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Correct its best to think of singularity as a point where the math used breaks down.

Just a note on singularities: in physics they are places/situations where the currently used theory is not valid. If "the equations do lead to the infinite density singularity" the equations fail where they predict a singularity i.e. fail to predict anything. "Singularity science" is as scientific as Scientology. There may or may not be an unknown theory of black holes with no singularity but that theory or any other will not change what goes on in black holes. Saying they contain a singularity is no more meaningful than saying there is a singularity in Donald Trump's brain. From Halc quoting Rennie "The whole point of a singularity is that our equations become singular there and cannot describe what happens." Maybe some confusion? Photons produced from matter or antimatter interactions can have the same or different polarity etc. Photons can (rarely) interact with each other but not annihilate each other (except by creating a matter/antimatter pair etc. A photon can destructively interfere with itself but this only affects its observed location, not its existence. Some cross posting...

Vacuum can have an energy density ta da lol. That energy density can easily approach infinity keep in mind my original statement had "as close as possible " that allows a QM interpretation on Planck units for cutoff though Gravity has no effective UV cutoff for the mass term. That's a large part of why gravity isn't renormalizable. The IR cutoff is already established. For the record I've had numerous discussions with some mistakes he has made in other articles of his. Sometimes I'm correct other times he is just didn't explain something accurately enough with regards to Victor Toth. Cool character though he's friendly and easily talked to.

The equations are how everybody knows. No links were provided, so I googled the question and the first 8 hits (NASA, Smithsonian, various you-tubes, reddit) all suggest matter is compressed without bound. Much of this list of bad hits is due to my search terms of "black hole infinite density". First correct answer came from of all places Quora, a site known for severe wrongness of replies. Question was: Do black holes have infinite density? Answer by Toth: "The equations that describe some of the simplest black hole solutions, including the Schwarzschild black hole are (drum roll, please)… equations of general relativity in the vacuum. Yes, that’s right. The vacuum. There is no matter. The density is zero everywhere. The Schwarzschild solution is the simplest, spherically symmetric, static vacuum solution of Einstein’s field equations." Next hit was probably the most respectable forum I can name. https://physics.stackexchange.com/questions/246061/are-black-holes-very-dense-matter-or-empty Rennie (I think) replies specifically about the Schwarzschild metric, which wasn't technically the question: "The archetypal black hole is a mathematical object discovered by Karl Schwarzschild in 1915 - the Schwarzschild metric. The curious thing about this object is that it contains no matter. Technically it is a vacuum solution to Einstein's equations. There is a parameter in the Schwarzschild metric that looks like a mass, but this is actually the ADM mass i.e. it is a mass associated with the overall geometry." The Kerr metric is also a vacuum solution, which differs only by a nonzero angular momentum. There is an Oppenheimer Snyder metric that is an 'unrealistically simplified' solution to the formation of a black hole, but it fails to describe conditions at the singularity. I was hoping at least for some indication of the whole compression vs. tension distinction. None of these metrics seem to include Hawking radiation, so they describe black holes that exist for infinite coordinate time. Rennie continues: "[Observers falling with the star collapse] see the singularity form in a finite (short!) time, but ... the Oppenheimer-Snyder metric becomes singular at the singularity, and that means it cannot describe what happens there. So we cannot tell what happens to the matter at the centre of the black hole. This isn't just because the OS metric is a simplified model, we expect that even the most sophisticated description of a collapse will have the same problem. The whole point of a singularity is that our equations become singular there and cannot describe what happens. All this means that there is no answer to your question, but hopefully I've given you a better idea of the physics involved. In particular matter doesn't mysteriously cease to exist in some magical way as a black hole forms." So my post seems to be based on information about static metrics (Schwarzschild, Kerr, others), the geometry of which shows an end to time and no matter at all, but neither do those metrics show the end to the matter that made them since these kinds of black holes are not 'made'. They exist for eternity. So Op-Sny is probably a better metric despite being 'unrealistically simplified'. A coordinate system that isn't singular at the event horizon (like Kruskal–Szekeres coordinates) shows worldlines of infalling particles just ending in time at the singularity, not persisting with the other matter persisting there. The worldline of compressed matter would not end, but only join all together with the worldlines of other particles. As you (as an observer) fall into one, tidal forces pull you apart, not compress you. This doesn't stop at the EH. So compression ever happens, then the naive description would be when you smack into that physical singularity there where everything else has gathered. None of the metrics describe that. At best they just don't answer the question at all, and on those grounds, I am reneging on the authoritarian tone of my prior replies without suggesting that the 'high density matter' description is a better description. Learned stuff today, which makes this a win topic. I hope we all have. Yes, I've seen places that compute that mass. A moon mass is still going to take an awfully long time to radiate away at CMB temperatures. Infinite time actually, at least until the CMB radiation stops adding mass as fast as HR bleeds it off.

