joigus

You do that and I'll be answering your previous points properly in the fullness of time. Don't worry, I won't see you inside the BH, but you will see me. If you can go back in time we'll meet here... I mean now.

Have you considered the possibility of, e.g., a BH that is ejected into an intergalactic void, and therefore experiments no accretion? What would happen to that BH? It must be a consistent object. Accretion is accidental; Hawking radiation is a function of BH's parameters. OK. So, in your model, do BH's radiate or not? You don't seem to have made up your mind about that. Do you realise that time transformations in QM or QFT are always represented by anti-unitary operators? You propose a unitary T operator, which is inconsistent with how the quantum states represent time inversions: https://en.wikipedia.org/wiki/Antiunitary_operator https://en.wikipedia.org/wiki/T-symmetry#Anti-unitary_representation_of_time_reversal Or Weinberg's Quantum Field Theory, vol. 1, p. 128, eq. 3.3.44, which you cite in your pre-print. Do you realise that one-particle states in QFT must have both "positive" and "negative" energies* if you want to preserve microcausality? The Dirac spinors that you obtain in the energy representation of the Dirac equation with either sign in, \[e^{\pm i\left(Et-\boldsymbol{p}\cdot\boldsymbol{x}\right)}\] are not one-particle states. The closest to the physical representation is the chiral one: https://en.wikipedia.org/wiki/Gamma_matrices#Weyl_(chiral)_basis You seem to want to deal with these time inversions as some kind of active transformation (something you actually do to a particle) rather than a passive transformation (a simple re-labelling of parameters). How does one interpret this flip in the particle's time? Why does the particle not experience its own past when it falls into the horizon? Does the particle's energy get inverted? If so, is energy not conserved at the horizon for the in-falling particles, going from E to -E and thus energy conservation being violated by an amount 2E? Be aware that the fact that something has been published is no guarantee that the scientific community at large considers it correct, or even worth discussing. *The quotation marks are there because the E's in the Dirac equation are not to be taken at face value as the particle's energy, but just as energy parameters that the particles "read differently" depending on whether they're particle or antiparticle. Bibliography: https://en.wikipedia.org/wiki/Rite_of_passage

This is something I don't understand either. +1 Neither do I understand how a growing BH implies the non-existence of Hawking radiation. Why couldn't it grow and evaporate? And we're not even getting a diagram, a simple equation. It's all blah blah. I haven't even seen the mysterious time transformation in terms of the metric and the coordinates. Something like t goes to i times t, g00 goes to minus g00 and such. Am I asking that much? Thank you. I share your confusion about negative energies. For all I know Hawking radiation has not been confirmed as yet. I don't think negative energies are necessarily prohibited, as far as one provides a mechanism to explain why they're not observed in the universe. I don't see that either in the "proposal". Thank you. +1

Thank you very much, although you cut short @MigL's answer only to show what you want (he telling you that you're right about something). And now I quote Wikipedia: https://en.wikipedia.org/wiki/Black_hole_information_paradox I would have to go in more detail into what @MigL was trying to tell you. Maybe he misunderstood you. I may have also misunderstood you, as it's very difficult to be sure what you're talking about (you never seem to get around to defining mathematically what you're saying). But further below he told you: Anyway... The information paradox has nothing to do with macroscopic entropy, which is the item you seemed to be referring to. It has to do with microscopic entropy, which is just volume of phase space. There are two versions for it; one classical (Liouville's theorem), and another quantum mechanical (unitarity, although I don't like that term; it's clearer if you say "pure states into strict mixtures"). Microscopic entropy (phase space volume) is strictly conserved in physics. Volume in phase space has two parts: One you can see by coarse graining (macroscopic) and another you can't see (total minus coarse-grained). The total is the one that concerns the paradox. Of course BHs create lots of macroscopic entropy, but that's not the problem, nor is it a paradox. It's actually the common pattern in Nature. What is a paradox is that BHs seem to require the violation of conservation of phase-space volume, which Leonard Susskind, e.g., calls "distinctions", because he is very careful about the concepts. Violation of the number of distinctions is not the same as irreversibility. Hossenfelder is also very careful to distinguish between what she calls "irreversibility" (it's actually non-conservation of distinctions) and violation of time-translation invariance. I think Hossenfelder (in what clearly is a popular video, not a lecture) does a very good job of explaining a difficult concept, but unfortunately she uses the word "irreversibility" which has a long tradition in thermodynamics, and is to do with macroscopic entropy. Nevertheless, she superimposes a movie explaining what she means, and it becomes very clear she means conservation of distinctions: Liouville's theorem. This "irreversibility" (it should never be called that way, and I stick to Susskind's term "conservation of distinctions") is what seems to be violated in Hawking's argument. If that's what your theory solves, well congratulations. I haven't seen a single formula yet proving that your "model" transforms pure states into pure states. Your insistence on time reversal only suggests to me that you keep confusing both (different) concepts, as explained by Hossenfelder. In the classical version, this would imply that two different initial states: \[q_{1},p_{1}\] \[q_{2},p_{2}\] merging into the same outgoing state: \[q,p\] Or the opposite (one trajectory splitting into two). That would also result in violation of Liouville's theorem. So "irreversibility" is an outstanding misnomer. It would be non-injective character in the evolution mapping, in either direction. I don't think that name will stick though. In the QM version of such violation, a pure incoming state: \[\rho_{\textrm{in}}=\frac{1}{2}\left(\left|\psi_{1}\right\rangle +\left|\psi_{2}\right\rangle \right)\left(\left\langle \psi_{1}\right|+\left\langle \psi_{2}\right|\right)=\left|\varphi\right\rangle \left\langle \varphi\right|\] comes out as a strict mixture: \[\rho_{\textrm{out}}=\frac{1}{2}\left(\left|\psi_{1}\right\rangle \left\langle \psi_{1}\right|+\left|\psi_{2}\right\rangle \left\langle \psi_{2}\right|\right)\] Now, it's not a matter of thermality, really. Thermality is not the crux of the matter. It can be added to the picture, it's probably there, but it only confuses things. It's rather a matter of one trajectory splitting into two, as Leonard Susskind very clearly explains in several lectures, available online. That's probably why Hossenfelder doesn't like to characterize it in terms of information. "Information" seems to imply an observer. In this case it's Nature itself that's erasing its distinctions. You see? Susskind's word "distinctions" is what conceptually cuts it. And even better is using some maths, they leave little or no doubt about what you mean. Edit: x-posted with MigL

