ChipperQ:
The idea that it takes an infinite of time to pass through the Event Horizon is mistaken on two points. First the result comes from a calculation that uses an arbitrarily small test mass i.e. there is no back reaction from the test mass on the BH. Second even that calculation only applies to eternally external observers, for the test mass the time to pass through the EH and all the way to the singularity is finite.

The geometry of the singularities is part of the overall solution of the fields. This is not a casual relationship but rather the singularities, EH and general geometry are all tied together. There are many cases in functional analysis wherein a behavior of the singularities serves as the descriptor of the function.

Both a singularity and an event horizon are emergent from calculations when the equations are solved.
Singularities will arise with just about any theory of gravity that is atttractive - barring some other effect/force that prevents unbridled contraction. It will appear regardless of choice of reference frame. When more stuff is added to an existing heap, gravity always adds more to it's effect and always sums across the whole heap. Other forces ( even electromagnetism! ) are in effect local, may subtract, and don't necessarily sum over the whole heap. For most configurations this means gravity wins given enough mass.
The event horizon ( at R = 2M in units where G = c = 1 ) gives special behaviour to a distant observer. Any body travelling in from a great distance will appear to gradually slow and fade at the event horizon. This is basically due to the infinite frequency shift of emitted radiation from that region. Unlike the singularity, you can remove the event horizon by choice of co-ordinates. A frame travelling with an ingoing observer will not evince any special behaviour at R = 2M. ( Except perhaps a sinking feeling in the stomach as the tidal forces rip organs apart, but thankfully not for long! ) 'Dark stars', 'Frozen stars' and other like ideas pre-dated General Relativity.
The point about back reaction is good. For instance to solve the hydrogen atom ( one proton, one electron ) via quantum mechanics, with a much larger mass the central proton is assumed fixed - being some 2000 odd times heavier than the electron. An exact treatment needs to drop that fixity and so results in really small adjustments to the energy levels. But not so with two black holes of similiar mass spiralling in close!
Cheers, Mike.

[aside] If you have an electromagnetic dipole - one positive charge separated by a distance from a negative one - then only up close is the force significant. If you go out an order of magnitude or two ( with respect to the dipole separation distance ) then it's basically zero. Unipolar ( single bare charge ) force goes like inverse square, dipole like inverse cube, and higher pole orders ( quadrupole etc ) quickly subside to nought. While the electromagnetic force is very strong, that also implies that really large amounts of separated charge are hard to achieve. It's really oscillation and other time dependent behaviour that give electromagnetism long range effects - like seeing starlight from afar - but that doesn't compete well in magnitude with gravity in determining movements of large masses.
[/aside]

I have made this letter longer than usual because I lack the time to make it shorter.Blaise Pascal

Thanks, Mark and Mike; if I understand your answers correctly, then the gravitational waveform should progress from 'chirp' pretty much straight to 'ringdown', with merger of the singularities themselves occurring during the progression from one waveform into the other, and otherwise unobservable.

Interesting point about the possibility that other forces may prevent complete contraction. It could also be fundamental principles in conjunction with forces, e.g., the well known uncertainty principle, that would by itself seem to forbid any â€œsharpâ€? singularity (meaning one that's well defined by any particular point inside the EH).

I was trying to imagine what it might be like inside an event horizon; wouldn't it be like a universe unto itself, sort of like an inverse of the one we're in (that is, swapping particles for empty space, and empty space for particles)? What's the speed of light on the inside of an EH?

Interesting point about the possibility that other forces may prevent complete contraction. It could also be fundamental principles in conjunction with forces, e.g., the well known uncertainty principle, that would by itself seem to forbid any â€œsharpâ€? singularity (meaning one that's well defined by any particular point inside the EH).
I was trying to imagine what it might be like inside an event horizon; wouldn't it be like a universe unto itself, sort of like an inverse of the one we're in (that is, swapping particles for empty space, and empty space for particles)? What's the speed of light on the inside of an EH?

