If any futuristic civilization wants to extract energy from a black hole, the first step will be to build a space elevator that violates the laws of physics
A day will come and the sun will die. The fuel fueling its nuclear fusion reactions will burn out, the skies will cool, and if the Earth survives at all, humanity will be thrown into eternal winter. If our descendants wish to remain alive, they will be forced to make alternative arrangements. First of all, they will exhaust the Earth's resources, then the solar system, and finally, all the stars in all the galaxies in the visible universe. With all sources of combustion eliminated, they will no doubt set their sights on the only source of energy left: black holes. Will they be able to collect this energy from them and save civilization?
I have bad news: this program will not work. The reasons for this lie in the physics of exotic entities such as quantum strings and the famous device favored by science fiction writers: the space elevator.
false hope
On the face of it, extracting energy (or indeed, anything else) from a black hole seems to be an impossible task. After all, black holes are enveloped in an "event horizon," a spherical envelope from which there is no return, within which the gravitational field becomes infinite. Anything that finds itself inside this shell, its fate is sealed. Therefore, any device that tries to eliminate a black hole and release its energy, will self-destruct, and be swallowed by the black hole along with its unlucky operator. A bomb thrown into the hole will not only not destroy it, but it will also enlarge it, by an amount equal to the mass of the bomb. What goes into a black hole never comes back out: not asteroids, not rockets, not even light.
At least that's what we're used to thinking. However, all of a sudden, in an article that for me is the most shocking and delightful article ever written in the history of physics, Stephen Hawking showed in 1974 that we were wrong. Hawking, based on earlier ideas conceived by Jacob D. Bekenstein, who currently works at the Hebrew University of Jerusalem, showed that black holes leak small amounts of radiation. You will still die if you fall in, but even though you yourself will never get out, eventually your energy will escape. This is good news for those who aspire to extract energy from black holes in the future: energy can escape.
The reason energy escapes lies in the deceptive world of quantum mechanics. One of the distinct phenomena of quantum physics is the possibility of a particle passing through a tunnel, i.e. passing through obstacles that would be impassable without quantum mechanics. A particle rolling towards a high barrier may sometimes appear on the other side. Don't try this at home: if you slam yourself into a wall, it's not that likely you'll be reincarnated without a scratch on the other side. But microscopic particles are more likely to pass through a tunnel.
It is quantum tunneling that allows alpha particles (helium nuclei) to escape from the jaws of a radioactive uranium nucleus, and it is quantum tunneling that allows "Hawking radiation" to leak from a black hole. Particles escape from the infinite gravitational field of the event horizon, not by hitting the walls but by tunneling through them. (Of course, no one has ever seen a leaking black hole, but this is such a compelling mathematical implication of applying quantum mechanics to curved spacetime that no one questions it.)
And since blacks are leaking, we can hope to absorb their energy. But the devil is in the details. No matter how we try to extract this energy, we seem to run into problems.
One simple approach would be to do nothing but wait. After enough time, the black hole will emit its energy, photon by photon, back into the universe and straight into our waiting bosom. With every drop of energy you lose, the black hole will shrink, until it eventually decays completely. In this sense, a black hole is like a delicious cup of coffee with everything touching its surface, one of its faults, gravitationally breaking into pieces. And yet, there is still a way to consume the deadly coffee: wait for it to evaporate, and inhale the vapors.
But there is a catch. The wait is indeed easy, but it is also terribly long. Black holes are extremely dim: a black hole with the mass of the Sun glows at a temperature of 60 nanokelvins. Until the 80s we didn't even know how to create something that cold in a lab. The time that would be required for the evaporation of a black hole whose mass is the mass of the Sun is 20 times greater than the current age of the universe, an incredibly long time. In general, the lifetime of a black hole is its mass to the third power, m1057. Our shivering offspring will probably want to speed things up a bit.
One of the reasons for optimism for them is that not every Hawking particle that escapes the event horizon continues on and escapes indefinitely. In fact, in practice, none of them do. Almost every particle that passes through a tunnel and crosses the event horizon is then recaptured by the gravitational field and forced to return to the lap of the black hole. If we can somehow dislodge these photons from the black hole's grip, extract them from its clutches after they escape the horizon but before they are recaptured, then we might be able to harvest the energy of black holes more quickly.
