Planck Stars: Carlo Rovelli & Francesca Vidotto

[marcus]

To re-iterate for clarity, what we are talking about are phenomena that could be observed at gamma or x-ray wavelengths if you assume the Rovelli Vidotto model of black hole.

So it is a possible test of the new RV model of BH, the "planck star" model as applied to primordial BH in this case. The model is interesting, different in significant ways, and could of course be wrong. We need observations to tell.

In order to talk about this you need to know the BASICS of this new BH model. In particular that it looks like a conventional BH for most of its lifetime but that its lifespan is only 65% as long for the same initial mass.

It evaporates by Hawking radiation at the same rate as a conventional BH of the same initial mass until its mass has dwindled to about 70% of initial (which takes about 65% of conventional lifespan) and then it blows up in a gamma burst. These are the short or very short GRB which could be studied.

Their energy is predicted by the theory and depends on when they exploded. Those that exploded in the past would have calculably less energy. Those exploding in the approximate present would have an energy mass-equivalent of about 140 megaton, or if you like 1.4 x 10¹¹ kg.
Folks can multiply that by the speed of light squared to get the ergs or joules if they like.

 

[Paulibus]

I'm convinced that the Rovelli-Vidotto model of a Black Hole, and how the gravitational collapse of such can be frustrated by a singularity-preventing bounce, is a landmark paper; it has really interesting implications for both Blackholery and Cosmology.

But despite having looked at (and not properly understood ) many of the technical background papers mentioned in this thread, I find the root cause of the bounce difficult to fit into my primitive background of Physics:

...The bounce is due to a quantum-gravitational repulsion which originates from the Heisenberg uncertainty, and is akin to the "force" that keeps an electron from falling into the nucleus. The bounce does not happen when the universe is of Planckian size, as was previously expected; it happens when the matter/energy density reaches the Planck density. In a matter dominated universe ... the bounce can happen at large values of the size of the universe: using current cosmological estimates, quantum gravity could become relevant when the volume of the universe is some 75 orders of magnitude larger than the Planck volume. Quantum gravity effects do not happen only over Planck volumes.

This introduction to the key point of the whole scheme is on p. 1 of the Rovelli-Vidotto paper. I'd appreciate some fleshed-out, low-level help in better understanding how this "quantum-gravitational repulsion" arises.

 

[marcus]

I'm convinced that the Rovelli-Vidotto model of a Black Hole, and how the gravitational collapse of such can be frustrated by a singularity-preventing bounce, is a landmark paper; it has really interesting implications for both Blackholery and Cosmology.
…
I find the root cause of the bounce difficult to fit into ...

Hi Paulibus, good to hear from you! I agree about the papers likely landmark role. I also share your sense that the bounce needs an intuitive explanation. I'll try to whittle away at that problem.

Notice that bounce is not unique to LQG, there are other cosmological models, whether classical or to some extent quantum, where a bounce occurs. As I recall there at least one "nonsingular" cosmologies review paper that lists and discusses several bounce models besides Loop. It would be too distracting to get into that so I will focus on Loop.

I can get SOME intuitive sense by thinking about electron degeneracy pressure that keeps ordinary matter from collapsing into neutron matter. I relate that in a general sort of way to Uncertainty Principle. Nature doesn't like being pinned down. Maybe geometry is analogous to matter in that regard, and resists being pinned down. Maybe geometry insists of some ultimate margin of freedom to be uncertain. But that's too vague, I want us to be able to contemplate something more quantitative.

Focussing just on Loop gravity, the bounce first appeared in cosmology around 2001. And in 2006 the original Loop cosmology dynamics were replaced by Ashtekar Pawlowski Singh improved dynamics, so then the bounce had to be checked all over again---at length. they were never sure it was going to occur, so kept exploring different cases. I get the impression that central people like Ashtekar do not themselves have an intuitive understanding of why the cosmological bounce has turned out to be such a robust feature of their model. They have acted as if they were surprised when it surfaced in 2001 and still cautious about it in 2006. But that shouldn't make US give up on getting an intuitive sense of why it happens.

Notice also that they did not immediately carry the bounce idea over from Cosmology to Black Holes! I remember for years being frustrated whenever I examined a new Ashtekar et al paper and found that he was doing almost anything to avoid concluding that BHs bounced. All but a very few LQG people were reluctant to accept the "baby universe" idea and I think BH bounce was equated to "baby universes" in everyone's mind. So all but a few avoided the BH bounce idea.

One reason this paper is a landmark is because it analyzes a bounce that rebounds back into OUR universe rather than budding off a baby one. So in that sense it is the first "mainstream" Loop BH bounce.

So far I am just giving an impressionistic and personal account of background and context. I want to unpack some intuition about the actual phenom. But I'll take some time to think and make a separate post for that.

One path towards bounce intuition might be to contemplate the fact that in Loop gravity there is an absolute fundamental maximum on acceleration.
I think that translates into some other geometrical and thermodynamic limits. Say on temperature, or on "the force of gravity" whatever that means , or on certain gradients like the temperature gradient, density gradient, maybe also on curvature...

Suppose we first talk about the Loop gravity limit on acceleration. It seems so unintuitive that there such be a maximal acceleration! Maybe if we can get over that first (simplest) intuition hurdle it will be easier to accept that nature's geometry could bounce.

 

[marcus]

I'm convinced that the Rovelli-Vidotto model of a Black Hole, and how the gravitational collapse of such can be frustrated by a singularity-preventing bounce, is a landmark paper; it has really interesting implications for both Blackholery and Cosmology.
…
I find the root cause of the bounce difficult to fit into ...