[total crap]
Without any strong basis other than disliking infinities as unrealistic, I prefer the idea of an entirely new force. This would be repulsive and only of significant strength at really short range, say around the Planck length. It would be intimately linked with the Uncertainty Principle. I have often wondered why the resistance to localisation of energetic particles implied by quantum mechanics had not been labelled as a force.
Take a massive star, toward the end of it's nuclear burning options, as it contracts down to a smaller volume. Gravity never sleeps. The star goes through a series of phases of material type. It is initially 'atomic', with electrons whizzing around a nucleon core, but all are relatively discrete and separated entities that are loosely bound - it is gaseous. Then as a white dwarf it is becoming quite solid in nature with a vast lattice that electrons crowd jowl by cheek - a fluid of sorts. As density increases, the preference is for electrons and nucleons to combine giving a really dense solid stuff - the neutron star. Proceed further and you've folded space around it and formed a black hole. This yields an event horizon, but maybe doesn't require a singularity. Distant observers will be largely indifferent to what's inside, but not completely. If a new phase ( with this new 'Planck Force' ) kicks in and prevents the ultimate scrunch then the centre will have some non-zero width, and it's characteristics will be definable by experimental measurement of gravity wave behaviour as a probe of this region ( with inspirals say ). Why not? Black holes aren't totally one-way, they still inform the local surrounds via gravity. If the original star's mass is all at the centre then how do the gravitons get out to tap me on the shoulder later on after the hole formed? Since the event horizon is not a 'real' barrier but simply a region where/when the character of measurement changes ( in some respects time and distance interchange ) then there isn't any discontinuity.
You'd could also solve the black hole entropy issue. The core state type ( whatever becomes of matter under the Planck Force ) would preserve information in it's internal quantum states - much like any atom does with it's electron population distribution changing/spreading through available energy levels when it interacts. It remembers it's history...
Speaking of which, the Planck Force easily supplies the Big Bang without even leaning on higher dimensions for help... :-)
I suppose someone wants me to produce a numerical prediction now..... :-(
[/total crap]

Cheers, Mike.

( edit ) Then again the Planck Force might simply be what gravity looks like up close. The side we never saw before.....

I have made this letter longer than usual because I lack the time to make it shorter.Blaise Pascal

Without any strong basis other than disliking infinities as unrealistic, I prefer the idea of an entirely new force. This would be repulsive and only of significant strength at really short range, say around the Planck length. It would be intimately linked with the Uncertainty Principle. I have often wondered why the resistance to localisation of energetic particles implied by quantum mechanics had not been labelled as a force.

Maybe something to do with the Pauli exclusion principle? Has this been attributed to any 'cause' beyond the bald statement that no two fermions can have the same quantum numbers?

ChipperQ:
The rules of physics would remain the same as you passed through the EH.
The larger the mass of the BH the lower the acceleration and tidal forces at the EH. For a BH of 1.5*10^12 solar masses the acceleration would be one gee and the tidal acceleration 2*10^-14 gee/meter. So you could easly pass through such an EH without noticing it.

The rules of physics would remain the same as you passed through the EH.

Certainly, but here's the crux of my questions; it's a quote from one of the articles in the SciAm Sp.Ed. 'A Matter of Time', the one by Paul Davies:

Quote:

...At the surface of a neutron star, gravity is so strong that time is slowed by about 30 percent relative to Earth time. Viewed from such a star, events here would resemble a fast-forwarded video. A black hole represents the ultimate time warp; at the surface of the hole, time stands still relative to Earth. This means that if you fell into a black hole from nearby, in the brief interval it took you to reach the surface, all of eternity would pass by in the wider universe. The region within the black hole is therefore beyond the end of time, as far as the outside universe is concerned...

I understand in the inertial frame of the falling object that time is marching on as ever, but the above description would seem to imply a kind of temporal region at the EH, akin to trying to cool something below absolute zero, in a time-wise sense. Does this apply to the physics on the inside of the EH? That is, does it mean that trapped matter is on an equal footing with light? (Since the amount of gravitational time dilation is otherwise equivalent with the amount experienced when v = c, velocity equals the speed of light...)

Maybe something to do with the Pauli exclusion principle? Has this been attributed to any 'cause' beyond the bald statement that no two fermions can have the same quantum numbers?

