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annaandherdad
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Quote: Originally posted by Zombie  |
I've asked a bunch of times. How do you model of an atom compacted infinitely?
Start simple... The energy of that atom at normal atmospheric pressure. Double it, double it, double it.
Does the energy go up? down? stay the same?
Common sense tells me the energy in that atom goes up. Force creates force right? |
This concerns the equation of state of matter at high pressures. Let's take the following question: What happens if you take a sample of ordinary
matter at ordinary temperature and pressure and compress it until the volume occupied by each atom becomes much less than originally? How do the
pressure, temperature and internal energy depend on the volume (which is getting smaller)?
Here is a rough way of thinking about this question that involves only simple considerations. Let each atom have a share of the volume of the system
given by V=L^3, so that L is the edge length of a cube whose volume is the average volume per atom. Initially, L is the Bohr radius times a number of
order of magnitude unity, that is L is roughly 10^{-8} cm, but L decreases as the sample is compressed.
The main physical process determining the pressure as L decreases is the confinement of the electrons to smaller and smaller volumes, which by the
uncertainty principle pushes their momentum to higher and higher values. If we model the electrons as particles in a box, then their momentum is of
the order of hbar/L, which goes up as L goes down. Being slightly more quantitative about this, the particle in a box model gives the pressure as a
function of the density as
P = (hbar^2/15 m*pi^2) x (3*pi^2*n)^{5/3},
where m is the electron mass and n is the number of electrons per unit volume. This is a standard result in statistical mechanics, and it applies at
zero temperature. The pressure goes as the 5/3 power of the density. The same applies to the internal energy, which goes up because of the work done
in compressing the sample.
This however ignores the electrostatic replusion of the electrons from one another, and the attraction of the nuclei for the electrons. For
example, if we use the formula above to compute the pressure of the valence electrons in a metal such as copper (at ordinary pressure), we find that
the pressure of the electron gas is enormously much larger than atmospheric pressure. The reason the copper doesn't explode from this pressure is the
net attraction caused by the electrostatic forces (including the positive nuclei), which reduces the pressure to nearly zero.
The formula above is the equation of state of a noninteracting electron gas at zero temperature, but it is valid as long as the actual temperature is
much less than the Fermi temperature. For normal copper metal, the Fermi temperature is much larger than 300K, so the temperature as far as the
electron gas is concerned is effectively zero. The actual temperature remains much below the Fermi temperature as the sample is compressed, so the
zero temperature formula continues to hold.
If we compress the sample until L is much less than its original value, L << the Bohr radius, then one thing that happens is that the effect of
the electrostatic forces between the electrons and nuclei becomes less and less important, so the formula above becomes a more and more accurate
description of how the pressure depends on the volume. That is, the pressure becomes dominated by the effects of the uncertainty principle, and the
effects of the electrostatic forces becomes negligible.
This continues until the momentum of the electrons at the top of the Fermi sea reaches relativistic values, p ~ mc. This happens roughly when L is
about alpha times the Bohr radius, where alpha is the fine structure constant, about 1/137. The volume is then alpha^3 times smaller than originally,
and the density 137^3 larger, that is, over a million times larger. Such densities are realized in white dwarf stars.
Above this transition to relativisitic electron velocities, the pressure shifts over to a 4/3 power of the density instead of 5/3.
At a certain point, as alluded to by blogfast, the energy of the electrons at the top of the Fermi sea becomes large enough to induce inverse beta
decay in the protons in the nucleus. This is the reaction,
e + p -> n + nu
where nu is an electron neutrino. It is very hard to confine neutrinos so they will escape. The effect is that the nuclei become more and more
neutron rich, and electrons are removed. This reduces the pressure and the material suddenly becomes much more compressible. At a certain point
there are so many neutrons that they cannot be bound by nuclear forces, and they start to drip off the nuclei, forming a gas of free neutrons. These
cannot beta decay (the normal fate of a free neutron) because the outgoing electron would have to occupy some state, and those are already filled up
to the top of the Fermi sea (and the energy of the outgoing electron in beta decay would be below the top of the Fermi sea at this level of
compression).
This is very roughly what lies behind the collapse of a white dwarf star to a neutron star (a type of supernova), but the model here is very
simplified. If further collapse stops at the neutron star stage, it is because the neutrons form a Fermi gas, whose pressure (for nonrelativistic
velocities) is the same formula above, except with the neutron mass instead of the electron mass.
