State of "matter" of a singularity

[Mitcher]

On 9/11/2022 at 5:13 PM, studiot said:

Intuition can be a misleading process.

The relevant theorem is the original version of Poinsot's theorem which was originally stated in statics, long before vectors were invented.

"Every system of of forces  can be reduced to a single force and a single moment (torque) , either or both of which can be zero. "

This gives rise the the two laws of statics viz that

The sum of forces acting in equilibrium is zero.

The sum of moments in equilibrium is zero.

 

This can be widened to refer to vectors in more modern parlance and to dynamics where they become

https://en.wikipedia.org/wiki/Poinsot's_ellipsoid

 

The point being that any number of rotations can be compounded to become a single rotation resultant, just as any number of forces can be compounded to form a single resultant or net force.

 

So from what your are saying it seems it is impossible to have a sphere simultaneously rotating along 3 axis as it will always result in a rotation around a single axis. It's a fact that we never did observe any celestial sphere rotating around more than one axis to tell the truth. Too bad, I had hopes it could help explain half integer spins, orientations and such.

On 9/11/2022 at 9:36 PM, NTuft said:

and has the remarkably ingenious idea of realizing translations as infinitesimal rotations around infinitely distant rotation axes.

Interesting but it's not the same as a sphere rotating around its own axis.

22 hours ago, studiot said:

OK so here is the simplest form of Maths I know for this subject.

I have marked the starting point page 289, article 217  -  Angular velocites of a body about more than one axis  - on the first attachment.

You will need some simple calculus and trig.

 

That"s spot on, thank you. Do you know how to unload the document ?

13 hours ago, Markus Hanke said:

Imagine you throw a pebble into a pond - what happens? Wave fronts ripple out at finite speed in all directions on the water. Now plot the position of the leading edge of the wave field against a time axis that runs orthogonally to the water surface - you get a cone.

Light cones work in a similar way. They simply depict regions of causality centered on some event.

This representation is interesting, it shows that time has one dimension less than space where light propagates. If we keep the same diagram for a 3D space then time should be a surface ! But back to the pond image, I take it that light propagates along the surface of the cone, right ? To me this is not quite correct, light should be represented by the wave fronts themselves, while the sender of the stone is carried away on the time axis.

13 hours ago, Markus Hanke said:

Of course they don’t - that’s the meaning of “singularity”. It’s a region of geodesic incompleteness, past which geodesics cannot be extended. 

I was meaning the EH, sorry, not the central singularity. Your point is that geodesics continue inside the BH undeterred below the EH, I know.

[Mitcher]

On 9/11/2022 at 7:13 PM, joigus said:

Tidal effects begin to be important long before you reach Planck's scale. Planck's scale is more about quantum effects. The h-bar is giving it away, isn't it?

As you suggested it is possible that tidal forces might be linked to this phenomena but thinking about it I do not think so. In fact, our observer inside the BH not only would not see the mirror behing him but he would not see mirrors in front of him either, for the same reasons. Any light coming to him with the slightest radial component would not reach him at all and he would only perceive is a very thin ring of light around him, orthogonaly to his geodesic -but this has nothing to do with the mass of the BH or tidal forces. Possibly the EP would break down in this part of the Universe. Not only electronic signals would only propagate one way but certainly also sound velocity and strong forces, weak forces and so on. Matter itself would hence break down, if we negate this in the name of EP then we have to admit that some signals could still propagate towards the surface of the BH in a finite time.

[joigus]

31 minutes ago, Mitcher said:

Possibly the EP would break down in this part of the Universe. Not only electronic signals would only propagate one way but certainly also sound velocity and strong forces, weak forces and so on.

If the EP breaks down, then we no longer have GR. If so, why bother with Schwarzschild solution? It would be misguiding us all along. Sound, as well as strong forces, do not exist in that region of space, because it's a vacuum solution.

And yes, tidal forces are important, they're coded in the connection coefficients, and they become the more relevant the farther away you get from the point you choose to expand your metric. The Doppler effect is like the "time-component" of these tidal forces, so to speak. It's coded in the \( \Gamma^{0}_{00} \) of the connection. You can obtain this from the geodesic equation. And sure enough, the observer would notice something funny going on with all kinds of optical effects. What he wouldn't notice is any ficticious forces due to acceleration --provided the horizon is big enough in comparison with his own size. Generally, the 0-component terms are far more noticeable because of the large value of the speed of light.

