Hawking's Legacy
Black hole thermodynamics and the Zeroth Law [1,2].
(a) black hole temperature: TH = hc3/16π2GkM
The LHS is intensive but the RHS is not intensive; therefore a violation of thermodynamics [1,2].
(b) black hole entropy: S = πkc3A/2hG
The LHS is extensive but the RHS is neither intensive nor extensive; therefore a violation of thermodynamics [1,2].
(c) Black holes do not exist [1-3].
Hawking leaves nothing of value to science.
REFERENCES
[1] Robitaille, P.-M., Hawking Radiation: A Violation of the Zeroth Law of Thermodynamics, American Physical Society (ABSTRACT), March, 2018, http://meetings.aps.org/Meeting/NES18/Session/D01.3
[2] Robitaille, P.-M., Hawking Radiation: A Violation of the Zeroth Law of Thermodynamics, American Physical Society (SLIDE PRESENTATION), March, 2018, http://vixra.org/pdf/1803.0264v1.pdf
[3] Crothers, S.J., A Critical Analysis of LIGO's Recent Detection of Gravitational Waves Caused by Merging Black Holes, Hadronic Journal, n.3, Vol. 39, 2016, pp.271-302, http://vixra.org/pdf/1603.0127v5.pdf
Well, to put it on a more concrete foundation, here's my view on his scientific achievement, not exhaustive, as I don't think I am entitled to judge on Hawking's scientific legacy.
His works on black hole theory are from about 50 years ago, and I would consider the singularity theorems he proved together with Roger Penrose quite the highlight of his scientific career. In a nutshell, what they say is that black hole creation takes place under very general conditions in space-time and is a necessary consequence of ART, and does not require very special, e.g. highly symmetric conditions.
With his work on Hawking radiation from teh mid-70s he applied semiclassical analysis to ART which paved the way to a more thorough treatment of quantum field theory on curved space/spacetime.
Although his scientific highlights might stem back from the 60s and 70s, I would nevertheless stress that his legacy surely comprises all that he did as an ambassador to science, as it seems. He surely was someone who gave inspiration to at least a complete generation of scientists many man years ago, his publicity starting to spread with the little booklet he wrote end of the 80s: "A Brief History of Time". I would never underestimate the importance of lighthouse figures like him with this regards, even though the hard-core scientific hightime had then already been past.
Well, to put it on a more concrete foundation, here's my view on his scientific achievement, not exhaustive, as I don't think I am entitled to judge on Hawking's scientific legacy.
His works on black hole theory are from about 50 years ago, and I would consider the singularity theorems he proved together with Roger Penrose quite the highlight of his scientific career. In a nutshell, what they say is that black hole creation takes place under very general conditions in space-time and is a necessary consequence of ART, and does not require very special, e.g. highly symmetric conditions.
With his work on Hawking radiation from teh mid-70s he applied semiclassical analysis to ART which paved the way to a more thorough treatment of quantum field theory on curved space/spacetime.
Although his scientific highlights might stem back from the 60s and 70s, I would nevertheless stress that his legacy surely comprises all that he did as an ambassador to science, as it seems. He surely was someone who gave inspiration to at least a complete generation of scientists many man years ago, his publicity starting to spread with the little booklet he wrote end of the 80s: "A Brief History of Time". I would never underestimate the importance of lighthouse figures like him with this regards, even though the hard-core scientific hightime had then already been past.
I bought a book by Hawkins many years ago. Nothing than chains of theories and abysmal speculations. He can not do any further demage.
Let the dead bury the dead.
Hawking contributed nothing of value to science. His equations for black hole temperature and black hole entropy stand in direct violation of the laws of thermodynamics, as my post above unambiguously attests. They are therefore outright nonsense. The Hawking-Penrose 'singularity theorems' are not theorems at all because they are nonsense [1]. Black holes do not exist [1-5]. Big bang cosmology is not science, never was science, and will never be science [1-5].
Hawking and his cosmologist colleagues have done massive damage to science, ruining it and the minds of their students and general readers, even children aged as young as 12 for whom Hawking wrote books of indoctrination poisoning their young minds with unbridled humbug long before they can think for themselves.
It is astonishing, although not unusual, that Hawking supporters, as on this very webpage, pay no heed to the content of the short and simple notes I posted above on Hawking's nonsensical equations for black hole temperature and entropy. Hawking's book "A Brief History of Time" is unscientific from cover to cover, replete with fantasies that beggar belief; a disgrace and insult to science and rational thought. It is no wonder that Hawking led the current attempts by cosmologists, spending $100,000,000.00 of Milner's thoughtless money, trying to contact aliens [5], the very same that fly saucers and UFO's, and who abduct people for experiments and vivisection, because they all come from outer space!
[1] Crothers, S. J. “On the Invalidity of the Hawking-Penrose Singularity ‘Theorems’ and Acceleration of the Universe with Negative Cosmological Constant”,Global Journal of Science Frontier Research Physics and Space Science, Volume 13 Issue 4, Version 1.0, June 2013, http://vixra.org/pdf/1304.0037v3.pdf
[2] Crothers, S.J., On Corda's 'Clarification' of Schwarzschild's Solution, Hadronic Journal, Vol. 39, 2016, http://vixra.org/pdf/1602.0221v4.pdf
[3] Crothers, S.J., A Critical Analysis of LIGO's Recent Detection of Gravitational Waves Caused by Merging Black Holes, Hadronic Journal, n.3, Vol. 39, 2016, pp.271-302, http://vixra.org/pdf/1603.0127v5.pdf
[4] Crothers, S. J., General Relativity: In Acknowledgement Of Professor Gerardus ‘t Hooft, Nobel Laureate, 4 August, 2014, http://vixra.org/pdf/1409.0072v9.pdf
[5] Crothers, S.J., The Painlevé-Gullstrand ‘Extension’ - A Black Hole Fallacy, American Journal of Modern Physics, 5, Issue 1-1 , February 2016, Pages:33-39, http://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmp.s.2016050101.15.pdf
Great contributions, Stephen. Please let the rest of us know if it makes sense to discuss with you at all or not. Maybe you are just a "provocateur" and like mocking other people, and that is fine then. Science can handle this. Just give us a hint whether people shall take you seriously or not. Cheers.
Oliver Tennert,
You are talking nonsense. The facts I presented speak for themselves. As I remarked previously, it is astonishing that supporters of Hawking, just like you, ignore the simple thermodynamic facts I presented in relation to my question. Study the references (it's obvious that you chose not to do so). Hawking's equations for black holes violate the laws of thermodynamics and the rules of pure mathematics. They are therefore bunkum.
Must scientists take cosmologists seriously as the latter try to contact aliens using radio telescopes all over the world, with the $100,000,000.00 they have of Milner's thoughtless money to fund them? Must scientists take Hawking and his colleagues seriously as they violate the laws of thermodynamics and the rules of pure mathematics? No, they don't! And why should they?
For those who can read French : https://blogs.futura-sciences.com/luminet/2018/03/15/stephen-hawking-1942-2018-travaux/
A more balanced and objective
analysis...
Do "black holes" really exist?
The collapse of a very massive star to a "black hole" would be comprehensible. But the mathematical formulation (Schwarzschild radius) of this theory predict, that also a small celesticel body as the moon or a particle like a proton can collapse to a small "black hole" - called as wormholes within the spacetime.
The question is what types of (material) matter would form this
different types of "black holes"? The massive star would collapse to assumed but speculative "neutron matter" (clusters of neutrons should be possible, they are never observed!). But in what state of matter would the moon or the proton pass over?
To say it clearly: The ideas about "black holes" are alchemistical ideas about the reality. There don't exist dozens types of matter according to unproven theories.
The question if "black holes exist" is still an open one in my opinion, and to be quite honest: I think that the ongoing discussion here as well as somewhere else is sometimes a complete mess.
First of all, black holes emerge as mathematical solutions of classical GRT, full stop. This is undebatable, the real question is: "what is the domain of validity of classical GRT"? Which set of physical parameters need to be given for GRT to leave its domain of applicability, and a new, adapted, enhanced, version of it, either quantized or whatever, needs to replace it? Of course, we still have to admit: this "quantized gravitational theory" is yet to be found, and all candidates as of today do not really earn the status of a "theory".
Plausibility arguments however, would lead to the assumption that the less quantum effects are to be expected, the more likely black hole creation is, as is the case for e.g. supermassive BHs in the middle of a galaxy.
As Hans G Hildebrandt correctly points out it is complete unknown what would really happen if a celestial body the size of a planet or moon collapses (for whatever, speculative reasons of course). Would a BH form, or would some "quantum gravitational theory" take over, and somehow prevent BH creation from happening? Maybe, we don't know yet. What about mini-black holes? In my opinion: a bogus discusssion, without any theoretical -- not to speak of experimental -- support.
And to be quite frank: it did not really support the credibility of scientists that CERN many years ago had this PR campaign about mini-black holes as a possible side-effect when running LHC at full energy. This maybe helped gain popularity and triggered Dan Brown to write a novel, but the BH discussion afterwards evolved into a complete mess. This is where I agree with some that physicists did sometimes a bad job explaining science to the public. I would consider it a professional physicist's responsibility to help tidy up this completely confused state, especially the public discussion going on in media etc. is in.
HAWKING'S LEGACY:
The Human Condition. The fact that Stephen Hawking survived for decades with a crippling medical condition inspired others with severe medical conditions to not give up on life. His efforts inspired able-bodied persons to strive with the gifts that they possessed.
