black hole. Maybe I wasn't too clear in my explanation, or maybe you mis-read.

 

I don't quite see how that follows as anything but an assumption on your part. A photon cannot have zero energy as that would defy Heisenberg Uncertainty. An infinitely long wavelength would still have an energy value. It would be infinitely small but not zero.

 

Don't follow your reasoning that

"a photon reaches an infinitely long wavelength then can it be said to actually exist?"

What does that mean?

An existing photon is red-shifted to infinity and CEASES to exist, so the energy/mass must go to the black hole!

 

The maximum wavelength anything can obtain cannot be larger than what it is contained within. Thus a wavelength longer than the "width" of the Universe would be less than a whole wavelength and thus cannot exist. Wavelengths don't come in fractions. The wavelength of the photon cannot be longer than the "width" of the Universe. Your assumption is that the photon crosses the EH (and thus adds its energy to the BH) but you yourself say it ceases to exist at the EH. It can't do both. Claiming that it "must go to the black hole" doesn't really cut it from where I'm standing.

 

Also I only used a photon to make the argument more manageable, but feel free to use an astronaut or a spaceship, they will both 'loose' their mass/energy at the event horizon, and it will have to go to the black hole since a black hole is the ultimate information shredder.

 

Which isn't correct either as you will never see anything reach the EH (even if you could see it). As I said above, an object falling toward a black hole would appear to stop moving but it won't actually stop moving. It will continue approaching the EH but never reach it. The closer it gets the slower it gets and because time is infinitely warped at the EH it will take an infinite amount of time for an observer to see anything cross the EH. ie. never.

 

In the case of a photon as it approaches the EH it gets more and more redshifted but it cannot reach infinite wavelength as it is bounded by the width of the Universe. Thus it's energy must always lie outside the EH for to cross it would need to have a wavelength longer than the "width" of the Universe.

 

Nor can the EH horizon "absorb" a photon as the EH is not a surface.

 

Incidentally thesame but reverse argument is responsible for evaporation ( Hawking radiation ). If mass/energy 'appears' next to an event horizon due to virtual particles, then even though the black hole absorbs one of the pair, it must repay the debt to the universe and LOOSES mass/energy ( instead of gaining ).

 

Well, my reading of HR seems to differ slightly to yours. I just dug out my copy of "A Brief History of Time" and will paraphrase: When virtual antiparticle-particle pairs are created near the EH one has positive energy and the other "negative" energy. The one with positive energy becomes a real particle and flies away from the BH whilst the one with negative energy becomes a real particle when it cross the EH (as, apparently, negative virtual particles can become real particles when they cross the EH). Thus a BH loses mass by the ingestion of negative energy ie. energy that is less than zero. The BH doesn't repay any debt to the Universe. The virtual particles becoming real particles - one negative energy, the other positive energy - balances the energy scales for the Universe. I'll let you figure out what the hell negative energy is!

 

This brings up the "trans-planckian" problem. If we measure a photon that has emanated from near the EH and it has a definite value then it has a wavelength smaller than the Planck length when it was created.

 

From your posts, then, I take it that it's your position that once a black hole initially forms it cannot gain any mass. Is this correct?

 

I made two conjectures initially and that was one of them. My other conjecture was that they cannot form at all, and as I learn more about the subject I am increasingly favouring the latter and that they cannot form at all.

 

Alan2here, your argument/assumptions have more holes than swiss cheese.

 

Slinkey, your argument ultimately reduces to "black holes cannot exist", since they cannot even ingest the original mass/energy that creates them.

If you would like to argue THAT point, I've gotta warn you, I have GR on my side, and helping me with my argument will be Einstein, Swartzchild, Oppenheimer, Wheeler, Kerr, Penrose, Thorne and Hawking.

 

Who's on your side ??

 

This is nothing but argument from authority and a known fallacy of argument.

 

As to GR helping you. It is GR that brings up the absurdity of watching something fall towards an EH forever which is what actually prompted my argument in the first place. As Hawking added to the mix that BHs radiate HR then it seems quite plausible that a BH will evaporate before we can see anything cross the EH because we can only ever watch something fall towards the EH but never cross it.

 

You are making the incorrect assumption that for an observation to be valid it must be able to be made from all frames of reference - the whole concept of SR, lightcones, simultaneity etc showed this to be false. This is a hangover from newtonian physics; the reality of Bob's observations from an accelerated reference frame do not compromise the reality of Alice's observations from the free-falling reference frame. I don't believe you are questioning the nature of blackholes - it is just a lack of engagement with altered frames of reference

 

No, it's nothing to do with reference frames. Events happen regardless of reference frame. We might disagree about their duration, position, or order, but events still happen.