One path towards bounce intuition might be to contemplate the fact that in Loop gravity there is an absolute fundamental maximum on acceleration...

Acceleration is interesting partly because of the "equivalence principle" that if you put a physicist in a box and uniformly accelerate the box then he can't tell the difference between that and the box sitting in a uniform gravitational field.

So if you put two physicists in the box and accelerate it, the forward one feels like he's upstairs and the aft one feels like downstairs, and their clocks run at slightly different rates. Nature functions slower downstairs. There's also the Unruh temperature thing, with acceleration. So establishing a maximal acceleration relates to a lot of things: time rate gradient, gravitational potential gradient…

Why should there be a maximal acceleration? It seems so unnatural! Could this paper be wrong?
What's the intuition behind this? (You may know the paper, Paulibus. But it could be worth our reviewing.)
http://arxiv.org/abs/1307.3228
Evidence for Maximal Acceleration and Singularity Resolution in Covariant Loop Quantum Gravity
Carlo Rovelli, Francesca Vidotto
(Submitted on 11 Jul 2013)
A simple argument indicates that covariant loop gravity (spinfoam theory) predicts a maximal acceleration, and hence forbids the development of curvature singularities. This supports the results obtained for cosmology and black holes using canonical methods.
Comments: 4 pages, 1 figure

Only 4 pages, how hard can it be?

 

[marcus]

In figure 1 the smaller the shaded area the more extreme the acceleration. You can see that the probe is coming in from the right almost at speed of light (i.e. nearly parallel to the incoming 45 degree line) decelerating madly and zooming off to the right again approaching speed of light (the outgoing 45 degree line).

Loop has an area minimum (one of the earliest results) which could enter into play here.

And why shouldn't there be a maximal acceleration after all? It has even been expected for several decades based on theoretical considerations.

Here's from conclusions on page 4:
"Maximal acceleration appears to cure strong singularities (in the terminology of [29, 30]) such as big bang, big crunch, black holes, as well as more exotic ones…"

Still unresolved but have to go to a rehearsal. Back later to look at this some more. Hope you have a look and find parts of it helpful.

 

[Paulibus]

Thanks for the full replies and pointing me at the interesting Rovelli-Vidotto paper on "Evidence for Maximal Acceleration" which I was unaware of. But I run aground easily; so far I have trouble checking the dimensions of even the simplest of their equations, e.g. [18], perhaps because they cleverly simplify by setting c = 1. I do wish this wasn't accepted practice.

Your comment in post #74 about physicists in an accelerated box set me puzzling also. The principle of equivalence between acceleration and gravitational fields extends also to their degree of uniformity, I hope. So the environment inside a uniformly accelerating box (say with chairs to stay relatively put in) is not quite equivalent to the radially not-quite-uniform gravitational field of the Earth. Inhomogeneity must be what makes Nature appear to function slower downstairs than upstairs. Maybe that's why Hell looks so eternal to those in Heaven? Gravitational red-shifts are, I think, caused by field gradients rather than uniform fields. Or are they?

But all this is just displacement activity. I'll get back to trying to understand Rovelli-Vidotto -- good stuff; I have a daughter Frances.

 

[MTd2]

Let me rephrase a bit my argument.

I suppose that primordial black holes would be caused by non uniformity of the inflaton process. Suppose that a volume A inflates, for a short moment, at a slightly lower than a volume B surrounding it. The area surrounding A will work like a compressor around B. It will squeeze the matter at A to a small black hole.

I also supposed that this non uniformity of the inflaton makes itself turbulent. So, I estimated how the rate of formation of primordial black holes, during inflation, would fall with the cooling of the universe at my post #51. It falls with the inverse of the 4th in relation to the temperature. Given that the temperature falls fast I supposed that the smallest ones would be the ones at the beginning, but I conjectured that the total volume of black holes would be bigger for those formed in the beginning of inflation, since we are talking about an overall adiabatic expansion of the universe, the rate of formation would fall faster then the fall of temperature. But, also, the earlier black holes would evaporate faster due its small mass, which I think due the fast cooling of the universe during inflation, would be always bellow the background temperature.

This would affect the CMB by accoustic oscillations, like this:

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

Even though these very early black holes should have a very high frequency, they should, this is only I guess, leave a mark due amplification by inflation and very high z.

This process may explain apparent violation to cosmological principle, like this(?): http://en.wikipedia.org/wiki/Huge-LQG

And formation of matter\dark matter concentrations beyond what would be expected by this principle, by the scattering process of non homogenous inflation and mini black hole explosions.

 

[marcus]

Let me rephrase a bit my argument.

I suppose that primordial black holes would be caused by non uniformity of the inflation process.
...
This would affect the CMB by accoustic oscillations, like this:
http://en.wikipedia.org/wiki/Baryon_acoustic_oscillations

Even though these very early black holes should have a very high frequency, they should, this is only a guess, leave a mark due amplification by inflation and very high z.

This process may explain apparent violation to cosmological principle, like this(?): http://en.wikipedia.org/wiki/Huge-LQG

And formation of matter\dark matter concentrations beyond what would be expected by this principle, by the scattering process of non homogenous inflation and mini black hole explosions.

Well this, as you indicate Daniel, is somewhat speculative. You are talking about mini primordial black holes (PBH) that may have formed during inflation and exploded promptly so as to be "amplified by inflation and very high z" so that they could have had an effect on "Baryon acoustic oscillations" and the like. Perhaps producing inhomogeneity at large enough scale to be visible in CMB.