Dear all
This issue needs to be addressed with due attention. If we read, albeit in a less profound way, the 230 publications of S. Hawking (these are the ones I know), we will recognize a serious researcher. A researcher who had deep mastery of the issues dealt with by him in his articles and books. A knowledgeable of the formalisms and experimental data relevant to the topics addressed by him during his academic life. The themes of his works were very relevant to the development of our knowledge about the Universe. So Hawking was a high-level researcher. Undoubtedly. He left important contributions regarding the deepening of the issues related to the limitations of General Relativity in the region of high energies and strong gravity, in subjects like the preservation of information in the study of black holes, or topics as the accelerated expansion of the Universe, brane theory, quantum mechanics of the Universe, large N cosmology, gravitational waves, and many other themes. So, as the question was put forward, it does not contemplate an adequate response. Perhaps the author of the question would like to question "the size" of the researcher S. Hawking in comparison with other renowned scientists. Still, to be answered with a minimum of depth would need to be reformulated, not to advance ethical limits. And, even though this is a democratic space, forgive me, we cannot treat this theme in superficial and vicious approaches. Democracy means the right of expression but not the right to disrespect someone. I think Reserachgate should establish a standard of ethics in the approaches.
Hawking radiation itself is kind of self-contradictory: it says that we can gather baryons into black hole, then transform them into massless EM radiation - it means that baryon number is not conserved, that they can be completely transformed into EM radiation.
If baryons can be destroyed as through Hawking radiation, there is some boundary condition for density/temperature when it happens. However, formation of black hole requires growth of event horizon from the center r=0. Schwarzschild radius is proportional to mass, so r->0 means that density -> infinity. Hence, before starting to form horizon of black hole, it should start "burying baryons" into energy instead - creating energy density and preventing collapse into singularity.
Hi Jarek
I presume you are talking about a scenario of baryogenesis from primordial black holes, assuming the presence of microscopic baryon (or lepton) number violation, due to the presence of an effective CP-violating operator which is a scalar function of the Riemann tensor and of the baryonic (leptonic) current,. In this scenario the time evolution of an evaporating black hole generates baryonic (leptonic) chemical potential at the horizon. Once the chemical potential is generated at the horizon, Hawking radiation produces lepton/baryon asymmetry. Is this the scenario?
“First of all, black holes emerge as mathematical solutions of classical ART, full stop. This is undebatable, the real question is: "what is the domain of validity of classical ART"?“ Oliver Tennert
Your assertion is demonstrably false. First, Hawking’s black hole temperature is nonsense because it violates the laws of thermodynamics, as proven above. So it is certainly false. Second, Bekenstein-Hawking black hole entropy violates the laws of thermodynamics, as proven above. So it too is certainly false. Third, the mathematical theory of black holes also violates the rules of pure mathematics because it requires that the absolute value of a real number take on negative values, which is impossible. In simple geometric terms it requires that a sphere centred at the origin of coordinates leaves its centre behind when it is moved away from the origin of coordinates, which is impossible. Also, once again, you did not study the references before making your demonstrably false claims. Address the proofs above and in the references instead of ignoring them because you want to maintain a false dogma.
“… of S. Hawking (these are the ones I know), we will recognize a serious researcher. A researcher who had deep mastery of the issues dealt with by him in his articles and books. A knowledgeable of the formalisms and experimental data relevant to the topics addressed by him during his academic life. The themes of his works were very relevant to the development of our knowledge about the Universe. So Hawking was a high-level researcher.” Cesar Zen Vasconcellos
Your claims are demonstrably false Hawking violated the laws of thermodynamics, proven above. He contributed nothing of value to science whatsoever. Hawking was quite incompetent. He does not get to violate the laws of thermodynamics and call it science.
Supporters of Hawking: stop shilly-shallying and prove that Hawking black hole temperature and Bekenstein-Hawking black hole entropy do not violate the laws of thermodynamics. The simple proofs are above. Stop ignoring the scientific facts in order to maintain a dogmatic fantasy.
Hi Cesar,
I am just expressing general concern about ignoring the state of matter in GRT singularities. Both Hawking radiation and baryogenesis allow for violation of baryon number in extreme conditions ( https://en.wikipedia.org/wiki/Proton_decay ). And any finite boundary for conditions will be exceeded before creating infinite density singularity in the center of neutron star (initial event horizon) - preventing the formation of singularity by destroying baryons in total mc^2 conversion into EM radiation (and neutrinos).
If considering baryon number violation in Hawking radiation and/or baryogenesis, it should be also considered in the center of neutron star.
Dear Stephen
Is not a matter to be a Hawking supporter. The main topic is: if someone is a scientist he shall be able to recognize the value of the scientific work of another scientist. I read carefully most of his papers. I have agreements and disagreements with his conclusions. This is normal in science. But I am able to recognize his value as a scientist. Now coming to the violation of the laws of thermodynamics, please make your statement more clear, logical and consistent in order I can understand exactly what do you have in mind and your physical background on General Relativity.
Stephen: you are continuously mixing up BHs as classical GRT solutions with Hawking radiation as an admittedly speculative but semiclassically effect, and the possibility of real-life BHs in whatever sort of adapted theory necessary for the domain under consideration. It would be great if you could see the difference here, and not continuously somehow revert back to your strong statements against Hawking, while at the same time promoting your "papers" that from your point of view nobody adequately appreciates.
If you think mathematicians get it all wrong, write a paper, face the discussion and get it published by a renowned journal. This is how you earn merits, not by telling everyone else on Researchgate that they have no clue.
It is a shame that rantings like this somehow depreciate the value of Researchgate as a high-quality discussion platform for scientific topics. And as I am afraid this debate here will not come to a good end, please feel free to go on without me then. At least you have given me the answer I was asking you for earlier. Cheers and have a nice day.
“you are continuously mixing up BHs as classical ART solutions with Hawking radiation as an admittedly speculative but semiclassically effect, and the possibility of real-life BHs in whatever sort of adapted theory necessary for the domain under consideration. It would be great if you could see the difference here, and not continuously somehow revert back to your strong statements against Hawking, while at the same time promoting your "papers" that from your point of view nobody adequately appreciates. If you think mathematicians get it all wrong, write a paper, face the discussion and get it published by a renowned journal. This is how you earn merits, not by telling everyone else on Researchgate that they have no clue. It is a shame that rantings like this somehow depreciate the value of Researchgate as a high-quality discussion platform for scientific topics. And as I am afraid this debate here will not come to a good end, please feel free to go on without me then. At least you have given me the answer I was asking you for earlier. Cheers and have a nice day.” Oliver Tennert
No, I did not confuse anything. You simply refuse to accept the facts that Hawking’s black hole temperature and the Bekenstein-Hawking black hole entropy are hogwash because they violate the laws of thermodynamics. The proofs are still above, just where I put them for all to see. This is the topic of this webpage, which you now seek to deflect to other quarters.
Furthermore, proof that the black hole is produced by irrational imagination and violation of the rules of pure mathematics has already been given to you. Again, you deliberately chose to ignore it too, because you don’t want the truth. Where the proofs are published is irrelevant. That they do not appear in journals of your choice has no bearing whatsoever. That you invoke “rantings” to evade the facts is quite pathetic, and all too common.
“Is not a matter to be a Hawking supporter. The main topic is: if someone is a scientist he shall be able to recognize the value of the scientific work of another scientist. I read carefully most of his papers. I have agreements and disagreements with his conclusions. This is normal in science. But I am able to recognize his value as a scientist. Now coming to the violation of the laws of thermodynamics, please make your statement more clear, logical and consistent in order I can understand exactly what do you have in mind and your physical background on General Relativity.” Cesar Zen Vasconcellos
Yet again you dodge the scientific facts. Anybody calling themselves a scientist who violates the laws of thermodynamics in order to advance their theory is not a scientist. Hawking violated the laws of thermodynamics. That he did not know he violated the laws of thermodynamics speaks for itself. That cosmologists at large do not know that they have violated the laws of thermodynamics also speaks for itself. The proof is already given to you above, in very simple terms. Hawking’s black hole temperature equation and his black hole entropy equation are thermodynamically unbalanced. They are therefore certainly false. Any thermodynamic equation must not only have the same units on each side, it must have the same thermodynamic character on each side. Hawking’s equations do not satisfy this essential requirement. Consequently they are false. Just examine the equations (a) and (b) above, thermodynamically. It seems you, like Hawking et al, do not know what intensive and extensive thermodynamic variables are. Is that really the case?
Dear Stephen
You said, "quoting" Hawking:
"Black holes do not exist."
And you said: "Hawking leaves nothing of value to science."
Certainly you are refering to title of his article on Nature: Hawking says there are no black holes.
But you are mistaken. Sorry. In the article, if you read it carefully, he does not say, despite the title, that black holes does not (really) exists...
Stephen Hawking simply tells us in the article that the event horizon is not a "fixed boundary" around a black hole and that the black hole is not accordingly a cosmic object like all the others.
@Jarek:
I am not sure if I have understood your question 100%.
"Hawking radiation itself is kind of self-contradictory: it says that we can gather baryons into black hole, then transform them into massless EM radiation - it means that baryon number is not conserved, that they can be completely transformed into EM radiation."
The Hawking radiation scenario includes pair creation, that is right. Pair creation by itself however does not violate baryon number conservation. What possibly could lead to baryon number nonconservation is the fact that while e.g. the particles is emitted in the process and escapes the BH, while the antiparticle gets "absorbed", similar to the "Klein paradox" scenario from relativistic QM. Nevertheless, with a full theory for quantum gravity still missing, it is simply completely unknown whether baryon number conservation holds or not. In fact, even without considering BHs and Hawking radiation and such, it is even unclear at all if there is some energy threshold for which baryon number conservation breaks down anyway. But this is probably a completely different topic by itself.
