Planck Stars: Carlo Rovelli & Francesca Vidotto

[marcus]

I just logged this on the biblio thread. This is in case there are questions, or things people want to discuss.
http://arxiv.org/abs/1401.6562
Planck stars
Carlo Rovelli, Francesca Vidotto
(Submitted on 25 Jan 2014)
A star that collapses gravitationally can reach a further stage of its life, where quantum-gravitational pressure counteracts weight. The duration of this stage is very short in the star proper time, yielding a bounce, but extremely long seen from the outside, because of the huge gravitational time dilation. Since the onset of quantum-gravitational effects is governed by energy density --not by size-- the star can be much larger than Planckian in this phase. The object emerging at the end of the Hawking evaporation of a black hole can then be larger than Planckian by a factor (m/m_P)ⁿ, where m is the mass fallen into the hole, m_P is the Planck mass, and n is positive. The existence of these objects alleviates the black-hole information paradox. More interestingly, these objects could have astrophysical and cosmological interest: they produce a detectable signal, of quantum gravitational origin, around the 10⁻¹⁴cm wavelength.
5 pages, 3 figures.

 

[Demystifier]

It's funny that authors comment their own paper as "nice paper".

Perhaps they meant "not too technical, easy to read"?

 

[MTd2]

I rather liked Stephen W. paper, concerning the non existence of Black Holes, that the horizon was apparent. Once I posted a similar idea on n-category cafe, a few years ago, then my posted got deleted and I got a warning on my own email because I was not allowed to promote my crackpot ideas of quantum gravity, heh. Note, that I was questioning an idea, not saying it was true...

What having a big name does for you! But fortunately S.W. put something worth, and I am happy that the idea is out, in a way.

 

[marcus]

It's funny that authors comment their own paper as "nice paper". ...

Funny! and also true. That's Francesca's light comic touch. It helps to keep the physical universe in a good humor.

 

[marcus]

I'll give a simplified paraphrase to help us (including myself) acquire some basic intuition.
They build on the LQC effective friedman equation which shows quantum corrections kicking in at high density and making gravity repellent.

So look at their figure 1. It shows TWO trapping horizons. The outer is the usual Schwarzschild horizon within which the light cones tilt more and more towards the center of collapse---UNTIL density gets high enough for quantum gravity corrections and the cones begin to straighten up.
When they are back up to a 45 degree tilt (as they originally were at the Schw horizon). Then again you have a trappingorizon.

An inner sphere that nothing can get out of. So picture this ball of very hot radiation at the center of collapse. That is what they call the "Planck star". It takes the place of the classical BH sing'ity.

And one of the beautiful things about this picture is that this Pstar ball of energy is undergoing a bounce in very slow motion

Rovelli and Smerlak have a paper in preparation where they estimate the time-scale. It is slow motion because of the extreme gravitational time-dilation.

Eventually the Schw out-horizon will shrink (about 1/3 of the mass eventually goes out as Hawking radiation) and the inner trapping horizon will grow until they meet and the Planck star bursts.

I picture a ball of hot photons, so dense that the photons are temporarily trapped, which seen from the outside has a time-dilated lifetime on the order of the age of the universe. And eventually the ball expands to where it bursts, releasing "cosmic rays".
Here's their reference [18] to the paper in preparation.

[18] C. Rovelli and M. Smerlak, “Proper time of life of a Planck star,” in preparation (2014) .

 

[marcus]

Maybe the best way to grasp the essential idea here is just to look at their summary at the conclusion of the paper (my bolding).
==quote==
The evaporation time, however, remains of the same order of magnitude, because it is proportional to m³; it is only reduced by a factor ∼ .6. Therefore for a long period the collapsed star behaves precisely as a conventional black hole. Nothing changes in conventional black-hole astrophysics.
The key difference with resect to the conventional scenario that disregards quantum gravity is that the inner core keeps memory of the original mass. Approximately one third of the mass is emitted in the Hawking evaporation; at the end of the evaporation, the star is still macroscopic. At this point there is no more horizon, the quantum gravitational pressure can disrupt the star and the information inside the hole can freely escape to infinity.
The physical picture is compelling: a star collapsing gravitationally can be understood as an object which rapidly shrinks to the size where its energy density is Planckian, then bounces back because of the quantum gravitational repulsion due to the quantum properties of spacetime. The bounce takes a short proper time (of the order of m, the time light takes to cover the star radius) in the star own frame. However, due to the huge gravitational potential, there is a high gravitational redshift that slows the local time with respect to the external world. An outside observer sees the collapse and the bounce of the star in “very slow motion”, and the entire process takes a long time of order m³. A black hole is essentially a collapsing and bouncing star that appears frozen because is seen in slow motion. The information that has fallen on the black hole is just there, frozen by the red shift, waiting to reappear as soon as the bounce is over.
==endquote==

 

[MTd2]

So, this picture is not much different from Hawking. The "event horizon" is actually an apparent horizon. It's always slowly receding.