To understand how we can set these photons free, we must start by examining the extreme forces that operate near a black hole. The reason most particles are recaptured is that these particles are not ejected in a straight line. Imagine you are projecting a laser beam just outside the event horizon. You must aim straight up for the light to escape; The closer you are to the horizon, the more carefully you have to aim. The gravitational field is so strong that even if you deviate from the vertical by a full thread, the light will bend and fall back in.
The fact that rotational speed can impair the escape process of the particle may seem strange. After all, the circular velocity is exactly what keeps the International Space Station aloft: it provides it with the centrifugal repulsion that opposes gravity. However, if you get too close to a black hole, the situation will be reversed: the rotational speed will delay the escapes. This phenomenon is a result of the theory of general relativity, which states that all mass and all energy are subject to the influence of gravity. Not only the rest mass of an object but also its rotational kinetic energy. Near a black hole (or more precisely, at a distance of less than one and a half times the radius of the event horizon), the gravitational attraction of the rotational kinetic energy is stronger than the centrifugal repulsion. From this radius onward, as the angular velocity of a particle increases, it will fall faster.
The meaning of this phenomenon is that if you slowly dangle yourself down towards the horizon of a black hole, you will get very hot in a short time. Not only the photons that managed to escape to infinity as Hawking radiation will be rained down on you, but also the photons that would never succeed in the task. The black hole has a "thermal atmosphere": the closer you get to the event horizon, the higher the temperature. This heat carries energy.
The fact that there is energy stored outside the event horizon gave birth to the ingenious proposal that we could "pump" the energy of a black hole by "reaching out", grabbing the thermal atmosphere and turning it out. Take a box near the horizon of the black hole, without crossing it, fill the box with hot gas and then pull it out. Some of the content would escape unaided, as normal Hawking radiation, but if we didn't intervene, most of the gas would be destined to fall back in. (Once this gas would have exited the area near the event horizon, it is relatively easy to transport it the rest of the way to Earth: simply load it on a rocket and fly it home, or convert the gas into a laser and beam it back.)
This strategy is similar to blowing on our delicious but dangerous coffee mug. Without external assistance, most of the water vapor that is released will fall back into the cup, but blowing on the surface removes the newly escaped vapor before it has a chance to recapture. The hypothesis is that if we peel off its thermal atmosphere from a black hole, we can quickly swallow the hole in a time period that is not of the order of m3, the time required for the hole to evaporate, but at a considerably faster rate, of the order of m.
But in my recent work, I have shown that this hypothesis is wrong. The problem does not arise from lofty reflections on quantum mechanics or quantum gravity. It stems from the least sophisticated consideration there is: you won't be able to find a strong enough rope. To pump out the thermal atmosphere, you need to be able to dangle a rope near the black hole, or in other words you need to build a space elevator. But I discovered that building an efficient space elevator near a black hole is an impossible task.
Elevator to heaven
A space elevator (sometimes called a skyhook) is a futuristic structure, made famous by science fiction writer Arthur C. Clarke in his 1979 book, The Fountains of Heaven (translated into Hebrew as "Fountains of Heaven" - the editors). Clark imagined a rope dangling from outer space down to the surface of the Earth. It is not held by a push from below (as happens in skyscrapers, where each floor supports the floors above it) but by a pull from above (each section of rope supports the section below it). The far end of the rope is anchored to a large mass that spins slowly far beyond the geostationary track, and it is this that pulls the rope outward and keeps the business hanging on a brake. The near end of the rope dangles down and reaches just above the planet's surface, where it stops. The balance between the various forces ensures that he will just float there, as if by magic (and as Clarke once said, magic is indistinguishable from sufficiently advanced technology).
The idea of this advanced technology is that when the rope is in place, it is much easier to move loads to the track. We will no longer need dangerous, ineffective and polluting missiles, which in the first part of their journey fly up mainly fuel. Instead, we will connect to an electric elevator rope. When the marginal cost of transporting cargo to a low orbit above the earth is no more than the cost of electricity, the price of putting a kilogram into space will drop from the amount of tens of thousands of dollars required by the space shuttle to the amount of two dollars. This is therefore a trip to space at a price lower than a bus ticket.
