QM + GR = black holes cannot exist

[nimbus]

Much as I disapprove of this "Farsight bashing" by members who seem to have no other interest than this (and certainly no demonstrated physics or maths knowledge), let me pick him up on a rather serious mis-reading.....

Farsight is fond of quoting Einstein's Leyden address, which I confess I haven't read. I paraphrase - "space-time is neither homogeneous nor isotropic." This, Farsight claimed, IS spacetime curvature (due to gravity)....

...Look - by "inhomogeneity" E. means that spacetime (the spacetime 4-manifold) cannot be covered by a single coordinate chart - in this circumstance of course this manifold is not literally (globally) flat, which is well known

By "non-isotropic" he appears to mean that the metric is semi-Riemann - that is that not all coordinate functions carry the same sign. Again this is well-known to differential geometers.

So, yes, Farsight is correct in this restricted sense, but seems not quite to understand why.

Sometime ago I said this (below) to farsigth when talking of this "inhomogeneity and isotropic" space.
Here

It’s telling us, that the spatial geometrical properties far away from mass are flat throughout or homogeneous throughout or Euclidean.
As against, the altered geometrical properties of space near a massive object. In other words, near mass, space is not homogeneous throughout in its geometrical properties.

You can read Farsight's reply, something about space being 'conditioned', I said that's old talk for altered. By altered I mean... you can't use Euclidean geometry thoughtout all spacetime.
Model gravity with forces or model it with an altered spacetime geometry, it doesn't matter if you get results explaining observations and making predictions who cares, since no one knows what gravity is for a fact.

To me, what you said about

"inhomogeneity" E. means that spacetime (the spacetime 4-manifold) cannot be covered by a single coordinate chart - in this circumstance of course this manifold is not literally (globally) flat, which is well known"

Seems to say the same thing, since a local frame can only be across a flat spacetime, tangent space, where your coordinates hold, in other words, in your local frame you can use Euclidean geometry.
Although the distant observer can use global Schwarzschild coordinates, but that's at the expense of 'seeing strange' things like a rock never reaching the event horizon because of slowing down, and other things.

 

[Farsight]

...who cares, since no one knows what gravity is for a fact.

I do. It's simple. Read this.

 

[Tiassa]

In Transition

As Professor Moore said, light doesn't get out because the light is stopped. The speed of light is zero. So that spin at nearly the speed of light is a problem.

The thing is that I am neither physicist nor mathematician, but the problem with your argument is so glaring that it's damn bloody apparent even to me.

Think of it this way:

←←←←|→→☀←←|→→→→​

The only way your point makes sense is if the gravitational influence of the singularity absolutely ends at the event horizon.

And that is observably absurd.

There would be no visible accretion disk if influence ended at the event horizon. Indeed, the vectors on which any light is traveling would not bend under gravitational influence if that was how gravity worked. But we already know that gravity does not work that way.

Thorne expects to get at least one paper published out of this, and maybe two. We don't allow monetary gambling here, so I'm uncertain what wager anyone could challenge you to, as I'm pretty sure none of us want to see you do a naked ice bucket challenge, but I am as certain as I can be that neither of those papers will include or even involve an absolute boundary for gravitational influence at the event horizon.

I may not be a physicist, but one doesn't need to be. I never got past PHYS122, because I was just filling my science credits with those classes. However, even I can tell that you're wrong.

In that far-off future that we imagine through impossible science fiction, when instead of chucking robots at comets we can shoot them out like an Imperial star destroyer, we'll be deploying probes at singularities like the czars threw peasants at the German guns. One of the most fascinating sights in the Universe, scientifically or aesthetically, will be found just outside the event horizon, where the light barely exceeds escape velocity.

That is to say, there is a transitional zone, and in order for your argument to make sense, there cannot be.

 

[nimbus]

I do. It's simple. Read this.

farsight, Is that based on your absolute frame thing, where time stops at the event horizon for all frames, including the in-faller's?
Spacetime is perfectly well behaved there for the in-faller, time does not stop for him.

 

[QuarkHead]

That's incorrect. Einstein said
space is neither homogeneous nor isotropic.

Space isn't curved where a gravitational field is. It's inhomogeneous.

No he doesn't. He means space is non-isotropic. That it isn't the same
in all directions. .

Then perhaps you can explain why the inhomogeneity and anisotropy of the spatial component of spacetime "compels us" to use a metric with 10 components.

For guidance notice that "space" in GR is 3-dimensional, so the matrix representation of any metric here can be AT MOST 3 x 3, whereas, if you work in 4-space your components are represented as a 4 x 4 matrix, and if it is symmetric (i.e. invertible) you easily reduce these components to $$\frac{4(4+1)}{2}=10$$ independent ones

No doubt you can help us; I for one am confused by what you are saying.