There is an interesting discussion of this process in the the book Gravitation by Misner, Thorne and Wheeler, although they don't worry about the
electrostatic effects at low pressure.
[Edited on 3-7-2015 by annaandherdad]
Any other SF Bay chemists?
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Zombie
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I recognize much of the discussion of this thread in your post. I also see much of what I speculated without any quantification on my part.
I'm happy to see Blogfasts statement that matter will at some point change included in your explanation.
This whole conversation started with me making a statement of a mathematical model, and 20.00 bucks.
You have no reason to trust me but PM me me an account I can send 20 bucks to, and its done. Even a PO box. I don't care...
Now. It's Friday, july 3rd. If you can imagine what a hootch drinkin' hillbilly would be doing on said date... I'm going to have to re-read this
post, and see what I understand, and how I can use the model you so generously supplied.
For the moment I will say thank you, and Happy 4th.
Later I will realize time travel, and sell you all rides to anytime you want to go. (Round trip not guaranteed)(alpha testing)
They tried to have me "put to sleep" so I came back to return the favor.
Zom.
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aga
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Very nice post annaandherdad
It should be said that notions such as Fermi liquids (see also Dirac and Landau) are postulations of what may be happening, not actual proven fact.
One of the biggest problems with mathematical extrapolation of known physics into very extreme conditions is that we have already experienced the
failure of linear extrapolation.
In very extreme conditions, all sorts of things can happen, even in reverse to what has been calculated or assumed.
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annaandherdad
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Zombie, aga, thanks for your responses. No need to send money, I'm just glad I could help. I delayed a couple of weeks in posting, because I had to
convince myself that I understood why the electrostatic forces become negligible as L /a ->0, where "a" is the Bohr radius.
Any other SF Bay chemists?
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aga
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'understanding' is always a good thing, but please be aware that what you seek to understand can only be 'understood' inside the confines of what is
known, and the reality may well be significantly different.
A Theory is not a fact.
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Zombie
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| Quote: Originally posted by aga |
In very extreme conditions, all sorts of things can happen, even in reverse to what has been calculated or assumed.
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This is exactly what I believe happened at the 3C303 event. Taking what is accepted as a model of a black hole, the event at 303 could not have
happened... but it did.
I believe this is information that should recreate the model(s).
I have no idea why but to me this is perhaps the most fascinating thing I have ever thought about. It seems that the answer to "free" energy is in
this somewhere. There has to be one atom of something that begins the entire process.
They tried to have me "put to sleep" so I came back to return the favor.
Zom.
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IrC
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| Quote: Originally posted by annaandherdad | | If further collapse stops at the neutron star stage, it is because the neutrons form a Fermi gas, whose pressure (for nonrelativistic velocities) is
the same formula above, except with the neutron mass instead of the electron mass. |
If the density were greater I imagine the neutron star could become a Quark matter star but from what it seems to me zombie is trying to describe he
is talking about exceeding the Tolman–Oppenheimer–Volkoff limit and I cannot fathom any other outcome than the formation of a black hole. Before
that density is reached we have the neutron star. From what I can discover on average 1 in 10 become magnetars. I am wondering if this relates to the
temperature during collapse to neutronium, if low enough with density high enough to form quark matter could the occurrence of Color superconductivity
be the reason 1 in 10 become magnetars.
In any case when all the lowest quantum states are filled in my mind higher densities must equate to formation of black holes. Or am I missing
something here?
"Science is the belief in the ignorance of the experts" Richard Feynman
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annaandherdad
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| Quote: Originally posted by IrC | | Quote: Originally posted by annaandherdad | | If further collapse stops at the neutron star stage, it is because the neutrons form a Fermi gas, whose pressure (for nonrelativistic velocities) is
the same formula above, except with the neutron mass instead of the electron mass. |
If the density were greater I imagine the neutron star could become a Quark matter star but from what it seems to me zombie is trying to describe he
is talking about exceeding the Tolman–Oppenheimer–Volkoff limit and I cannot fathom any other outcome than the formation of a black hole. Before
that density is reached we have the neutron star. From what I can discover on average 1 in 10 become magnetars. I am wondering if this relates to the
temperature during collapse to neutronium, if low enough with density high enough to form quark matter could the occurrence of Color superconductivity
be the reason 1 in 10 become magnetars.