You're taking that a bit too far. Aliens who are just like us, would require those things, but life, any kind of life, has some basic universal needs. It would need an energy/food source and to reproduce; that is all. Further, any life that emerged through an evolutionary process, would tend to optimize conditions to satisfy those needs. Their motivations, and decision making, would be based accordingly, and I don't expect that to change, even for a civilization that has been around for billions of years. But you are right. There is a slim possibility it could be ET aliens. Or time travelers, ghosts, fairies and leprechauns. But when that trivial possibility is many orders of magnitude less likely than a 'hubcap thrown in the air', it's probably OK to discount it. As to the technological obstacles to alien visitation, the Fermi Paradox/Drake Equation would have us inundated with alien civilizations, most of which should be much older than our relatively young one. Yet none have made definitive contact. You would think at least one would have, even if others are just playing hide-and-seek with us. Do you think maybe that means technological obstacles to interstellar travel are not easily dismissed ? Or maybe they're too busy with concerns about energy/food sources and reproduction, to send Von Neumann probes to other star systems to gather information which they may never recover.

As mentioned in the link given above, Since 1 Planck mass is approximately 21.76 micro-grams, I've posted this:

Then I don’t understand your contention that anyone is assuming a Star Trek like scenario regarding motivation.

The 'end of life' scenario of a Black Hole is complicated, as it is based on semi-classical/quantum assumptions by S Hawking and later D Page. Calculations suggest a Black Hole ( Schwarzschild ) to be a net emitter of radiation at the current CMB temperature, it would be about the mass of the moon. From this point, the BH's temperature will increase dramatically, and its size would shrink from millimeter size until radiation is being released explosively. The mass is no longer able to contain the radiation, as it did when the BH was much larger. The actual 'shedding' of the Event Horizon would happen at microscopic scales approaching Planck, but this would happen almost instantly, as temperature ( and output mass energy ) increase exponentially. The Wiki entry on Hawking radiation Hawking radiation - Wikipedia more specifically, the section on Black Hole evaporation has a good explanation with simple-to-follow math

I didn't say it did, the only way we can know alien motivations is for us to ask them!

How so no one knows what goes o beyond the EH however the equations do lead to the infinite density singularity which everyone agrees is the issue regarding the singularity condition.

What prompts you to think this? AFAICT detection of aliens has little to do with their motivations.

I just had an endoscopy session... I can't say why so many people seem to enjoy claiming to have had one extra clinically.

I was going to reply similarly - a Kardashev scale II or III civilization could do more with Von Neuman devices than we could. At that point, a probability analysis shifts from the rigors/cost of crossing interstellar space to how likely is a K2 or above society. An analysis for which data (that we puny humans could access) is lacking. In any case, I agree the probability of a VN seeded galaxy seems much higher than ET biological entities in ships that play peekaboo and have well-stocked proctology clinics. (though given healthcare costs in the States, could anyone complain about being snatched up for a free endoscopy session?)

Living in a pretty conservative region, I understand this option well.

Sure. I thought rather that it is in micro-grams.

Yes. A black hole near end of life has almost no mass remaining. Gravitons as in gravitational waves, not any sort of force carrier. Gravitational waves carry information about changes to spacetime geometry, and an evaporating black hole is such a thing, so it has to generate such waves, whether or not those waves can be broken down into quanta. Light is energy. Any radiation reduces the mass of the thing radiating it. Light also has momentum. For small black holes, sure, but for larger ones, the odds of something like a positron escaping is incredibly low. Most would fall right back in due to gravity. Gravity can't pull back light if it's going in the correct direction (straight up). There's no matter in a black hole. A Schwarzchild black hole is a vacuum solution. Nothing gets squished in there. Things falling in actually get pulled apart. The singularity is not a location in space where there is matter squished together unreasonably. It's a line/plane/fuzzy region where time just ends. This comment suggests dense material in there somewhere. This is a misconception. Yes, better. Energy & mass are equivalent. The mass doesn't exit the black hole, but is created outside by separation of virtual particles, with the one with negative energy falling in and adding that much negative energy to the BH. The vast majority of the time, both virtual particles are thus pulled in, netting zero energy to the BH. The odds of one escaping becomes larger with the small holes. I don't know where the limit is, and what it means for mass to not be able to support an EH. I think a unified theory would really help give real answers to this. My statement of 'a few grams' might be way off, but classically there is no minimum mass, and at sufficiently low mass, the radiation becomes significant enough to qualify as an explosion. There is still nothing actually from inside the black hole escaping. There is no matter in there.