PS an argument free of quotes and analogies would be ideal

 

[tashja]

Hello, Rajesh Trivedi. Here's Prof. Moore's reply:

If a star has collapsed to an extent that its radius has fallen below Rc, then doomed. For r < Rc it is actually r = 0.

The prof statement is unintentionally off the mark when he says " as measured by an observer on the surface". actually inside the EH, time has only spatial meaning, that is a singular move from r = Rc to r = 0. I do not think it can be calculated (or even sensible ?) to find out the time in surface reference for travel of surface between r = Rc to r = Rc/2 etc.

Prof. Moore:

The respondent is thinking about the Schwarzschild t coordinate. Inside the event horizon, t has a spatial meaning, and the Schwarzschild r component has a time meaning (with r = 0 in the future). So the person is correct that one cannot assign a sensible t-coordinate difference to the observers travel to r = 0.


However, I was thinking about the time that the observer measures with his/her own clock, that is, the observer's proper time. This time is not linked to the Schwarzschild t-coordinate inside the event horizon. Once the observer has passed through the event horizon, the time that his/her clock measures is well defined and finite (indeed, for a solar-mass black hole, very short) to get to r = 0.

One of the core features of GR is that physics is completely ordinary in freely falling frames. So the observer's clock will run just fine inside or outside the event horizon. That is the time I was referring to.

 

[paddoboy]

That's incorrect. Einstein said space is neither homogeneous nor isotropic. And note this Baez article which says this:

"Similarly, in general relativity gravity is not really a 'force', but just a manifestation of the curvature of spacetime. Note: not the curvature of space, but of spacetime. The distinction is crucial."

Space isn't curved where a gravitational field is. It's inhomogeneous.

The inhomogeneous nature of space, or more correctly spacetime, is "curvature"...Simple as that.
Oh, and of course.....
Henceforth, space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.
H. Minkowski:

 

[paddoboy]

And if you put a stopped observer in front of a stopped clock, you still have an undefined result. Zero divided by zero is not one. It is undefined. The stopped observer does not see the stopped clock ticking normally "in his frame". Light has stopped. So he sees nothing.

Your mistake!
For the umpteenth time, nothing is seen to stop in any FoR....Light does not stop, clocks to not stop. From any remote FoR, they are redshifted and gravitationally dilated to infinity.
From any local frame of anyone or any thing falling into the BH, nothing is seen to happen. No redshift, no time dilation, and one will cross the EH and reach the Singularity in a finite amount of time.

 

[paddoboy]

I do. It's simple. Read this.

No you don't. You are giving a description. You fail to tell us why curved spacetime in the presence of mass, should exhibit the phenomenon we call gravity.
We certainly know that happens but we do not know what gravity actually is...FACT!

 

[paddoboy]

Hello, Rajesh Trivedi. Here's Prof. Moore's reply:

I like the final paragraph.....

One of the core features of GR is that physics is completely ordinary in freely falling frames. So the observer's clock will run just fine inside or outside the event horizon. That is the time I was referring to.

 

[tashja]

Thanks tashja. I'm a little surprised by the reply from S Shapiro, in that he hasn't answered the question.

Perhaps he needs reminding of this: "The proposed experiment was designed to verify the prediction that the speed of propagation of a light ray decreases as it passes through a region of decreasing gravitational potential". The reply by Baez looks better, though I think he made a typo when he said it actually does slow down as it ascends. It speeds up. Again for reference:

This is essentially the same answer as Moore's correct answer: the light doesn't get out because it's stopped. Good stuff. But he goes on to say this which seem a little confusing:

What chain of reasoning? The question was why doesn't the light get out? And he's answered it correctly. But nevermind. I'm encouraged that nobody has come out with the "infalling space" crackpot nonsense.

You're welcome, Farsight. I'm sorry you are not getting the desired replies from the professors, but as you may well know, they are very busy people and perhaps can't spend too much time focusing on the post's intricacies, and many don't want to get involved in online debates because it's too time-consuming. Actually, I didn't expect we would get this many replies, much less follow-ups, so I was happily surprised when the answers started to roll-in

 

[tashja]

I like the final paragraph.....

One of the core features of GR is that physics is completely ordinary in freely falling frames. So the observer's clock will run just fine inside or outside the event horizon. That is the time I was referring to.

Me too. Prof. Moore's primary research interest is in General Relativity theory and computer modeling of problems in relativistic astrophysics. I thinks he knows what he's talking about

 

[paddoboy]

This is essentially the same answer as Moore's correct answer: the light doesn't get out because it's stopped. Good stuff. But he goes on to say this which seem a little confusing:

What chain of reasoning? The question was why doesn't the light get out? And he's answered it correctly. But nevermind. I'm encouraged that nobody has come out with the "infalling space" crackpot nonsense.

Moore did not say that. The following is what he said....