It's you who doesn't understand the information paradox. It has nothing to do with disappearance of macroscopic information. It's about volume of phase space (classical mechanical picture) or, in QM, violation of unitarity. It's about disappearance of microscopic distinctions. Irreversibility is not involved. How would macroscopic irreversibility be at odds with the physics we know if it is a universal law of physics? Don't you have a grasp of basic thermodynamics? How can you claim to have solved a problem you clearly don't understand? I'm back.

Good question. +1 Let's see how it goes unanswered.

It serves me well for trying to be intuitive. I didn't mean physically going. I meant transformations and mappings. May I point out that you haven't shown your "model" yet? You really have no model, do you? Your transformation? You have defined no transformation. I've got a purple one-eyed winged elephant. Do you want me to talk about it? I bet I can google for something resembling it and come up with some links to keep this going. At this point, I take my leave.

Qualitative conclusions: The conclusions could be qualitative. You see? This is the problem. This is what I meant when I said: (Point number 1.) It's the opposite. First order effects cannot be detected. Second order ones can. Those are called tidal forces. If a small BH went through you, you would notice, believe me. But if it were you who's small in comparison to a quiet silent BH, you would notice nothing remarkable when going through the event horizon. Einstein's EP is the essence of gravity. How could it exclude gravitational effects? Markus has told you that too. You seem to be just insisting on what we know not to be true. Continuity, differentiability and injective mappings are very important in GR. In fact it's a paragon of these features. Intrinsic to its very foundations. Basically, whenever something takes you from A to B, it must be possible to reconstruct the going from B to A. Otherwise it's a can of worms you're opening. It's up for grabs for any ad hoc thinking basically.

The Lorentz group splits into 4 chunks. Only one of them is connected to the identity, the so-called proper ortochronous. The other pieces are not even groups and you cannot continuously go from one to another. It's as if they lived each in their own island. The only solution I see for defining time inversions and/or changes in the metric is to extend the number of dimensions and try to figure out what the Einstein equations are as a projection from that richer space. Maybe in that higher-dimensional space the transformations that you're envisioning do make sense as a connected group of transformations. Next step would be to make your assumptions as clear as possible. Formulate a plausible set of approximations to draw clear mathematical conclusions. They don't have to be numerical. They could be qualitative. Now find a suitable publication that is open to more speculative thinking. Send your paper. Be cautious and understate things, rather than make big announcements. Be prepared for something more than a battle of words. If you think what you've found here is stubborn opposition to your ideas, that's nothing compared to what you're going to be up against in the peer-review world. Be prepared for some heartbreaking trashing. As to time stopping, pay heed to what Markus told you. That's very very likely just an artifact of the coordinates. That's what it looks to be. They only well-referred unambiguous observers in GR (IMO, there could be differences of opinion here) are free-falling ones. And when you change coordinates to locally minkowskian (free falling observer) the weird "inversion" (which is actually a swap radius <--> time) disappears. If the BH is big enough, the observer feels nothing. That's what the maths say. As to wiping out the singularity, Ghideon has pointed to the possibility of alternative heuristic toy models, Markus has told you about torsion or going to the more realistic Kerr metric. I would like to mention also that, if the BH is of stellar origin, there may be what remains from the dead star playing a part there. The only serious alternative I can see for what you want to do is to generalize GR. That's quite a challenge. And that's about what I can think of right now. I'm trying to be as helpful and constructive as possible.