The technological obstacles facing the construction of a space elevator are enormous, the biggest of which is finding a suitable material for the rope. The ideal material should be strong and light. Strong so that it doesn't stretch or tear due to the twist, and light so that it doesn't put too much weight on the rope above.
Steel is not strong enough, not even close. A steel section must carry, in addition to everything below it, its own weight, so the cable must be thicker and thicker as you go higher. Steel is so heavy in relation to its strength that near the earth the cable would have to double its thickness every few kilometers. Long before it reaches the geostationary point, it will be so thick that its use will no longer be practical.
Building a space elevator around the earth using 19th century construction materials simply cannot be done. But 21st century building materials are already starting to show promising signs. Carbon nanotubes, which are long cylinders of carbon whose atoms are arranged in a honeycomb-like hexagonal pattern, are 1,000 times stronger than steel. Carbon nanotubes are excellent candidates for building an extraterrestrial space elevator.
This operation will cost many billions of dollars, will be the largest mega-project that humanity has ever undertaken, without any competitors, will require finding a way to weave the nanotubes into threads that are tens of thousands of kilometers long, and will face additional obstacles. But for a theoretical physicist like me, once you've decided that some structure doesn't in principle violate the known laws of physics, everything else is just an engineering problem. (According to the same principle, the problem of building a nuclear fusion reactor has also been "solved" already, despite the conspicuous absence of such reactors providing energy to humanity, except for one notable exception - the sun).
Black hole elevator
Around a black hole, of course, the problem is much more difficult. The gravitational field is stronger, and the attempt to adapt to the task what operates around the earth is doomed to a ridiculous crash on the ground of reality.
It can be shown that even if we use the impressive strength of carbon nanotubes, a putative space elevator arriving near the event horizon of a black hole would have to be either so thin near the black hole that a single Hawking photon would break it, or so thick far from the black hole that the rope itself will collapse under its own gravity and become a new black hole.
These limitations rule out the possibility of carbon nanotubes. But just as the Iron Age came after the Bronze Age, and just as carbon nanotubes will one day replace steel, so too can we expect material scientists to invent stronger and lighter materials. Indeed it is not impossible. But this process cannot go on forever. There is a limit to this process, a limit to engineering, a limit to the ratio between tensile strength and weight in any given material, a limit set by the laws of nature themselves. This limit is a surprising result of Albert Einstein's famous formula, E=mc2.
The tension in the rope means how much energy you have to invest to make it longer: the tighter the rope, the more energy is required to extend it. A rubber band has elasticity because in order to extend it, an investment of energy is needed to rearrange its molecules: when it is easy to organize the molecules (that is, not much energy is required for this), the elasticity is small; When the energy cost of the organization is high, the tension is high. But instead of putting the energy into rearranging existing rope sections, we can always just make a new rope section and glue it to the end. The energetic cost of extending a rope in this way is equal to the energy contained in the mass of the new rope segment, and is calculated using the formula: E=mc2, that is, the mass (m) of the new rope segment times the speed of light squared (c2).
This is a very energetically expensive way to extend a rope, but it is also a safe way. It provides an upper barrier to the energy cost of extending a rope and in any case also sets a limit to the tension of a rope. The tension can never be higher than the mass per unit length times c2. (You might think that two braided ropes would be twice as strong as a single rope. But they would also be twice as heavy and therefore not improve the strength-to-weight ratio.)
This fundamental limit on the strength of materials leaves a lot of room for technological progress. This limit is hundreds of billions of times stronger than steel, and even when weight is taken into account, it is hundreds of millions of times stronger than carbon nanotubes. And yet, this means that we cannot improve our materials without limit. Just as our efforts to propel ourselves faster and faster must stop at the speed of light, so our efforts to build stronger and stronger materials must stop at E=mc2.