Edited May 16, 2011 by Slinkey

[imatfaal]

 

No, it's nothing to do with reference frames. Events happen regardless of reference frame. We might disagree about their duration, position, or order, but events still happen.

 

 

Slinkey - it's everything to do with reference frames. The outside observer is in an accelerated reference frame compared to the free-falling victim. The event happens - the outside observer can never see any form of EMR that comes from that event. The whole point of spacetime diagrams with lightlike lines is to show that some events are not observable by measurement from a distance position or different FoR. You mentioned that you had read the black-hole war - although how you got anything out of it if you cannot believe these foundations - Susskind regularly uses the pond with a drain analogy. If the drain is fast flowing enough there is a point at which the boat with fastest engine cannot escape the drag - if the fastest engine (EMR) is too slow what can send a message? It isn't that a message isn't sent from the striken boat nor that the event didnt take place it's that after a certain point the message itself which has a finite speed cannot get to any observer.

 

 

[MigL]

Check your basic physics, slinkey, a photon's energy is inversely proportional to its wavelength, so when the wavelength becomes infinite, its energy becomes undefined. Alternately, if infinities make you unconfortable, a photon's energy is proportional to its frequency, ie when it becomes zero, the photon has no enrgy.

 

Negative and positive energy are just conventions which make the math more manageable. Read more advanced Hawking, rather than "A Brief History of Time" for a more complete explanation. Always keep the physics of the situation in mind, what exactly would be the properties of 'negative' energy ??

 

I'm at work, will try to get back later for more discussion.

[Slinkey]

Slinkey - it's everything to do with reference frames.

 

Err, no, it's not. The event is outside the EH thus it is in principle observable from any reference frame outside the EH. Secondly, to all outside observers an entity will never be seen to cross the EH the event of crossing the EH does not happen for any observer outside the EH. To argue that in the reference frame of the entity falling towards the EH that he experiences the event of crossing the EH is to argue there are two distinct histories for the entity falling towards the EH. History 1, for all observers outside the EH, and history 2, for the observer falling towards the EH are at odds with each other.

 

Remember the premise is that an object falling toward an EH will continue to fall towards the EH at an ever decreasing rate for all outside observers and will never be seen to cross the EH. As BHs evaporate then the object will not cross the EH before the BH evaporates.

 

So, you have to reconcile two distinct and contradictory histories.

 

Check your basic physics, slinkey, a photon's energy is inversely proportional to its wavelength, so when the wavelength becomes infinite, its energy becomes undefined.

 

And non-zero. Basic physics also tells us that a photon cannot have an infinite wavelength, hence my point that it cannot cross the EH horizon as at that point its wavelength would be longer than the width of the Universe.

 

Alternately, if infinities make you unconfortable, a photon's energy is proportional to its frequency, ie when it becomes zero, the photon has no enrgy.

 

Which means it ceases to exist. Thus preserving Heisenberg Uncertainty.

 

Negative and positive energy are just conventions which make the math more manageable. Read more advanced Hawking, rather than "A Brief History of Time" for a more complete explanation. Always keep the physics of the situation in mind, what exactly would be the properties of 'negative' energy ??

 

Sure, I understand that it's a convention to do with the math. That's precisely the point and hence my statement "I'll leave you to figure out what negative energy is". The one property I am concerned with here is an energy <0.

 

I'm at work, will try to get back later for more discussion.

 

Cool.

[imatfaal]

Err, no, it's not. The event is outside the EH thus it is in principle observable from any reference frame outside the EH. Secondly, to all outside observers an entity will never be seen to cross the EH the event of crossing the EH does not happen for any observer outside the EH. To argue that in the reference frame of the entity falling towards the EH that he experiences the event of crossing the EH is to argue there are two distinct histories for the entity falling towards the EH. History 1, for all observers outside the EH, and history 2, for the observer falling towards the EH are at odds with each other.

 

Remember the premise is that an object falling toward an EH will continue to fall towards the EH at an ever decreasing rate for all outside observers and will never be seen to cross the EH. As BHs evaporate then the object will not cross the EH before the BH evaporates.

 

So, you have to reconcile two distinct and contradictory histories.

Cool.

Your points in order

 

The events outside the EH are observable - the crossing of the EH is not as it is not outside the EH.

