Planck Stars: Carlo Rovelli & Francesca Vidotto

[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?)

 

[marcus]

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?)

I think you are right about the fourth line being metrically just slightly awkward. Let's try this slight change in that line, so the stress comes naturally on the second syllable "time" just as it does on the second syllable of the first line "star".Planck star, you dark rebounder,
what mass were you at first?
"Point six billion tons."

Deep time, in you, must founder.
How long before you burst?
"I'm almost done!"Let's let it sit like that for a while and get used to it before we try further changes. You've already helped improve the little rhyme quite a lot. I'd rather not make changes too fast. Let's look at it again tomorrow.

BTW the shadow pop song structure I'm hearing as a kind framework is Righteous Brothers "Unchained melody". It's on YouTube. Was popular in the mid-Sixties.
The third line in the RB original is:
"a LONG lonely time" and we are saying
"point SIX billion tons" as a partial echo with their stress pattern

The sixth line in the RB original is:
"are you still MI-I-I-NE?!" and we are saying
"I'm almost DONE!" again partially echoing the stress pattern.

Here's a 1965 recording of the Righteous Brothers song I'm referring to for stress pattern:

 

[marcus]

For people who have already taken a look at 1401.6562, and 1404.5821, I'm repeat some things I found interesting and/or surprising.

One thing I found interesting is the detection range that Barrau Rovelli calculate in 1404.5821 (the phenomenology paper) namely with an assumed square meter detector surface a range of only 200 light years!

This is for an explosion wattage which is, for a brief interval like one second, roughly 100 times the wattage of the sun. Namely the "mc²" energy equivalent of 0.4 billion tons mass*, delivered in, say, one second. If that power were presented in the usual starlight spectrum---the UV-visible-IR range---it would be detectable much farther off than 200 light years. What they point out in 1404.5821, that I didn't think of earlier myself[/color] is that since the power is presented in very high energy photons there are way fewer photons.

The photons are comparatively speaking so sparse that beyond a certain range (like 200 LY) they might be so spread out that they entirely miss the finite area detector. If you assume a larger detector you get a longer detection range of course---with 4 square meters the range doubles to 400 LY. But the detector has to be up outside the atmosphere so there are reasonable cost limits on what area one wants to assume is practical.

BTW what this seems to imply is that one couldn't rule out primordial Planck stars as a significant fraction of dark matter, merely because then we would be seeing lots and lots of them. Since we would only detect the explosions if they are within 200 light years there could be a substantial amount of dark mass out there in the form of the ASTEROID-MASS objects which would not show up in LENSING SEARCHES.
Of course primordial PS might NOT constitute a significant fraction of dark mass, but it looks like we cannot rule it out so easily. One needs to search for nearby gamma ray bursts with predicted photon energy around 10 MeV (wavelengths around a tenth picometer) and get some STATISTICS before one can put constraints on the relevance to dark matter.

That detection range limit only applies to seeing INDIVIDUAL EVENTS. They also start investigating the implied effect of Planck star model primordial black hole explosions on the gamma ray BACKGROUND.
That means integrating the diffuse radiation that one would expect from more distant, earlier, younger explosions as well: "hotter" radiation because from lower mass smaller size primordial BH that exploded earlier e.g. in distant galaxies, and on the other hand redshifted, e.g. z=2 or z=3. The redshifting and the "hotter" partially cancel each other. So Barrau Rovelli also look at the phenomenological consequences to the gamma background as distinct from what one expects in the individual GRB events department.

*the final mass is the initial mass divided by sqrt(2), so final is about 70% of initial. For primordial Planck stars exploding at present time, initial is .6 billion tons, so final is about 0.4 billion tons.
Their more precise figure is 0.43, see eqn 2.7.

http://arxiv.org/abs/1401.6562
http://arxiv.org/abs/1404.5821

 

[Paulibus]

In my post #72 I found the root cause of the bounce difficult to fit into my primitive background
of Physics. I’m still having difficulty with this, by Rovelli and Vidotto:

http://arxiv.org/abs/1401.6562, p.1, paraphrased ...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...

This introduction to the key point of the whole ‘bounce’ scheme is on p. 1 of the Rovelli-Vidotto
paper.

But I’d still like to have help to better understand how this "quantum-gravitational repulsion"
arises. In fact I wonder if the bounce is not better related to the Pauli Exclusion principle, rather
than to Heisenberg’s uncertainty principle?

The reason that two particles (say Fermions; particles with half-integral spin, like electrons) can’t
occupy the same state is that electrons are all identical, so when their wave functions overlap they
can’t be kept track of as individuals. Indeed there is a

.. deep physical connection between transformation of states under spatial
rotations (like spin?).. and the statistics of many-particle systems...

that leads to failure
for repeatedly deploying a quantum-mechanical ‘creation’ operator to place more than one
electron in a state labelled with the same quantum numbers.