There is one hypothetical material for the rope, which reaches exactly this limit, i.e. as strong as any material can be. This substance has never been observed in the laboratory, and some physicists doubt its existence, but others have dedicated their lives to researching it. And although no one has ever seen the strongest rope in nature, it already has a name: string. The people who study strings, string theorists, hope to discover that they are the basic building blocks of matter. For our purposes, it doesn't matter how basic the strings are, what matters is their strength.
Strings are strong. On a section of rope made of strings, the length and weight of which is like a shoelace, you can hang Mount Everest. The toughest engineering challenges require the use of the toughest materials, so if we want to build a space elevator around a black hole, our best chance would be to use strings. Where carbon nanotubes have failed, elementary strings may succeed. If there is a material that can do this, that material is strings. Conversely, if strings cannot, black holes are not in danger.
It turns out that although strings are strong, they are not strong enough. In fact, they manage to skim right on the edge of sufficient strength. If they were a little stronger, it would be easy to build a space elevator even around a black hole; If they were a little weaker, the project would be hopeless because the string itself would snap under its own weight. Strings are right on the edge because while a rope made of strings dangling towards the surface of a black hole is indeed strong enough to support its own weight, it has no strength left to support the cargo on the elevator. The rope can support itself, but for that we have to give up the box.
This is therefore what protects black holes from poking around. The laws of nature themselves limit our building materials, and this means that while a rope can reach the compressed thermal atmosphere of a black hole, it cannot effectively rob it. Since the strength of a string is precisely finite, we can extract a limited amount of energy from the high, thin atmosphere with a shorter string.
However, this meager and inadequate menu is not much better than waiting: the lifetime of the black hole will remain on the order of m3, the same order of magnitude as the lifetime of independent evaporation. If we hunt down stray photons here and there, we might be able to shorten the black hole's lifespan by some small amount, but we won't be able to get the industrial pumping needed to feed a hungry civilization.
In the case of black holes, the finite speed of light repeatedly hinders our steps. Since we cannot travel faster than light, we cannot escape the event horizon of a black hole. Since we cannot extract more energy from our fuel than mc2, we are doomed to stare at black holes with dark eyes. And since a rope will never be stronger than the speed of light squared times its mass per unit length, we cannot swallow the contents of the hole.
When summer ends on the sun, we will live in eternal winter. We may covet the vast stores of energy in a black hole's thermal atmosphere, but trying to get hold of them could cost us dearly. If we reach too deeply, or too eagerly, then instead of our box robbing the black hole of its radiation, it is the black hole that will rob us of our box. A cold winter awaits us.
About the author
Adam Brown is a theoretical physicist at Stanford University. When he's not thinking about black holes, he's thinking about the big bang and bubbles of nothingness.
in brief
When the sun dies in a few billion years, humanity will have to find a new source of energy to survive. One candidate could be black holes, which are full of energy.
A thought experiment suggests using an idea from the world of science fiction, a space elevator, to "pump" the thermal radiation from a black hole.
A space elevator would use the box attached to the rope dangling down to near the event horizon of the black hole to collect radiation from there. However, it turns out that even the strongest material in the universe, an elementary string, will not provide us with a rope that can withstand the enormous gravitational pull at the event horizon of a black hole.
More on the subject
Fountains of Paradise. Arthur C. Clark, translation: Omer Nebo. Odyssey Publishing, 2006.
Acceleration Radiation and the Generalized Second Law of Thermodynamics. William G. Unruh and Robert M. Wald in Physical Review D, Vol. 25, no. 4, pages 942–958; February 15, 1982.
Learn more about the latest research on space elevators
ScientificAmerican.com/feb2015/brown
The article was published with the permission of Scientific American Israel
More of the topic in Hayadan:
The space elevator is coming down from the episode?
Who will ride the space elevator?
Huge magnetic fields are found near supermassive black holes at the centers of galaxies
How do black holes form?
38 תגובות
are happy They have no worries. I worry about what will happen to the world in the next year or two. Not the sun and its lack will destroy the world. We humans are bringing the end to our great-grandchildren. Either in overheating or in endless wars.