"If baryons can be destroyed as through Hawking radiation, there is some boundary condition for density/temperature when it happens. However, formation of black hole requires growth of event horizon from the center r=0. Schwarzschild radius is proportional to mass, so r->0 means that density -> infinity. Hence, before starting to form horizon of black hole, it should start "burying baryons" into energy instead - creating energy density and preventing collapse into singularity."
This is where you need to explain to me again what you mean by that question. In the simplest scenario of the gravitational collapse of say a normal-sized star, the Schwarzschild radius normall grows outward from r=0 to r=R, that is right. It is right that an event horizon may form even before the outer shells of the collapsing object pass the final horizon. But the exact process highly depends on the initial radial density distribution of the collapsing object, and in any case there is no initial infinite density to start with.
Dear Oliver,
Hawking radiation/black hole evaporation says that what was initially baryons, through formation of black hole, is finally transformed into massless radiation - a positive number of baryons is transomed into zero baryons, what obviously violates the baryon number conservation (also baryogenesis).
A (hypothetical) possibility of such complete matter->energy conversion means that structure of baryon can be destroyed - while it is a local energy minimum, it is not global energy minimum - providing sufficient amount of energy we can take it through barrier from local to global minimum - destroying the baryon. If it is possible, there should be some huge but finite energy/temperature/density threshold above which baryons are just destroyed thermodynamically.
Regarding formation of event horizon in the center of neutron star, before growing from r=0 to R, from one side Schwarzschild radius r is proportional to mass inside, from the other this mass inside is proportional to density * r^3. Hence, r->0 requires density -> infinite.
A natural conclusion seem that neutron star should start burning baryons in its center before/instead collapsing into black hole ... unless baryon number is ultimately conserved, what means that baryogenesis and Hawking radiation are impossible.
Dear Jarek,
my apologies if I am still misunderstanding you, but maybe there is some basic misunderstanding here: first of all I don't see where a potential problem with baryon number nonconservation comes in. For example, proton/antiproton annihilation is a completely allowed process in physics, no matter if black holes are around or not. It is the absorbing of either the particle oder the anti-particle by the BH ("Klein paradox effect") that _possibly_ leads to baryon number nonconservation. And it is neither clear (a) whether this is a problem at all in the first place, or if baryon number nonconservation takes place anyway in nature above an energy threshold, and (b) if it occurs at all because we do not know what the final state of an evaporating BH is as of today.
Furthermore, the interior of a collapsing object is not given by the Schwarzschild solution, so the calculation you did is not correct. You *must not* apply the Schwarzschild solution in a region filled with matter. Rather, we have to apply some model for matter (i.e. dust) and put it e.g. in the Tolman-Oppenheimer-Volkoff equation for the spherical symmetric case. By this, initial infinite densities can be avoided, and the solution you get (if approximate) is the resulting spacetime geometry for the interior of the collapsing object.
I might add: once an event horizon -- which is a null surface! -- has formed, everything that is inside the horizon will eventually end up in a time-like singularity. Due to the causal structure inside the horizon, it is problematic to speak of anything like a "density" inside the horizon.
Dear Oliver,
Sure creation/annihilation of baryon-antibaryon pairs is possible - it conserves baryon number, and happens all the time e.g. in LHC. However, the problem is that both black hole evaporation and baryogenesis violate this conservation law.
There is absolutely no doubt that electric charge is ultimately conserved, as Gauss law says that the entire universe guards total charge being fixed. However, there is nothing like Gauss law for baryon number - hence there is considered its violation, especially as proton decay: nearly total matter->energy conversion, like while annihilation but without antimatter.
Its search in room temperature water pools bounded proton decay time by ~10^34 years ( https://en.wikipedia.org/wiki/Proton_decay ). However, if it is possible, the final decay time will be reduced in extreme temperatures, like during baryogensis (just after Big Bang), in evaporating black hole, and maybe also in the center of neutron star - especially if it is going to collapse into black hole.
If you believe that some finite matter density is sufficient to start creation of event horizon of black hole in the center of neutron star, what density is it? Sure after creation of event horizon everything is trapped inside, but what was density of matter just before starting this singularity?
Dear Jarek,
I would assume your last question is easy to answer with the help of the TOV equation once one agrees upon a state equation for nuclear matter -- at least in the spherical symmetric model of a neutron star. I admit I am no expert in the subject matter of exotic or large-scale nuclear matter, but I would think that the upper mass limit for neutron stars of something between 2 and 3 solar masses is roughly correct. Given the size of a pulsar of around 20 km in diameter, one can calculate the matter density for a stable pulsar configuration. If, for whatever reasons like matter aggregation, the total pulsar mass by the time gets higher than some upper limit however, for all that we know as of today, complete and unstoppable gravitational collapse sets in.
Nevertheless, I do not see any infiinite matter density outside the emerging horizon during the process.
Dear Oliver,
Schwarzschild radius is r=2MG/c^2. From the other side, M~r^3 * density, naively requiring density -> infinity for r->0. Also, black hole lifetime due to evaporation is proportional to M^3, hence r->0 initial horizon should immediately evaporate (converting baryons -> massless radiation).
Anyway, the initial point of singularity is mathematically problematic, black hole diagram is usually drawn as having "spike": infinite curvature (and so density) in the central point. There is needed an explanation that it can start with a finite density - if you don't know such calculations, maybe somebody else could point an article showing that this infinite density singularity gets to infinity some nonzero time after the start of event horizon?
If violation of baryon number is considered in baryogenesis or through Hawking radiation, why it isn't considered in the center of neutron star, e.g. just before collapsing into black hole? The standard view doesn't understand enormous energy production behind gamma-ray bursts, or e.g. for M82 X-2 ( https://en.wikipedia.org/wiki/M82_X-2 ) - pulsar radiating ~10 million times more energy than our sun, according to Wikipedia: "shining about 100 times brighter than theory suggests something of its mass should be able to". Total matter->energy conversion in baryon burning could repair this lack of understanding.
Dear Stephen
Let me explain a bit more about your claim that Hawking would have said that "black holes do not exist". I make in the following an analogy with the celebrated debate between Albert Einstein and Niels Bohr about quantum-mechanical reality.
Probably you know that in 1935, Albert Einstein, Boris Podolsky and Nathan Rosen published an article containg an argument that quantum mechanics is not a complete theory in terms of providing a complete description of physical reality.
Title: Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? A. Einstein, B. Podolsky, and N. Rosen. Phys. Rev. 47, 777 – Published 15 May 1935
ABSTRACT:In a complete theory there is an element corresponding to each element of reality. A sufficient condition for the reality of a physical quantity is the possibility of predicting it with certainty, without disturbing the system. In quantum mechanics in the case of two physical quantities described by non-commuting operators, the knowledge of one precludes the knowledge of the other. Then either (1) the description of reality given by the wave function in quantum mechanics is not complete or (2) these two quantities cannot have simultaneous reality. Consideration of the problem of making predictions concerning a system on the basis of measurements made on another system that had previously interacted with it leads to the result that if (1) is false then (2) is also false. One is thus led to conclude that the description of reality as given by a wave function is not complete.
The basic argument of the paper (know as EPR Paradox), against the completeness of quantum mechanics was the definition by the author of a reality criterion:
“If, without in any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity”.
The authors then complement this statement:
“ Regarded not as a necessary, but merely as a sufficient, condition of reality, this criterion is in agreement with classical as well as quantum-mechanical ideas of reality”.
In the end of the EPR paper, the authors state: “We are thus forced to conclude that the quantum mechanical description of physical reality given by wave functions is not complete. One could object to this conclusion on the grounds that our criterion of reality is not sufficiently restrictive”
The main legacy of Hawking are the studies of black holes and the Beginning of the Universe. He is right that the source of the Universe is a black hole. Because our World is the fractal, the Universe must include small black holes --- quasars, nucleus of galaxies, collapsed stars... But it is wrong to study black holes as usual ((regular) objects. Every black hole is out our system of reference of real observer, who can move only with the velocities v
" Let me explain a bit more about your claim that Hawking would have said that "black holes do not exist"." Cesar Zen Vasconcellos
Your comment and citation are irrelevant to the matter at hand. You are deliberately diverting from the scientific facts to avoid addressing them.
(1) Hawking black hole temperature and Bekenstein-Hawking black hole entropy stand in violation of the laws of thermodynamics, so they are hogwash. Since you are intent on defending Hawking then provide your proofs that the aforesaid black hole temperature and black hole entropy are not in violation of the laws of thermodynamics; and answer my question to you on intensive and extensive thermodynamic quantities.
(2) The mathematical theory of back holes violates the rules of pure mathematics, to wit, it requires that the absolute value of a real number must take negative values; that a sphere centred at the origin of coordinates when moved away from that centre leaves its centre behind; that the so-called 'event horizon removable singularity' is in fact an isotropic point and therefore an insurmountable invariant; so the theory of black holes is hogwash. You have been provided with citation to the proofs. Since you are intent on defending Hawking and the theory of black holes provide your proofs that the foregoing are not true.
I reiterate: black holes do not exist - they are products entirely of irrational imagination, wishful thinking, violations of the laws of thermodynamics, and violations of the rules of pure mathematics, as the proofs unambiguously attest. Astronomers and cosmologists do not get to alter the laws of thermodynamics and the rules of mathematics so that they can advance fantasy in the guise of science. It is no wonder that cosmologists are now trying to contact aliens, using radio telescopes all around the world, funded to the tune of Milner's $100,000,000.00 US, as my citations reveal.