But it seems that, whatever black hole it is, even a 1 billion solar mass black hole will evaporate. An the final mass will be only 30% at the end. It's radius as a classical black hole is 3 billion km km of radius. But it will shrink to 10,000km at the end.

That's a huge ball of fire. But since there is an equilibrium at the end, shouldn't there be a GUT star. Followed by an inflaton star? Or maybe inflation was caused by the radiation pressure from several mini black holes?

 

[marcus]

Hi MTd2, fortunately we don't have to worry about the end of solar mass BH or billion solar mass BH because they take so long to evaporate.
But on page 4, down around equation (23) they consider primordial BH formed at start of expansion which could be much less massive---say a TRILLION kg.
They estimate that these might be ending their life right now, since their estimated evaporation lifetime is about equal to the 14 billion year age of universe.
the bursting of these modest-size objects, they estimate, could contribute GeV-scale radiation and be detectable in cosmic rays.

 

[MTd2]

Sure, it will take long. But the marks on CMB from Penrose's last eons should be harder to find, I think. A so sudden explosion...

 

[marcus]

Sure, it will take long. But the marks on CMB from Penrose's last eons should be harder to find, I think. A so sudden explosion...

I see the sense of your comment. But I am not sure that a supermassive Planck star (i.e. the central body in a supermassive black hole trapping horizon) would ever have a chance to explode!
Remember we are thinking in the context of Loop cosmology bounce.

At least, that is how I am thinking since it is Loop gravity paper and the Planck star mechanism described is Loop type (a slow motion bounce)

So I don't switch over to Penrose "Eons". So I am thinking that only moderate-size Planck stars would have a chance to explode, before some kind of global crunch occurs, and a bounce, leading to our expanding phase. I don't see how such Planck star explosions that occurred in the prior contracting phase could leave a mark on OUR sky.

But maybe they could.

 

[marcus]

The "planck stars" paper is very clearly written on the whole. I like it that the two primary motivations of the paper are presented in the first 25 lines of the lefthand column on page 1.
And the first seven references cited there at the outset provide a well-chosen solid basis.
IOW the presentation has been carefully thought out. The whole thing is deliberate. E.g. here are the first 7 references.

[1] S. Liberati and L. Maccione, “Quantum Gravity phenomenology: achievements and challenges,” arXiv:1105.6234.
[2] S. Hossenfelder, “Experimental Search for Quantum Gravity,” arXiv:1010.3420.
[3] A. Barrau and J. Grain, “Quantum gravity in the sky,” arXiv:1206.1192.
[4] A. Almheiri, D. Marolf, J. Polchinski, and J. Sully, “Black Holes: Complementarity or Firewalls?,” JHEP 1302 (2013) 62, arXiv:1207.3123.
[5] S. B. Giddings and W. M. Nelson, “Quantum Emission from Two-Dimensional Black Holes,” arXiv:9204072 [hep-th]. http://arxiv.org/abs/hep-th/9204072.
[6] D. Page, “Information in black hole radiation,”Physical Review Letters 71 (Dec., 1993) 3743–3746, arXiv:9306083 [hep-th].
[7] S. Giddings, “Black holes and massive remnants,”Physical Review D 46 (Aug., 1992) 1347–1352, arXiv:9203059 [hep-th].

The first three tell you that of the two primary motives for this line of thought, one is to be able to detect "quantum gravity in the sky": in this case to derive (from theory) features of the cosmic ray spectrum we can look for.

The next three tell you that the other main motive is to resolve some persistent puzzles about the fate of information falling into black holes that have led numerous people into bizarre contorted speculations such as the recent "firewall" buzz.