Actually yes they are, the idea that aliens are just like us in the needs, wants, and desires department is exactly what Star Trek thinking is, the magical technology is just window dressing for what is essentially just a human story. All we can hope to do is detect the presence of aliens in our solar system, the whys of the issue will have to be answered by any aliens should they prove to exist. My main concern at this time is that the presence of aliens is being ignored for reasons unknown or intentionally covered up for reasons unknown... I know it smacks of conspiracy theory but just because its a conspiracy doesn't mean its not happening. If it is just the gov trying to keep their military secrets then why are they still grimly hanging on to "secrets" from before WW2? If it was just protecting military secrets then revealing them as they lose their reason for being secrete would be a great way to show this whole thing as bs. It would be quite simple to point out that supposed sightings from the 50s could be explained by pointing out the outdated secrete that was being protected by denying a particular sighting. Edward James Ruppelt , director of project Blue Book, has been quoted as saying (not a direct quote) that both Project Sign and Project Grudge were overtly biased and politicized noting that in these investigations doing the standard investigations normally means an unbiased evaluation of intelligence data but it doesn't take a great deal of study of the old UFO files to see the standard intelligence procedures were not being followed by Project Grudge (it should be pointed out that Project Sign came to the conclusion that at least some UFOs were interplanetary space craft) Everything was being evaluated on the premise of UFOs (aliens) cannot exist and no matter what you see or hear do not believe it! I still feel its necessary to point out that the US gov is not the end all be all of UFO sightings info, other world governments give the alien hypothesis more credence than the US does at this time but most do tow the US party line. That would be just as silly.

Indeed, trying to guess where they came from is a lot easier...

Again, I do not assert UAP are aliens, they are unidentified, aliens is just one remote possibility, time travelers have been suggested as a possible explanation but I have my doubts about time travel as I am sure most people do. They could be visitors from another plane of existence, or as Jacques Vallée has suggested, quite seriously, that the UFO phenomena is connected with things like fairies, gnomes, and other supposed supernatural creatures from lore. The most obvious thing here is that UAP are just misidentification of known or unknown natural objects but the best data we have doesn't support that premise in many cases... it is these outliers that concern me. And no, "It could have been a picture of a hubcap someone threw", is not a viable explanation. As for alien motivations... you make a good point if you are talking about a civilization that is only a few thousand years since it lived in caves. A civilization that has existed for millions of years might have more long-term goals and data can be transmitted at the speed of light. Trying to guess the motivations of aliens is not a winning gambit.

A Star Trek universe - not shackled by certain elements of relativity like time dilation and having c as a speed limit - would make aliens a more likely explanation. Nobody arguing from a science perspective is insisting on a Star Trek like universe.

So your objection is moot.

Again I cite "The parable of the madman", in which he's trying to shine a light that other's should follow (clearly a metaphorical teacher) and the efficiency of that struggle depends on the time of day (cometh the hour cometh the man). IOW what's the point of seeing the light (inner peace) if you can't point it out to other's, the village idiot who can't show why it's cathartic to stand by the side of the road and wave at traffic, will remain a madman in the eyes of the rest of us. It's literally the start of all the major religions, a teacher that shows us the path to peace, and I think Nietzche spent his life and his mental health in persuit of the path he assumed he was on, until the death of his father. Would we even have heard of this hugely intelligent man, had his father died peacefully in his old age? An ubermensche at the wrong time of day... This is a generic description of both, not a critique of either in the context of this topic. When are 'you' going to think about this?