I can't fault this as a speculation, nor does it contradict what I was discussing which was evidence of more massive longer lived PBH as gamma ray bursts (GRB) and as contributors to the gamma ray and x-ray background. Your idea is a completely separate subject of inquiry!

But we are talking about the Planck stars BH model with SLO-MO REBOUND replacing the "singularity". It is not clear to me how your conjectured effect on CMB could TEST this model. How would the disruption of CMB isotropy look any different with the Planck star PBH than with the conventional PBH?

If the imagined effect on CMB does not DISTINGUISH between conventional and Planck star model then it does not seem related to the topic of this thread. Or does it simply need a lot more quantitative/numerical work before you can tell whether it relates to the Planck star model or not?

 

[marcus]

... the interesting Rovelli-Vidotto paper on "Evidence for Maximal Acceleration"... But I run aground easily; so far I have trouble checking the dimensions of even the simplest of their equations, e.g. [18], perhaps because they cleverly simplify by setting c = 1. I do wish this wasn't accepted practice.

... the environment inside a uniformly accelerating box (say with chairs to stay relatively put in) is not quite equivalent to the radially not-quite-uniform gravitational field of the Earth. Inhomogeneity must be what makes Nature appear to function slower downstairs than upstairs. Maybe that's why Hell looks so eternal to those in Heaven? Gravitational red-shifts are, I think, caused by field gradients rather than uniform fields. Or are they?

... I'll get back to trying to understand Rovelli-Vidotto -- good stuff; I have a daughter Frances.

Hello to F, I hope her interests include some physics and or cosmology! They're good things for a young person to keep an eye on IMHO.

I'll have a look at equation [18] on the off chance I can help.

You are certainly right about radial inverse square being different from uniform, even though with a large enough radius the one can approximate the other. I believe gravitational redshift would still be caused by a uniform field, there is still a potential gradient (an idea of depth, a downstairs and an upstairs). I'd be embarrassed to learn I was mistaken about this, it seems so intuitive, but you might be right.

I think of the steadily accelerating box with the forward and aft (to use nautical terms) physicists who have been told by a duplicitous Experimenter that they are in a gravitational field. Upstairs sends a flash of light to downstairs and by the time it gets there the receiver is coming to meet it faster! So he detects a blueshift. And so on. This confirms their mistaken belief (suggested to them by the guileful Experimenter) that they are in a gravitational field.

 

[MTd2]

Or does it simply need a lot more quantitative/numerical work before you can tell whether it relates to the Planck star model or not?

There is, indeed, a need of numerical inference. But, I don't think these problems are not unrelated, indeed, since I cannot think there is any kind of "compressor" mechanism capable of producing small black holes with any range of masses, other than inhomogeneities during inflation as I described. You know that the smaller the black hole, the greater is the pressure for a given matter density.

Outside the inflation range, only a ~2-10 solar (outside this range, I am not aware of any process other than simply falling mass to a stellar black hole or black hole merging) mass can be compressed enough to form a black hole, as far as I can imagine.

So, I think both are related. Since, after the supposed numerical calculation, the abundance of primordial black explosions should be related to a given time of the inflation, where it was generated. So, studying both the CMB and the remains of explosions, should help to understand inflation, when it began, how much it lasted, among other things.

Do you have any other idea of how such black holes might be formed? I initially formed about quantum gravity fluctuations before inflation, but it seems that by CDT the universe becomes homogeneous at a very small scale, hundreds of plank scale, at least homogenous enough not to form a black hole

 

[marcus]

Daniel, a lot has been written about primordial BH, specifically as sources of gamma ray bursts and such-like high energy radiation. I think if one is interested in the possibility of visible disruption to the CMB caused by PBH explosions then one needs to start reading the technical literature on PBH. At this point it doesn't seem to have a specific connection with the Planck star BH model, so maybe a separate thread?

As a reminder, here's the reference to the paper Paulibus and I (hopefully others as well!) were considering:

Acceleration is interesting partly because of the "equivalence principle" that if you put a physicist in a box and uniformly accelerate the box then he can't tell the difference between that and the box sitting in a uniform gravitational field.

So if you put two physicists in the box and accelerate it, the forward one feels like he's upstairs and the aft one feels like downstairs, and their clocks run at slightly different rates. Nature functions slower downstairs. There's also the Unruh temperature thing, with acceleration. So establishing a maximal acceleration relates to a lot of things: time rate gradient, gravitational potential gradient…

Why should there be a maximal acceleration? It seems so unnatural! Could this paper be wrong?
What's the intuition behind this? ...
http://arxiv.org/abs/1307.3228
Evidence for Maximal Acceleration and Singularity Resolution in Covariant Loop Quantum Gravity
Carlo Rovelli, Francesca Vidotto
(Submitted on 11 Jul 2013)
A simple argument indicates that covariant loop gravity (spinfoam theory) predicts a maximal acceleration, and hence forbids the development of curvature singularities. This supports the results obtained for cosmology and black holes using canonical methods.
Comments: 4 pages, 1 figure
...

Paulibus mentioned equation (18). I'll have a look and also anybody else's explanatory comment is welcome!

 

[MTd2]

I just want to know if these things can be generated. Existing mathematically may be just like talking about the reality of a Godel universe.