 

An event that happens to Alice does not happen to a remote entity Bob in any circumstances; it happens to Alice and is observed by Bob - the difference between the two and the necessity of transmission of this information is where you are failing. There is no history for Bob apart from that communicated from the distant Alice. Bob and all outside observers knows what has happened because they understand the principle that stops any observation from exiting the BH and provides an ever slowing picture of the near approach.

 

Your premise is fine for outside observers - what they see is affected by the gravitational time dilation, but it is only the message/the observation that is affected; Alice ploughs on without even noticing the EH. Time dilation is relative to outside observers it is not internal to Alice's FoR - you do realise that Alice never sees her own clock get slower!

 

 

 

[MigL]

My point, slinkey, is that frequency and wavelength are inversely related , ie a zero frequency is equivalent to an infinite wavelength. When a photon's frqequency becomes zero at the event horizon, its wavelength becomes infinite, and it ceases to exist. Oh, and yes, a wavelength can be greater than its containment, it happens all the time at quantum mechanical levels and leads to what we call tunneling ( Please don't ask me if the infinite wavelength photon can then 'tunnel' out of our universe, because at infinite wavelength THERE IS NO MORE PHOTON ! ).

 

Just a thought, do you think a photon's wavelength is related in any way to its size ( since you say an infinite wavelength means it is wider than the universe and so cannot cross the event horizon ) ????

 

If so, you really need to check your basic physics.

[Slinkey]

My point, slinkey, is that frequency and wavelength are inversely related , ie a zero frequency is equivalent to an infinite wavelength.

 

A zero frequency does not equal an infinite wavelength. Zero frequency equals zero energy and zero wavelength.

 

When a photon's frqequency becomes zero at the event horizon, its wavelength becomes infinite, and it ceases to exist.

 

So nothing passes the EH. As a photon moves toward an EH it's wavelength tends towards infinity.

 

Oh, and yes, a wavelength can be greater than its containment, it happens all the time at quantum mechanical levels and leads to what we call tunneling ( Please don't ask me if the infinite wavelength photon can then 'tunnel' out of our universe, because at infinite wavelength THERE IS NO MORE PHOTON ! ).

 

No, at infinite wavelength you have an undefined but non-zero frequency. At zero frequency you simply have nothing. Tunneling occurs when barriers get so small that their own wave properties come into play and aren't barriers in the classical sense. At quantum dimensions "barriers" is not a meaningful term.

 

This is all moot anyway because you don't see photons unless they hit your retina or equipment and this whole discussion is based upon an entirely ambiguous point which I really should've known better than to discuss.

 

Just a thought, do you think a photon's wavelength is related in any way to its size ( since you say an infinite wavelength means it is wider than the universe and so cannot cross the event horizon ) ???? If so, you really need to check your basic physics.

 

So you want to argue that the size of a photon has nothing to do with its wavelength? You want to think of a photon as a point particle that has a wavelength that is longer than a point?

 

As we are talking about an unmeasured photon it is in a super-position. ie. it is completely uncertain and its size could be anything from planck scales up to infinity.

 

We can't say anything about a photon until we measure it and we measure it by its energy content from which we can infer its wavelength and frequency. ie. when it hits a detector and deposits its energy we can work out its frequency and wavelength from how much energy it registers (or with the eye by what colour you "see"). You may now wonder how a photon can deposit its energy all in one go when it has a "length" which would seem to imply that the energy would take time - proportional to its wavelength - to deposit all its energy, and the longer the wavelength the longer it takes to deposit its energy. Well, a "photon" exists at every point from where it was emitted to where it lands, but "once it lands" the wave-function collapses to that point in no time at all. Thus you could argue that a photon is as big as the distance between where it was emitted to where it is absorbed.

 

Its wavelength could then be described as the distance between these two points divided by a whole number.

 

Your points in order

The events outside the EH are observable - the crossing of the EH is not as it is not outside the EH.

 

No. That wasn't my point.

 

An event that happens to Alice does not happen to a remote entity Bob in any circumstances; it happens to Alice and is observed by Bob - the difference between the two and the necessity of transmission of this information is where you are failing.

 

No, it's not. It's actually where you are failing because you are still failing to understand that you will never see anyone reach the EH if you are outside the EH. It will take an infinite amount of time for them to reach the EH from any observer outside the EH. ie. never.

 

There is no history for Bob apart from that communicated from the distant Alice. Bob and all outside observers knows what has happened because they understand the principle that stops any observation from exiting the BH and provides an ever slowing picture of the near approach.