Happily for us, a lot follows from the quantum quirk of being able to sort fundamental particles
into Bosons and Fermions. This distinction prevents electrons from all collapsing into a common
ground state. Via short-range repulsion it stabilizes structures with electrons, like atoms and
metals. Indeed it enables the Periodic table and let's electricity flow easily along metal wires into
our houses. Great stuff. But in this case without a shattering bounce.

Perhaps some more esoteric quantum-mechanical quirk related to the Pauli principle could helps
to violently rip apart collapsing Planck stars and so avoid a singularity?

...I want us to be able to contemplate something more quantitative...
...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.

. Agreed.

 

[Ken G]

That's an interesting point about the exclusion principle, it suggests that a black hole made of a distinguishable mixture of Fermions, like different quarks, or even of bosons, like gluons or photons, would have very different "quantum bounce" properties than one made up of identical fermions. That's a problem, it seems to me, because if one wants to use the bounce to solve the information paradox, and if the bounce spits out a bunch of gamma rays (which are bosons), how can it retain the information of what kinds of particles went in there in the first place? Or put differently, if they are "primordial" black holes, they might have been there "from the beginning", and so it might not be well defined what kinds of particles created them, one might only know the mass of the primordial black hole. That can't be if the bounce needs to know if they are bosonic or fermionic. Perhaps one simply expects them to form from the quark-gluon plasma, but the quarks are fermions and the gluons are bosons, so wouldn't they need to know the relative proportion to know how the bounce happens?

 

[Paulibus]

I should warn that my temerity in suggesting that a Rovelli-Vidotto remark is wrong (their writing that the gravitational-quantum bounce is caused by the Uncertainty Principle) is based on my pretty shaky understanding of the whole 'bouncing loop-quantum-gravity' scenario.

My further suggestion that one should look rather to the Exclusion Principle for intuitive understanding of such a 'bounce' scenario should therefore be taken with a pinch of salt.

But the Exclusion Principle is known to be such an effective condensation or collapse preventer, while the Uncertainty Principle hardly fits this needed role, so it's faute de mieux!

 

[marcus]

Hi Paulibus, I've been slow to respond. It's a good question. there should be a path of INTUITIVE reasoning from some basic principle such as HUP (or some other if not that) to, say, the discreteness of the LQG area operator---a minimum positive area eigenvalue.

After that it seems intuitive---curvature is reciprocal of area. A minimum positive area means a maximum curvature (so collapse can't go all the way to classical singularity). Also you may remember the paper where Rovelli and Vidotto showed there is a maximum ACCELERATION in Lqg and argued that the BH singularity is thereby avoided. that was also based on the discrete areas spectrum as I recall.

I went back to the January Planck Star paper http://arxiv.org/abs/1401.6562 to see what their reference was. One of their references, [17], was to http://arxiv.org/abs/1310.8654 which I want to check out. It might help.
==quote http://arxiv.org/abs/1401.6562 page 1==
For instance, a collapsing spatially-compact universe bounces back into an expanding one. 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 [16]. 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 [17].
==endquote==
The two references are to
http://arxiv.org/abs/gr-qc/0612104
http://arxiv.org/abs/1310.8654

In the latter paper (October 2013) I see the Heisenberg uncertainty principle appearing on page 2 in a discussion of bounce dynamics. But I can't give you an intuitive account, as yet. I don't understand this well enough yet. I see the simple Friedman universe being modeled using Heisenberg dynamics and a CONJUGATE pair of variables (in the classical development) which become operators in the quantum version. I see a Heisenberg dynamics equation using the commutator of these operators. I see the HUP applied to the conjugate pair "c" and "p" where p is associated with the scale factor---the "size" of the universe in the Friedmann cosmic model. And where c is conjugate to that. Maybe analogous to how momentum is conjugate to position---could "c" be a rate that the scale factor is changing? Could "c" be related to energy density? I keep seeing an HUP-like expression involving ΔcΔp or the operator version of that, with the tildes. I don't understand this well enough to discuss it. Anyway maybe some intuition can be dug out of the October 2013 paper (by Rovelli and Wilson-Ewing) or else out of the earlier December 2006 paper that was referred to also.