 

[marcus]

Paulibus, I put the c back into equation (16), as I believe you wished.
Also I think equation (5) says A = c⁴/(2a²)
So one can solve for a:
a = (c⁴/2A)^1/2
==quote==
Restoring physical units, we have a minimal nonvanishing value of the area
A_min = 4πGℏ/c³, …………..(16)

which, recalling (5), gives a maximum physical value of the accelerations

a_max= (c⁷/8πGℏ )^1/2…………..(17)
The existence of a maximum value of acceleration is of course something long expected in quantum gravity…
==endquote==

Paulibus you were right about their setting c=1 and removing all the c from the equations (16 thru 18), and elsewhere, but I have restored the c raised to what I think are the appropriate powers. So we ought to be able to find out what actually IS the max acceleration. It will be stupendously abrupt acceleration, I expect . Have to run some errands, but will get back to this later!

Francesca used to post here frequently and made a valuable contribution to BtSM forum as a PF member. Now we have her occasional research papers.

 

[marcus]

For continuity:
What's the intuition behind this? ...
http://arxiv.org/abs/1307.3228
Evidence for Maximal Acceleration…

... the interesting Rovelli-Vidotto paper on "Evidence for Maximal Acceleration"... But I run aground easily; so far I have trouble checking the dimensions of even the simplest of their equations, e.g. [18], perhaps because they cleverly simplify by setting c = 1. I do wish this wasn't accepted practice.

... I'll get back to trying to understand Rovelli-Vidotto -- good stuff; I have a daughter Frances.

(c⁷/8πGℏ )^1/2 unpacked for the google window's calculator is:

(c^7/(8pi hbar*G))^(1/2)

When I put that in the google window, I get

1.10924269 × 10⁵¹ m/s²

So if you put the appropriate power of the speed of light back into Rovelli and Francesca's expression for the maximal acceleration, the google calculator is able to parse it and gives back an acceleration in standard format.

Probably it is something an aficionado would recognize as "Planck acceleration" aka one Planck unit of speed per Planck time unit. Or that times a numerical factor of order one.

 

[marcus]

The introduction of the July 2013 "Evidence for Maximal Acceleration" paper has a brief paragraph that summarizes how the a_max derivation goes:

==quote page 1 of http://arxiv.org/abs/1307.3228 ==
... The key to our derivation relies on a core aspect of the covariant approach: the proportionality between generators of boosts and rotations [15]. This ties space-space and space-time components of the momentum conjugate to the gravitational connection and transfers the discretization of the area spectrum to a discretization of a suitable Lorentzian quantity, which, we show, is related to acceleration. The mechanism indicates the existence of a maximal acceleration. This, in turn, yields a bound on the curvature and on the energy density in appropriate cosmological contexts, supporting the results in loop quantum cosmology and for black holes…
==endquote==

It's easy to see that they were already anticipating results about the density maximum, the bounce, and the Loop black hole model, back in July 2013 when they were deriving the Loop acceleration max.

SO THERE ARE TWO things to become conversant with here: the discrete area spectrum and the boost-rotation proportionality. They are too technical for us to enter into detail explanation right now. Let's just be aware of them as keywords, and as essential features of Loop gravity.

The discrete area spectrum was one of the earliest results of LQG, going back to around 1990. It's constantly coming up in discussion and being applied (along with analogous discreteness results for some other geometric operators).

The proportionality between boost and rotation generators is here being used to link acceleration with area and as they said, to "transfer" the discreteness. That proportionality is associated with the basic function on which spinfoam dynamics is built, the so-called "Y map". I first recall seeing it in connection with some work by Eugenio Biachi around 2006 or 2007. The idea is we have two important groups SU(2) (basically spatial rotations) and SL(2,C) (basically spacetime symmetries, the Lorentz group). To take on DYNAMICS we have to map one into the other! Abstract groups are concretized by their matrix "representations" so we need an algebraic map from the SU(2) reps to the SL(2,C) reps. The Y map does this.
So Loop dynamics is built on it and ALSO it establishes that proportionality we were talking about.

Now for a moment everything becomes overly algebraic and a bit incomprehensible. I'll just quote some words from one of the many paper where Y map has appeared in the spinfoam literature during recent years. For a concise summary (minus explanatory background) one can refer to any of numerous papers. One I like is by Chirco, Haggard, Riello, Rovelli. E.g. have a look at page 6 of this:

==quote page 6 of http://arxiv.org/abs/1401.5262 ==
The dynamics of the theory is obtained mapping these states to unitary representations of SL(2,C). A unitary representation (in the principal series) [25] is labelled by a discrete spin k ∈ N/2 and a continuous parameter p ∈ R⁺ and the representation space is denoted H_(p,k). This space decomposes into irreducible representations of the SU(2) subgroup as follows

H_(p,k) = ⊕_j=k^∞H_j . . . . . (40)

where H_j is the (finite dimensional) SU(2) representation of spin j. Therefore H_(p,k) admits a basis |(p, k); j, m⟩ obtained diagonalizing the total angular momentum L² and the L_z = L⃗ · ⃗z component of the SU(2) subgroup. The map that gives this injection, and defines the loop quantum gravity covariant dynamics is given by

Y_γj→H_j^γ
|j,m⟩→ |(γj,j);j,m⟩ . . . . . . . . (41)

Here [the gamma] γ ∈ R⁺ is the Immirzi parameter.
….
….
On the image of the map Y_γ, the boost generator K⃗ and the rotation generator L⃗ satisfy
⟨K⟩ = γ⟨L⟩ . . . . . . . . (43)
as matrix elements.
==endquote==

I tried not too successfully to make the lowercase italic gamma visually distinguishable from the capital Y. Gamma is just a positive real number--it's used in constructing SL(2,C) Lorentz group representation matrices and it turns out to actually BE the proportionality we were looking for.