"As the planet's mass approaches the black hole limit, the signal emitted from the surface will seem to move more and more slowly away from the surface (and will also be seen to be increasingly red-shifted as observed from infinity). When the surface of the planet coincides with the black hole's event horizon, the signal will stop moving outward from the surface (and the redshift observed at infinity will go to infinity). So light no longer escapes.

This also does not contradict the statement about an observer at rest on the surface seeing the signal to have speed c, because as event horizon moves beyond the planet's surface, that surface can no longer remain at rest, but in fact must go to r = 0 in a finite time (as measured by an observer on the surface), just as surely as the past must go towards the future. Even then, an observer on the surface will *still* see the light moving outward at speed c, but from the perspective of the global coordinate system, it is simply that the observer is falling faster toward r = 0 than the signal is.

To understand all this fully, I strongly recommend that the questioner take a course in general relativity!"


That is further supported by....

Prof. Shapiro said:
Once you are inside the event horizon (surface) of a Schwarzschild black
hole, you cannot remain stationary but must fall inward. The
force of gravity, if you like, is sufficiently strong that nothing can
remain or orbit on a sphere of constant area, but must fall inward
and, in a finite time as measure on your watch, plunge into the
singularity at the origin. While you are falling inwards, all light
rays you emit must plunge inward as well.

Prof. Baez said:
It actually does slow down as it ascends... if you time it using a clock on a distant star. Light always has the same speed as measured by someone right next to it. But you've probably heard how "a gravitational field slows down time":

http://en.wikipedia.org/wiki/Gravitational_time_dilation

This means that someone on a distant star will see things near the surface of your super-massive planet moving slower than normally. This applies to light coming out of the planet, too. At some point, the light no longer escapes at all!

None of this stuff makes real sense until you go ahead and do the math. Purely verbal explanations are much too vague. So, I really recommend some books on general relativity to help you get to the bottom of this stuff:

http://math.ucr.edu/home/baez/einstein/node15.html

My rough "explanation" is aimed merely at pointing you toward the weak link in your chain of reasoning."

Now those are the answers from the experts.
My own preference is the spacetime/waterfall/fish swimming upstream analogy.
as follows...
http://jila.colorado.edu/~ajsh/insidebh/waterfall.html
Where it says in part......
"
The picture of spacing falling into a black hole has a sound mathematical basis, first discovered in 1921 by the Nobel prize-winner Alvar Gullstrand2, and independently by the French mathematician and politician Paul Painlevé3, who was Prime Minister of France in 1917 and then again in 1925.
It is not necessary to understand the mathematics, but I do want to emphasize that, because the concept of space falling into a black hole is mathematically correct4, inferences drawn from that concept are correct.

The Gullstrand-Painlevé metric is

ds2=−dt2ff+(dr−vdtff)2+r2(dθ2+sin2θdϕ2)
which is just the Schwarzschild metric expressed in a different coordinate system. The free-fall time tff is the proper time experienced by observers who free-fall radially from zero velocity at infinity. The velocity v in the Gullstrand-Painlevé metric equals the Newtonian escape velocity from a spherical mass M
v=−2GMr−−−−−√
with a minus sign because space is falling inward, to smaller radius.
Physically, the Gullstrand-Painlevé metric describes space falling into the Schwarzschild black hole at the Newtonian escape velocity. Outside the horizon, the infall velocity is less than the speed of light. At the horizon, the velocity equals the speed of light. And inside the horizon, the velocity exceeds the speed of light. Technically, the Gullstrand-Painlevé metric encodes not only a metric, but also a complete orthonormal tetrad, a set of four locally inertial axes at each point of the spacetime. The Gullstrand-Painlevé tetrad free-falls through the coordinates at the Newtonian escape velocity.

It is an interesting historical fact that the mathematics of black holes was understood long before the physics. Einstein himself misunderstood how black holes work. He thought that the Schwarzschild geometry had a singularity at its horizon, and that the regions inside and outside the horizon constituted two separate spacetimes. I think that even today research into general relativity is too often dominated by abstract mathematical thinking at the expense of conceptual understanding.



So much for your "crackpot" inference.
Of course those answers, and the analogies given, do invalidate the "real crackpot" idea, of light stopping.

 

[tashja]

Prof. Olum's reply to Farsight's gedanken:

Prof. Olum:

The original poster is right that the light does not curve round and so is always going radially outward at the speed of light. But if it is emitted at the black hole horizon, it nevertheless makes no outward progress and is trapped in the horizon forever. The situation is somewhat similar to ripples on the surface of a river which is falling over a waterfall. Some of the ripples move upstream at their usual speed, but if they are too close to the brink, they don't make any upstream progress. If the light is emitted from inside the horizon, then it gets closer and closer to the singularity, even though it is always directed outward and moving at the speed of light.