You forgot to read the abstract: Relativistic quantum mechanics is a play-toy. If you want to get serious you need to use QFT. When you do that, first thing that happens is that Dirac 4-spinors go in the rubbish bin, because they're not irreducible representations of the Poincaré group (particles). That's one of the reasons why the SM is formulated in terms of Weyl spinors. The authors don't say to be proposing any plausible mechanism or making any strong claim. They seem to me to be arguing that negative energies are not as crazy as it may seem if you use a unitary CT operator that they introduce in the naive wave function formalism. That's all. You've read too much into it. No. That's not a Wick rotation. What Hilbert did there was to absorb the minus sign in the metric by re-defining time as pure imaginary. I suppose Hilbert was much more familiar with Kronecker deltas than Minkowski pseudometrics. That's kind of a re-labelling, a convention rather than a transformation. I don't know if I'm explaining myself: You take the sign from the metric and absorb it into the time definition. That's why I asked you about the changes both in the metric and in the coordinates. Nothing sacred about the metric coefficients in relativity, but the contraction of metric with coordinate differentials is next-to-sacred. And there are good reasons for it. A Wick's rotation is very different. The metric doesn't change, but time does. This is called a Euclidean-time calculation. You calculate the partition function, pretend time is imaginary, and obtain a nicely convergent result, from which you guess the actual solution by arguments of analytic continuation. You're not swapping the sign from one place to the other; you're actually changing it, obtaining a "fake" solution, and guessing the physical one. You're keeping your ideas behind a horizon in many senses. I suspect it's all because you don't want anybody to really see them. It's all like behind a thin veil of heuristic censorship (GR joke.) I certainly don't want to go through the same ordeal as other brave warriors, getting fired from behind the bunker of a conceptual horizon. I'm just trying to give them a temporary relief in battle.

That's the direction I was going when I said that naive hydrodynamical calculations seem to produce ridiculous results. A back-of-the-envelope calculation in time saves a lot of work. Responsible for this could be the occurrence of exponentials. If you take a look at how spherically symmetric, self-gravitating fluids behave: https://en.wikipedia.org/wiki/Lane–Emden_equation.: You will realize that the dependence of density with the radius follows some kind of power law depending on the polytropic index n, which would have to be guessed. Your problem, I think, is still more complicated, because the fluid is not purely self-gravitating, but also is being subject to an external potential.

Yes, the fact that there are lots of methane and ethane could be very useful to obtain energy/store it for different purposes. I don't know about how efficient electrolysis of water in Titan would be. Maybe someone can help about that. My personal favourite in terms of generating oxygen is analogues of cyanobacteria that could work in Titan's conditions. You would need a microorganism that liberates oxygen... It seems that the most abundant source of oxygen in Titan is water. Not much CO2 from volcanos. Bacteria and archaea of some kind on Earth manage to exploit virtually any redox-reaction that the chemists have been able to draw on the whiteboard. So, possibilities there are. https://en.wikipedia.org/wiki/Titan_(moon) Magnetosphere. Stars and gas giants have very powerful magnetic fields around them that, in the case of Saturn, whip their moons with very strong and potentially very damaging ionizing radiation. This radiation is mutagenic, and most mutations would result in cancer. The Earth, e.g., is protected against the Sun's magnetosphere by its own magnetic field. The problem with these moons is that generally they are geologically inactive, so the don't have own magnetospheres to act as shields. https://en.wikipedia.org/wiki/Magnetosphere_of_Saturn Here they seem to suggest the opposite of what I was saying, that Saturn's magnetosphere shields the moon from solar wind. [?] Maybe it's a question of prevailing winds... As to soil minerals, the problem with life is that you must move all the chemicals in cycles: nitrogen, carbon, water, iron... That would take a massive engineering grand scheme of recycling. Because Titan is being the subject of intense study now, I wouldn't take anything we know now as set in stone. I'm no expert on this. I only want to entice nice and informed conversation here, because the topic is interesting. +1

I will add some points to what Markus, MigL and Ghideon have already said. You talk about violation of energy conditions. What energy conditions? From what I know about energy conditions, they are imposed on the matter tensor; and there is no matter tensor in the Schwarzschild problem, as there is no RHS of Einstein's equations. It's a vacuum solution. Maybe you're implying a matter tensor with negative T00 for the interior. If that's the case, what you should do is solve the Einstein equations with that source, patch them up with the exterior solution and prove that no singularities in the metric happen from the outside to the inside. You cannot do physics in vague concepts and claim that it must make sense in the face of all criticism. You talk about quantum jumps at the horizon as possible justification for your jumps in the metric. Do you realize that you're talking about quantum gravity? You seem to suggest a Wick rotation. Can I see a mathematical formula? How does it act on the metric coefficients and the coordinates? You've been very ambiguous about this. Is it a Wick rotation or an time inversion? Those are different things. And may I ask what has been suggested to you before?: What are your predictions?