You asked if they possibly could have meant Pauli exclusion instead. I think that primarily involves Fermionic matter and here we are mainly concerned with geometry, sometimes with a scalar field as token matter. As best I can see right now, probably they really mean HUP, not Pauli exclusion. but I can't be sure! Hope to understand this better in a few days and be able to respond with a bit more competence

 

[marcus]

Since we've turned a page, I'll bring forward a quote from discovery.com that describes the basic Planck Star idea rather well, for genera audience:

, 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==

 

[Paulibus]

Thanks for that very full reply to my muddled post on the cause of repulsion that causes the bounce. I'd not properly read the Rovelli-Wilson-Ewing paper, which explains the relevance of the Heisenberg uncertainty principle to the bounce. I'm still baffled by the c in the their uncertainty relation, which seems to be defined as a "configuration variable" in "Mathematical structure of loop quantum cosmology" by Ashtekar, Bojowald and Lewandowski (arXiv:gr-qc/0304074v4 24 Dec 2003). It's way above my head. But c must represent something physical and measurable, but I can't see quite what, yet. I'll think about your suggestions.

 

[marcus]

Thanks for that very full reply to my muddled post on the cause of repulsion that causes the bounce. I'd not properly read the Rovelli-Wilson-Ewing paper, which explains the relevance of the Heisenberg uncertainty principle to the bounce. I'm still baffled by the c in the their uncertainty relation, which seems to be defined as a "configuration variable" in "Mathematical structure of loop quantum cosmology" by Ashtekar, Bojowald and Lewandowski (arXiv:gr-qc/0304074v4 24 Dec 2003). It's way above my head. But c must represent something physical and measurable, but I can't see quite what, yet. I'll think about your suggestions.

I'm still far from being able to get my mind around the significance of the HUP and how it plays a role here. But maybe there is hope. A friend writes suggesting that I should think more about PHASE SPACE. You know in conventional dynamics of an N particle system each particle has a 3D position and a 3D momentum. So there are a pair of conjugate variables for each particle. Phase space is this large dimension vector space recording these 2N variables.

It seems that the Planck's hbar is the natural RESOLUTION SCALE of phase space! It indicates how fine you can grind it or how clear you can see it. It seems significant that the UNIT of hbar is length*momentum, or equivalently time*energy. which is also the separation unit in phase space!

So if n is the dimension of phase space the volume of a "phase-fuzz element" or "blur-cell" of phase space is hbarⁿ. Not sure what that means. It is the volume of a blob that your eyes can resolve into two blobs. It is interesting that, if the system has 5 particles and hence ten 3d degrees of freedom and so phase space is 30 dimensional Euclidean R³⁰ that then there should be this small volume which we can calculate by taking the 30th power of Planck constant: hbar³⁰

and the units work out, that is the right unit of volume because the unit along the axes in R³⁰ is in fact length*momentum. Not only am I not sure I know what this means, I know I am NOT sure what it means.

It seems that Nature holds the line against precision, defies being pinned down, beyond a certain point. If I understood conventional dynamics better I might be able to grasp how this defiant existential frivolity of nature could lead to a bounce. Today I shall just have lunch and not try anymore to understand her.

 

[Paulibus]

Yes, I'm familiar with resolving power, say of the human eye (about 1/10th of a mm). And of limits to resolution imposed by the wavelength of light, or electrons, used as observing probes. I suppose one can regard the lattice spacing of say, a copper crystal, as a graininess akin to a resolving power, which controls some of the measured physical properties of copper, like mechanical strength and electrical conductivity. But I'm talking here of limited 'resolution' in an observer-related sense that's quite 'real' for me.

When it comes to 'limited resolution', 'phase-fuzz element' or 'blur cell' connected with abstract human constructs like multi-particle phase space, my understanding starts to totter. But I often wonder, idly, if regular, simple-seeming, everyday space-time will eventually be revealed as grainy, in which case I'd be more comfortable with a grainy phase space.

Perhaps the abstract physics of a bouncing cosmos described in terms of a grainy phase space defines a path that leads this way, hopefully to be someday confirmed by prediction and observation. In the meantime I'll watch this space with interest and just enjoy Sunday lunch.

 

[marcus]

... In the meantime I'll watch this space with interest and just enjoy Sunday lunch.

We had a really enjoyable Sunday. It was my wife's birthday. Our son (I almost wrote sun) came over and did some redwood carpentry and told us latest tech/geek news and we watched a movie called *quartet* that Dustin Hofmann directed, about very old retired musicians at a place in English countryside. Redwood is a really nice material. Durable but soft, easy to handle, and lovely to look at as rich chocolate is to taste.

I think of you sailing one of those over-sailed planing-hull scows equipped with a trapeze. Must be an unforgettable excitement.

You mentioned that graininess of PHASE-SPACE would be more intuitive if one already had the idea of graininess of space. One does have it in LQG geometry, in a very interesting sense. GEOMETRIC MEASUREMENTS in LQG are always grainy because of the oldest most basic theorem in Loop, the discreteness of the area operator spectrum. There is a smallest positive area eigenvalue which can occur from a measurement of area. (Similar facts about volume, angle etc.)