Ken Olum

 

[Billy T]

I don't / can't do GR calculations* but made a short story and posted it here several years ago, which I think uses correct BH physics. In the not too distant future some sick are sent to the hospital in orbit just out side the event horizon of a BH where they wait / age less than a year but back on earth several hundred or even 1000 years have passed and a cure for their illness has been discovered, so the space ship bring (via space time warp?) new ill to the near BH hospital takes them back to earth where an old doctor who's grandfather was not even born when they went to the near BH hospital treats them with the new cure, but they often have psychological problems adjusting to Earth that is 1000 years older than they are.

* This is why I don't enter the discussion. In general I think it un wise to comment on subject I lack the ability to compute / work with. I have no ability with lots of things, so I can only paraphrase what others who can do the work / analysis say, but rarely does real understanding survive the translation into layman's language.

 

[paddoboy]

Prof. Olum's reply to Farsight's gedanken:

Again, appreciate the professional replies tashja....
With the one from Prof Olum, though, while agreeing with the bulk of what he said, I was of the opnion that the light emitted just at the EH but outside, would actually arc or curve back to secumb to the EH, unless it is emitted directly radially away.
Then it will appear to hover forever just outside that EH [as the professor says] which in my understanding reinforces the "space falling in" and "water fall" analogy as I illustrated in my previous post.

My querie is with photons that are not emitted directly radially away.
I was always of the opinion that with that scenario, from a local FoR, they would indeed arc back and secumb to the BH's EH.
Not wanting you to wear out your welcome, but if that position could be clarified, I would appreciate it.
Thanks.

 

[paddoboy]

* This is why I don't enter the discussion. In general I think it un wise to comment on subject I lack the ability to compute / work with. I have no ability with lots of things, so I can only paraphrase what others who can do the work / analysis say, but rarely does real understanding survive the translation into layman's language.

One can only do the best he can, and speaking as a layman, I have read plenty of what I see as reputable books, [by Thorne, Davis, Rees, Hawking, Begalman, Kaku, and others] listened and learned from reputable forum frequenters here and elsewhere, and apply a smidgin of common sense.
I harp on the scientific method, the peer review system, why our alternative hypothesis pushers do not align with that system, and apply in my opinion some common sense and logic.
That common sense and logic I see as...
[1] Mainstream theories become mainstream because they have run the gauntlet and passed....
[2] In most cases, the reputable scientist is hard at it at the coal face, and would not have too much time to frequent forums such as this.
[3]There is no reason why anyone with any alternative hypothesis should not be able to put in the hard yards and through the scientific method, undergo the proper peer review.
[4] Most though offer conspiracy crap regarding the intrangensence of mainstream science and unfair treatment.
That coupled with my limited knowledge, but reasonable logic, has me forming the opnions that I do have.
In actual fact, I'm quite an Imaginative and Innovative sort of bloke, but what I speculate, and what others speculate, without observational/experimental or mathematical evidence, must remain just that....speculation.

 

[RajeshTrivedi]

Hello, Rajesh Trivedi. Here's Prof. Moore's reply:

Thanks Tashja...

I messed up the fact that 'proper time' equations under gravitational impact in Schwarzchild solution is for a frame which is situated at a distance r. Certainly this will not make a sense if r < Rc, not only mathematically (results into negative Sqrt) but qualitatively also as at r < Rc none can stay put, it has to necessarily move into r= 0, in a free fall, and as prof Moore reminds us the basic postulate of relativity that under free fall frames are gravitational invariant. Mathematically this time is 2Rc/c (from EH to r = 0), but how an observer sees this time (due to gravitational time dilation) at earth...no comments.

Can we say that we cannot have any fixed FOR between r = 0 to r = Rc ?? The only FOR which we can have is under free fall only in this range.

 

[paddoboy]

Can we say that we cannot have any fixed FOR between r = 0 to r = Rc ?? The only FOR which we can have is under free fall only in this range.

If that's the same as saying that all paths lead to the Singularity and oblivion, between the EH and the Singularity then I say BINGO!!!

 

[tashja]

Thanks Tashja...

No problem, Rajesh.

Again, appreciate the professional replies tashja....
Not wanting you to wear out your welcome, but if that position could be clarified, I would appreciate it.
Thanks.

I forwarded your post, Paddoboy. I'll post a reply if I get one. In the meantime, here's Prof. Begelman's comment on Farsight's thought experiment:

Prof. Mitch Begelman:

I think the key assumption is that you are somehow able to remain stationary at the surface of the planet as it becomes a black hole. At the instant that the horizon engulfs the surface of the planet you actually would feel infinite gravitational force --- you only feel zero gravity if you are in free fall. The beam from the laser pointer then undergoes infinite gravitational redshift while rising an infinitesimal distance. This means that a photon carries no energy in an upward direction.