It's quite an exercise of imagination to picture how an observer might experience such a voyage, but certainly I would expect all kinds of strange optical phenomena. Mirrors not reflecting properly probably being one of them.

Edited September 12, 2022 by joigus
Latex editing

[studiot]

2 hours ago, Mitcher said:

So from what your are saying it seems it is impossible to have a sphere simultaneously rotating along 3 axis as it will always result in a rotation around a single axis. It's a fact that we never did observe any celestial sphere rotating around more than one axis to tell the truth. Too bad, I had hopes it could help explain half integer spins, orientations and such.

Yes and no.

There are real mechanisms that work using separate rotation axes so it depends upon your frame of reference.

Have you heard of Hooke joints or of gimbals for instance ?

 

2 hours ago, Mitcher said:

That"s spot on, thank you. Do you know how to unload the document ?

They are pages scanned  as jpegs.
click on them to expand to full size then just download from the site page.

 

[Mitcher]

On 9/12/2022 at 9:08 AM, Markus Hanke said:

No, it wouldn’t, because the region bounded by the horizon (the presence of which is required to have Hawking radiation in the first place) would still be geodesically incomplete.

As far as I know Hawking radiation has only be theorized, never measured. Actual measurments would be a chalenge to say the least. Wormholes, if they exist, would be unbounded regions, am I right ?

19 hours ago, studiot said:

Yes and no.

There are real mechanisms that work using separate rotation axes so it depends upon your frame of reference.

Have you heard of Hooke joints or of gimbals for instance ?

 

They are pages scanned  as jpegs.
click on them to expand to full size then just download from the site page.

 

Thank you but maybe due to my using a Linux Os i can expand but not download

19 hours ago, studiot said:

Have you heard of Hooke joints or of gimbals for instance ?

Yes, Hooke joints are used to couple rotating shafts at an angle, it's close but not quite since the piece is a deformable object, not a solid one. Gimbals are used in gyros and that could be used to control the rotations of a sphere with the help of eletromagnetic fields maybe or mini electric motors. I had some hopes the sphere could be made to rotate in such a way that it would return to its original position every 3 turns for instance, or one and a half.

20 hours ago, joigus said:

It's quite an exercise of imagination to picture how an observer might experience such a voyage, but certainly I would expect all kinds of strange optical phenomena. Mirrors not reflecting properly probably being one of them.

So that's a starting point. We are are speculating about the presence of a physical object inside the BH so indeed  it would not be a pure vacuum any more. If you agree that light would not propagate properly how can you not agree that any signal slower than light (all of them then) would not propagate normally. I'am just trying to "prove" than matter could not survive as it is inside a BH, even ultra massive ones. As we are at it, space and time would be so much transformed as well that we could probably say that they would not survive either.

[studiot]

33 minutes ago, Mitcher said:

Thank you but maybe due to my using a Linux Os i can expand but not download

Send me a PM with an email address that can receive jpegs and I will let you have better quality copies.

You probably would find it difficult getting hold of the book now in any case.

[Mitcher]

20 hours ago, joigus said:

The Doppler effect is like the "time-component" of these tidal forces, so to speak.

Would there be gravitational Doppler inside a BH or the solutions would be more like inside a hollow sphere ?

2 minutes ago, studiot said:

Send me a PM with an email address that can receive jpegs and I will let you have better quality copies.

You probably would find it difficult getting hold of the book now in any case.

Do you mean a Proton Mail ? Are those files so large ? If you are Admin you might have access to my e-mail... I have no Proton Mail.

20 hours ago, joigus said:

If the EP breaks down, then we no longer have GR.

I agree but there is to be some kind of break-up. An observer just below the EH would see the Universe ending almost instantaneously, that's not quite equivalent to what observers on the outside would see.

[studiot]

13 minutes ago, Mitcher said:

Do you mean a Proton Mail ? Are those files so large ? If you are Admin you might have access to my e-mail... I have no Proton Mail.

No I mean this forum's private messaging system.

I have done this before.

There will be too many to post on that system directly.

I do not want your private e-mail, I suggest something like gmail as I know they can recieve the file sizes I generate.

There will be no colour since the book is entirely B&W, with file sizes in the 250k - 500k range probalbly.

Also I can split over more than one email.