Dear Stephen
In his reply to Bohr, Enstein could for instance have written an article with a provocative title: "The Moon Does not Exist!". Einstein would be contesting the existence of the Moon. No! He would only be taking his arguments about the understanding of quantum mechanic reality to an extreme limit and challenging Bohr's view of quantum mechanic reality.
- The present discussion is based on what you said:
- (c) Black holes do not exist [1-3].
- Hawking leaves nothing of value to science.
Steven Hawking proceeds in a similar way to what I wrote above in his contextualizations. What Hawking contextualizes is the meaning of "event horizon" of black holes (a region around a black hole from which nothing, not even light, can escape), one of the most puzzling problems in theoretical physics.
He was not really claiming that black holes do not exist. He was in reality proposing a new explanation for this puzzling problem.
The title above is just provocative! To stimulate the debate about the understanding of event horizon.
The celebrated german physicist, Walter Greiner, did something similar in his article: "There are no black holes," using general relativity pseudo-complex.
http://www.cesarzen.com/GREINER.pdf
Dear Stephen
You said that Hawking had said that black holes do not exist. I did not say that. I'm just telling you that your statement is completely wrong.
Dear Stephen
There was a missing link involving my arguments again your (fail) statement about Hawking stressing that "black holes dot not exist" involving my view about EPR and Bohr and Hawking that I fill now below:
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Niels Bohr argued against EPR by providing a careful analysis of quantum measurements from the point of view of complementarity. For Niels Bohr, in the absence of an experiment to determine the reality, it has no existence at all.
Einstein then objected Bohr: “Do you really believe the moon is not there when you are not looking at it?”
In his reply to Bohr, Enstein could for instance have written an article with a provocative title: "The Moon Does not Exist!". Einstein would be contesting the existence of the Moon. No! He would only be taking his arguments about his understanding of quantum mechanics' reality to an extreme limit and challenging Bohr's view of quantum mechanics' reality.
- The present discussion is based on what you said:
- (c) Black holes do not exist [1-3].
- Hawking leaves nothing of value to science.
Steven Hawking proceeds in a similar way to what I wrote above. Read the paper. What Hawking contextualizes is the meaning of "event horizon" of black holes (a region around a black hole from which nothing, not even light, can escape), one of the most puzzling problems in theoretical physics.He was not really claiming that black holes do not exist. He was in reality proposing a new explanation for this puzzling problem.The title above is just provocative! To stimulate the debate about the understanding of the so called "event horizon".The celebrated german physicist, Walter Greiner, did something similar in his article: "There are no black holes," using pseudo-complex general relativity.
http://www.cesarzen.com/GREINER.pdf
I come back soon to discuss with you your statements about thermodynamics, that the mathematical theory of back holes violates the rules of pure mathematics (I honestly do not know what you mean by this), about neutrons stars, and so on. I feel compelled to write because students read these posts and such statements are completely meaningless, sorry.)
Dear Stephen
Concerning your arguments about thermodynamics, the laws of black hole thermodynamics can be described, in synthesis, as:
(1) The temperature inside a black hole is in equilibrium with the outside temperature. According to the first law of thermodynamics, the interrnal black hole temperature is : T−1=∂S/∂E, This temperature must be also equal to the temperature of the radiation.
(2) For a static black hole of mass M, the element of mass dM follows a relationship with the surface gravity κ of the black hole dM=κ8πdA. This expression is analogous to the first law of thermodynamics dE=TdS, with the identification κ8πdA=TdS (black holes radiate a thermal spectrum of particles and that the temperature of this radiation depends on the surface gravity κ of the black hole ).
(3) The entropy of a black hole is proportional to its horizon area; the sum of the entropy of a black hole and the ordinary entropy of matter in the outside region of the black hole never decreases.
(3) The temperature T > or = 0.
So, I did not understand your arguments. What kind of thermodynamics' laws are you talking about?
"So, I did not understand your arguments. What kind of thermodynamics' laws are you talking about?" Cesar Zen Vasconcellos
The laws of thermodynamics. Once again you did not address intensive and extensive thermodynamic quantities. Your arguments are false and clearly reveal that you do not understand intensive and extensive thermodynamic quantities; no cosmologist does and thereby violate thermodynamics at every turn. Temperature is always intensive, mass is always extensive, area is neither intensive nor extensive, entropy is always extensive. Hawking's black hole temperature equation stands in violation of thermodynamics because it makes temperature move inversely with mass. The Bekenstein-Hawking black hole entropy equation violates the laws of thermodynamics because it makes entropy move with area. It's also obvious that you chose not consult the references I provided.
" He was not really claiming that black holes do not exist." Cesar Zen Vasconcellos
Hawking never retracted black holes - that's the point. Black holes do not exist. Hawking's black holes do not exist. The mathematical theory of black holes also violates the rules of pure mathematics as I described. But you chose not to consult the references so you don't know why.
" that the mathematical theory of back holes violates the rules of pure mathematics (I honestly do not know what you mean by this), about neutrons stars, and so on. I feel compelled to write because students read these posts and such statements are completely meaningless, sorry.)" Cesar Zen Vasconcellos
Again, you don't know what I mean because you chose not to study the proofs in the references I provided. Unless you study the references you are just regurgitating the usual fallacies. Students will do well not to follow your example. They should study the references to learn, instead of reproducing the standard false dogma as you do.
Dear Stephen
Words, just words. You have to prove mathematically/theoretically/experimentally what you mean. Your words do not prove anything. Words just words...
One cannot apply the extensive/intensive arguments, valid in standard thermodynamics, in the case of black hole thermodynamics since the latter results are based on general relativistic and quantum mechanical arguments (for systems having a horizon) which often are counter-intuitive.
"One cannot apply the extensive/intensive arguments, valid in standard thermodynamics, in the case of black hole thermodynamics since the latter results are based on general relativistic and quantum mechanical arguments (for systems having a horizon) which often are counter-intuitive." Patrick Das Gupta
Incorrect. The laws of thermodynamics cannot be ignored in order to advance theories that violate the laws of thermodynamics. Hawking claims black hole thermodynamics. He did so in violation of the laws of thermodynamics. His black hole thermodynamics is therefore false.
Furthermore, there is no such thing as an 'event horizon'. Black holes do not exist. I refer you back to the references I provided, which contain detailed proofs. It's astonishing that you too chose not to consult the references before launching into your argument.
" Words, just words. You have to prove mathematically/theoretically/experimentally what you mean. Your words do not prove anything. Words just words... "
Cesar Zen Vasconcellos
No, its not just words. The scientific facts have been adduced but you deliberately chose to ignore them. You have also demonstrated by your comments that you do not understand thermodynamics. You also chose to ignore the references which contain more detailed proofs of the falsity of Hawking's black hole theories. It's obvious that the scientific truth is not on your agenda.
Dear Stephen
You have to prove using mathematical/physical developments/statements that you are rigth! Not just words...
I wish to know where is the mistake on the statement below. Show me your conception about the thermodynamics of a black hole.
(2) For a static black hole of mass M, the element of mass dM follows a relationship with the surface gravity κ of the black hole dM=κ8πdA. This expression is analogous to the first law of thermodynamics dE=TdS, with the identification κ8πdA=TdS (black holes radiate a thermal spectrum of particles and that the temperature of this radiation depends on the surface gravity κ of the black hole ).
Dear Stephen
See the argument of Patrick Das Gupta:
"One cannot apply the extensive/intensive arguments, valid in standard thermodynamics, in the case of black hole thermodynamics..."
" See the argument of Patrick Das Gupta:
"One cannot apply the extensive/intensive arguments, valid in standard thermodynamics, in the case of black hole thermodynamics..." Cesar Zen Vasconcellos
Your remark carries no scientific weight whatsoever. In your usual fashion, you have chosen to ignore my reply to Das Gupta. I refer you back to it.
I reiterate: consider a homogeneous mass on Earth of uniform temperature. Divide the mass in half. The two resultant parts have half the mass of the original, half the volume of the original, but the temperature does not change. Temperature is always intensive, mass is always extensive, and area is neither intensive nor extensive in 3 dimension space. Hawking's black hole temperature is T = K/M, K a constant, so the temperature is halved with doubling of the mass, in violation of reality and the laws of thermodynamics. Hawking's black hole temperature is therefore invalid.
Entropy is defined generally dS = dQ/T. The quotient is extensive because change in heat dQ is extensive. Entropy is therefore always extensive. The Bekenstein-Hawking black hole entropy is S = KA, where K is a constant, A the area of the 'event horizon' enclosing the black hole. But area is neither intensive nor extensive, so the black hole entropy is invalid. Moreover, the area of the 'event horizon' is 4π(RS)2 where RS = 2GM/c2. So for the black hole,
S=16πKG2M2/c4.
On the right side all are constants but M. Mass M is extensive, but M2 is not extensive because it is not additive as required for an extensive property. Thus S is not extensive, in violation of the laws of thermodynamics.
Nobody is allowed to redefine temperature so that it is no longer intensive. As a result black holes cannot exist. Dr. Robitaille's argument is correct.
Hi Stephen
The rate of particle emission from the horizon is proportional to the change in the black hole entropy: Gamma ~ e^(beta Delta E) with beta = T^(-1)
Hi,
Black holes are thermodynamical systems with a temperature proportional to the surface gravity and having pure geometrical entropy equal to one-fourth of the horizon area.