 

[marcus]

Rovelli and Vidotto have posted a new version of the "Planck Stars" paper as of today,
with a bunch of minor corrections and additions.
If you liked either of the two earlier you might want to print off this version.
Google "planck stars" or click on http://arxiv.org/abs/1401.6562BTW tomorrow Tuesday 4 Feb Bianca Dittrich will speak at the online ILQGS seminar about a new way of constructing Loop quantum gravity. If it catches on it could have considerable impact on future research. Here's where you find the audio and slides files:
http://relativity.phys.lsu.edu/ilqgs/

 

[marcus]

A black hole is essentially a collapsing and bouncing star that appears frozen because it is seen in slow motion. The information that has fallen into the black hole is just there, frozen by the red shift, waiting to reappear as soon as the bounce is over.
--quote from page 4 of http://arxiv.org/abs/1401.6562

The Planck star model of a BH seems to solve a number of problems at once.

1. Explains why VSGRB are so powerful.
It says very short gammaray bursts are the final explosions of those primordial black holes (PBH) whose lifetimes are of the order of 14 billion years. In this model a PBH explodes while it still has 70% of its initial mass. In the original Hawking model the final flash came after a much longer time when there was almost no mass left, and all Hawking model BH made the same puny terminal flash because in every case it came when the mass ran out. So the picture of what explosions to expect is very different.

2. Resolves the BH info paradox.
Restores unitarity in a simple elegant way. The information reappears as soon as the slo-mo bounce is over.

3. Distinctive predictions--solves problem of making QG testable.
a. characteristically shorter BH lifetime, so different mass-class of PBH are now exploding
b. distinctive large mass remnant predicts powerful very short bursts
c. size prediction gives handle on the observed burst's gammaray spectrum of wavelengths

4. Possible solution to the problem of what constitutes dark matter.

Since we know the concentration of DM in the sun's neighborhood, the model affords a way to check the DM hypothesis. It gives a lower bound on the masses of PBH that could comprise DM, thus a possible handle on the numbers of PBH in our neighborhood, the number of explosions that should be visible, and their magnitude. Some statistics (2011 Cline et al) on observed VSGRB already exist.

Cline et al http://arxiv.org/abs/1105.5363 Do Very Short Gamma Ray Bursts originate from Primordial Black Holes?
Cline et al http://arxiv.org/abs/1006.1470 see page 18 Observational constraints on the nature of VSGRB
distance estimates ~6 ly based on idea that final mass is around 100,000 kg.
Cline Otwinowski http://arxiv.org/abs/arXiv:0908.1352

 

[marcus]

After looking at the numbers I've decided that point 4 above (which is not one raised by the authors of the Planck star paper) probably does not work. Primordial black holes (PBH) in this context would not be a major constituent of dark matter. If they were sufficiently abundant to constitute dark matter then more GRB explosions would be detected than we actually see. I'm not at all expert in this so can't rule it out, but I'll set the idea aside for the time being. It was not an idea raised in the Rovelli Vidotto paper (although it does get studied in some of the papers they reference.)

 

[MTd2]

Bee have a blog post here!

http://backreaction.blogspot.com.br/2014/02/can-planck-stars-exist.html

 

[marcus]

Bee have a blog post here!

http://backreaction.blogspot.com.br/2014/02/can-planck-stars-exist.html

Thanks for the pointer! Bee is skeptical and raises objections. Carlo has a nice answer to them, numerous other people comment, and Phil Helbig says there are more comments at the arXiv blog. I must have a look!

If anyone has a link to the comments @arxiv, please post it! I suppose I'll be able to find it starting at the abstract page: http://arxiv.org/abs/1401.6562

Well, I see this "trackback" link but AFAIK it is just to ONE POST at "The Physics ArXiv Blog":

https://medium.com/the-physics-arxiv-blog/6cf7ec0ed28b

Anybody know where the comments plural could be, which Phil Helbig mentioned?

 

[marcus]

Just to check my understanding of some of the estimates in the Planck star paper, I think in the usual model the lifetime of a 228 metric ton BH is one second. Unless I've made a mistake, you can see why the final flash of a conventional BH is considered an "explosion" because all that mass has to convert to energy in one second. One point about that is in the conventional model ALL holes lead to the same size final flash, because they all eventually evaporate down to that. The flash has no memory of the original collapse mass.