 

[marcus]

The Planck star (delayed rebound) model of black hole has several interesting things about it.

It resolves the "information loss paradox" because all the info comes back in a simple way, in a long-delayed bounce gamma ray burst (GRB)

It resolves the BH singularity with something physical (no infinities: a bounce).

It doesn't lead to bizarre complicated stuff (e.g. Leonard Susskind's "firewalls") that torment other BH models.

It doesn't get into the "baby universe" business--the rebound is back into OUR space, it does not create a new expanding region (which some earlier black hole bounce concepts depicted).

There are possible PREDICTIONS.
=================

This last point is important: the size of the explosion is not the same for all BH (as in the conventional Hawking evaporation model) but instead the explosion size goes as the cube root of the lifespan.

So that makes the issue of PRIMORDIAL black holes (PBH) crucial to testing the model. The model can be used to predict the energy of pbh GRB that we should now be observing if PBH of the required sized were in fact created in the early universe.

So we may have use for this REVIEW article about PBH by Anne Green. It will be published as the PBH chapter in a book on Quantum BH edited by a former Physicsforums poster named X. Calmet.

Useful review, could serve as source for Planck star discussion:
http://arxiv.org/abs/1403.1198
Primordial Black Holes: sirens of the early Universe
Anne M. Green
(Submitted on 5 Mar 2014)
Primordial Black Holes (PBHs) are, typically light, black holes which can form in the early Universe. There are a number of formation mechanisms, including the collapse of large density perturbations, cosmic string loops and bubble collisions. The number of PBHs formed is tightly constrained by the consequences of their evaporation and their lensing and dynamical effects. Therefore PBHs are a powerful probe of the physics of the early Universe, in particular models of inflation. They are also a potential cold dark matter candidate.
21 pages. To be published in "Quantum Aspects of Black Holes", ed. X. Calmet (Springer, 2014)

 

[Paulibus]

Marcus: thanks for restoring (in your post #84) the factor of c^7 in eqn. 17 of the Rovelli-Vidotto acceleration paper. The maximal acceleration is then easily remembered as roughly 50 orders of magnitude bigger than familiar g. It's reassuring to know that this fundamental limit to acceleration is too large to affect sports like aerobatics or drag racing!

I believe gravitational redshift would still be caused by a uniform field, there is still a potential gradient (an idea of depth, a downstairs and an upstairs). I'd be embarrassed to learn I was mistaken about this, it seems so intuitive, but you might be right.

You are probably right. Think of a photon that carries energy and therefore mass 'upwards' in a perfectly uniform gravitational field. The field exerts a force on this mass and work is done by the photon: force x distance. Work saps photon energy, reduces its frequency, increases its wavelength and red-shifts the photon. But I can't help feeling that this argument is somehow naive, and now I'm somewhat confused by the fact that photons can't just slow down, like vertically thrown objects. But Nature is cunning at extracting work, just as the taxman is at extracting payment.

Lastly, fore and aft; ok with me. I'm an ex Fireball yachtie.

 

[marcus]

Marcus: thanks for restoring (in your post #84) the factor of c^7 in eqn. 17 of the Rovelli-Vidotto acceleration paper. The maximal acceleration is then easily remembered as roughly 50 orders of magnitude bigger than familiar g. It's reassuring to know that this fundamental limit to acceleration is too large to affect sports like aerobatics or drag racing!

You are probably right. Think of a photon that carries energy and therefore mass 'upwards' in a perfectly uniform gravitational field. The field exerts a force on this mass and work is done by the photon: force x distance. Work saps photon energy, reduces its frequency, increases its wavelength and red-shifts the photon. But I can't help feeling that this argument is somehow naive, and now I'm somewhat confused by the fact that photons can't just slow down, like vertically thrown objects. But Nature is cunning at extracting work, just as the taxman is at extracting payment.

Lastly, fore and aft; ok with me. I'm an ex Fireball yachtie.

Six photos here, #5 in sequence is especially gratifying:
http://www.fireball-international.com
Specs:
http://sailboatdata.com/viewrecord.asp?class_id=2945
History:
http://www.fireball-international.com/the-boat/history/

Handling a light planing hull with more than enough sail area must surely be a good preparation for learning physics intuition. Misjudge and you get a dunking. Or so I guess. :^D

 

[Ken G]

I wonder what is the connection between uncertainty and the minimum quantum of action, h. You don't really need uncertainty to get degeneracy support if you have a minimum quantum of action, so it may be more the latter that is the analog of maximum acceleration. A maximum geometric curvature would connect to a minimum sized circle, and the connection between action and acceleration is that action associates with only the fundamental constant h and acceleration associates with the inverse square root of the product of h and G (I don't think c is of importance, it's just a kind of medium of exchange between the various scales, I think we could understand the situation just with h and G, action and gravity). So maximum acceleration seems to combine the minimum action h with a minimum of something else that associates with gravity. It reminds me of how many systems acquire a maximum kinetic energy when their action is minimal, we may have something here where a spacetime system acquires a maximum curvature when some generalized version of action reaches a minimum of the geometric mean of h and G.

