Unlike a mathematical fundamental constant such as pi, the fine structure constant can only be determined by experiment.
The statement in your link (https://physics.nist.gov/cuu/Constants/alpha.html) that the famous number 1/137 is not unique or especially fundamental comes as a surprise!
Quote: "At an energy corresponding to the mass of the W boson (approximately 81 GeV), α [alpha] is approximately 1/128 compared with its zero-energy value of approximately 1/137."
I'll just stick with what your mentor John Baez has said:
"[The fine structure constant] is about 1/137.03599. Nobody knows why it equals this. At present, it's a completely mysterious raw fact about the universe!"
You could make the same argument about any physical constant. We know that if these constants had any other value, the universe would be very different. It is what it is.
I'm not sure what the analogy is there. 🤔
Steve and I were each comparing the size of something to the size of something else.
The numerical values of constants which involve units of mass, length and time etc. depend on the units we use. The numbers would change if we used different units.
However, certain constants, like the fine structure constant, do not depend on the units we use. These are called "dimensionless" constants and they tell us facts about nature that are completely independent of our choices of units.
The reason black holes are so small is because there is so much space between electrons and the nucleus before being crunched by gravity to grapefruit size. If a sports analogy is preferred substitute soccer ball for grapefruit. I met John Baez’ father by accident one time, he was visiting a friend of mine who had suffered a spinal injury.
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That now makes it clear that your analogy referred to the size of the nucleus compared to size of an electron orbit. 😎
I was talking more from the angle of if the constants were fundamentally different - not so much from the units of measurement. You often hear that the universe is so ‘highly tuned‘ it must imply that it is the creation of a supreme being, or ‘OMG, we are 1 centillionth away from anhilation.
To which I say ‘so what? We are where we find ourselve, as does the rest of the universe’
Me either. You could certainly (theoretically, an hopefully far away from our solar system) have a black hole that's actually the size of a grapefruit, or soccer ball. The Earth's mass compressed to a black hole would have a diameter around 1cm, the size of a grape (for fruit) or marble (for games).
There are formulas and tables for these things surely many places on the Web. I recall avidly reading Jerry Pournelle's writings around 40 years ago (he wrote and edited a quarterly or so MMPB-format magazine "A Step Farther Out"), he had attended a conference given by Stephen Hawking circa 1980 where he announced Hawking radiation. Pournelle described a bunch about black holes, and included formulas for things like the lifetime of a black hole, how long it would last before it radiated all its mass away due to Hawking radiation. Really large ones (solar mass and more) last practically the lifetime of the Universe, whereas I recall that really small ones (the mass of a mountain) are microscopic and last only microseconds.
I too used to read Jerry Pournelle in the 1980s. His column in the high level BYTE computer magazine "Computing at Chaos Manor".
His old MS DOS computer always had problems, which he was usually able to solve! He might start by saying something like "Roberta's computer locked up recently. Now you don't OFTEN need a disk editor, but when you do, you need one BADLY"! 🤣
I was a bit of a Apple/DOS computer hacker in those days too... Norton Utilities was my favourite software.
He co-wrote some hard science fiction with Larry Niven. Niven won a Hugo for a short story about a Black Hole the mass of a mountain called "The Hole Man" IIRC.
Idea was "The Aliens" had contained a hot Black Hole as an energy source...
Still a website for him, but sadly his wife Roberta has passed too: https://www.jerrypournelle.com/
I think Stephen Hawking let loose his theory about Black Holes having a temperature in 1974. Certainly Niven's story was 1975. But I really don't know.
There is a calculator for this here, which one hopes is reliable:
https://www.omnicalculator.com/physics/black-hole-temperature
That is the sort of practical temperature you find in Nuclear Reactors without melting the metal pipes.
I would guess it corresponds to a Black Hole made from a 300 mile diameter asteroid like Vesta, if such a thing were possible.
I believe an Earth size Schwarzchild Black Hole would have a radius of 9mm. And not vary hot at all.
The formula for the radius of a Black Hole is around 3km X Number of Solar masses. Thus if you double the mass, the radius doubles too.
Which means Black Holes get rapidly less dense as they get bigger since the volume is related to the cube of the radius.