Earlier I was talking about BHs on the order of billion metric tons. I estimate that to narrow that down to rough numbers (not just orders of magnitude) we need to be talking about
0.2 billion metric tons. Let's check to see what the corresponding lifespan would be. Then the Rovelli Vidotto (RV) lifespan would be about 60% or 65% of that.

To use Google calculator to get the conventional lifespan I have to paste in
(2*10^8/228)^3 seconds in years
which gives 21.4 billion years

And then to get the RV lifespan I paste in
0.65*(2*10^8/228)^3 seconds in years
and indeed we do get 13.9 billion years.

 

[marcus]

In a way my doing numerical calculations is premature because the presentation so far has been basically intuitive. A more quantitative treatment is expected with a paper that Rovelli and Smerlak have in preparation. Details of the equations may change, I suppose. What counts at this point is the fundamental intuitive concept:

If you work in Loop gravity context, collapse that achieves near Planck density bounces. This is a fairly robust conclusion in Loop cosmology, from trying a lot of different cosmic models. All cases rebound, so that is how one tentatively visualizes the start of the expansion we now see happening.

It's plausible therefore to carry that over to BHs.
A black hole is a bounce.
But then gravitational time dilation enters the picture.

One realizes that deep in a gravity well, the processes of geometry and matter happen with enormous slowness---or so it would seem to an outside observer.

RV estimate that the slo-mo bounce bursts out through the conventional Event Horizon and becomes visible to outsiders after what seems to outsiders to have been about 65% of the conventional-model lifespan. That number is only a preliminary approximation---they say about 0.6 and that at that time the remaining unevaporated mass is M/√2
the initial mass divided by the squareroot of 2. So about 70% of the initial mass.

So although it's premature to be overly precise about this, the energy that is released by an hypothetical primordial BH that blows today and is detected as a VSB (very short gamma ray burst) has a mass equivalent of about 70% of 0.2 billion metric tons.

That is, 0.14 billion metric tons. I'm curious to know if that corresponds to the brightness of VSBs originating in our galaxy, or in our local group.
The interesting thing about this is that it immediately exhibits both an observational and a QG theoretical side.

 

[marcus]

If you paste this into google 5120*pi*G^2*(228000 kg)^3/c^4/hbar
you get 1 second, or more exactly 0.99682…seconds. Close enough.
That is the formula for the lifetime of a conventional BH with mass 228 tons.
Probably it will work without the asterisks stuck into show multiplication. Google calculator is rarely picky about that.
This standard formula for BH evaporation time you also see for example in equation (18) of the RV paper.

5120 pi G² M³/(hbar c⁴)

It just happens if you put 228 metric tons in for M you get an evaporation time of one second.
For me that is easier to remember and use than the standard formula and when you know the time for 228 tons then you can easily find it for any other mass because the time goes as the cube of the mass.

The authors of the Planck star paper (http://arxiv.org/abs/1401.6562) simply TRUNCATE the last third or so of the conventional lifespan. The idea is that the thing starts with mass M and behaves like a conventional BH for a long time, until its mass is down to M/√2 and then it blows.
So the amount its life is shortened by is proportional to the cube of M/√2.
In other words the RV lifespan is proportional to the conventional multiplied by
(1 - .5^3/2)
That is 0.6464… which for convenience I'm calling 65%

 

[marcus]

According to the RV model, a primordial black hole, formed in the early universe with a mass of one fifth of a gigaton has a lifespan just under 14 billion years, i.e. comparable to the current expansion age, so would be almost done with its invisible bounce and getting ready for its gamma ray burst finale.

…[primordial] BHs on the order of billion metric tons. ... to narrow that down to rough numbers (not just orders of magnitude) we need to be talking about
0.2 billion metric tons. Let's check to see what the corresponding lifespan would be. Then the Rovelli Vidotto (RV) lifespan would be ... 65% of that.

To use Google calculator to get the conventional lifespan I have to paste in
(2*10^8/228)^3 seconds in years
which gives 21.4 billion years

And then to get the RV lifespan I paste in
0.65*(2*10^8/228)^3 seconds in years
and indeed we do get 13.9 billion years.

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

Your time goes by so slowly...
What mass were you at first?
A fifth gigaton!

related melody:

 

[marcus]

Intuitively, the Planck star model of BHs (as I see it) is fairly straightforward. Loop quantized gravity repels at extreme density and leads to a bounce.

If the bounce is a REBOUND back into the home universe that cancels info-loss and firewall jokes.