"If our descendants ask to stay alive, they will be forced to make alternative arrangements. First of all, they will fully exploit the Earth's resources, then the solar system, and finally, all the stars in all the galaxies in the visible universe."
I stopped reading when I saw this
Who said that the only way is to "physically" transfer the energy.
Can't you chain there a device that will use the energy, turn it into radiation and then radiate it out?
Find how many contradictions there are in this article
Maybe in physics you understand something, but in astrophysics you understand nothing.
"This is good news for those who aspire to extract energy from black holes in the future: energy can escape"
How will you bring the energy to the earth?
"I have bad news: this program will not work. The reasons for this lie in the physics of exotic entities such as quantum strings and the famous device favored by science fiction writers: the space elevator."
I have bad news: humanity will be extinct long before the sun dies
I have more bad news: man will find a substitute for energy long before the sun dies out
"They will exhaust the Earth's resources, then the solar system, and finally, all the stars in all the galaxies in the visible universe."
"All the stars in all the galaxies in the visible universe."
Yeah sure
we will get there
We'll see you get to Uranus first
Even if we had a rope it wouldn't work: because the rope has to be tied to something on the other side. And if it is tied to the Earth and the gravitational force of the black hole captures the box then the attempt to rewind the rope will pull the Earth towards the black hole and not the other way around.
Yehuda,
First of all, there is nothing fictional here. This is science. Although this is theoretical physics, but as someone who has read the articles and also discussed the subject with the author, I can assure you that this is physics in the purest sense of the word.
I can't understand why your argument "energy can be produced in simpler ways, anyway we can't produce more energy than the mass of the black hole" is not valid for nuclear reactors as well. Why didn't we have to tell the people who studied nuclear reactors in the middle of the last century "leave it, it's easier to burn coal and you won't be able to produce more energy than the mass of the nuclear contains anyway"? You need to do research to know how you can produce energy, how cheaper, how simpler, how you can achieve higher efficiency, how you can do it in the cleanest and safest way. I fail to understand how you know the answers before you have done the research.
The practicality is indeed problematic today simply because we don't have black holes nearby. In addition, the article claims that even if there were, there is no process that can extract energy at a reasonable rate (and I'm not convinced we agree on that). But what is impractical today is tomorrow's everyday technology. In the 18th century, electricity was the most impractical thing there is, yet it was studied...
Finally, if you read you will see that all the processes in question take place outside the black hole. We know *exactly* what's going on there. We have very accurate theoretical models. We have many observations. There are no surprises. The big question marks are regarding the horizon itself and the interior of the black hole.
Yehuda, did you read the first paragraph of the article?
"With all sources of combustion eliminated, they will undoubtedly set their sights on the only source of energy that will remain: black holes. "
I don't understand what is the great advantage of going on a crazy journey and maybe in fiction beyond the range known in science when we absolutely do not know what will happen next to a black hole and what "surprises" will be irradiated to us on the way to the blessed energy.
What is simpler than creating energy from matter in the known way from ordinary matter, in the end even from a black hole we will not receive more energy than the matter contained in it. It would be wiser to investigate fusion options or simple reactors that would be powered by simpler and cheaper materials than uranium or plutonium.
This whole article may just be a thought exercise but it doesn't seem practical to me.
Successfully.
Albentezo
Weird, I just saw the comment you were talking about.
It's upsetting to find out that I wasted quality time on the train on an illiterate troll
Strong
Comment before he said he didn't read the article, you have nothing to worry about.
It's possible...
Here is the definition of science fiction from Wikipedia:
"Science fiction is a literary genre that deals with the description of fictional future plots through the development of existing ideas and trends in the fields of science, technology... a realistic hypothesis about possible future events, based solidly on knowledge and recognition of the real world, past and present, and with an understanding of nature and the importance of the scientific method...
Many tend to confuse science fiction and fantasy or treat the two types as one, but the two are different from each other... science fiction is based on scientific laws... while fantasy takes place entirely in an imaginary world"
It's possible...
"By its very definition, science fiction ignores the laws of physics..."