I think I read somewhere that a supermassive Black Hole the size of the orbit of Neptune would have a density around that of our atmosphere, which is surprising.
A grapefruit size Black Hole would be about 5 Earth masses.
To address the "Anthropic Principle", the phrase was invented by Fred Hoyle who (brilliantly) theorised the Triple Alpha process in star fusion:
https://en.wikipedia.org/wiki/Triple-alpha_process
It is remarkably finely tuned to convert Helium 4 into Beryllium 8 into our needed Carbon 12 and Oxygen 16 elements in fusion in stars, without which we would not exist.
Against the Anthropic Principle, some scientists reckon about 30% of possible Universes might sustain life of some sort even if some physical constants were different.
Because life adapts to the Universe we find ourselves in by their notion. Might be Methane or Ammonia based! It is interesting that basic Amino Acids are formed quite naturally in interstellar space.
I wonder if they will find them in that recent asteroid Bennu sample that NASA grabbed?
His old MS DOS computer always had problems, which he was usually able to solve! He might start by saying something like "Roberta's computer locked up recently. Now you don't OFTEN need a disk editor, but when you do, you need one BADLY"! 🤣
I was a bit of a Apple/DOS computer hacker in those days too... Norton Utilities was my favourite software.
He co-wrote some hard science fiction with Larry Niven. Niven won a Hugo for a short story about a Black Hole the mass of a mountain called "The Hole Man" IIRC.
Idea was "The Aliens" had contained a hot Black Hole as an energy source...
Still a website for him, but sadly his wife Roberta has passed too: https://www.jerrypournelle.com/
I think Stephen Hawking let loose his theory about Black Holes having a temperature in 1974. Certainly Niven's story was 1975. But I really don't know.
There is a calculator for this here, which one hopes is reliable:
https://www.omnicalculator.com/physics/black-hole-temperature
That is the sort of practical temperature you find in Nuclear Reactors without melting the metal pipes.
I would guess it corresponds to a Black Hole made from a 300 mile diameter asteroid like Vesta, if such a thing were possible.
I believe an Earth size Schwarzchild Black Hole would have a radius of 9mm. And not vary hot at all.
The formula for the radius of a Black Hole is around 3km X Number of Solar masses. Thus if you double the mass, the radius doubles too.
Which means Black Holes get rapidly less dense as they get bigger since the volume is related to the cube of the radius.
I think I read somewhere that a supermassive Black Hole the size of the orbit of Neptune would have a density around that of our atmosphere, which is surprising.
A grapefruit size Black Hole would be about 5 Earth masses.
To address the "Anthropic Principle", the phrase was invented by Fred Hoyle who (brilliantly) theorised the Triple Alpha process in star fusion:
https://en.wikipedia.org/wiki/Triple-alpha_process
It is remarkably finely tuned to convert Helium 4 into Beryllium 8 into our needed Carbon 12 and Oxygen 16 elements in fusion in stars, without which we would not exist.
Against the Anthropic Principle, some scientists reckon about 30% of possible Universes might sustain life of some sort even if some physical constants were different.
Because life adapts to the Universe we find ourselves in by their notion. Might be Methane or Ammonia based! It is interesting that basic Amino Acids are formed quite naturally in interstellar space.
I wonder if they will find them in that recent asteroid Bennu sample that NASA grabbed?
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system7 wrote, “I think I read somewhere that a supermassive Black Hole the size of the orbit of Neptune would have a density around that of our atmosphere, which is surprising.”
I’m flabbergasted.
I’m flabbergasted.
You read it in my post on page 42!
"A billion solar mass black hole would have an event horizon 3 billion km in radius, roughly the distance of Neptune to the Sun.
The resulting density would be roughly 1/1000 of a gram per cc - and that’s the density of air!"
The short story involves a micro black hole which tunnels through a scientist's entire body, fatally injuring him with tidal forces as it falls towards the centre of the planet Mars.
https://en.wikipedia.org/wiki/Micro_black_hole
Jerry Pournelle himself wrote a short story called "He Fell Into a Dark Hole", the plot of which involves the mystery of why spaceships keep disappearing!