But then we have the question "why does the bounce take so long?" seen from outside.

So the authors have to come up with a plausible model in which the bounce occurs under extreme time dilation.

And surely the "event horizon" concept (which traditionally depended on knowing the whole future of the universe so you could be sure stuff never gets out) does not apply. They have to work with (temporary) TRAPPING HORIZONS, borders where the lightcones tilt inward.

Technically the paper makes considerable use of a paper by Sean Hayward, actually two, his 1994 "General Laws of BH Dynamics" Physical Review D, http://arxiv.org/abs/gr-qc/9303006, and his 2006 piece in Physical Review Letters.

http://arxiv.org/abs/gr-qc/0506126
Formation and Evaporation of Non-singular Black Holes

 

[marcus]

Technically the paper makes use of a paper by Sean Hayward, actually two, his 1994 "General Laws of BH Dynamics" Physical Review D, http://arxiv.org/abs/gr-qc/9303006, and his 2006 piece in Physical Review Letters.
But more importantly, Hayward's 2005 Non-singular BH paper:
http://arxiv.org/abs/gr-qc/0506126
Formation and Evaporation of Non-singular Black Holes

Several of the equation in the Non-singular BH paper seem ready-made to be adapted by Rovelli and Vidotto for their purposes in http://arxiv.org/abs/1401.6562
Also I found the FIGURES in this 4-page conference paper by Sean Hayward very helpful:
http://arxiv.org/abs/gr-qc/0504037 (e.g. diagrams of trapping horizons, the essentials of a conference talk he gave challenging the info-loss paradox.)
For a wide-audience intuitive presentation of Hayward's argument debunking conventional black holery and info-loss:
http://arxiv.org/abs/gr-qc/0504038 (popularlzed version of the conference talk)

 

[marcus]

At first sight the slo-mo rebound model black hole could seem a bit disturbing, if you happen to imagine the (supernova-size) final explosion of a stellar mass BH, but it might allay such concerns to consider how far that would be in future, should it ever happen.

Solar mass is 2*10^30 kg, aka 2*10^27 metric tons, so paste in:
0.65*(2*10^27/228)^3 seconds in years
and you get 10^67 years
ten million trillion trillion trillion trillion trillion years
it's essentially never---something else more significant is bound to have happened before astrophysical black holes explode.

And so called "supermassive" black holes at the center of galaxies? Well small ones, like the one at the center of Milky, are on the order of a million solar masses, so paste in:
0.65*(2*10^33/228)^3 seconds in years
and you get 10^85 years
which is even more never

 

[marcus]

Rovelli's next installment of Planck star research is expected to be a paper currently in preparation with Matteo Smerlak (at Perimeter Instititute). To get an idea of what this might entail we can check out two recent Smerlak BH papers.

This one came out April 2013 and was published in Physical Review D:
http://arxiv.org/abs/1304.2858
New perspectives on Hawking radiation
Matteo Smerlak, Suprit Singh
(Submitted on 10 Apr 2013)
We develop an adiabatic formalism to study the Hawking phenomenon from the perspective of Unruh-DeWitt detectors moving along non-stationary, non-asymptotic trajectories. When applied to geodesic trajectories, this formalism yields the following results: (i) though they have zero acceleration, the temperature measured by detectors on circular orbits is higher than that measured by static detectors at the same distance from the hole, and diverges on the photon sphere, (ii) in the near-horizon region, both outgoing and incoming modes excite infalling detectors, and, for highly bound trajectories (E<<1), the latter actually dominate the former. We confirm the apparent perception of high-temperature Hawking radiation by infalling observers with E<<1 by showing that the energy flux measured by these observers diverges in the E->0 limit. We close by a discussion of the role played by spacetime curvature on near-horizon Hawking radiation.
14 pages, 7 figures

This one received honorable mention in the 2013 Gravity Research Foundation essay competition and was published in the International Journal of Physics D:
http://arxiv.org/abs/1307.2227
The two faces of Hawking radiation
Matteo Smerlak
(Submitted on 5 Jul 2013)
What happens when Alice falls into a black hole? In spite of recent challenges by Almheiri et al. -- the ""firewall" hypothesis -- the consensus on this question tends to remain "nothing special". Here I argue that something rather special can happen near the horizon, already at the semiclassical level: besides the standard Hawking outgoing modes, Alice can records a quasi-thermal spectrum of ingoing modes, whose temperature and intensity diverges as Alice's Killing energy E goes to zero. I suggest that this effect can be thought of in terms a "horizon-infinity duality", which relates the perception of near-horizon and asymptotic geodesic observers -- the two faces of Hawking radiation.
7 pages, 2 figures