Absolutely not, science fiction is (among other things) also what is currently technologically impossible, it doesn't have to be something that ignores the laws of physics or conflicts with them. For example, the things described in the book 20 thousand miles under water by Jules Verne were considered science fiction at the time, but after less than 100 years the things became reality.
It's possible..
Answer one.
Where did you see a disregard for the laws of physics in the article?
The article asks a question and tries to answer it by relying on the known laws of physics.
What is fiction here?
Strong
by definition,
Fiction ignores the laws of physics...
Response to Eitan - this is exactly the point. How can all the variables be weighted to reach a certain result? . In the Mossad books, Asimov developed what is called psychohistory by understanding all the electrical currents in the brain and he presented them as mathematics. - So we have a point body and we can so to speak "control" all the variables. But how do you do such a thing a black guy? Or even in the calculation of the effect of the movement of a pigeon's wingspan on the climate in South Africa. Is it even possible to define them as functions? . I guess not. Is it possible ? for sure . The very ability to think about it, in my opinion, is already 50 percent of the way. - I lost the point of the link of what I wanted to convey, never mind. I exhausted the discussion.
Albertoso
beginning
The very length of the article raises suspicions about its purpose...
I assume that this is a "standard" size black guy.
That is, one that draws into it any material close to it...
So how can you get close to him in order to draw energy from him without drawing into him?
By the way, I didn't even think to bother and read the article...
It is possible,
After you have demonstrated unprecedented knowledge in the study of gravitation, perhaps you can tell us what exactly is science fiction presented in the article? I'm sure you read the articles, internalized and understood everything the writer showed in them, and you can tell us why this is not real science but just fiction, right?
What is fictional about what you read?
You have a serious failure in reading comprehension
Strong
Science fiction is fiction…
When you mix it with real science,
Real science is also becoming fiction...
It's possible..
What is the problem with science fiction?
What's the problem with taking a scenario, which is currently science fiction and analyzing it scientifically?
This is basically the definition of classic science fiction: a story based on scientific or future speculation.
And finally a small question: is it possible that science fiction according to your definition is anything you don't understand?
Continued comment to possibly: because it is possible that this is the last one, so even Clifford Simak in the city book - tried to speed up insights - the city of ants for example. Now that sounds like science fiction. But who says it's not possible?
A possible response: without science fiction, things would not have started to take shape. - Jules Verne spoke at the time about a super cannon that would throw us into space, Goddard or someone with a c in the name that I don't remember his name but there is some building on it somewhere in NASA - he suggested The use of rockets to reach space, before that he was laughed at. Heinlein predicted this in one of his books even before the man received the respect he deserved. Even Clark predicted the use of satellite communications - science fiction is the mistress you can't get rid of.
I'm sorry that this
has become this respected site is becoming
of science fiction…
interesting
Another way (in my view simpler) is to utilize the vacuum energy that exists according to the uncertainty principle (the uncertainty principle is also the basis for Hawking radiation). The statement that it is simpler of course does not mean that it is simple.
Discovering a way to harness void energy would be an amazing breakthrough if it did happen.
When trying to isolate a quark despite the strong force, the quark creates another quark from the void.
Perhaps its operation can be imitated in a similar way to collect energy, but this is of course provided that the investment in energy
Bringing such a situation will not be higher than the value.
I'll explain to you Noam - it's easier to extract energy from a black hole by extraterrestrials like in Asimov's book "The Gods themselves". ] . Here and there there is the presence of bacteria whose memory is a blessing from space. But the aliens haven't arrived yet... a few months ago they posted an article about a space elevator that will be fixed by an asteroid and a space station will be built on top of it. But we haven't even gotten there yet... so an elevator inside a black hole? I guess they meant a metaphor. In the article there is a link to Clark's book "The Fountains of Paradise" - I strongly recommend reading it. In general, all his books are great.
Can someone explain to me why energy can only be extracted from the black hole by a space elevator?
After all, particles can arrive at a high speed from afar and pass outside the event horizon and return to space (like any asteroid in an elliptical orbit) and then heat up from the same energy and thus "steal" Hawking radiation at a higher rate than usual.
Or they will move to a younger parallel universe each time. It is more likely that humanity will not last more than a few million years.