Yup, indeedy! Fermions, those particles with half integral spin, when passing into indistinguishable/identical final states subtract probability amplitudes. Thus such probabilities go to zero and you don't find several Fermions together. Bosons with integral spin add and probabilities go to non-zero hence they huddle up. But this is the simply the mechanics of the theory, and only de-references your question one step back. 'Spin' would be a mere label for this 'associative' behaviour, except that one can actually macroscopically detect it - as a form of angular momentum. The Stern-Gerlach experiment, where atoms with unpaired electrons are passed through a magnetic field gradient, separates atoms out with different values of nett spin. It's a bit like a postal letter sorter.
The deeper truth is that most of matter is fermionic, but interacts via bosons. What would the centre of a black hole do to that?
[aside]
If you and I shoot hoops with a ball each, then after a while we may come up with a law like 'No two basketballs can occupy the same place at the same time'. Being ever so humble I let you dub it the Odysseus Exclusion Principle, but I'll get the Hewson Lemma '......particularly at the ring'. Then Chipper comes along, clever lad, and blows us away with Chipper's Laws of Motion - action/reaction, inertial stuff, conservation of basketballs.... whatever. So we find that 'our' law was derivative from Chipper's, and pine for the good old days we could be burning young Chipper at the stake. :-)
The Van De Vaals force is a similiar case. It has four 'bands' of behaviour.
#1 - Molecules when placed far enough apart have no interaction.
#2 - Move them closer together and they repel.
#3 - Closer in they are somewhat attractive.
#4 - But yet further in they really, really repel.
Electromagnetism plus atomic theory supercedes this.
#1 - The plusses and minuses of all the dipoles in a molecule cancel to zippo far out.
#2 - Mainly the outermost parts of the molecules feel each other. As these are the electron clouds, of same charge sign, they repel.
#3 - Now the electrons can feel the other guy's protons and vice versa. The electrons are still repelling electrons, and the protons the protons, but the nett effect is to cuddle.
#4 - Same as #3, only the repulsion overrides because those nuclei are really unfriendly to each other when that close up. They have charge in a lot more concentration than those diffuse electron clouds.
If left alone for a while, two molecules will sit in a happy valley of minimum energy - nett attraction compared with the far off case - but can be bumped apart with a good whack. An enormous amount of everyday stuff can be understood with this type of model, and you can even be predictive.
My ( long laboured ) point is: whatever is given the title of a force is really just a mechanism for producing the result of an interaction. Newton, Gallileo, Einstein, Mach, Poincare and all the other guys said much the same - if it goes off course from a straight line then look for the force. That's how you define it!
[/aside]

I have made this letter longer than usual because I lack the time to make it shorter.Blaise Pascal

... 'Spin' would be a mere label for this 'associative' behaviour, except that one can actually macroscopically detect it - as a form of angular momentum. The Stern-Gerlach experiment, where atoms with unpaired electrons are passed through a magnetic field gradient, separates atoms out with different values of nett spin. It's a bit like a postal letter sorter. [...]

Thanks; I didn't realize quantum spin had such 'literal' manifestations; I'd thought of it more like "flavour" or "colour" in quarks.

Regarding Van der Waals forces, when I was taking chemistry in the late '70s they were still very much alive as a paedogogical or simplified model, despite the fact that we 'knew better' from having been introduced to orbitals &c. IIRC drawing benzene rings with circles (instead of doubling every other side of the hexagon) to represent the shared pi-bonds was just coming into fashion then ...

Regarding Van der Waals forces, when I was taking chemistry in the late '70s they were still very much alive as a paedogogical or simplified model, despite the fact that we 'knew better' from having been introduced to orbitals &c. IIRC drawing benzene rings with circles (instead of doubling every other side of the hexagon) to represent the shared pi-bonds was just coming into fashion then ...