 

[marcus]

The way I see it, that's the best post on this thread so far. It's really interesting. I've avoided posting for a couple of days so as not to "cover it" but leave it visible on the menu. what you suggest here is a line of research that somebody could do, analogous to that by Vidotto and Rovelli in the "Evidence for Maximal Acceleration" paper http://arxiv.org/abs/1307.3228 but about an action quantity instead of acceleration.

You refer to it as "the geometric mean of h and G" which is a nice way to think of the Planck length. BTW here's how I remember some of those natural units quantities, since my memory is not great and I can use a mnemonic now and then:
Obviously hbar∗c is energy∗length = force∗area
and the natural unit of force is c⁴/G (the one thing I have memorized).
So divide force∗area by force and you get hbar∗G
You say neglect factors of c, so I leave off the /c³ denominator.
So then the square root of that hbar∗G is the length.

 

[Ken G]

Exactly. I don't claim to understand the meaning of that, but it suggests to me that there is a quantity, analogous to action, that is also quantized, and thereby has a minimum possible value. Perhaps G, some kind of gravity related quantity (minimum inverse curvature? Like a duality where acceleration has a maximum because some kind of dual to curvature has a minimum?). And together, perhaps it is the combination of the quantized action and the quantized other thing in the duality that get together and have a geometric mean that underpins the Planck scale, the basic scale of our universe. These are not well-formed thoughts, but perhaps the reason the Planck length is the geometric mean of h and G is related to the AdS/CFT duality, where the G comes from AdS and h comes from CFT, and the duality is not a single aspect of the universe that obeys one of the laws, and then coincidentally the other applies to the duality, but rather the universe combines both aspects of that duality, that either by itself doesn't make a universe. That might also help explain why there are so many Planck lengths in the universe-- the usual expectation is that a universe built of Planck lengths should have order-unity Planck lengths in it, but not if the Planck length itself originates from a kind of collision of two vastly different scales. Admittedly this word salad is badly in need of a more constructive formulation!

 

[marcus]

Exactly. I don't claim to understand the meaning of that, but it suggests to me that there is a quantity, analogous to action, that is also quantized, and thereby has a minimum possible value. Perhaps G, some kind of gravity related quantity (minimum inverse curvature? Like a duality where acceleration has a maximum because some kind of dual to curvature has a minimum?). And together, perhaps it is the combination of the quantized action and the quantized other thing in the duality that get together and have a geometric mean that underpins the Planck scale, the basic scale of our universe. ...

In LQG one of the most basic results proved is that you do have a minimum positive area (measured by the area operator, eg. the area observable constructed in Loop gravity has a minimum eigenvalue) and this is compatible with the theory being Lorentz invariant. So there is a maximum curvature (the duality with area you mentioned) and indeed "acceleration has a maximum" as you said, in LQG. See, for comparison,

... that by Vidotto and Rovelli in the "Evidence for Maximal Acceleration" paper http://arxiv.org/abs/1307.3228 ...

Paulibus, you were talking about Planck quantities, I'll bring this forward since we're on a new page:

... here's how I remember some of those natural units quantities, since my memory is not great and I can use a mnemonic now and then:
Obviously hbar∗c is energy∗length = force∗area
and the natural unit of force is c⁴/G (the one thing I have memorized).
So divide force∗area by force and you get hbar∗G
You say neglect factors of c, so I leave off the /c³ denominator.
So then the square root of that hbar∗G is the length.

Getting back to the PLANCK STARS topic, there's a rather good popular news article about the idea in "discovery.com" magazine:
http://news.discovery.com/space/could-black-holes-give-birth-to-planck-stars-140211.htm

===sample excerpt===
What goes on inside a black hole’s event horizon has actually caused a theoretical conflagration and now, two theoretical physicists have proposed a new idea that may marry quantum mechanics with gravity, extinguishing the tricky “firewall” and finding a solution to the “information paradox.”
==endquote==

==more from the discovery.com article==
…Rovelli and Vidotto looked at this problem from a different perspective. While working on models of a collapsing universe — i.e. the opposite to the Big Bang, known as the Big Crunch — they found that the fundamental quantum structure of the Universe prevents an infinitely dense singularity from forming. The collapse of the Universe therefore reaches a fundamental density, causing the universal collapse to rebound, or “bounce.”...

Say if a similar model can be used to describe a black hole?

A Planck Star Rises

If a massive star explodes as a supernova, creating a black hole in its wake, what if the superdense material that formed the black hole actually didn’t form a “singularity”? Sure, the material is unimaginably dense, but the object in the core of the black hole still has structure. Rovelli and Vidotto argue that the inward force of gravity is counteracted by the quantum structure of the Planck density.

If we were to zoom in, far beyond the size of quantum particles, it is theorized that we will reach a fundamental scale known as the Planck length. Should matter be compressed to these scales, rather than disappearing into an “infinitely dense” singularity — a solution that doesn’t make a whole lot of sense — perhaps the contraction stops at the Planck density, creating a “Planck Star” and the object rebounds, or “bounces.” From the perspective of the Planck Star, it will be a very short-lived affair; it’s collapse and bounce would occur rapidly. But to outside observers elsewhere in the Universe (i.e. us), as space-time surrounding the Planck Star is so extremely warped, time dilation makes the black hole (and the Planck Star it contains) seem static and unchanging.