Hi Stephen
With respect to non-extensive thermodynamics, its aim is to describe dynamically and statistically entangled systems, and also the quark-gluon plasma at the moment of hadronization.
Hi Stephen
very good, instead of cursing you are bringing mathematical arguments to the discussion ... now we can talk with seriousness
Hi, Stephen
Let me tell you the following about entropy, thermodynamics second law and black holes.
According to the conventional understanding about the second law of thermodynamics, the entropy of a closed system should increase. Assume for instance that the system is in one of many possible microstates. Then, you know that we can describe the state of the system in terms of a density matrix ρ. The second law places restrictions on values of density matrices ρ(t) which are thermodynamically accessible from some initial density matrix ρ(0). The second law is a necessary condition which conforms any state transformation (regardless of the underlying physical laws). The 2nd law allows to understand macroscopic properties of physical systems.
According to Bekenstein and Hawking, the event horizon of a black hole carries entropy gS = A/4G;
A: the surface area of the black hole’s horizon; G:Newton’s constant.
Now, if you apply the second law of thermodynamics to this expression, you will find that the area of the event horizon must always increase!
This condition was geometrically proven, for any classical processes, by
- S. W. Hawking, “Black holes in general relativity,” Commun. Math. Phys. 25 (1972) 152.
- S. W. Hawking and G. F. R. Ellis, “The Large Scale Structure of Space-Time,” (Cambridge University Press, Cambridge, 1973).
- These results show the consistency of Black Holes and thermodynamics.
Hi Stephens
I just quote Daniel Grumiller, Robert McNees and Jakob Salzer as a hint to track the consistency of black holes thermodynamics:
"Black hole thermodynamics emerged from the classical general relativistic laws of black hole mechanics, summarized by Bardeen–Carter–Hawking, together with the physical insights by Bekenstein about black hole entropy and the semiclassical derivation by Hawking of black hole evaporation. The black hole entropy law inspired the formulation of the holographic principle by ’t Hooft and Susskind, which is famously realized in the gauge/gravity correspondence by Maldacena, Gubser– Klebanov–Polaykov and Witten within string theory. Moreover, the microscopic derivation of black hole entropy, pioneered by Strominger–Vafa within string theory, often serves as a consistency check for putative theories of quantum gravity."
" You seem to believe that everybody, except you, is completely ignorant, wrong, irrelevant – including Hawking and his rather large group of collaborators and students (many of whom are professors of physics, cosmology, etc. at top universities)." Wulf Rehder
Rubbish. It is about what is proved. Professor Robitaille is correct - black hole temperature and entropy violate the laws of thermodynamics. You did not address this issue.
"According to Bekenstein and Hawking, the event horizon of a black hole carries entropy gS = A/4G; A: the surface area of the black hole’s horizon; G:Newton’s constant. Now, if you apply the second law of thermodynamics to this expression, you will find that the area of the event horizon must always increase!" Cesar Zen Vasconcellos
You continue to ignore the fact that entropy is always extensive and temperature is always intensive. Hawking's black hole temperature is not intensive, so it is certainly false. The Bekenstein-Hawking black hole entropy is not extensive, so it is certainly false. Nobody, including Hawking, gets to arbitrarily alter the laws of thermodynamics in order to advance theories that violate the established laws of thermodynamics. Professor Robitaille is correct - black hole thermodynamics violates the laws of thermodynamics. To argue otherwise you had better prove that temperature is not always intensive and that entropy is not always extensive. I await your proofs.
Hi Stephen
Maybe you did not realize the limitations for the applicability of standard thermodynamics. For instance, long‐range forces may have far‐reaching consequences for the applicability of standard thermodynamics.
Dear Stephen
The inclusion of gravity into any physical theory alters, in a fundamental way, its basic assumptions and formal structure . You must understand in particular the changes induced by gravity in the underlying principles of thermodynamics. This is the reason for the creation of a new branch in physics: gravitational thermodynamics. In this domain, you must review your basic concepts about standard thermodynamics. As for instance the concepts of extensive and intensive variables. Because, otherwise, it becomes a dialogue between people who speak completely different languages and unable to create some line of communication.
"The inclusion of gravity into any physical theory alters, in a fundamental way, its basic assumptions and formal structure . You must understand in particular the changes induced by gravity in the underlying principles of thermodynamics. This is the reason for the creation of a new branch in physics: gravitational thermodynamics. In this domain, you must review your basic concepts about standard thermodynamics. As for instance the concepts of extensive and intensive variables. Because, otherwise, it becomes a dialogue between people who speak completely different languages and unable to create some line of communication." Cesar Zen Vasconcellos
You have again attempted to evade the issues: Professor Robitaille is correct - black hole thermodynamics violates the laws of thermodynamics. To argue otherwise you had better prove that temperature is not always intensive and that entropy is not always extensive. I await your proofs.
I reiterate: Hawking et al do not get to arbitrarily alter the laws of thermodynamics, and call it "creation of a new branch in physics", in order to advance 'theories' that violate the established laws of thermodynamics, and that necessarily includes intensive and extensive variables: dS = dQ/T.
Hi Stephen
I understand your point about extensive variables in standard thermodynamics
You imagine that the physics of a black hole, to be consistent with the laws of standard thermodynamics, should respect the conditions of extensivity of thermodynamic variables, i.e., the entropy S of a black hole should be proportional to its free mass, M, in the form S ~ M, to the extent that, in the standard (classical) formulation of thermodynamics, entropy corresponds to an extensive quantity.
You are right about that! However, as I told you before:
"...In this domain, you must review your basic concepts about standard thermodynamics. As for instance the concepts of extensive and intensive variables. "
This is the main point: you must review in particular your conception in this case about the definition of the free mass of a black hole.
If you do that, you will see that black hole thermodynamics becomes extensive.
Using the predictions of Hawking and other authors, what you would get, from their definition of the black hole entropy, S ~ A (surface area of the black hole), is S ~ M^2. According to the extensive condition you should expect S ~M. Now, M defines the free mass of the black hole? No!
(Of course in order to obtain this expression you should consider the known Schwarzschild relationship embedded in the Tolman-Oppenheimer-Volkoff (TOV equations) , which relates the Schwarzschild radius and the "gravitational mass" of the black hole, that is, R = 2GM /c^2 and one should use the relation A~R^2.)
What you should differentiate when considering compact stars (neutron stars, black holes, strange stars, quark stars, and so on) is the difference between two different concepts,
gravitational mass, MG, and baryonic mass, MB.
The gravitational mass, as defined by the TOV equations, corresponds to the integral of the energy density of the system. The baryonic mass in turn corresponds to the integral which comprises the ratio between the baryonic number density, n(r), and the term 1 - 2GM(r)/(r c^2) of the Schwarzschild metric. This integral is further multiplied by the mass of the baryon.
MB represents the free mass of the black hole. Not MG!
They are diverse concepts. That is, as you can see, the mass M(r) contained in the second integral corresponds to the internal gravitational mass of the black hole.
There is another ingredient that should be considered in this composition: the gravitational binding energy: -|BE| = (MB - MG)c^2.
You can see from this expression, since BE < 0, that
MB = MG - |BE|
and because the gravitational binding energy is negative, the baryon mass, which represents the free mass of the black hole is bigger than the gravitational mass:
MB > MG.
According to Leonard Susskind, MB, the free mass of the black hole, is related to MG in the form
MB ~MG^2.
So when you combine the previous "non-extensive" equation S ~ M^2, replacing M by MG, from the above equation, you get
S ~ MG^2 ~ MB !
ie, you get a thermodynamically consistent extensive expression for the black hole entropy in the realm of the black hole thermodynamics!
"For more, see: https://rationalwiki.org/wiki/Stephen_J._Crothers"Wulf Rehder
Wulf Rehder, your comments and your citation above do not contain anything scientific. That you stoop to reference a link to immature people of no scientific account scribbling ad hominem graffiti in all consuming anger attests to your own immaturely and lack of scientific acumen. No reasonable person, beyond the age of 12, could possibly give any credence to what you have said and done here, for all to see. It is of note that Cesar Zen Vasconcellos congratulates you on posting such drivel and contributed a 'recommendation' to your unscientific post.
Dear Wulf
Concerning your comment let me add the folliwing.
I ike Researchgate, largely because people interested in science, who are not necessarilly part of the conventional form of what we call official science, participate intelligently and democratically in debates of scientific aspects allegedly well known by the official science. I prepare many of my theoretical physics classes bearing in mind the issues that are discussed here.
Are there elements of plague-science and pseudo-scientism in Researchgate? There are. But this is part of the debate of ideas and the basic idea of democratization of this debate as proposed by Reserchgate. It is very simple to identify, and this is clearly not your case, such pseudo-scientists. They are usually masters of the truth, they do not accept proven facts, and when confronted they offend people and they bcome absolutely angry at confronting their "genius ideas", never recognized by the international scientific community. And they only publish on journals without peer review.
Dear Wulf
Thanks for the long and so profound message. I really appreciate. Will adopt, from now on, your definition of "categories" ...
In my opinion, his legacy is that the hardest problems can be progressed and never be disappointed and And he taught everyone that we must believe ourselves only to achieve the goal
(1) “This is the main point: you must review in particular your conception in this case about the definition of the free mass of a black hole. If you do that, you will see that black hole thermodynamics becomes extensive.” Cesar Zen Vasconcellos
First you claimed that temperature is not always intensive and mass not always extensive, and entropy not always extensive, so that you can arbitrarily change the laws of thermodynamics to bring into the ambit of the new ‘thermodynamics’ things that do not exist – black holes. Now you invoke the thermodynamic requirement of extensive mass to make ‘black hole thermodynamics’ extensive. You can’t have it both ways, so your argument is nonsense. Temperature is always intensive, mass is always extensive, entropy is always extensive.