Yes, Waals not Vaals, sorry...
My theme here is that of 'effective theories', where each scale ( size, time, mass .. ) or combination of scales has it's own 'best' theory. You need to have continuity at the boundaries between those theories ( ie. they make the same predictions at some overlapping scale ) so that one can move back along the causal chain to the human region. Otherwise we cannot assess the measurement. Alot of the time we do this implicitly, mentally modelling some series of interactions without realising it. The LIGO's have a very thorough analysis of those linkages, alas they still can't find that low frequency hum ( traffic was the last guess ). The 'electron' is actually a model constructed ( albeit very accurately and consistently ) to explain a vast raft of apparently disparate phenomena. I like the Stern-Gerlach because it brings the microscopic up to our size with so few steps. Compare that, say, with the detection of the top quark! Those humungous detectors! Not to mention all the rigamarole just to create the reaction vertex. With care, you have some hope of doing the Stern-Gerlach in your own back shed. But no feasible method exists for checking out the top in the home garage. Another good one is the Millikan experiment - charges on oil droplets kept hovering in mid-air by an electric field - which measures, nay proves, the discreteness of the electronic charge. I actually did at that one at University.
Cheers, Mike.

I have made this letter longer than usual because I lack the time to make it shorter.Blaise Pascal

Another good one is the Millikan experiment - charges on oil droplets kept hovering in mid-air by an electric field - which measures, nay proves, the discreteness of the electronic charge. I actually did at that one at University.
Cheers, Mike.

I did it too but F.J.Dyson almost got killed. See his book "Disturbing the universe". Theoretical physicists beware!
Tullio

## RE: ChipperQ: The idea that

)

Both a singularity and an event horizon are emergent from calculations when the equations are solved.

Singularities will arise with just about any theory of gravity that is atttractive - barring some other effect/force that prevents unbridled contraction. It will appear regardless of choice of reference frame. When more stuff is added to an existing heap, gravity always adds more to it's effect and always sums across the whole heap. Other forces ( even electromagnetism! ) are in effect local, may subtract, and don't necessarily sum over the whole heap. For most configurations this means gravity wins given enough mass.

The event horizon ( at R = 2M in units where G = c = 1 ) gives special behaviour to a distant observer. Any body travelling in from a great distance will appear to gradually slow and fade at the event horizon. This is basically due to the infinite frequency shift of emitted radiation from that region. Unlike the singularity, you can remove the event horizon by choice of co-ordinates. A frame travelling with an ingoing observer will not evince any special behaviour at R = 2M. ( Except perhaps a sinking feeling in the stomach as the tidal forces rip organs apart, but thankfully not for long! ) 'Dark stars', 'Frozen stars' and other like ideas pre-dated General Relativity.

The point about back reaction is good. For instance to solve the hydrogen atom ( one proton, one electron ) via quantum mechanics, with a much larger mass the central proton is assumed fixed - being some 2000 odd times heavier than the electron. An exact treatment needs to drop that fixity and so results in really small adjustments to the energy levels. But not so with two black holes of similiar mass spiralling in close!

Cheers, Mike.

[aside] If you have an electromagnetic dipole - one positive charge separated by a distance from a negative one - then only up close is the force significant. If you go out an order of magnitude or two ( with respect to the dipole separation distance ) then it's basically zero. Unipolar ( single bare charge ) force goes like inverse square, dipole like inverse cube, and higher pole orders ( quadrupole etc ) quickly subside to nought. While the electromagnetic force is very strong, that also implies that really large amounts of separated charge are hard to achieve. It's really oscillation and other time dependent behaviour that give electromagnetism long range effects - like seeing starlight from afar - but that doesn't compete well in magnitude with gravity in determining movements of large masses.

[/aside]

I have made this letter longer than usual because I lack the time to make it shorter. Blaise Pascal

## Thanks, Mark and Mike; if I

)

Thanks, Mark and Mike; if I understand your answers correctly, then the gravitational waveform should progress from 'chirp' pretty much straight to 'ringdown', with merger of the singularities themselves occurring during the progression from one waveform into the other, and otherwise unobservable.

Interesting point about the possibility that other forces may prevent complete contraction. It could also be fundamental principles in conjunction with forces, e.g., the well known uncertainty principle, that would by itself seem to forbid any â€œsharpâ€? singularity (meaning one that's well defined by any particular point inside the EH).