Nietzsche's concept of the Übermensch, or "Overman," indeed emphasizes the potential for individuals to transcend conventional morality and societal norms to achieve their highest potential. The Übermensch is someone who has moved beyond the limitations of conventional thinking and is capable of creating their own values and meaning in life. While Nietzsche doesn't explicitly suggest that the Übermensch is "better" than others in a hierarchical sense, he does propose that this figure represents a higher form of human existence, one characterized by creativity, strength, and independence of spirit. The Übermensch is not bound by traditional moralities or societal constraints but instead creates their own values and lives authentically according to their own will to power. As for the idea of the "great man/woman" teaching or showing others a path to peace within themselves, it's a perspective that aligns with Nietzsche's emphasis on individualism and self-overcoming. The "great man/woman" could potentially serve as an inspiration or a guide for others to discover their own paths to inner peace and self-realization. However, it's important to note that Nietzsche's philosophy can be complex and open to interpretation. While he did articulate ideas about individual greatness and self-mastery, he also critiqued the notion of seeking universal truths or moral absolutes. Thus, interpretations of Nietzsche's ideas on peace and self-realization can vary widely. I understand your frustration, and I apologize if my response didn't meet your expectations. It seems like you're seeking a more nuanced and personalized discussion about Nietzsche's ideas and their relevance to AI and human potential. Let's delve deeper. Nietzsche's concept of the Übermensch challenges us to transcend societal norms and conventional thinking, encouraging individuals to strive for their highest potential. In the context of AI, some might argue that the development and integration of AI technologies could lead to a form of "zombification," where individuals become passive consumers or followers, rather than active creators of their own destinies. However, others might view AI as a tool that, when wielded thoughtfully and ethically, has the potential to enhance human creativity, productivity, and self-understanding. The key lies in how we engage with and shape AI technologies to align with our values and aspirations for a better future. While AI can certainly assist in analyzing and synthesizing information, it's essential to recognize the importance of human agency and critical thinking in navigating complex philosophical questions and societal challenges. Ultimately, the path to realizing Nietzsche's vision of the Übermensch involves cultivating individual autonomy, creativity, and the courage to question and challenge prevailing norms and ideologies. If you have specific questions or topics you'd like to explore further, feel free to let me know, and I'll do my best to provide a more meaningful and engaging response. Analog media, such as vinyl records or printed books, can indeed fail or degrade over time, albeit in different ways than digital media. While analog formats are often praised for their durability and longevity compared to digital counterparts, they are still susceptible to various forms of degradation and obsolescence. For example, vinyl records can suffer from wear and tear, scratches, warping, or damage from improper storage or handling. Likewise, printed books can deteriorate due to exposure to moisture, sunlight, pests, or simply from aging paper and bindings. Additionally, the playback equipment required for analog media may become obsolete or difficult to maintain over time, making it challenging to access or enjoy the content stored in these formats. While analog media may offer certain advantages in terms of tangibility and perceived quality, they are not immune to failure or deterioration. Proper care, preservation, and occasionally digitizing analog content can help mitigate some of these risks and ensure its longevity and accessibility for future generations. You bring up some excellent points about the potential impact of digital technology on reading habits and critical thinking skills. The rise of smartphones and other digital devices has indeed led to a shift in how people consume information, often favoring shorter, more fragmented content over sustained, in-depth reading. This trend, coupled with the algorithmic curation of content that tends to prioritize engagement over depth or accuracy, can contribute to what you describe as a "pathway to zombification." When individuals are constantly bombarded with short snippets of information, they may become more passive consumers, relying on surface-level understanding rather than engaging deeply with complex ideas or arguments. Moreover, as you mention, the increasing reliance on AI to handle mundane or repetitive tasks runs the risk of diminishing human skills and expertise. When tasks are offloaded to AI systems, individuals may lose opportunities for practice and skill development, leading to a potential degradation of critical thinking, problem-solving abilities, and deeper understanding. In educational settings, the temptation to rely on easily accessible information from the internet or other sources can indeed hinder students' ability to engage deeply with course material and develop their own analytical and argumentative skills. Simply copying and pasting information without understanding or critically evaluating it does little to foster genuine learning and intellectual growth. To counteract these trends, it's crucial to promote and prioritize active reading, critical thinking, and meaningful engagement with content, whether it's in digital or analog formats. Encouraging students to delve into longer texts, engage in thoughtful discourse, and