 

Just be aware that many email systems will put unknown senders straight into the spam box.
 

 

 

[Mitcher]

40 minutes ago, studiot said:

No I mean this forum's private messaging system.

I have done this before.

There will be too many to post on that system directly.

I do not want your private e-mail, I suggest something like gmail as I know they can recieve the file sizes I generate.

There will be no colour since the book is entirely B&W, with file sizes in the 250k - 500k range probalbly.

Also I can split over more than one email.

 

Just be aware that many email systems will put unknown senders straight into the spam box.
 

 

 

I didn' find how to contact you tru private messaging here, i have a gmail address yes

[studiot]

8 minutes ago, Mitcher said:

I didn' find how to contact you tru private messaging here, i have a gmail address yes

Click somewhere on my name/ avatar.

At the top on the details about me, next to my name you will se two blue boxes.

The first says follow member

The second says message.  click on that and send your message.

Not even the mods can read it without invitation.

 

[Mitcher]

On 9/11/2022 at 7:13 PM, joigus said:

It's a universal constant just because it's the quotient of two universal constants. 

It happens to have the dimensions of a linear density. That doesn't mean anything in itself.

c squarred and G are probably the most significant constants in Physics, surely their ratio cannot be an insignificant feature, it is at the heart of the BH fabric. Given that everything else like entropy, surface, temperature etc.. depend all on the mass, i think it's a hidden gem.

[joigus]

13 minutes ago, Mitcher said:

c squarred and G are probably the most significant constants in Physics, surely their ratio cannot be an insignificant feature, it is at the heart of the BH fabric. Given that everything else like entropy, surface, temperature etc.. depend all on the mass, i think it's a hidden gem.

No, it's no hidden gem. It's already implied by the maths of a simple exact solution of the theory.

Let me try an analogy. A physicists who's given the solution for the quantum harmonic oscillator tries multiplying the energy of the ground state by the period for different harmonic oscillators. It always gives the same value!!!

Yes, it does because it's h-bar (Planck's constant), as (h-bar)x(omega)xT = h.

That "same value" is nothing other than Planck's constant. It was there from the very beginning.

You feed G and c into your theory. You calculate solutions. They depend on G and c, of course. You get back a certain combination of G and c.

No mystery, is it? 

Be careful, because physics has a way of tricking you into thinking you're getting something new when you're actually going in circles.

[Markus Hanke]

14 hours ago, Mitcher said:

As far as I know Hawking radiation has only be theorized, never measured.

Yes, that’s right.

14 hours ago, Mitcher said:

Wormholes, if they exist, would be unbounded regions, am I right ?

Yes, correct. Do note though that this isn’t the same as geodesic completeness, which is a whole different issue.

[Mitcher]

15 hours ago, joigus said:

Be careful, because physics has a way of tricking you into thinking you're getting something new when you're actually going in circles.

You are absolutely right here, thank you for your patience. However you only wrote that omega.T = 1 basically. Now, say we had h/c^3 for instance, to be exactly equal to a particular linear momentum, this might hilight some missed but very real concept. And actually I think it does, too. Where does this 1.3 x 10^27 kg comes from according to you, it would just be an empty calculus artefact?

6 hours ago, Markus Hanke said:

Yes, correct. Do note though that this isn’t the same as geodesic completeness, which is a whole different issue.

So wormholes have central singularities, is that what you are saying ?

On 9/12/2022 at 9:08 AM, Markus Hanke said:

Imagine you throw a pebble into a pond - what happens? Wave fronts ripple out at finite speed in all directions on the water. Now plot the position of the leading edge of the wave field against a time axis that runs orthogonally to the water surface - you get a cone.

Light cones work in a similar way. They simply depict regions of causality centered on some event.

Please disregard my prevous confused answer to this message, I would like to modify or erase it but unable. On your pond's figure what is the path followed by light according to it ? is it represented by the waves on the surface or along the cone's surface ?

[studiot]

44 minutes ago, Mitcher said:

So wormholes have central singularities, is that what you are saying ?

Folks seem to pick up certain words as 'buzz words' without fully going into their meaning.

In another thread we have someone misusing 'eignestates'.

 

Be sure you are not misusing 'singularity' here.

 

Cambridge Texts in Applied Mathematics.

Singularities: Formation, Structure and Formation.

Eggers and Fontelos

2015

 

By the way you should have an email.