Available to buy now as Kindle, Paperback and Audiobook versions.
The rotating Kerr solution is the most realistic black hole scenario, and involves a ring singularity.
This is a 2D ring with zero thickness but non-zero radius, and is often referred to as a ringularity.
A Schwarzschild non-rotating black hole which involves a point singularity (r=0) probably doesn’t exist.
As to the diameter of a ring singularity, perhaps the answer is in here! https://physics.stackexchange.com/questions/471419/metric-diameter-of-a-ring-singularity#:~:text=The ring singularity has coordinates r = 0,,/ 2 cos θ d θ = a
The weak force is involved in the fusion of hydrogen into helium.
If the weak force were weaker, the Sun would never have lit up, and life on Earth would never have existed!
There are three sorts of decay associated with unstable heavy atoms,
Strong Force for Alpha (Helium 4 nucleus) decay.
Weak Force for Beta (Electron) decay.
Electromagnetic Force for Gamma radiation decay.
In al cases an energetically favourable pathway is required to the end products.
In Beta decay, the down quark in a neutron changes to an up quark which results in a proton and a higher atomic number.
The W- boson is the intermediate (virtual?) particle here, and it decays into an emitted electron and an antineutrino to preserve fermion number.
I recall I measured the gamma ray spectrum from Caesium 137 in the 2nd. year Physics lab. The sample was kept in a little locked metal box on the bench, and you handled it with tongs.
The Caesium often decays to an excited state of stable Barium 137, which quickly fires off a gamma. It has a peak energy around 700 keV apparently. Which is more than the rest mass energy of an electron.
Anyway, my take on this is if the cross-section of the weak force was stronger, half-lives by Beta decay would be shorter, and the W and Z Bosons would be lighter than 80-90 GeV / c^2 mass.
Strong Force for Alpha (Helium 4 nucleus) decay.
Weak Force for Beta (Electron) decay.
Electromagnetic Force for Gamma radiation decay.
In al cases an energetically favourable pathway is required to the end products.
In Beta decay, the down quark in a neutron changes to an up quark which results in a proton and a higher atomic number.
The W- boson is the intermediate (virtual?) particle here, and it decays into an emitted electron and an antineutrino to preserve fermion number.
I recall I measured the gamma ray spectrum from Caesium 137 in the 2nd. year Physics lab. The sample was kept in a little locked metal box on the bench, and you handled it with tongs.
The Caesium often decays to an excited state of stable Barium 137, which quickly fires off a gamma. It has a peak energy around 700 keV apparently. Which is more than the rest mass energy of an electron.
Anyway, my take on this is if the cross-section of the weak force was stronger, half-lives by Beta decay would be shorter, and the W and Z Bosons would be lighter than 80-90 GeV / c^2 mass.
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Of the four fundamental forces, the weak nuclear force is the least understood.
It's only about five years ago that physicists managed to measure the weak force between electrons and protons.
The weak force represents just a fraction of the force between a negatively charged electron and a positively charged proton, by that didn't put the smart guys off trying to measure it.
Apparently, parity symmetry (i.e. when swapping all positives and negatives in the Universe makes everything look pretty much the same) is violated only in the weak force, so provides a tool with which to measure it.
https://www.nature.com/articles/s41586-018-0096-0
What the physicists actually measured was the proton's weak charge. The value obtained was 0.0719 ± 0.0045, a dimensionless number which is in almost perfect agreement with the Standard Model prediction.
https://www.sciencenews.org/article/protons-weak-charge-just-feeble-physicists-thought
It's only about five years ago that physicists managed to measure the weak force between electrons and protons.
The weak force represents just a fraction of the force between a negatively charged electron and a positively charged proton, by that didn't put the smart guys off trying to measure it.
Apparently, parity symmetry (i.e. when swapping all positives and negatives in the Universe makes everything look pretty much the same) is violated only in the weak force, so provides a tool with which to measure it.
https://www.nature.com/articles/s41586-018-0096-0
What the physicists actually measured was the proton's weak charge. The value obtained was 0.0719 ± 0.0045, a dimensionless number which is in almost perfect agreement with the Standard Model prediction.
https://www.sciencenews.org/article/protons-weak-charge-just-feeble-physicists-thought
Attachments
The Weak Force is a very mysterious thing indeed. It acts with a biased handedness with matter and antimatter. CP violation in short.