(2) “What you should differentiate when considering compact stars (neutron stars, black holes, strange stars, quark stars, and so on) is the difference between two different concepts, gravitational mass, MG, and baryonic mass, MB. … There is another ingredient that should be considered in this composition: the gravitational binding energy: -|BE| = (MB - MG)c^2.” Cesar Zen Vasconcellos
Now you want to invent another kind of black hole mass to save it from oblivion. From your equation for black hole ‘binding energy’, the unit on the left side is Joules: [BE] = J. Thus, the unit for MG and MB on the right is certainly kg: [MG] = kg, [MB] = kg.
“You can see from this expression, since BE < 0, that MB = MG - |BE| and because the gravitational binding energy is negative, the baryon mass, which represents the free mass of the black hole is bigger than the gravitational mass: MB > MG. According to Leonard Susskind, MB, the free mass of the black hole, is related to MG in the form MB ~MG^2. So when you combine the previous "non-extensive" equation S ~ M^2, replacing M by MG, from the above equation, you get S ~ MG^2 ~ MB ! ie, you get a thermodynamically consistent extensive expression for the black hole entropy in the realm of the black hole thermodynamics!” Cesar Zen Vasconcellos
But the unit of MG and MB is kg. From your expression S ~ MG^2 ~ MB it obtains in accordance with your equation for binding energy that [MG2] = kg2 and [MB] = kg. Thus, your expression S ~ MG^2 ~ MB violates dimensional balance, so it is again nonsense. And again you invoke the thermodynamic requirement that mass and entropy are extensive to make black hole entropy extensive after claiming that mass and entropy are not always extensive.
(3) Putting Susskind-Vasconcellos MB ~ MG2 into the Hawking black hole ‘temperature’ equation gives,
TH = hc3/16π2Gk√MB
Then [TH] = Kelvin, but [hc3/16π2Gk√MB] ≠ Kelvin because [√MB] = √kg, so the equation is not only a violation of thermodynamics but also violates dimensional balance.
Hi Stephen
Concerning your 2nd statement let me tell you the following. The concepts of gravitational mass, MG, and baryonic mass, MB, are two concepts very well known for researchers in nuclear physics, cosmology and astrophysics! I can give a list of references on this topic. Concerning your first topic there are many researchers nowadays working in a not so new area of research, the so called non-extensive thermodynamics. So, if you adopt Tsallis quantum mechanical statistics, for instance, you are on the domain of a non extensive thermodynamics. And the black hole thermodynamics would be non extensive. I gave you an explanation based on my area of research, nuclear astrophysics. Concerning your calculations I just use the symbol ~ to indicate to you the order of magnitud, not the balance of units...so if you want the balance of units, according to Susskind, MG^2 = cte MB, and the constant "cte", in a rigorous proof, carries the right dimensions for the entropy and so on...moreover concerning your argument about the expression MB = MG - |BE|, I am using the usual convention "c = h/2pi = 1". In this domain E = M, for instance!
A Brazilian Tsalis invented the non-extensive statistical mechanics and the non-extensive thermodymics. It is a very interesting branch of physics with many important applications and surprising results. Specially in black hole physics and quantum mechanics. You have to try to get out of box...
“I gave you an explanation based on my area of research, nuclear astrophysics. Concerning your calculations I just use the symbol ~ to indicate to you the order of magnitud, not the balance of units...so if you want the balance of units, according to Susskind, MG^2 = cte MB, and the constant "cte", in a rigorous proof, carries the right dimensions for the entropy and so on...moreover concerning your argument about the expression MB = MG - |BE|, I am using the usual convention "c = h/2pi = 1". In this domain E = M, for instance!” Cesar Zen Vasconcellos
Nonsense! The defining equation you adduced on this very webpage is:
-|BE| = (MB - MG)c^2
Thus MB and MG have units of kg. Now confronted with your dimensional imbalance you seek sanctuary in yet more double-talk and Susskind. Provide your constant “cte” and your ‘rigorous proof’. Baryons include protons and neutrons. They have masses in kg. Proton mass = 1.6726485(86) x 10-27 kg [1]. Neutron mass = 1.674954(9) x 10-27kg [1].
You have the same violation of the laws of thermodynamics in the temperature of gaseous stars: the temperature equation is not intensive. From the kinetic theory of gases combined with Newtonian gravity via the Virial Theorem:
T = GMmp/5kr
The terms G, mp, and k are constants. Radius r is neither intensive nor extensive, and M is extensive. Thus, the left is intensive but the right is extensive, in violation of the laws of thermodynamics
By means of the equations of hydrostatic equilibrium:
Tc = 8μGMρ/3Rrρc
where Tc is central temperature, μ the dimensionless molecular weight, ρ the average density, ρc the central density. The left side is intensive, but the right is not a combination of properties leading to an intensive property, again in violation of the laws of thermodynamics. Furthermore, a gas cannot do work on itself to raise its own temperature. Gravitational collapse, i.e. self-compression, of a gas to form stars, permits perpetual motion machines of both the first and second kind, which are forbidden by the laws of thermodynamics [2, 3].
The black hole does not exist so all attempts to give it thermodynamics is nonsense (see citation [3], at the top of this webpage for the proofs, again as [4] below) . Cosmologists and astronomers do not get to arbitrarily alter the laws of thermodynamics, the rules of pure mathematics, and the nature of mass, in order to include in physics things that don’t exist.
REFERENCES
[1] Radin, S.H., Folk, R.T., Physics for Scientists and Engineers, Prentice-Hall, Inc., 1982
[2] Robitaille, P.-M., How are Stars Formed? The Standard Model: Gravitational Collapse, Black Holes, and The Big Bang! https://www.youtube.com/watch?v=LoqsG7V13G8
[3] Robitaille, P.-M., The Sun is Not Hollow! Solar Collapse, the Core, Density, and the Tachocline Layer!
https://www.youtube.com/watch?v=ox1GNuCV5M0
[4] Crothers, S.J., A Critical Analysis of LIGO's Recent Detection of Gravitational Waves Caused by Merging Black Holes, Hadronic Journal, n.3, Vol. 39, 2016, pp.271-302, http://vixra.org/pdf/1603.0127v5.pdf
Well Stephen
It's clear you are not a researcher. Just an outsider...this discussion is over!
"Well Stephen
It's clear you are not a researcher. Just an outsider...this discussion is over!" Cesar Zen Vasconcellos
You can't even balance dimensions in an equation. No wonder physics is such dire straits. Any reasonable person reading this page can easily see that you and the cosmologists are wrong.
I am not in the position to judge Hawking. He can be a great thinker even if black holes and Hawking radiation do not exist. It is not true that black holes must be there in GRT. It really depends on what you have on RHS of the Einstein equation. If you put NULL or just electromagnetic field in the theory you got black holes. But what happens if you put Yang-Mils, Dirac and Higgs fields (not quite quantum gravity yet, but as some prelude of quantum theories), black holes might not exist any more. The situation when gravity exists without any matter or just with electromagnetism, according to my understanding is not real. So the existence of black holes or anything in a unjustified situations is not necessarily a reality.
"I am not in the position to judge Hawking. He can be a great thinker even if black holes and Hawking radiation do not exist." Nguyen Ai Vet
Black holes are central to Hawking's entire career. That they don't exist attests that Hawking was not a great thinker. His violations of the laws of thermodynamics again attest that he was not a great thinker. His violations of the rules of pure mathematics again attest that he was not a great thinker. That Hawking led the charge, with $100,000,000.00 of Milner's money, to try to contact aliens, using radio telescopes all around the world, also attests that he was not a great thinker.
General Relativity violates the usual conservation laws for a closed system. It is thereby in conflict with a vast array of experiments. It is therefore false, no matter what is on the right side of Einstein's 'field equations'.
Dear Dr Nguyen Ai Viet
As a Doctor of Philosophy your opinion about Hawking, black holes and so on reveals you are a wise man. Congrats.
"Dear Dr Nguyen Ai Viet
As a Doctor of Philosophy your opinion about Hawking, black holes and so on reveals you are a wise man. Congrats." Cesar Zen Vasconcellos
So says Vasconcellos, who has demonstrated on this very webpage that he cannot even balance dimensions in an equation.
Well, the last statement comes from someone that doesn't know the difference between the mathematical symbols "=" and "~", that never heard about the concepts of "black hole gravitational mass" and "black hole baryonic mass", so used in cosmology, that does know the great physicist Susskind and his publications that still cause a huge impact on cosmology, that doesn't know the definition of the "natural system of units" (c= h/2pi=G), that still uses "Kg" to express the masses of protons and neutrons (and not the natural mass units "amu", i.e. atomic mass units), that thinks that only neutrons and protons belong to the "family of baryons (he doesn't know the large number of remaining members of the baryon family: the fundamental baryon octet + other higher orders of the SU(N) members), that never heard about the non-extensive thermodynamics, that does not believe on black holes, general relativity, that does not understand Lorentz transformations, that does not believe on gravitational waves .. what comes next? That the Earth is flat?
@Cesar,
is this the first time that you (Don Quijote) encounter the phenomenon of pseudo-science (wind mills)?