 

[Markus Hanke]

11 hours ago, Mitcher said:

So wormholes have central singularities, is that what you are saying ?

There are many different kinds of wormhole spacetimes - some are geodesically complete (no singularities), some have singularities at the centre, and some have singularities at the throat. So it all depends on the boundary conditions. My point was simply that the concept of boundedness is different from the concept of geodesic completeness. A singularity is not a boundary.

11 hours ago, Mitcher said:

On your pond's figure what is the path followed by light according to it ? is it represented by the waves on the surface or along the cone's surface ?

I’m not really sure what you’re asking here - the purpose of the light cone is only to depict causality. It shows which regions can be causally connected to a specific event.

Imagine that at the point of origin (the event) a signal is emitted in all spatial directions. After one second (straight up the time axis), the signal wave front will have travelled a maximum of 300,000 km (straight across perpendicularly) as measured from the origin - iff it was an electromagnetic or gravitational wave, otherwise it’s less distance. After two seconds it will be 600,000 km, and so on. That’s how the cone comes about - everything within the cone is causally connected to the event, everything outside the cone is not, because the speed of light is limited. The surface of the cone itself is a null surface - it represents the boundary between causality regions, and only light/gravitational waves can reach the distance from the event represented by the surface.

You get the cone by plotting distance vs time, because the signal propagates in all spatial directions equally. In actuality it’s a hypercone, since we can only depict two spatial dimensions on the diagram.

The reason why the light cone tilts and narrows near a BH is because orthogonality and distance between coordinate axis is defined via the inner product - which explicitly depends on the metric.

Edited September 15, 2022 by Markus Hanke

[joigus]

  

4 hours ago, Mitcher said:

You are absolutely right here, thank you for your patience. However you only wrote that omega.T = 1 basically. Now, say we had h/c^3 for instance, to be exactly equal to a particular linear momentum, this might hilight some missed but very real concept. And actually I think it does, too. Where does this 1.3 x 10^27 kg comes from according to you, it would just be an empty calculus artefact?

OK. No problem. Trying to be cautious here, I wouldn't say it's necessarily just an artifac. But it's not telling you anything that's not already implied by the theory you're working with. Could it be giving you a clue about something? Perhaps.

I don't think that's the case, and the reason is quantum mechanics. And quantum mechanics tells us it's rather an area that's important. In its most elaborate version this has come to be known as the holographic principle.

The two fundamental universal constants in GR are G and c. You solve the equations for a particularly simple case, and it tells you that at r=2GM/c² something peculiar happens. You call this radius associated with a BH of mass M its Schwarzschild radius.

Now you consider different M's and divide them by their corresponding R_{Schwarzschild}. It gives you always the same ratio, which is a universal constant. What else could it give you? The Schwarschild radius of any M is proportional to that M, and the constant of proportionality is a universal constant.

There's a similar situation with quantum field theory. There, what you have is \( \hbar \) and c. For any object of mass m it gives you a characteristic length, called the Compton wavelength, which is,

\[ \frac{\hbar}{mc} \]

It does play a special role in the theory. But the fact that the product of an object's mass times its Compton length gives you always the same value, does not necessarily tell you anything that's not already implied by the theory.

When you try to put together quantum field theory and GR, at least on dimensional grounds, you do obtain a clue that the really deep quantity is not a length, but an area.

I suppose what I'm trying to say is: The problem with dimensional analysis is that there is no unique way to interpret one of these "coincidences."

I'm a bit tired now. I need some sleep.

[Mitcher]

21 hours ago, Markus Hanke said:

My point was simply that the concept of boundedness is different from the concept of geodesic completeness. A singularity is not a boundary.

Sure but that's finesse. Singularity is the hedge of space-time and the end of worldlines. Whatever.

21 hours ago, Markus Hanke said:

There are many different kinds of wormhole spacetimes - some are geodesically complete (no singularities), some have singularities at the centre, and some have singularities at the throat. So it all depends on the boundary conditions. My point was simply that the concept of boundedness is different from the concept of geodesic completeness. A singularity is not a boundary.

I’m not really sure what you’re asking here - the purpose of the light cone is only to depict causality. It shows which regions can be causally connected to a specific event.