In any case when all the lowest quantum states are filled in my mind higher densities must equate to formation of black holes. Or am I missing
something here? |
You're talking about some current ideas in astrophysics (magnetars, quark matter stars etc) and not being an expert in the field all I can say is that
there is much speculation about these hypothetical objects. The simplest theoretical game one can play (ie a gedankenexperiment) is to imagine
compressing a sample of matter at zero temperature, allowing any reactions (nuclear etc) to take place as they will, allowing the resulting heat to
escape so that we remain at zero temperature, and then continue the compression. This game is discussed in the book Gravitation by MTW which I
mentioned. That book is out of date and won't tell you about current speculation about exotic objects, but the basic physics hasn't changed and is
discussed well. This gedankenexperiment is only indirectly related to what happens in actual stars, because they are not at zero temperature nor
even in thermal equilibrium. For example, actual white dwarfs typically have cores of made of carbon, and if one increases the compression by adding
matter accreted from a companion, then instead of compressing the carbon to higher and higher densities what happens at a certain point is the
temperature in the core reaches the stage where the carbon can undergo fusion to heavier elements, a process that runs away and blows the star apart.
The energy for this comes from carbon fusion. This is one type of supernova.
In more massive stars the core fuses stably to heavier elements, reaching finally iron after which there is no more energy to be obtained via fusion.
Then at a certain point the Chandrasekhar limit is reached in the core (when the pressure of degenerate electrons can no longer support the star
against gravitational collapse) and the core collapses to a neutron star or black hole, depending on the mass. This is another type of supernova, and
the energy released is mostly gravitational.
The formula I gave for the pressure as a function of the electron density treats the electrons as an ideal gas of nonrelativistic particles.
Actually if we could carry out our gedankenexperiment the actual pressure would not follow the formula exactly because the electron gas is not ideal.
I mentioned the problem of corrections due to electrostatic forces, and mentioned that these are proportionally less important as the density
increases. Also, the formula needs to be modified when the electrons become relativistic; this is necessary to get the Chandrasekhar limit, which
doesn't exist in the nonrelativistic model. The usual derivations of the Chandrasekhar limit also don't take into account inverse beta decay, which
I mentioned, but certainly there is an upper limit to the velocities of the electrons due to this effect. In any case, inverse beta decay certainly
takes place in the core collapse of a massive star, we know this because the neutrinos have been observed (in the Magellanic cloud supernova in the
1980's).
If you wish to model a neutron star as an ideal gas of neutrons at zero temperature, supporting itself against gravitational collapse due to the
pressure of degenerate neutrons, then you can use the same formula I gave or its relativistic generalization, but with the "m" being the neutron mass
and "n" being the number of neutrons per unit volume. This leads to a new limit on the maximum mass supportable against gravitational collapse, a
version of the TOV mass limit. But the basic idea is the same as in the Chandrasekhar limit. This is only a model, however, because the neutron
matter is not an ideal gas, and the equation of state of compressed neutron matter is poorly known. The nuclear physics of working out something more
realistic is complicated and difficult. So there is some uncertainty about the TOV limit or what physics goes on inside a neutron star, but no one as
far as I know doubts that there is an upper limit to the mass of a neutron star. After that it has to be a black hole, and there seem to be plenty of
those around.
Any other SF Bay chemists?
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aga
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| Quote: Originally posted by annaandherdad | | This is only a model, however, because the neutron matter is not an ideal gas, and the equation of state of compressed neutron matter is poorly known.
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This is the biggest problem when applying Science to the big stuff.
Impossible to do a controlled experiment to test and find out.
Observing stuff is about all we can do, and attempt to draw conclusions from occluded observations.
It's a bit like determining the way the bearings inside an internal combustion engine are constructed by examining the exhaust pipe emissions from 4
light years away.
[Edited on 4-7-2015 by aga]
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Zombie
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I still think it is simpler than that.
We/I am talking about the forces involved with one atom. A seed if you will. There has to be something that initiates the process.
Perhaps this is cyclic, and involves stars / supernovas / white dwarfs or perhaps it is a specific atom that we do not know or understand, or perhaps
it is dimensional... I really think that following the math will provide answers or maybe the correct questions.
Think of examples on an atomic scale that can occur in space. Fission? Fusion? What about light waves... Perhaps a frequency that is so energetic it
can compress an atom.
when you take harmonic frequencies they amplify each other. Perhaps the frequency of a complete galaxy is the power source that begins the process.
There is always a "sweet spot" where the frequency is at it's strongest. Maybe this is where a BH is "born".