Which may be why matter dominates our Universe.
This amusing Neutrino enthusiast is interested if Neutrinos and Antineutrinos oscillate differently between the three fllaours of Electron, Mu or Tao types:
https://www.sciencenews.org/article/neutrino-particle-universe-matter-antimatter-mystery
Only about 6 minutes, but decent science speculation IMO.
But I have been investigating the topical small mountain size Black Hole for our edification:
10^11 kg by all accounts, lasts about as long as our current Universe:
https://www.omnicalculator.com/phys...ow-to-use-the-schwarzschild-radius-calculator
Bit buggy that calculator, but have gleaned some things from it.
https://jila.colorado.edu/~ajsh/bh/hawk.html
With some extremely back of a beermat calculations, I make that about 10^ -15 m in size. A mere femtometer. About the radius of a Proton. I have also learned that the lifetime of a Black Hole (in an effectively cold Universe) is as the cube of the mass, like its reducing density. 😎
Which may be why matter dominates our Universe.
This amusing Neutrino enthusiast is interested if Neutrinos and Antineutrinos oscillate differently between the three fllaours of Electron, Mu or Tao types:
https://www.sciencenews.org/article/neutrino-particle-universe-matter-antimatter-mystery
Only about 6 minutes, but decent science speculation IMO.
But I have been investigating the topical small mountain size Black Hole for our edification:
10^11 kg by all accounts, lasts about as long as our current Universe:
https://www.omnicalculator.com/phys...ow-to-use-the-schwarzschild-radius-calculator
Bit buggy that calculator, but have gleaned some things from it.
Evaporation of a mini black hole
Black holes get the energy to radiate Hawking radiation from their rest mass energy. So if a black hole is not accreting mass from outside, it will lose mass by Hawking radiation, and will eventually evaporate. For astronomical black holes, the evaporation time is prodigiously long — about 10^61 times the age of the Universe for a 30 solar mass black hole. However, the evaporation time is shorter for smaller black holes (evaporation time t is proportional to M3), and black holes with masses less than about 10^11kg (the mass of a small mountain) can evaporate in less than the age of the Universe. The Hawking temperature of such mini black holes is high: a 10^11 kg black hole has a temperature of about 10^12 Kelvin, equivalent to the rest mass energy of a proton (Ed: Huh, what is that to do with temperature? system7). The gravitational pull of such a mini black hole would be about 1 gee at a distance of 1 metre.
It is not well established what an evaporating mini black hole would actually look like in realistic detail. The Hawking radiation itself would consist of fiercely energetic particles, antiparticles, and gamma rays. Such radiation is invisible to the human eye, so optically the evaporating black hole might look like a dud. However, it is also possible that the Hawking radiation, rather than emerging directly, might power a hadronic fireball that would degrade the radiation into particles and gamma rays of less extreme energy, possibly making the evaporating black hole visible to the eye. Whatever the case, you would not want to go near an evaporating mini black hole, which would be a source of lethal gamma rays and energetic particles, even if it didn’t look like much visually.
The animation at left is a fanciful depiction of the final moments of the evaporation of a hypothetical mini black hole. In the final second of its existence, the mini black hole radiates about 10 tonnes of rest mass energy. Such an explosion is large by human standards, but modest by astronomical standards. An evaporating black hole would be detectable from Earth only if it went off within the solar system, or at best no further away than the nearest star.
What’s the cross shape? Telescopic diffraction spikes, added for artistic effect. Compare these beautiful Hubble Space Telescope pictures of the Orion nebula or of stars in the Messier 4 globular star cluster.
https://jila.colorado.edu/~ajsh/bh/hawk.html
With some extremely back of a beermat calculations, I make that about 10^ -15 m in size. A mere femtometer. About the radius of a Proton. I have also learned that the lifetime of a Black Hole (in an effectively cold Universe) is as the cube of the mass, like its reducing density. 😎
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