Those who have had a look at Planck stars paper http://arxiv.org/abs/1401.6562 will have realized that INGOING hawk.rad. plays an important role. So these two papers of Smerlak may help us get a firmer grip on what is going on during the rebound. There is obviously a time mismatch. The insider thinks it all happens in a the twinkling of an eye, meanwhile the same amount of information falls down on him as goes out in the form of hawk.rad. in a process which to an outsider looks like it takes billions of years. It's late here (1 am Pacific time) so I'll have a look at these Smerlak papers in the morning and try to see then how Smerlak's analysis might add to what we already have from 1401.6562 (which already cites the Rovelli-Smerlak work in prep on Planck star lifespans/timelines).

 

[Nugso]

Thanks for the all links marcus. I'm really trying to read all of them despite my terrible English. Since they're both in English and "Scientific", they're both giving me two times a hard time.

I don't know why I said those, but I felt like I'd feel better by doing so!

 

[marcus]

Thanks for the all links marcus. I'm really trying to read all of them despite my terrible English. Since they're both in English and "Scientific", they're both giving me two times a hard time.

I don't know why I said those, but I felt like I'd feel better by doing so!

I got the impression that your English is pretty good for a second language, definitely not terrible.
I'm wondering now what your first language is. I know a little German, for instance, but my German is nowhere near as good as your English.

I should do something like "color-code" the links. Or rank them in some other way. So far only the main article matters. It is, say, BLUE (top priority). I am gathering others partly just as a reading list for myself, or for other readers who might be coming to this at a technical level. Call them GREEN (not essential, potential source material, lower priority).

When the Rovelli Smerlak paper comes out it will be "blue". but don't feel as if you need to read any of the lower priority stuff. We should try to make this idea easy to understand. People shouldn't have to work so hard to assimilate and enjoy a good idea like this. But I don't feel we are there yet. For now, I am just accumulating a reading list, and sniffing around--nosing around for clues.

 

[Nugso]

I got the impression that your English is pretty good for a second language, definitely not terrible.
I'm wondering now what your first language is. I know a little German, for instance, but my German is nowhere near as good as your English.

I should do something like "color-code" the links. Or rank them in some other way. So far only the main article matters. It is, say, BLUE (top priority). I am gathering others partly just as a reading list for myself, or for other readers who might be coming to this at a technical level. Call them GREEN (not essential, potential source material, lower priority).

When the Rovelli Smerlak paper comes out it will be "blue". but don't feel as if you need to read any of the lower priority stuff. We should try to make this idea easy to understand.

Turkish. I'm also learning German along with English! Well, you don't need German as much as I need English at least.

Well, I'd really appreciate if you did 'color-code' the links, but even the idea of it sounds sort of difficult and you're already quoting, I guess, the most important parts.

 

[marcus]

I remember one time you posted this Carl Sagan link:

I like that quite a lot. It is inspiring. I also like this (but it is music-only, no video):
https://soundcloud.com/kenley-kristofferson/cosmos
I'll hunt for a music+video version

EDIT: Yes! Here is a pretty nice video. It alternates sky and nature imagery with spoken words by C.S. and with the singers performing the choral work at a planetarium (part of the science museum in Alberta Canada):

 

[Nugso]

I remember one time you posted this Carl Sagan link:

I like that quite a lot. It is inspiring. I also like this (but it is music-only, no video):
https://soundcloud.com/kenley-kristofferson/cosmos
I'll hunt for a music+video version

Carl Sagan, the man! If it weren't for Carl Sagan and Richard Feynman, I'd not be interested that much in science.(Not that anyone cares or it's imporant to anybody else, but anyway)


Sorry for digressing the topic.

 

[marcus]

I think both Sagan and Feynman were comparatively honest as popularizers, unlike some recent authors who are selling string and multiverse fantasies. Both of them had a feeling for poetry but stayed more grounded in real empirical science.

...
Sorry for digressing the topic.

I take full responsibility for the digression in a slowly growing topic like this there is not such great urgency to stay focused.