 

Your premise is fine for outside observers - what they see is affected by the gravitational time dilation, but it is only the message/the observation that is affected; Alice ploughs on without even noticing the EH.

 

No, that's an assumption that you have no evidence for and the point under discussion.

 

Consider this:

I measure the mass of a BH and find it is 5 solar masses. I take Hawking's equations and work out that the BH will exist for 8.268976e+85 seconds. I then dive towards the BH. As I fall toward the BH I look back to where I came from and see that as I get closer to the BH the Universe is speeding up relative to me. At some point before I reach the EH - where time dilation is infinite - the dilation will be so great that 8.268976e+85 seconds will pass in a tiny fraction of a second as measured by me and the BH will have had enough time to evaporate.

 

So when did I cross the EH?

 

I'm sure you agree that 8.268976e+85 seconds is a lot less than infinite, no?

 

Time dilation is relative to outside observers it is not internal to Alice's FoR - you do realise that Alice never sees her own clock get slower!

 

I'm well aware that clocks in the same reference frame tick at the same rate. I think rather it is you that is not understanding what I am saying.

[MigL]

You're now spouting garbage as metre long waves have low enough energy to be localised at a much maller dimension according to Heisenberg's uncertainty principle. Do the math, then you can make such statements. A photon's wavelength is not linearly proportional to its size .

By the way , the definition of frequency is repititions per second. An infinite wave cannot by definition repeat.

 

 

[imatfaal]

1. No. That wasn't my point.

 

 

 

2. No, it's not. It's actually where you are failing because you are still failing to understand that you will never see anyone reach the EH if you are outside the EH. It will take an infinite amount of time for them to reach the EH from any observer outside the EH. ie. never.

 

 

 

3. No, that's an assumption that you have no evidence for and the point under discussion.

 

4. Consider this:

I measure the mass of a BH and find it is 5 solar masses. I take Hawking's equations and work out that the BH will exist for 8.268976e+85 seconds. I then dive towards the BH. As I fall toward the BH I look back to where I came from and see that as I get closer to the BH the Universe is speeding up relative to me. At some point before I reach the EH - where time dilation is infinite - the dilation will be so great that 8.268976e+85 seconds will pass in a tiny fraction of a second as measured by me and the BH will have had enough time to evaporate.

 

So when did I cross the EH?

 

I'm sure you agree that 8.268976e+85 seconds is a lot less than infinite, no?

 

 

 

I'm well aware that clocks in the same reference frame tick at the same rate. I think rather it is you that is not understanding what I am saying.

 

1. if it wasn't your point why did you say

The event is outside the EH thus it is in principle observable from any reference frame outside the EH

Events outside EH are observable - those inside are not.

 

2. you are erroneously linking the event and its observation by a distant third party observer. I know that an observer in an accelerated reference frame will never see Alice cross the event horizon; but I also understand that this does not preclude the fact that Alice does fall through the barrier. It is not two separate histories causing a paradox as you are insisting upon it is a single history and an observation. An observation of a signal by a distant observer does not affect the passage of Alice through space - it is the signal that is affected not the history.

 

3. No - it is widely accepted physics and the reason why you cannot reconcile yourself to agreed views. In order to understand what is happening to Alice in a physical sense you do not calculate her progress using coordinate time what you must do is calculate her progress using a coordinate independent proper time - and she will reach the singularity (let alone the EH) in a finite amount of time.

[math] \tau = \left( \frac{\pi}{2\sqrt{2m}} \right) r^{3/2}[/math]

 

 

4. Immaterial - the black hole could evaporate in a couple of months and my logic would remain. By the way - you are thinking in terms of Schwarzchild coordinate system and that is a bit of a problem; whilst Gravitational time dilation in a the vicinity of a gravitating spherical nonrotating mass can use schwarzchild coordinates with a black hole one must use eddington-finkelstein coordinates. In Schwarzchild coordinate the sums at R=2m are very dodgy indeed as the result is singular and this might be the root of your misunderstanding.

Edited May 17, 2011 by imatfaal

[Slinkey]

1. if it wasn't your point why did you say

The event is outside the EH thus it is in principle observable from any reference frame outside the EH

 

The event of falling toward the EH is outside the EH and is in principle observable by anyone outside the EH.

 

2. you are erroneously linking the event and its observation by a distant third party observer. I know that an observer in an accelerated reference frame will never see Alice cross the event horizon;

 

And you also accept that BHs evaporate, yes? So if you never see Alice cross the EH and the BH evaporates then on which side of the EH was/is Alice?