It's amazing that until 100 years ago (or a little less [?]) we lived in a static universe and there was no big bang... and today we have above these lines the above mentioned article and assumptions that most likely in a not too long time will seem a bit irrelevant (not to mention a billion years ).
Anyway, I enjoyed reading what was written.
but
Sometimes when I read articles of this kind I remember those films / books / radio programs that were made long before I came here and I always have the feeling that when they did it - they knew they were doing something ancient, even before photography became elephants (there was such a thing) developed.
For those who are curious to know what I'm talking about - watch, for example, The Beatles...
Our rate of progress has undoubtedly exceeded the fast track and against it our ability to predict (meaning: the faster we progress - the less well we predict) and this is pretty bad news (in my opinion)
I personally deal with programming and here too you need the ability to predict. And when my prediction fails - I find myself deciphering things that I did - and it takes many hours (and sometimes days) - a kind of mental work where each layer (code in this case) depends on the one before it and the more layers are piled up - the more difficult the work of decoding becomes.
In life (in my opinion) the matter is doubly complicated - I have a feeling that if for some reason we have to restart the technology that exists today (let's say as a result of a magnetic storm [or an angry virus]) the knowledge to start the systems simply does not exist.
And to the point of the delightful article: it was fun to read - like reading a science fiction book (or a cartoon when I was 5 years old) but nothing more than that.
No way - I have to go back to work...
Miracles so it is not written there relative to the mass in the third, but it is written that it is the mass in the third. But after us, Albanzo explained the issue that this is about taking constants as a unit in what we will call natural units. An interesting idea and this is probably the explanation. From all my educated teachers (:)) Thank you.
to call units other than mass, energy, etc. In theoretical physics - for reasons of convenience - it is customary to take c=1, that is to determine the speed of light. As a result, speed becomes a unitless quantity and therefore time and distance have the same units. Obviously, this is not really true for measurements we will make in the laboratory, but it is very convenient for theoretical calculations. If we wanted to apply a theoretical calculation in the lab, we would have to return the correct units by multiplying by the correct power of c (obviously the reason we allow ourselves to do this is because there is only one way to return units correctly).
Similarly, it is customary to take Planck's constant as 1. When the speed of light and Planck's constant are 1 (called "natural units") then it is directly accepted that all sizes in nature have units that are some power of mass. For example, length is mass to the minus one power. Energy is mass to the 1st power. Angular momentum is mass to the 0th power, etc. Therefore, energy and mass can be measured in the same units, etc. Of course, if you want to translate to the laboratory - you have to return the constants c and Planck in the correct powers.
In the physics of gravitation, it is customary to use "geometric units", in which, in addition to the above-mentioned constants, Boltzmann's constant and Newton's G are also 1. In these units, no quantity in nature has units - everything comes out without units. In these units it is also accepted that the life time of a black hole goes as its mass in the third. As usual, in order to translate the time into a result that can be tested in the laboratory (ie, seconds) you need to return all the constants in the correct units.
"A day will come and the sun will die. The fuel fueling its nuclear fusion reactions will burn out, the skies will cool, and if the Earth survives at all, humanity will be thrown into eternal winter. If our descendants wish to remain alive, they will be forced to make alternative arrangements. First of all, they will fully exploit the Earth's resources, then the solar system, and finally, all the stars in all the galaxies in the visible universe."
This part seems a bit... when the sun dies we won't be here because before then it will be a red giant. exploit the resources of the earth, the solar system. All the stars and all the galaxies. how? It's easier to move. And how will we reach all the galaxies in the visible universe?
Yehuda
Your first correction makes sense to me. I don't understand the second amendment. All that is said is that life expectancy is relative to mass in one third. No one claimed equivalence.
I see two jarring inaccuracies in the article:
In the article it is written: "Particles escape from the infinite gravitational field of the event horizon." End quote.
The event horizon of a black hole does not have infinite gravity but the escape velocity from the horizon is the speed of light.
It is also written in the article: "In general, the lifespan of a black hole is its mass to the third power". End quote.
Well, mass can be measured in units of energy but not in units of time.
sorry if i'm wrong (:))