@Crothers:
"a) black hole temperature: TH = hc3/16π2GkM
The LHS is intensive but the RHS is extensive; therefore a violation of thermodynamics [1,2]. "
The right hand side is not extensive. The mass is in the denominator, not in the numerator. It would be useful, if you got the facts right first. Then we might discuss whether this is a problem or not. Gravitation produces many counterintuitive thermodynamic results. For example, the specific heat of a star is negative. Violation of thermodynamics? No.
You just have to think more precisely and note the limitations of the preexisting theory and how it has to be extended to overcome the apparent contradiction.
Dear Ulrich
I think you are correct in your observation. Pseudo science is a complete new world for me...
Dear Kassner
Your comments are really precise. Congrats! As you said, GR produces
many counterintuitive thermodynamic results. And this is the beauty of science, allways challenging our imagination.
@Kassner
"a) black hole temperature: TH = hc3/16π2GkM
The LHS is intensive but the RHS is extensive; therefore a violation of thermodynamics [1,2]. " Crothers
"The right hand side is not extensive. The mass is in the denominator, not in the numerator. It would be useful, if you got the facts right first. Then we might discuss whether this is a problem or not. Gravitation produces many counterintuitive thermodynamic results. For example, the specific heat of a star is negative. Violation of thermodynamics? No." Kassner
Since you don't like the fact that mass is in fact extensive, then the LHS is intensive but the RHS is not intensive. This is a violation of thermodynamics. Gravitation does not produce violations of the laws of thermodynamics, cosmologists do. You also ignore the fact that black holes do not even exist, so all attempts to assign them thermodynamics are also bunkum. I refer you to my references above, which you also obviously chose to ignore. Try as you might to save face, cosmology and its black holes are not science.
The negative specific heat of a star is also nonsense. It is derived from self-compression of a gas to form a star. Whether by application of the Virial Theorem or the hydrodynamic equations, nothing can compress itself to do work on itself and thereby raise its own temperature. To argue otherwise stands in violation of the laws of thermodynamics [1]. Similarly, the temperature relations obtained for stars by these methods stand in violation of the laws of thermodynamics [1]. Temperature is intensive, yet the stellar temperature equations obtained from self-compression of a gas are not thermodynamically balanced, equating intensive to something not intensive [1].
REFERENCES [1] Professor Pierre-Marie Robitaille, How are Stars Formed? The Standard Model: Gravitational Collapse, Black Holes, and The Big Bang! https://www.youtube.com/watch?v=LoqsG7V13G8
“Well, the last statement comes from someone that doesn't know the difference between the mathematical symbols "=" and "~", that never heard about the concepts of "black hole gravitational mass" and "black hole baryonic mass", so used in cosmology, that does know the great physicist Susskind and his publications that still cause a huge impact on cosmology, that doesn't know the definition of the "natural system of units" (c= h/2pi=G), that still uses "Kg" to express the masses of protons and neutrons (and not the natural mass units "amu", i.e. atomic mass units), that thinks that only neutrons and protons belong to the "family of baryons (he doesn't know the large number of remaining members of the baryon family: the fundamental baryon octet + other higher orders of the SU(N) members), that never heard about the non-extensive thermodynamics, that does not believe on black holes, general relativity, that does not understand Lorentz transformations, that does not believe on gravitational waves .. what comes next? That the Earth is flat?” Cesar Zen Vasconcellos
So yet aqain says Vasconcellos, who has demonstrated on this very webpage that he cannot even balance dimensions in an equation. The defining equation you adduced on this very webpage O Cesar is:
-|BE| = (MB – MG)c^2
So the mass units of MB and MG are exactly the same, and in balance. Then you asserted: “MG^2 = cte MB and the constant "cte", in a rigorous proof, carries the right dimensions for the entropy and so on.. ”.
But it does not matter what units you want to use for mass, (mass units)2 ≠ mass units, so, as I said before, you don't even know how to balance dimensions in an equation. And please give us your miraculous constant cte, O Cesar.
“Concerning your calculations I just use the symbol ~ to indicate to you the order of magnitude” Cesar Zen Vasconcellos
So I did and still do understand your symbols “=” and “~”. Order of magnitude does not obviate necessity for dimensional balance: (mass units)2 ≠ mass units, in either case, O Cesar.
“that still uses "Kg" to express the masses of protons and neutrons” Cesar Zen Vasconcellos
There is certainly nothing wrong with using kg for the masses of protons and neutrons [1], so your protest is ignorant drivel.
“that thinks that only neutrons and protons belong to the "family of baryons”. Cesar Zen Vasconcellos
Here you resort to outright lie to try to save face. Anybody can see for themselves that what I wrote previously is in fact this: “Baryons include protons and neutrons. They have masses in kg. Proton mass = 1.6726485(86) x 10-27 kg [1]. Neutron mass = 1.674954(9) x 10-27 kg [1]."
“that does not believe on black holes, general relativity, that does not understand Lorentz transformations, that does not believe on gravitational waves .. what comes next? That the Earth is flat? “ Cesar Zen Vasconcellos
Au contraire, O Cesar. It is not a matter of my 'belief', but what can be proven. Cosmologists indulge routinely in their mere beliefs, demonstrably false as they are. Black holes do not exist, general relativity violates the usual conservation laws for a closed system and is thereby in conflict with a vast array of experiments, General Relativity cannot localise its gravitational energy so there are no 'gravitational waves', and the speed of propagation of these fantastic waves is not uniquely the speed of light because the speed of propagation is entirely coordinate dependent – chose a different set of coordinates then the speed is altogether different to that of light. As for Lorentz Transformation, Einstein's tacit assumption that his systems of clock-synchronised stationary observers are consistent with Lorentz Transformation is certainly false. Systems of clock-synchronised stationary observers consistent with Lorentz Transformation do not exist! All the proofs are in the references I cited previously, but, as usual, you deliberately chose to ignore them because you simply want to cling to your false beliefs, your violations of the laws o physics, and your violations of the rules of pure mathematics. Susskind can't save you because he is just like you. And as for the 'flat earth' that is your ridiculous embellishment, not mine. Don't forget that you cosmologists are now off, initially led by Hawking, spending $100,000,000.00 of Milner's thoughtless money, using radio telescopes all around the world, trying to contact aliens; the very same aliens that fly saucers and UFO's, and who kidnap people for experiments and vivisection – because they all come from outer space! [2]
REFERENCES
[1] Radin, S.H., Folk, R.T., Physics for Scientists and Engineers, Prentice-Hall, Inc., 1982
[2] http://www.independent.co.uk/news/world/australasia/scientist-warns-world-to-think-twice-before-replying-to-alien-signals-from-outer-space-10408201.html
So Stephen, you believe in "aliens that fly saucers and UFO's, and who kidnap people for experiments and vivisection – because they all come from outer space!". Splendid.
Entropy: A concept that is not a physical quantity
https://www.researchgate.net/publication/230554936_Entropy_A_concept_that_is_not_a_physical_quantity
Hi Zhang
I did not get it...it is not a quantity in what sense?
Physical quantity = physical property?! Entropy is not a physical property?
In conventional" thermodynamics:
Entropy per unit mass = intensive thermodynamical property.
Total Entropy of a system = extensive thermodynamical property.
A very perceptive question posed by you, dear Stephen.
I dare add here my own seven footnotes:
https://www.researchgate.net/post/Hawking_was_a_didactic_Genius_Seven_Footnotes
I find the long discussion above too combative and not enough to the point.
Can I bring-in here my return to the Einstein of 1907 before he gave up on the global constancy of c (which happened only in 1911)?
I believe that none of the deep thinking discussants disagrees that the equivalence principle, which is based alone on special relativity with its global c, in the end confirms c-global. It only took a century to see how.
Or is there one voice saying that the equivalence principle (based on c-global) entails c-non-global?
It was this inconsistency which forced Einstein to fall silent on gravitation from 1907 until early 1911.
In the absence of quantum mechanics, he saw no other way than to follow his good friend Paul Ehrenfest's advice to live with the inconsistency and go on nonetheless, given his great strength. "Eventually" everything would come out right -- even if this would take a century.
I think it was a good advice since the time of "re-consistification" has begun.
My thanks to everyone who cares to comment.
Dear Otto
Thanks for your comment. Let me see if I understand your point of view. Your claim about c-global means that you believe that the speed of light is a constant if measured in an local inertial frame of reference, as well as well as if measured in a global non inertial frame? That's it?
Dear Cesar:
I am more pragmatic. I claim that c in the vacuum is not only everywhere locally valid, as everyone accepts, but that it holds globally.
Specifically, in the case of a black hole, this means that if light takes infinitely long to touch down (as is known to be the case), then also the distance from the outside world towards the horizon is infinite.
Specifically, the famous Flamm's paraboloid is now replaced by a funnel that coincides in only its uppermost part with the paraboiloid but then gets more and more stretched so that the horizon, the waist of the former paraboloid, is only reached infinitely deep down. So that the second half of the paraboloid vanishes altogether.
Is this naive description a bit helpful?
“So Stephen, you believe in "aliens that fly saucers and UFO's, and who kidnap people for experiments and vivisection – because they all come from outer space!". Splendid.” Cesar Zen Vasconcellos
So says Vasconcellos, the man who can't even balance dimensions in an equation, and now can't even read the written word. I reiterate: it's very clear:
"Don't forget that you cosmologists are now off, initially led by Hawking, spending $100,000,000.00 of Milner's thoughtless money, using radio telescopes all around the world, trying to contact aliens; the very same aliens that fly saucers and UFO's, and who kidnap people for experiments and vivisection – because they all come from outer space! [2]"
REFERENCES
[1] Radin, S.H., Folk, R.T., Physics for Scientists and Engineers, Prentice-Hall, Inc., 1982
[2] http://www.independent.co.uk/news/world/australasia/scientist-warns-world-to-think-twice-before-replying-to-alien-signals-from-outer-space-10408201.html
Dear Otto
I understand your point. I thank you for your delicate approach to the problem.