 

but I also understand that this does not preclude the fact that Alice does fall through the barrier.

 

It's not a fact. It's a conjecture that has never been evidenced except by math that is known to be incomplete.

 

It is not two separate histories causing a paradox as you are insisting upon it is a single history and an observation. An observation of a signal by a distant observer does not affect the passage of Alice through space - it is the signal that is affected not the history.

 

I suggest you read Leonard Susskind's "The Black Hole War" because he disagrees with you. In fact the only way he can reconcile it is by invoking "black hole complementarity" in the same vein as particle-wave complementarity.

 

3. No - it is widely accepted physics and the reason why you cannot reconcile yourself to agreed views.

 

Actually this is still hotly debated.

 

You're now spouting garbage as metre long waves have low enough energy to be localised at a much maller dimension according to Heisenberg's uncertainty principle. Do the math, then you can make such statements. A photon's wavelength is not linearly proportional to its size .

 

So what you're arguing is that the wavelength of a photon can be longer than the photon itself? So we have a wavelength of 1 meter and you are saying the photon would not actually be 1 meter long? Please explain that one to me.

 

By the way , the definition of frequency is repititions per second. An infinite wave cannot by definition repeat.

 

An infinite wavelength would have a non-zero frequency. Period.

[csmyth3025]

The original premise was that black holes cannot be entered; specifically, that nothing can be seen to cross the event horizon (for the purposes of this thought experiment we were ignoring gravitational redshifting and tidal forces) by an outside observer due to the time dilation when an infalling object nears the event horizon.

 

So, in order to do this thought experiment correctly you have to take that into account when talking about the CMBR. As the premise was that nothing can be seen to enter a black hole this would include the CMBR. ie. a black hole does not absorb the CMBR as it defies the postulate being put forward. Thus black holes cannot gain mass they can only "evaporate".

 

As to the evaporation itself. I haven't read up on it for a long time but from what I remember the mass loss of a black hole is due to the creation of particle-antiparticle pairs at the event horizon allowing one of the pair to fly off to infinity and the other to fall back into the black hole(!) (whereas normally they would annihilate in short order) creating a mass deficit for the black hole and thus reducing its mass (correct me if I am wrong here. I always welcome correction as the purpose of this discussion was/is to learn more). However, this view of Hawking radiation would defy the postulate of the thought experiment also. Thus when there is particle-antiparticle creation at the event horizon, according to the thought experiment, they must both escape to infinity.

 

Conclusion: the time it takes for a black hole to "evaporate" is less than that postulated by Bekenstein and Hawking.

This also means that evaporation of black holes is not subject to the temperature of the CMBR (which is after all just photons at a specific wavelength) and would seemingly be in contradiction to the laws of thermodynamics. This leads to another interesting question: as photons do not fill every point in spacetime what is the actual temperature of spacetime when there is no CMBR photon present? The temperature we measure is not spacetime itself but photons that are whizzing about within it.

 

Further, we call a photon a massless particle and one of the laws of physics is that massless particles must travel at the speed of light. You would therefore assume that if you "pointed" photons in the direction of a black hole they would cross the EH in pretty short order. However, as I reiterated above the premise was that nothing can cross the EH, and a photon is something. So, I postulate that something is happening to spacetime at the EH that allows a photon to continue moving at light speed but to never cross the EH.

(Bold added for emphasis by me) This statement is not logical. If nothing can pass through the event horizon either way, the black hole cannot gain or lose mass (or, equivalently, energy) - even over an infinite length of time. I'm guessing that your argument is that neither mass nor so-called "negative mass" (from one of the virtual particle pairs) can pass through the event horizon in a finite time.

 

Lets suppose - for the sake of argument - that an event horizon manages to spring up around a very concentrated point-like mass of 6 x 10^11 kg (600,000,000,000 kg or, alternately, 600 billion kg).

(ref. http://www.wolframal...---.*--&x=8&y=9 )

The Schwarzschild radius for this mass is 8.911 x 10^-16 meters. The diameter of this event horizon would be

1.782 x 10^15 meters. This is about the diameter of a proton.

(ref. http://en.wikipedia..../Atomic_nucleus )

 

By your reasoning, this point-like black hole can never get any larger, nor can it "evaporate".

 

Is this your claim - or are you proposing that it's impossible for black holes to exist at all?

 

Chris

 

Edited to correct spelling errors

Edited May 18, 2011 by csmyth3025

[Slinkey]

Chris,

 

I'm inclined to think they don't exist at all.