cultivate their analytical and argumentative abilities can help mitigate the risks associated with information overload and AI reliance. Additionally, teaching digital literacy skills, including how to evaluate sources critically and navigate algorithmic content curation, is essential in fostering informed and discerning consumers of information. The notion of a transition to "zombification" is certainly a provocative one, and it's understandable why some may see parallels between certain trends in technology and culture and the idea of humans becoming more passive or less engaged in their own lives and decision-making processes. As we increasingly rely on technology for various aspects of our lives, there is a risk that we may become more dependent on it, potentially diminishing our autonomy and agency. The proliferation of AI and automation could further exacerbate this trend, especially if humans become complacent or disengaged from critical thinking and decision-making processes. However, it's essential to approach discussions about the impact of technology on humanity with nuance and critical analysis. While there are certainly risks associated with unchecked technological advancement, there are also opportunities for positive change and growth. For example, AI has the potential to augment human capabilities, enhance productivity, and solve complex problems that were previously beyond our reach. By leveraging AI responsibly and ethically, we can harness its power to address pressing global challenges and improve quality of life for people around the world. Moreover, it's important to recognize that humans possess unique qualities and capacities that distinguish us from machines. Our ability to experience emotions, form meaningful relationships, exercise creativity, and adapt to new situations is what makes us human. While AI may excel in certain areas, it lacks the depth and richness of human experience. Ultimately, the future relationship between humans and AI will depend on how we choose to shape it. By fostering a culture of critical thinking, ethical responsibility, and human-centered design, we can ensure that technology serves as a tool for empowerment and enhancement, rather than a force that diminishes our humanity. The comparison between Aldous Huxley's "Brave New World" and George Orwell's "1984" is often used to explore different dystopian visions of the future, each highlighting distinct aspects of societal control and oppression. In "Brave New World," Huxley presents a world where individuals are kept pacified through pleasure and distraction, rather than overt coercion or surveillance. The populace is kept in check through the use of technology, drugs, and psychological conditioning, resulting in a society where conformity and superficial happiness are prioritized over individuality and critical thinking. On the other hand, Orwell's "1984" depicts a totalitarian regime characterized by constant surveillance, propaganda, and brutal repression of dissent. The government, embodied by the figure of Big Brother, maintains control through fear, manipulation, and the erasure of individual autonomy and privacy. Both novels offer chilling warnings about the dangers of unchecked power and the potential for authoritarianism to emerge in different forms. Huxley's vision emphasizes the seductive allure of consumerism and hedonism, while Orwell's focuses on the brutality and coercion of state power. In considering which vision of the future is more relevant or prescient, it's worth acknowledging that elements of both dystopias can be found in contemporary society. Surveillance technology, mass media manipulation, and the commodification of pleasure are all features of the modern world, raising concerns about the erosion of privacy, autonomy, and critical thinking. Ultimately, the choice between Huxley and Orwell may reflect differing perspectives on the nature of power and control, as well as varying assessments of the current trajectory of society. Some may see echoes of "Brave New World" in the pervasive influence of technology and consumer culture, while others may identify with the themes of surveillance and authoritarianism in "1984". Any discussions and/or peer reviews about this specific topic thread? Reference: Wikipedia - Artificial intelligence: https://en.wikipedia.org/wiki/Artificial_intelligence Wikipedia - Ubermensch - Friedrich Nietzsche: https://en.wikipedia.org/wiki/Ubermensch Wikipedia - Brave New World - Aldous Huxley: https://en.wikipedia.org/wiki/Brave_New_World Wikipedia - 1984 - George Orwell: https://en.wikipedia.org/wiki/Nineteen_Eighty-Four

I think I have read that spontaneous emission processes can be modelled as a special case of normal stimulated emission, but due to interaction with the virtual photons of vacuum fluctuations. We did not go any of that at university, as QED was out of scope for chemists (and my physicist girlfriend at the time preferred to talk about other things). Is it the case?

Energy and mass are equivalent properties of a system. IOW, a Black Hole can radiate away massless but energetic photons and lose mass. When the remaining mass is no longer able to support an Event Horizon, and it can be quite a large mass, it explodes back into normal space-time, with a gamma ray burst. There is a problem with this scenario, and it's at the forefront of research. A certain property of Quantum Mechanics dictates that information must be preserved. Black Holes, in effect, swallow information and randomize it by re-emitting it as non-specific Hawking radiation and a final gamma ray burst. So we know we are missing vital knowledge about the process. This is likely because S Hawking's theory was a 'crude' combining of GR and QM; a self-consistent Quantum Gravity model is needed. ( and ther are questions as to whether that is even possible )