Hells bells... Tesla was correct! There is free energy. We just need a better receiver...
They tried to have me "put to sleep" so I came back to return the favor.
Zom.
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IrC
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http://laplace.physics.ubc.ca/000-People-matt/200/gravitatio...
Thanks for mentioning the book, hopefully I can find some time to look at it in the near future.
-----------------------------------------
I moved this post so I can comment after opening the PDF, I was half tempted to just remove the link but it is the only free to view source for this
book I can find. Whoever scanned it did an unimaginably bad job as well as scanning about half of the pages upside down. This forces you to rotate the
page 180 degrees to read it. I will leave the link but be warned reading the text is very annoying. I can think of no better example of the wisdom in
just saying no to drugs to whoever scanned this book.
------------------------------
Zombie, If what you are thinking had a probability far above zero, nearly empty space would be forming black holes all the time. The process occurs
due to the effect an incredibly large number of atoms have on each other. Thus the reason there is a line between a ball of particles which turns into
a black hole and one that does not. I do not see how you are going to get there with individual atoms outside of building a powerful enough
accelerator which thankfully CERN has been unable to do thus far.
A mini black hole getting loose on earth is not a comforting thought. No evidence has thus far been found that any process out in space would focus
enough energy on such a small location for this to occur naturally. At least not since the first seconds of the universe. Think about it. If even a
small probability existed, by now one would think spacetime would be well on the way to being eaten alive. In nearly 14 billion years there would be
many mini black holes wandering around out there.
"Science is the belief in the ignorance of the experts" Richard Feynman
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Zombie
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I obviously don't know about all that...
If you take a "big bang" for example. This could appear to be what happened at 303, potentially.
This is a spontaneous release of energy, and perhaps matter. I imagine it is the opposite of the formation of a BH but maybe not the end of one
either. Just a release of electrostatic energy.
In thinking about resonant or harmonic frequencies, look at what Tesla did in his apartment building with a simple machine. He rocked a 4 story
building with frequency.
I can only guess that the galaxy as a whole has enough energy to compress an atom. The process has to have a beginning, and why not one atom. One
attracts two, two attract 4, and so on.
I kind of like the idea of making your own mini BH's... Of course I do.
Remember when the theory was an atomic detonation would ignite the atmosphere? Imagine the runaway process of a BH.
They tried to have me "put to sleep" so I came back to return the favor.
Zom.
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IrC
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I am not quite sure why you are so taken by 303 or how it has all that much to do with the thread title. Lots of jet spewing black holes exist out
there. Not much special here. Moving charged particles IS a current flow. If 303 is the largest one still not all that applicable to the thread.
Anyone close enough to actually use any of that energy within several hundred generations would be vaporized anyway. Remember being 2 billion light
years away it would take 2 billion years for the power in EM radiation form to get to your toaster oven. Even longer for the particles themselves.
"Science is the belief in the ignorance of the experts" Richard Feynman
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aga
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Zomb likes the idea it seems.
The thoughts in this thread are a bit random, but then the OP Title is too.
Falling 'into' a BH is ambiguous, seeing as it isn't a Hole at all.
Not as if you'd randomly be able to 'fall' or 'into' one.
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Zombie
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I've never really cared much for Quantum sciences. Same thing for theories.
I'm a prove it to me or I have better things to do sort. Just as random as falling into an open sewer that leads you to some other dimension the
process of thinking about what makes BH's 'tick" sort of fell into my lap.
The 303 deal is fascinating because just as everyone is telling me that nothing can escape the "gravitational pull of a BH... one goes, and pukes all
over it's galaxy. Pretty much in sync as I am believing that according to what we understand about physics, the event logically must occur.
The thing that gets me is when I am told that physical laws can not be changed or altered to fit a theory, the same persons will state that another
form of understanding that only a handful of people can understand applies (see John Smith) yet the math involved is tailored to the answer(s) sought.
Besides getting me thinking about something that I have never thought about, this entire process is allowing me t understand things I never
understood.
I have to go insulate my thumper now. I'm experimenting with sound waves as my heat source. It gets pretty warm just yelling at it.
They tried to have me "put to sleep" so I came back to return the favor.
Zom.
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IrC
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I'm not quite sure what your thinking but hopefully you understand the jet coming from 303 is not coming out of the black hole (from inside it).
Rather the disk of matter outside the horizon is being accelerated (some of it) outward in a jet. These highly charged particles moving very fast and
in large quantities in a line constitute the electric current. Anyway there is one simple answer to the thread title.