I have difficulties to accept your classical extrapolation as a strong argument to claim that c is global. I do not see any theoretical framework in your argumentation to get this conclusion. If you remember how Maxwell deduced the constancy of c in the vacuum you see that he does not assume a global, universal, absolute frame of reference.
What he did was, starting for instance from Faraday's law relating the rotational of the electric field, then taking the rotational of the rotational of Faraday's law, combined with Gauss law for the electric field and Maxwell-Ampere law, all these laws described in the Lab frame.
But, see:
In 1687, Sir Isaac Newton established the principle known today as the Weak Equivalence Principle (WEP) which states that the mass of a body is proportional to its weight and he established this way the universality of free fall of massive bodies, in the sense that trajectories of freely falling “test” bodies are independent of their masses, structures and compositions. The Einstein Equivalence Principle (EEP), on the other hand, is a more comprehensive concept, since it not only establishes the validity of the WEP, but also that the outcome of any local non-gravitational experiment is independent of the speed of the reference system in free-fall (LLI) as well as from its space-time location at the universe. Thus, special relativity is locally valid. EEP states this way the strict equivalence between gravity and inertial acceleration; this means that the laws of motion of free- falling frames in gravitational fields are completely equivalent to the corresponding laws of motion in uniformly accelerating inertial frames. These experiments are also independent of where and when in the Universe they are performed (LPI). Nowadays, we speak of the strong equivalence principle (SEP), which differs from EEP due to the inclusion of bodies with self- gravitational interactions (planets, stars) and of experiments involving gravitational forces (Cavendish experiments, gravimeter measurements). Notice that SEP contains the EEP as a special case in which the local gravitational forces are ignored. Additionally, nowadays we speak of two fundamental classes of metric theories, purely dynamical and prior-geometric, i.e., metric theories for which gravitational fields have their structure and evolution determined by coupled partial differential field equations and metric theories that contains fields or equations whose structure and evolution are given a priori, and are independent of the structure and evolution of the other fields of the theory. General relativity belongs to the second class of metric theories.
In the June 1905, Einstein predicted from his postulates the Lorentz transformations of the electric field E and the magnetic field B, for inertial frames in relative motion with constant velocity v. Einstein has shown that Maxwell equations are invariant by assuming a flat spacetime metric and Lorentz transformations.
A bit later he has shown that, in the presence of gravitation characterized by the potential field Φ(r), the speed of light in vacuum becomes a position-dependent quantity, c(r) = c_0 [1 + Φ(r)/c^2 ], where c_0 denotes the speed of light in vacuum without gravity. Analogous to the speed of light being c/n in a medium of refractive index n, the gravitational potential produces, in effect, a variable index of refraction, n = (1 + Φ/c^2 )^(−1). As you know, in physical optics, different optical paths lead to different vales for the speed of light. A similar effect occurs here with the bending of light. In flat spacetime, the smallest distance between two points is a straight line. In curved spacetime, a geodesic.
So therefore I have conceptual difficulties to agree with you about c-global. In order to accept the idea of c-global you have to assume a global frame, in reality an absolute frame. This is meaningless in the context of GR. And from the logical point of view, a c-global means that c has the same value in any part of the universe, regardless if the "observer" is inertial or not, without taking into account the presence of local gravitational fields, etc.
Thanks for the patient.
Dear Otto
Moreover, when you talk about black holes and other stars and cosmological objects or clusters of objects, should not forget rotation as an important ingredient in GR. Because clocks run more slowly on the surface or within a star than at infinity, an observer in a local inertial frame within the star will measure at a point r would measure angular velocities larger than those at infinity by a factor e^(−ν(r,θ)) , the so called gravitational time dilation. When a compact star rotates, spacetime around it not only bent due to its mass, but it is also twisted due to its rotation. This effect, frame dragging, is one of the most important predicted effects in general relativity. In this context, rotating astrophysical objects as neutron stars and black holes represent laboratories for the study of general relativity. As a consequence, the centrifugal force acting on a fluid element of the star and the inertia moment I of a rotating neutron star must depend on the difference between the frequency F and the frequency ω(r, θ) of the local inertial frame at the location of the fluid element. This changes completely your picture.
“Thus, special relativity is locally valid.” Cesar Zen Vasconcellos
No, it isn't [1-4].
[1] Special Theory of Relativity: Logical Inconsistencies : American Physical Society Ohio Meeting, 17th April, 2018: http://meetings.aps.org/Meeting/APR18/Session/Y13.6
[2] Crothers, S.J., On the Logical Inconsistency of the Special Theory of Relativity, American Journal of Modern Physics. Vol. 6, No. 3, 2017, pp. 43-48, http://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmp.20170603.12.pdf
[3] Crothers, S.J., Special Relativity: its Inconsistency with the Standard Wave Equation, Physics Essays (in press), 2018, http://vixra.org/pdf/1708.0055v2.pdf
[4] Crothers, S.J., Minkowski-Einstein spacetime: insight from the Pythagorean theorem, http://vixra.org/pdf/1803.0208v1.pdf
“Moreover, when you talk about black holes and other stars and cosmological objects or clusters of objects, should not forget rotation as an important ingredient in GR.” Cesar Zen Vasconcellos
Black holes do not exist. Not only do they violate the laws of thermodynamics as explained above, they violate the rules of pure mathematics as well [1-4].
[1] Crothers, S.J., On Corda's 'Clarification' of Schwarzschild's Solution, Hadronic Journal, Vol. 39, 2016, http://vixra.org/pdf/1602.0221v4.pdf
[2] Crothers, S.J., The Painlevé-Gullstrand ‘Extension’ - A Black Hole Fallacy, American Journal of Modern Physics, 5, Issue 1-1 , February 2016, Pages:33-39, http://vixra.org/pdf/1512.0089v1.pdf
[3] Crothers, S. J. On the Generation of Equivalent ‘Black Hole’ Metrics: A Review, American Journal of Space Science, v.3, i.2, pp.28-44, July 6, 2015, http://vixra.org/pdf/1507.0098v1.pdf
[4] Crothers, S. J., General Relativity: In Acknowledgement Of Professor Gerardus ‘t Hooft, Nobel Laureate, 4 August, 2014, http://vixra.org/pdf/1409.0072v9.pdf
Dear Otto As I told you before, I have conceptual difficulties to agree with you about c-global. According to the principle of special relativity, the laws of physics are invariant in all inertial reference frames. The experimental basis of this statement is the Michelson-Morley experiment, which shows that the speed of light is constant and equals to c in every inertial frame. In GR we call local if locally flat. Particularly, I like very much the following statement from Rindler: "...Newton’s mechanics possesses the relativity of the so-called Galilean group, SR possesses the relativity of the Poincare (or ‘general’ Lorentz) group, GR possesses the relativity of the full group ´ of smooth one-to-one space-time transformations, and the various cosmologies possess the relativity of the various symmetries with which the large-scale universe is credited. Even a theory valid only in one absolute Euclidean space, provided that is physically homogeneous and isotropic, would possess a relativity, namely the group of rotations and translations. " In order to accept the idea of c-global you have to assume, the way I see, the idea of a global inertial frame, in reality an absolute inertial frame, valid in a absolute Euclidian space. This is meaningless in the context of GR. And from the logical point of view, a c-global means that c has the same value in any part of the universe, regardless if the "observer" is inertial or not, without taking into account the presence of local gravitational fields, etc. In my view, you are talking about the "aether"... According to Rindler: " Einstein’s solution of the aether puzzle was more drastic: it was like cutting the Gordian knot. In his famous relativity principle (RP) of 1905 he asserted that all inertial frames are equivalent for the performance of all physical experiments. That was the first postulate. For Einstein there is no ether, and no absolute space. All inertial frames are totally equivalent. " And at end, no absolute time. Should remember again that in the presence of gravitation characterized by the potential field Φ(r), the speed of light becomes a position-dependent quantity, c(r) = c_0 [1 + Φ(r)/c^2 ], where c_0 denotes the speed of light in vacuum without gravity.Analogous to the speed of light being c/n in a medium of refractive index n, the gravitational potential produces, in effect, some kind of variable index of refraction, n = (1 + Φ/c^2 )^(−1). As you know, in optics, different optical paths lead to different vales for the speed of light. A similar effect occurs here with the bending of light. In flat spacetime, the smallest distance between two points is a straight line. In curved spacetime, a geodesic. So, if you consider c-global the situation is even worst in terms of assuming a constant velocity of light. Now with respect to the concept of horizon in black hole physics, I presume you are talking about the regularity of the horizon. Now if you consider the Schwarzschild metric and consider also a a spherical mass M of uniform density ρ and radius r; for r > 0, it can be shown that the Schwarzschild metriic satisfies the vacuum field equations for some given conditions. What Rindler says is that nothing untoward occurs at the horizon. To show that this statement is correct he has solved the 14 independent invariants of the Riemann curvature tensor and has verifyied that the curvature remains finite there.
📷
Dear Otto
Concerning the black hole thermodynamics since we do not know the volume of a black hole it is reasonable to me to assume that the black hole entropy behave as a monotonic function of the area of the event horizon instead of a function of its volume.
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