From what I know the only liquid in Titan is mostly methane (and maybe other light hydrocarbons.) Water is frozen solid so hard that geologically it plays the role of rocks there. I don't think there would be even the remotest possibility of growing crops or pigs because of that. Also, Saturn's magnetosphere would be deadly to the flying pigs. Although I love the picture of flying pigs in Titan.

Hard to believe. I'm trying to picture a land swallower who had big knees. Maybe something was lost in translation? Perhaps the original meaning was something like "strong knees" and "conqueror of land"... Anyway, eponyms and toponyms are a constant source of drift in meaning and spawning of new vocabulary. Interesting that Walpiri loaned grammatical structure from English, rather than loan nouns, adjectives, verbs, and adverbs. For example, the "'em" in "pick'em", "tell'em" etc. became a mark of direct object in Walpiri. So grammar also flows from one language to another.

Oh, I hadn't seen that. Here's a higher resolution: There are further inconsistencies, as the city of Shambala has been identified, for all I know, and geology and known biology easily debunk this picture. It's actually kind of a challenge to spot all the inconsistencies with known facts. I find the comment "inner Earth to be re-drawn by someone who has been there! Thank you..." particularly endearing. Edit. With this picture, we would have plants that grow in presumably inverted microgravity...

My original idea was about scientific principles, but poetic, inspirational mottoes are certainly useful too. So I personally welcome them. Another very well-known one by John Wheeler: There is another one which captures the essence of Darwin's theory of evolution, that I can't remember now, and I must rescue from somewhere. If anybody remembers...

I think your idea is not very out there, and I'll tell you why from my own reasoning. The first time you hear about the Plank scale, you find the lp and the tp to be very reasonably in the range of what a minimal distance and time must be. Well below anything event-related that makes sense. Very small. Inconceivably small. But... mp is nothing like that. It's neither here nor there. It isn't at all interpretable as the minimum conceivable mass; nor is it the opposite. It's close to the mass of an amoeba: https://www.google.com/search?client=ubuntu&channel=fs&q=mass+of+an+amoeba&ie=utf-8&oe=utf-8 Coincidence? I don't think so. To me, Plank's mass is to do with information, and there must be some kind of power law behind it. What that power law could be I don't know. But I don't think it's to do with humans; I think it's probably to do with severe constrictions on how a macroscopic system stores and processes information of the world around it. As long as we are in the arena of speculation...

I misunderstood the problem here. Of course you guys are right: Gravitational field inside a shell of spherical mass is zero. For some reason I kept thinking of the "real" Earth, or an approximate model to it.

Love requires many letters. 26 fall short. You almost got me. Although love letters are a thing of the past, probably. I once learnt that in Wales there is a place which has one of the longest toponyms. There seems to be a Maori toponym that is longer. How about a weekend in, Taumatawhakatangihangakoauauotamateaturipukakapikimaungahoronukupokaiwhenuakitanatahu? If that's too much of a stretch, you can always stay at, Llanfairpwllgwyngyllgogerychwyrndrobwllllantysiliogogogoch I'm sure those are sentences in disguise!

Also, maybe Cadabra, for symbolic calculations, especially suited for field theory: https://cadabra.science/ I haven't tested it, to tell you the truth.

You've got a free web portal: https://www.wolframalpha.com/ And if you need more computation power and time, server dedication, (plus access to some packages, etc.), you can download an app for about not much more than 2€, if I remember correctly. I think it's money well spent.

Birkhoff's theorem: https://en.wikipedia.org/wiki/Birkhoff's_theorem_(relativity) Sorry. I hadn't noticed that Markus had already said it. +1

No. I learnt about Django Reinhardt from within my light cone, by gathering signals. Very nice mnemonics. +1 The left ear is inverted. I mentioned Django Reinhardt because he had two fingers burnt, and managed to play beautifully with only eight fingers.

I posted the solution here: Gravitational field at centre is zero. It can be solved by using Gauss' theorem. For interior solution spherical symmetry must be assumed. Goes down linearly with the distance to the centre. I agree that there's nothing else remotely scientific in OP. Any hollow in the Earth's interior would be crushed by the enormous pressure, obviously.