Help I've fallen and I can't get up.
"Science is the belief in the ignorance of the experts" Richard Feynman
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Fulmen
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| Quote: Originally posted by Zombie | | just as everyone is telling me that nothing can escape the "gravitational pull of a BH... one goes, and pukes all over it's galaxy
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This actually happens "everywhere", google quasars.
We're not banging rocks together here. We know how to put a man back together.
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IrC
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If you remembered the news stories in the 50's and 60's the newly discovered quasar was big. Companies were even naming products after them. I do not
know if before or during that time if black holes were discussed or commonly accepted at least in the astrophysics realm of science. So the name sort
of bothers me because it was sold as some new fundamental thing unknown in origin. It was not thought of as what today we are sure they are so the
idea the impossible energy could be accounted for by a black hole jet pointed at us was unknown as far as I know. They were not some new unique thing
as was portrayed in popular mags. So calling it a Quasar just does not jive for me. It was merely a special form of something already known. Theories
most popular went along the lines of several galaxies all squished into a big ball to account for the energy. I never once read any article that
considered the analogy of staring at a hundred watt light bulb compared with looking into the same power laser beam. Lasers were known by then I am
sure, even before the Ruby laser of fame circa 1963 or around then. I need to look up the history but I think HeNe was known around the time the
Quasar was discovered. A long winded poor explanation I guess but back then Quasar meant a new fundamental unique entity and knowing what it really is
at least to me discounts the use of a 'special' name. Unless it makes sense to say Quasar rather than one of over 200,000 known 'odd black holes which
shoot beams'. Or is this just me.
"Science is the belief in the ignorance of the experts" Richard Feynman
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aga
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You been watching the film 'Dune' again ?
https://www.youtube.com/watch?v=_Twmc6jUrNw
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IrC
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Usul no longer needs the weirding module.
"Science is the belief in the ignorance of the experts" Richard Feynman
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Zombie
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No. I need the weirding thing... I made one from my tinfoil hat, and a gallon of EtOH.
There was another part but I think I swallowed that.
I'm kind of preoccupied with another project, My mind is swimming in this one so I am having a hard time following my own train(s) of thought.
I've told you all that I keep busy to keep partially sane. When projects are at 1/2 way stages I can easily follow but right now I have 4 projects of
my own, and 2 for customers that are almost completed. I'm losing my mind at the moment.
Thinking about BH-s will drive me over the top.
They tried to have me "put to sleep" so I came back to return the favor.
Zom.
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IrC
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Theres your problem, one cannot operate the weirding module on a tinfoil hat, and a gallon of EtOH alone. You need Mata Hari.
"Science is the belief in the ignorance of the experts" Richard Feynman
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Fulmen
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IrC:
From Wikipedia: Quasar or quasi-stellar radio sources ... Their spectra contain very broad emission lines, unlike any known from stars, hence the name
"quasi-stellar."
We're not banging rocks together here. We know how to put a man back together.
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IrC
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| Quote: Originally posted by Fulmen | IrC:
From Wikipedia: Quasar or quasi-stellar radio sources ... Their spectra contain very broad emission lines, unlike any known from stars, hence the name
"quasi-stellar." |
True but my point was based upon the reality of the definition.
quasi- ˈkwāˌzī,ˈkwäzē/ combining form prefix: quasi- seemingly; apparently but not really.
Even the definition proves my point. It was not really a new unique thing. Rather just a newly discovered rare form of an already known thing. The
point is moot to discuss it based upon the knowledge and thought of today with hindsight. I am talking about the news stories of the early 60's taken
in with the knowledge and though (mindset) at that time. If you were there you know. If not it can only be thought about in terms of today. Which was
not the point I was making. I guess one would have to have been there to see my point. Or owned the new Quasar TV with astounding color and ultrasonic
remote control. Equally exciting in 1967.
"Science is the belief in the ignorance of the experts" Richard Feynman
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Fulmen
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Ah, I wasn't around to experience that hype. From what I can gather they were discovered before BHs were commonly accepted as real objects. And it
wasn't until the 70's that accretion disk models were able to explain the observations. So I don't agree that they were already known, in fact it
seems that our understanding of BHs were advanced by the discovery and explanation of these quasars. While BHs were predicted from GR without any
observable evidence I don't think anybody predicted the extreme physics of the accretion disk before the quasars were observed.
We're not banging rocks together here. We know how to put a man back together.
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