I was trying to imagine what it might be like inside an event horizon; wouldn't it be like a universe unto itself, sort of like an inverse of the one we're in (that is, swapping particles for empty space, and empty space for particles)? What's the speed of light on the inside of an EH?

## RE: Interesting point about

)

[total crap]

Without any strong basis other than disliking infinities as unrealistic, I prefer the idea of an entirely new force. This would be repulsive and only of significant strength at really short range, say around the Planck length. It would be intimately linked with the Uncertainty Principle. I have often wondered why the resistance to localisation of energetic particles implied by quantum mechanics had not been labelled as a force.

Take a massive star, toward the end of it's nuclear burning options, as it contracts down to a smaller volume. Gravity never sleeps. The star goes through a series of phases of material type. It is initially 'atomic', with electrons whizzing around a nucleon core, but all are relatively discrete and separated entities that are loosely bound - it is gaseous. Then as a white dwarf it is becoming quite solid in nature with a vast lattice that electrons crowd jowl by cheek - a fluid of sorts. As density increases, the preference is for electrons and nucleons to combine giving a really dense solid stuff - the neutron star. Proceed further and you've folded space around it and formed a black hole. This yields an event horizon, but maybe doesn't require a singularity. Distant observers will be largely indifferent to what's inside, but not completely. If a new phase ( with this new 'Planck Force' ) kicks in and prevents the ultimate scrunch then the centre will have some non-zero width, and it's characteristics will be definable by experimental measurement of gravity wave behaviour as a probe of this region ( with inspirals say ). Why not? Black holes aren't totally one-way, they still inform the local surrounds via gravity. If the original star's mass is all at the centre then how do the gravitons get out to tap me on the shoulder later on after the hole formed? Since the event horizon is not a 'real' barrier but simply a region where/when the character of measurement changes ( in some respects time and distance interchange ) then there isn't any discontinuity.

You'd could also solve the black hole entropy issue. The core state type ( whatever becomes of matter under the Planck Force ) would preserve information in it's internal quantum states - much like any atom does with it's electron population distribution changing/spreading through available energy levels when it interacts. It remembers it's history...

Speaking of which, the Planck Force easily supplies the Big Bang without even leaning on higher dimensions for help... :-)

I suppose someone wants me to produce a numerical prediction now..... :-(

[/total crap]

Cheers, Mike.

( edit ) Then again the Planck Force might simply be what gravity looks like up close. The side we never saw before.....

I have made this letter longer than usual because I lack the time to make it shorter. Blaise Pascal

## RE: Without any strong

)

Maybe something to do with the Pauli exclusion principle? Has this been attributed to any 'cause' beyond the bald statement that no two fermions can have the same quantum numbers?

## ChipperQ: The rules of

)

ChipperQ:

The rules of physics would remain the same as you passed through the EH.

The larger the mass of the BH the lower the acceleration and tidal forces at the EH. For a BH of 1.5*10^12 solar masses the acceleration would be one gee and the tidal acceleration 2*10^-14 gee/meter. So you could easly pass through such an EH without noticing it.

## RE: The rules of physics

)

Certainly, but here's the crux of my questions; it's a quote from one of the articles in the SciAm Sp.Ed. 'A Matter of Time', the one by Paul Davies:

I understand in the inertial frame of the falling object that time is marching on as ever, but the above description would seem to imply a kind of temporal region at the EH, akin to trying to cool something below absolute zero, in a time-wise sense. Does this apply to the physics on the inside of the EH? That is, does it mean that trapped matter is on an equal footing with light? (Since the amount of gravitational time dilation is otherwise equivalent with the amount experienced when v = c, velocity equals the speed of light...)

## RE: Maybe something to do

)

Yup, indeedy! Fermions, those particles with half integral spin, when passing into indistinguishable/identical final states subtract probability amplitudes. Thus such probabilities go to zero and you don't find several Fermions together. Bosons with integral spin add and probabilities go to non-zero hence they huddle up. But this is the simply the mechanics of the theory, and only de-references your question one step back. 'Spin' would be a mere label for this 'associative' behaviour, except that one can actually macroscopically detect it - as a form of angular momentum. The Stern-Gerlach experiment, where atoms with unpaired electrons are passed through a magnetic field gradient, separates atoms out with different values of nett spin. It's a bit like a postal letter sorter.