Over time, as the black hole loses mass to Hawking Radiation and the Planck Star continues to expand after the rebound, the event horizon of the black hole will slowly contract, eventually reaching the surface of the Planck Star contained within. At this point, argue the researchers, all of the information the black hole ever consumed over its lifetime will be suddenly released to the Universe — solving the “information paradox.” What’s more, we should be able to detect this deluge of information.
...
...
“(Planck Stars) produce a detectable signal, of quantum gravitational origin, around the 10^-14cm wavelength,” they write. This signal could embody itself in cosmic rays of energies in the GeV range, a signal that can be easily detected by gamma-ray observatories.
==endquote==

 

[Ken G]

Interesting, I must say that is a cute possibility. It seems to dovetail nicely with the idea that every black hole is its own universe, ready to eventually "Big Bang" as the Planck star is exposed by the contracting event horizon. If so, then if the object did not form from matter that fell in from infinity, but rather fell in from a gravitationally bound object (like the core of the star), it would also not expand to infinity when it re-emerges. Maybe the original "bounce" is the inflationary epoch, and there is a kind of second "Bang" when the contracting event horizon reaches the Planck star and it pops out of its gravitational cocoon. Could that end up looking like dark energy?

 

[marcus]

That sounds like food for further research! In their first paper on the subject, Rovelli and Vidotto assume that the entire mass of a Planck star is converted to gamma ray.

So what results is something that looks like a so-called "very short" type of GRB. There is some evidence that these are isotropic, and of a different mechanism from the longer GRB. There is data on short and very short GRB, see refs. in R&V paper.

R&V estimate the typical wavelength of the Planck starburst GRB, and the energy to be expected if they currently occur as finale of primordial BH.

Different analysis might lead to other kinds of radiation, but I think intuitively according to R&V analysis the only primordial BH which short enough lifetime (14 billion years) to be exploding NOW are ones with comparatively small mass and very small size. Their analysis suggests an initial mass on the order of 100 million metric ton and a BH of such a small mass is extremely small. So when the burst occurs there simply is not space or time enough for matter particles to form. The energy is all GRB. Just an intuitive argument but you see what I'm saying.

The lifetime goes as the cube of the initial mass. So the kind of Planck star bursts we conceivably could see in the present era are all of this small BH with lifetime no longer than 14 billion years, the expansion age of the universe.

What you are talking about is a different matter---explosion of much more massive BH. That's an interesting line of thinking---as you suggest, we are not likely to ever SEE such an explosion, but its conceivable that we are IN such an explosion. IOW that some of the stuff we around us was MADE in such an explosion. Interesting idea but on a very different track from the observational checks that Vidotto and Rovelli are talking about.

 

[Ken G]

That sounds like food for further research! In their first paper on the subject, Rovelli and Vidotto assume that the entire mass of a Planck star is converted to gamma ray.

It seems to me, if one will solve the information paradox this way, then to get GRMs the black hole must originally have been made from gamma rays, but I guess if they are primordial, they can be anything.

Different analysis might lead to other kinds of radiation, but I think intuitively according to R&V analysis the only primordial BH which short enough lifetime (14 billion years) to be exploding NOW are ones with comparatively small mass and very small size. Their analysis suggests an initial mass on the order of 100 million metric ton and a BH of such a small mass is extremely small. So when the burst occurs there simply is not space or time enough for matter particles to form. The energy is all GRB. Just an intuitive argument but you see what I'm saying.

Yes I do, I guess you can make the primordial BH out of anything, so the information that comes out can be anything too.

What you are talking about is a different matter---explosion of much more massive BH. That's an interesting line of thinking---as you suggest, we are not likely to ever SEE such an explosion, but its conceivable that we are IN such an explosion. IOW that some of the stuff we around us was MADE in such an explosion. Interesting idea but on a very different track from the observational checks that Vidotto and Rovelli are talking about.

Yes, I see what you mean, they are thinking about small primordial BHs that we can now observe. It would be interesting if observational checks on that kind of animal end up suggesting that the whole universe is a much bigger version of the same thing! It would certainly usher in anthropic arguments, because a GRB is not going to spawn a universe in which intelligent life can develop, but information about the distribution of those very short GRBs might allow extrapolation to a full Planck-star IMF, which might then allow anthropic arguments over the "landscape" of that IMF, extrapolated all the way up to universes that can create life. What has always bothered me about anthropic arguments is that to use them, you already need some constraint on the distribution, but instead the distribution must usually be cooked to get the expected result.

 

[MTd2]

It seems to dovetail nicely with the idea that every black hole is its own universe, ready to eventually "Big Bang" as the Planck star is exposed by the contracting event horizon.

Not exactly a different universe. Here, we have a bouncing star, that is, a 2-sphere, plus its volume, bouncing. A universe would be a 3 sphere, plus its hypervolume, bouncing.

 

[marcus]

Hi KenG and MTd2,
I wanted to share the results of a calculation. First, though, I think KenG has a point, but it is not about a "new universe" so much as it is about asking what could the explosion debris be from a more massive Planck star BH. I don't know the answer.

This is different from (for example) Smolin's baby universe idea where a BH collapse produces a new expanding spacetime region entirely separate from the mother universe and we never see that. It is an explosion "out the bottom" of the BH collapse.

In R&V picture no new spacetime is created, there is simply an explosion of whatever went into the BH in the first place after it has undergone the complete physical transformation one expects near Planckian density and rebounded outwards. some kind of matter AND/OR radiation. As I picture it, radiation more likely than matter, but one has to allow for pair-production (radiation producing particle-antiparticle pairs).

In the standard picture the universe has only been expanding for 14 billion years, so we have no chance of SEEING the debris of an explosion of more than small primordial BH. It has been repeatedly conjectured by various people that this would simply be a GRB. So that is all Rovelli and Vidotto are considering---a simple very brief comparatively small GRB. Violent by our standards but small" compared with other sorts of longer-duration GRB that are often observed.