But geometry in LQG is also grainy in another sense. This is more involved and more work to understand. You know that in 1915 GR the geometry is an *equivalence class* of metrics defined on manifolds. There is no preferred representative of the geometry. No preferred manifold or set of points, and no preferred metric ON whatever manifold happens to be be used.
Because of general covariance and background independence there is no fixed material space which could be grainy, no aether which could have grains.

Space is nothing but the gravitational field itself. Nothing but the geometry field. Nothing but the abstract equivalence class of metric-and-matter layouts. (no underlying point-set) So ontologically it is somewhat analogous to the electromagnetic field. Something one cannot see, but believes physically real, and which is experienced by matter through interactions e.g. measurements of the field by some event.

Space IS geometry. Geometry is finally nothing but geometric measurements, interactions that occur. This points to the deeper discreteness than what I already mentioned. Geometry is a quantum field, inferred continuous but experienced by matter in discrete facts (interactions). Just as the electromagnetic field although inferred continuous is experienced in discrete quanta, in discrete PHOTON interactions.

In a quantum field theory phenomena are intermittent. They occur here and there, with this or that bit of matter, now and then.
Phenomena are discrete, continuities are inferred.

So geometry IS grainy, in response to your question, in both the simple sense that e.g. the area observable has discrete spectrum,
and what I think is a deeper sense that all quantum fields (whether they are geometry or matter) are grainy in their phenomena.

 

[MTd2]

Hey Marcus, have you seen my post on the LQG thread? Do you think LQG can describe a de sitter space like that? The curious thing it is that (despite trying to solve the non existent problem of boltzman brains), it seems that the end of the universe is like the beginning.

 

[Paulibus]

The enthusiasm you have for Loop Quantum Gravity's conclusion that geometry (and its manifestation as gravity) is grainy in the quantum sense is heartening, Marcus. Thanks for that illuminating post. I hope that such granularity will in time be revealed by the tried and tested physics cycle of prediction and observation, which distinguishes our subject's imaginings from prolific human fantasies; sample below.

Quantum phenomena seem to me to be often linked to the phenomenon of resonance, which in turn couples our familiar dimensions of time and space. Bohr's concept of atomic energy levels being linked to integral numbers of wavelengths is an example; standing waves. Maybe the Pythagorean concept of 'the music of the spheres' was prescient?

And that's enough mystic nonsense!

 

[marcus]

The enthusiasm you have for Loop Quantum Gravity's conclusion that geometry (and its manifestation as gravity) is grainy in the quantum sense is heartening, Marcus. Thanks for that illuminating post. I hope that such granularity will in time be revealed by the tried and tested physics cycle of prediction and observation, which distinguishes our subject's imaginings from prolific human fantasies; sample below.

Quantum phenomena seem to me to be often linked to the phenomenon of resonance, which in turn couples our familiar dimensions of time and space. Bohr's concept of atomic energy levels being linked to integral numbers of wavelengths is an example; standing waves. Maybe the Pythagorean concept of 'the music of the spheres' was prescient?

And that's enough mystic nonsense!

Frank Wilczek (nobel for the tricolor glue that holds quarks and stuff) wrote a nice article a while back about the engrained stubborn Pythagorishness of modern physics. He's part humanist (not all Vulcan so to speak) and has composed some decent sonnets. You might like the article.

How do you know how much is enough mystic nonsense? Isn't it true that there's never enough of the right kind?

Have you watched Rovelli's June 2013 Oxford "cosmology and quantum theory" YouTube?

Let me google rovelli cosmology relational and see if it comes up.

Yes, it is the first hit.

compared to that talk, the Wilczek piece is casual light reading but if curious google the title
"world's numerical recipe" and the author's name. Probably
wilczek world recipe would get it
Yes, just those three words.

 

[marcus]

About making sense of the bounce…that's the essential topic here: it's common to both the Planck star concept of BHs and Loop cosmology…so I may as well have another go at it.
A friend recently sent me an intuitive take on it part of which I'll quote:
==excerpt from private message==
...regarding ...heisenberg uncertainty principle,... there is a standard argument for the stability of atoms because of quantum theory. the electron cannot fall into the nucleus because HUP forbids it to be too localised without zipping away. i would see the cosmological bounce and the core of the Planck stars as possible manifestations of the very same thing. as you say, nature does not like to be pinned down too precisely. discreteness and therefore the area gap is a manifestation of the same: in the classical phase space, a system cannot be squeezed in a region smaller than hbar (hbar has the dimensions of phase space ...). so we cannot have an eigenvalue of the energy of a harmonic oscillator, or of the electron in a coulomb potential, or of the area of a region, or of the volume of a symmetric universe, so small as to require the corresponding state to be squeezed in too small a region of phase space. ...
==endquote==