The deeper truth is that most of matter is fermionic, but interacts via bosons. What would the centre of a black hole do to that?

[aside]

If you and I shoot hoops with a ball each, then after a while we may come up with a law like 'No two basketballs can occupy the same place at the same time'. Being ever so humble I let you dub it the Odysseus Exclusion Principle, but I'll get the Hewson Lemma '......particularly at the ring'. Then Chipper comes along, clever lad, and blows us away with Chipper's Laws of Motion - action/reaction, inertial stuff, conservation of basketballs.... whatever. So we find that 'our' law was derivative from Chipper's, and pine for the good old days we could be burning young Chipper at the stake. :-)

The Van De Vaals force is a similiar case. It has four 'bands' of behaviour.

#1 - Molecules when placed far enough apart have no interaction.

#2 - Move them closer together and they repel.

#3 - Closer in they are somewhat attractive.

#4 - But yet further in they really, really repel.

Electromagnetism plus atomic theory supercedes this.

#1 - The plusses and minuses of all the dipoles in a molecule cancel to zippo far out.

#2 - Mainly the outermost parts of the molecules feel each other. As these are the electron clouds, of same charge sign, they repel.

#3 - Now the electrons can feel the other guy's protons and vice versa. The electrons are still repelling electrons, and the protons the protons, but the nett effect is to cuddle.

#4 - Same as #3, only the repulsion overrides because those nuclei are really unfriendly to each other when that close up. They have charge in a lot more concentration than those diffuse electron clouds.

If left alone for a while, two molecules will sit in a happy valley of minimum energy - nett attraction compared with the far off case - but can be bumped apart with a good whack. An enormous amount of everyday stuff can be understood with this type of model, and you can even be predictive.

My ( long laboured ) point is: whatever is given the title of a force is really just a mechanism for producing the result of an interaction. Newton, Gallileo, Einstein, Mach, Poincare and all the other guys said much the same - if it goes off course from a straight line then look for the force. That's how you define it!

[/aside]

I have made this letter longer than usual because I lack the time to make it shorter. Blaise Pascal

## RE: ... 'Spin' would be a

)

Thanks; I didn't realize quantum spin had such 'literal' manifestations; I'd thought of it more like "flavour" or "colour" in quarks.

Regarding Van der Waals forces, when I was taking chemistry in the late '70s they were still very much alive as a paedogogical or simplified model, despite the fact that we 'knew better' from having been introduced to orbitals &c. IIRC drawing benzene rings with circles (instead of doubling every other side of the hexagon) to represent the shared pi-bonds was just coming into fashion then ...

## RE: Regarding Van der Waals

)

Yes, Waals not Vaals, sorry...

My theme here is that of 'effective theories', where each scale ( size, time, mass .. ) or combination of scales has it's own 'best' theory. You need to have continuity at the boundaries between those theories ( ie. they make the same predictions at some overlapping scale ) so that one can move back along the causal chain to the human region. Otherwise we cannot assess the measurement. Alot of the time we do this implicitly, mentally modelling some series of interactions without realising it. The LIGO's have a very thorough analysis of those linkages, alas they still can't find that low frequency hum ( traffic was the last guess ). The 'electron' is actually a model constructed ( albeit very accurately and consistently ) to explain a vast raft of apparently disparate phenomena. I like the Stern-Gerlach because it brings the microscopic up to our size with so few steps. Compare that, say, with the detection of the top quark! Those humungous detectors! Not to mention all the rigamarole just to create the reaction vertex. With care, you have some hope of doing the Stern-Gerlach in your own back shed. But no feasible method exists for checking out the top in the home garage. Another good one is the Millikan experiment - charges on oil droplets kept hovering in mid-air by an electric field - which measures, nay proves, the discreteness of the electronic charge. I actually did at that one at University.

Cheers, Mike.

I have made this letter longer than usual because I lack the time to make it shorter. Blaise Pascal

## RE: Another good one is the

)

I did it too but F.J.Dyson almost got killed. See his book "Disturbing the universe". Theoretical physicists beware!

Tullio