Imagine that at the point of origin (the event) a signal is emitted in all spatial directions. After one second (straight up the time axis), the signal wave front will have travelled a maximum of 300,000 km (straight across perpendicularly) as measured from the origin - iff it was an electromagnetic or gravitational wave, otherwise it’s less distance. After two seconds it will be 600,000 km, and so on. That’s how the cone comes about - everything within the cone is causally connected to the event, everything outside the cone is not, because the speed of light is limited. The surface of the cone itself is a null surface - it represents the boundary between causality regions, and only light/gravitational waves can reach the distance from the event represented by the surface.

You get the cone by plotting distance vs time, because the signal propagates in all spatial directions equally. In actuality it’s a hypercone, since we can only depict two spatial dimensions on the diagram.

The reason why the light cone tilts and narrows near a BH is because orthogonality and distance between coordinate axis is defined via the inner product - which explicitly depends on the metric.

Yes, so the pond's surface represents the 3D space and light is represented by the waves on it, yes ? That was my question. In that case the cone is virtual, it's called light-cone but light does not travel along it, right ?

[Mitcher]

21 hours ago, joigus said:

I'm a bit tired now. I need some sleep.

ok, take a few days leave   

[MigL]

A light cone doesn't 'represent' anything physical.

It is a plot of time vs distance, and if the units are seconds, on the time scale, and ct , on the distance scale, then light is constrained to travel on the 45^o slope separating timelike and spacelike motion.

See here       Light cone - Wikipedia

[Mitcher]

21 hours ago, joigus said:

For any object of mass m it gives you a characteristic length, called the Compton wavelength

In the gravity regime the caracteristic lenght is proportional to M while in the quantum regime it is inversely proportional, that's allowed Planck to construct his constants, just where the equations meet. From the Compton relationship (lambda).M = h/c does not give a meaningfull quantity since M does not cancel but maybe the Compton's wave lenght of the Universe itself corresponds to a very small quantum of mass and could play a role in the holographic principle since its volume would also be equal to a Planck's volume, surprinsingly. And for the most fundamental dimension, although h ultimately represents an angular quantum I think that it should rather be velocities, with time and space being only their apparent components. Everything is nothing but velocities and momenta.

4 minutes ago, MigL said:

A light cone doesn't 'represent' anything physical.

It is a plot of time vs distance, and if the units are seconds, on the time scale, and ct , on the distance scale, then light is constrained to travel on the 45^o slope separating timelike and spacelike motion.

See here       Light cone - Wikipedia

So the cone is supposedly formed by light ! That's exactly my understanding when I was saying that's it is not quite right. Light travels in pure space, not in time.

[joigus]

9 minutes ago, Mitcher said:

In the gravity regime the caracteristic lenght is proportional to M while in the quantum regime it is inversely proportional, that's allowed Planck to construct his constants, just where the equations meet. From the Compton relationship (lambda).M = h/c does not give a meaningfull quantity since M does not cancel but maybe the Compton's wave lenght of the Universe itself corresponds to a very small quantum of mass and could play a role in the holographic principle since its volume would also be equal to a Planck's volume, surprinsingly. And for the most fundamental dimension, although h ultimately represents an angular quantum I think that it should rather be velocities, with time and space being only their apparent components. Everything is nothing but velocities and momenta.

Mmm. Part of what you say makes sense, and is correct AFAIK. The Schwarzschild radius of an object is essentially its mass. The Compton wavelength of an object is essentially its inverse mass. That's right. Both lengths meet at a particular scale we call Planck's scale. So you could define Planck's mass, eg, as the mass of an object of which its Compton length is the same as its Schwarzschild radius. Those are not ordinary objects, as you can imagine.

Something that, in my mind, is extremely peculiar is that Planck's length and time are unfathomably small, while Planck's mass is roughly the size of an amoeba.

Another very peculiar thing is that ℏ appears in the denominator of the entropy of a BH. IOW, it acts as a regularising factor for the entropy of a BH. If you make it go to zero, the entropy of the BH becomes infinite... Classically!! Now, there's a clue for you.

Another part of what you say, I find more difficult to grasp, let's say. The Compton wavelenght of the universe doesn't make a lot of sense to me. The Compton wavelength is relevant in a context of quantum fields. When you try to probe a massive quantum field at scales of order its Compton wavelength, what happens is that, instead of getting a more detailed picture of it, you produce more quanta of the field and its associated anti-particle (2mc² and beyond). IOW, you enter the regime of pair production. This is known as Klein's paradox --well, the solution to it, to speak more properly. I can't wrap my head around that for the universe!! Creation of universe-antiuniverse pairs?