This has to do with the calculation I wanted to show you.

If you put this into google
((hbar*c^4*14 billion years)/(5120pi*G^2) )^(1/3)
you get 1.738 x 10¹¹ kilograms

If you look at equation (18) of the Planck stars paper, on page four, you see that this must be the INITIAL mass of a conventional Hawking BH that evaporates in 14 billion years.
Check it out http://arxiv.org/abs/1401.6562 you'll see what I mean.

And then if you look at equation (22) you will see that the initial mass of a PLANCK STAR black hole that lasts 14 billion years before exploding as GRB has to be that multiplied by the square root of two.
Putting into google
2^(1/2)*((hbar*c^4*14 billion years)/(5120pi*G^2) )^(1/3)
gets you
2.4584 x 10¹¹ kilograms

This is a quarter of a billion metric tons

About one THIRD of that remains (has not evaporated) when the Planck star finally blows.
That is how much mass is converted into GRB energy. So that gives an idea of the energy of now of these predicted gamma ray bursts. It is on the small side as GRBs go. A lot of them are far more energetic---the term "hypernova" is used.

Earlier I estimated a FIFTH of a billion tons, but I think I should use this revised estimate of a QUARTER which is more carefully derived. And to remember it (you may think this ridiculous but it helps me recall it) I have this rhyme of an imagined conversation with a primordial BH that is now ready to go hyper nova, if the theory is right.

Oh Planck star, you dark rebounder,
how long before you burst?
"I'm almost done!"

But your time goes by so slowly,
what mass were you at first?
"Quarter billion tons!"

 

[Ken G]

Another issue to bear in mind is, in what environment is the evaporation of such a BH going to proceed more slowly than accretion of additional mass? For Bondi-Hoyle accretion, one gets the scale of the mass accretion rate to be
4 pi G^2 M^2 rho / v^3
which makes the timescale to add mass M
v^3 / 4 pi G^2 M rho
and using any reasonable numbers for that makes it way longer than the age of the universe, so it seems that mini BHs really don't accrete anything to worry about.

 

[MTd2]

Marcus, well, I was not saying baby universe. I was talking about a new universe. A big bounce seems to be a recycle of an old universe...

BTW, where does this old universe comes from? A previous aeon?

 

[marcus]

Another issue to bear in mind is, in what environment is the evaporation of such a BH going to proceed more slowly than accretion of additional mass? For Bondi-Hoyle accretion, one gets the scale of the mass accretion rate to be
4 pi G^2 M^2 rho / v^3
which makes the timescale to add mass M
v^3 / 4 pi G^2 M rho
and using any reasonable numbers for that makes it way longer than the age of the universe, so it seems that mini BHs really don't accrete anything to worry about.

KenG, thanks for that comment. I think you are right, for nearly all the expansion age the density has been so low that accretion would not amount to much. Maybe one can check that also by comparing temperatures. the temperature of the primordial BH versus the temperature of the surrounding medium, background radiation and so forth.

MTd2, I think we understand that we are not talking about daughter universes, or new spacetime regions resulting from a bounce. We are talking about matter/radiation explosions that happen in THIS universe.

 

[marcus]

I was just going to post this on the Loop&allied QG bibliography and found MTd2 beat me to it by barely a minute:

http://arxiv.org/abs/1404.5821

Planck star phenomenology

Aurelien Barrau, Carlo Rovelli
(Submitted on 23 Apr 2014)
It is possible that black holes hide a core of Planckian density, sustained by quantum-gravitational pressure. As a black hole evaporates, the core remembers the initial mass and the final explosion occurs at macroscopic scale. We investigate possible phenomenological consequences of this idea. Under several rough assumptions, we estimate that up to several short gamma-ray bursts per day, around 10 MeV, with isotropic distribution, can be expected coming from a region of a few hundred light years around us.

It's 5 pages, with 4 figures.

 

[marcus]

Barrau and Rovelli have an interesting calculation of the range at which a PBH explosion can be detected, say with a reasonable size (1 square meter) detector in orbit.

The GRB explosion is powerful, but it is carried by a comparatively small number of high-energy photons, not enough are likely to hit the finite area of the detector to register, if the explosion is more than a few hundred LY away.

Check out their calculation. they also recalculated what the initial mass has to be in order for the thing to explode at present, digging in more detail into the evaporation process, and using a numerical integration.

0.61 billion metric tons. So the mnemonic rhyme has to say "Point six" for 0.6, or words to that effect.

Planck star, you dark rebounder,
how long before you burst?
"I'm almost done!"

Deep time in you goes slowly,
what mass were you at first?
"Point six billion tons!"
_____________

 

[Ken G]

(if I may presume to improve on your fine poem, how do you feel about "doth founder" instead of "goes slowly" to create an even deeper rhyming connection between the verses?)

 

[marcus]

(if I may presume to improve on your fine poem, how do you feel about "doth founder" instead of "goes slowly" to create an even deeper rhyming connection between the verses?)

"Founder" is an excellent suggestion! Let's try this:


Planck star, you dark rebounder,
what mass were you at first?
"Point six billion tons."

Deep time in you does founder,
how long before you burst?
"I'm almost done!"



________

 

[Ken G]

Yes, I like that reversal in the order, it gives a punchline in the end and still serves to help you recall the putative mass of these potential denizens of the otherwise dark corners of space. (Does "deeply" fit the meter better?)