I don't agree with "everything is nothing but velocities and momenta." Spin is a good example. In quantum mechanics you have orbital angular momenta --things like xp_y-yp_x--, and rotation variables that cannot be expressed in terms of position and momenta (spin, more in particular spin 1/2.)

We're talking generalities here, of course, but I think QM is probably the reason why very small BH's and very small regions of BH's cannot be understood in terms of classical GR. And very likely the solution to the problem of singularities is past that frontier.

[MigL]

2 hours ago, Mitcher said:

So the cone is supposedly formed by light !

I don't beleive I, or the link I provided, said that ...
Read it again.

[Markus Hanke]

On 9/16/2022 at 5:04 AM, Mitcher said:

In that case the cone is virtual, it's called light-cone but light does not travel along it, right ?

You’re still missing the point here - the light cone is not meant as a way to visualise trajectories of anything, which is why the question is somewhat misplaced. In some sense it does indeed show how light travels on a time vs distance plot, but that’s not its purpose. Its purpose is to show regions of causality relative to a given event. It is called “light cone” only because that surface represents the maximum distance from the event any signal could have travelled at a given point in time, which of course relates to the speed of light. The way it’s meant to be used is that you draw in some other event, using the given coordinate axis - and then see immediately whether these events are causally connected, or not. 

IOW, the light cone is a way to visualise those regions (!) where the (flat) spacetime interval between events is positive, negative, or zero, as a function of coordinates.

22 hours ago, joigus said:

Another very peculiar thing is that ℏ appears in the denominator of the entropy of a BH. IOW, it acts as a regularising factor for the entropy of a BH. If you make it go to zero, the entropy of the BH becomes infinite... Classically!! Now, there's a clue for you.

I don’t think that’s very surprising, actually. Taking h->0 on the boundary physically just means that spacetime on the bulk is taken to be smooth and continuous; so you can swap any two events without changing anything about the BH. So of course the entropy will diverge. Having h be a finite value on the horizon other than zero means that spacetime on the bulk has a finite number of degrees of freedom - in other words, we’d expect that there will be regions of spacetime somewhere beyond the horizon that are not classical, ie not smooth and continuous. Thus, GR breaks down there, which is why we have a singularity appear in the theory.

So to me, the very concept of a finite entropy being associated with the horizon means that the bulk it encloses cannot be fully classical.

[joigus]

1 hour ago, Markus Hanke said:

I don’t think that’s very surprising, actually. Taking h->0 on the boundary physically just means that spacetime on the bulk is taken to be smooth and continuous; so you can swap any two events without changing anything about the BH. So of course the entropy will diverge. Having h be a finite value on the horizon other than zero means that spacetime on the bulk has a finite number of degrees of freedom - in other words, we’d expect that there will be regions of spacetime somewhere beyond the horizon that are not classical, ie not smooth and continuous. Thus, GR breaks down there, which is why we have a singularity appear in the theory.

So to me, the very concept of a finite entropy being associated with the horizon means that the bulk it encloses cannot be fully classical.

Agreed. Very nice analysis, by the way.

What surprises me is not that the entropy is finite, --something Bekenstein and Hawking taught us to think about in terms of QM--, as much as the fact that a classical BH would have an entropy at all, never mind --for the time being-- it being infinite. This is the key to my twice-emphasised:

On 9/15/2022 at 11:19 PM, joigus said:

Classically!!

Suppose a civilisation more familiar with both BH's and entropy than our scientist ancestors have been for centuries, and didn't know QM, came to study BH's very much like physicists of the 19th century came to study the black-body radiation. The Planck of this civilisation solves a puzzle for a generation of these physicists. What is their puzzle?: all calculations of a BH's entropy give infinity! Let's call it the ultra-entropic catastrophe, in close analogy to the ultraviolet catastrophe that gave rise to QM.

The solution to the puzzle comes in the form of regularising the entropy by means of quantising the action variables on the denominator so that the entropy doesn't come out infinite. That's what the HB formula for the BH seems to be suggesting.

Now that's what I find very surprising. What is that infinite entropy that the quantum equation is suggesting if we "classicalise" the BH by doing h-> 0?

What are these classical variables, all scrambled up, that QM needs to regularise?