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Thread: how does 'particle in a box' relate to compact bodies?

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    how does 'particle in a box' relate to compact bodies?

    if you took a rock and compress it to a speck of dust, would that mean that the atoms would have high momentum?

    in a neutron star does the compression add to the degeneracy pressure?

    I was wondering about a 'pre-Hawkin' type radiation, where under compaction, the collective momentum of the particles leads to evaporation...
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    Quote Originally Posted by Mudskipper View Post
    if you took a rock and compress it to a speck of dust, would that mean that the atoms would have high momentum?

    in a neutron star does the compression add to the degeneracy pressure?

    I was wondering about a 'pre-Hawkin' type radiation, where under compaction, the collective momentum of the particles leads to evaporation...
    Line 1, Would the rock get intensely hot? Yes.

    Line 2. Can't have degenerate matter without the compression, lack of compression forces causes degenerate matter to turn back into normal matter "energetically". So yes.

    Line 3. Word salad, as far as I can tell.
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    Quote Originally Posted by BigDon View Post
    Line 3. Word salad, as far as I can tell.
    I mean does the general momentum get so high that some particles have so much speed that they fly off, ie evaporation..?
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    A rock is already an essentially degenerate object, i.e., the electrons are already degenerate. That's why it's so hard to compress a rock. So the answer is, in order to compress a rock, you need to completely change the forces responsible for the rock, thus completely changing the nature of the degeneracy in the rock. But yes, to do that would mean putting a lot of kinetic energy into the rock (that's better than momentum, given the vector nature of the latter).

    Now, it's true that a lot of people think degeneracy is about very high density (because they are told that in so many places, sadly), but actually degeneracy has nothing at all to do with density. It has to do with being in the quantum mechanical ground state, whatever that is for the system in question. The density of the ground state depends on the forces in the system, and usually the forces are so strong (as in electric forces in solids) that the density of a ground state is rather mundane. But so many people are introduced to the concept of degeneracy in the context of astronomy (white dwarfs or, as in this case, neutron stars) that they think it must happen for super high density. The reason ground states in astronomy have such high densities is that the long-range relevant force is so famously weak-- gravity, not electric forces. There's also the strong force in neutron stars, but it's a short range force, so even though it is strong, it only appears at very high density. Nothing to do with degeneracy by itself, it is all about the forces and the approach to the ground state those forces produce. I've tried in many places to dispell the myths of degeneracy, but trust me, they are so deeply ingrained by now it's almost an impossible task!

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    Quote Originally Posted by Ken G View Post
    A rock is already an essentially degenerate object, i.e., the electrons are already degenerate. That's why it's so hard to compress a rock. So the answer is, in order to compress a rock, you need to completely change the forces responsible for the rock, thus completely changing the nature of the degeneracy in the rock. But yes, to do that would mean putting a lot of kinetic energy into the rock (that's better than momentum, given the vector nature of the latter).

    Now, it's true that a lot of people think degeneracy is about very high density (because they are told that in so many places, sadly), but actually degeneracy has nothing at all to do with density. It has to do with being in the quantum mechanical ground state, whatever that is for the system in question. The density of the ground state depends on the forces in the system, and usually the forces are so strong (as in electric forces in solids) that the density of a ground state is rather mundane. But so many people are introduced to the concept of degeneracy in the context of astronomy (white dwarfs or, as in this case, neutron stars) that they think it must happen for super high density. The reason ground states in astronomy have such high densities is that the long-range relevant force is so famously weak-- gravity, not electric forces. There's also the strong force in neutron stars, but it's a short range force, so even though it is strong, it only appears at very high density. Nothing to do with degeneracy by itself, it is all about the forces and the approach to the ground state those forces produce. I've tried in many places to dispell the myths of degeneracy, but trust me, they are so deeply ingrained by now it's almost an impossible task!
    so, are you saying that the atoms in a rock are like particles in a box?
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    Squish

    The Wiki article on degenerate matter is here:

    https://en.wikipedia.org/wiki/Degene...er#Singularity

    and it's good.

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    Quote Originally Posted by Mudskipper View Post
    so, are you saying that the atoms in a rock are like particles in a box?
    Yes. So are the electrons within those atoms. But then, every bound state is like a particle in a box, that's just quantum mechanics. You see how bad the myths of degeneracy are-- people are told "degeneracy appears when particles act like they are in a box," but all bound particles always act like that in every situation. All degeneracy means is the particle-in-box is near its ground state, but you're never told that. Notice how common it is for various subsystems to reach their ground states, so "degeneracy" is a completely mundane condition that does not in any way require high density. This should be obvious-- if you put a gas of noninteracting particles in a box, and just keep removing heat from the box, the gas will be completely degenerate eventually-- without ever changing its density!
    Last edited by Ken G; 2018-Jan-09 at 02:22 PM.

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    Quote Originally Posted by John Mendenhall View Post
    The Wiki article on degenerate matter is here:

    https://en.wikipedia.org/wiki/Degene...er#Singularity

    and it's good.
    Except that it has nothing to do with degeneracy. Look at the first words in that subsection-- they start by saying degeneracy cannot be relevant, and go from there! It would produce better understanding of degeneracy to start with "In systems that do not have a ground state due to self-gravity..." instead of "At densities greater than those supported by any degeneracy, gravity overwhelms all other forces," which tends to promote the misunderstandings (like that degeneracy is a force in the first place).
    Last edited by Ken G; 2018-Jan-09 at 02:35 PM.

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    Strings and Sealing Wax

    Quote Originally Posted by Ken G View Post
    Except that it has nothing to do with degeneracy. Look at the first words in that subsection-- they start by saying degeneracy cannot be relevant, and go from there! It would produce better understanding of degeneracy to start with "In systems that do not have a ground state due to self-gravity..." instead of "At densities greater than those supported by any degeneracy, gravity overwhelms all other forces," which tends to promote the misunderstandings (like that degeneracy is a force in the first place).
    Whoops. Did not mean to link to susbection. Let's try again:

    https://en.wikipedia.org/wiki/Degenerate_matter

    Yes, the subsection on Singularity is too speculative..

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    Quote Originally Posted by Ken G View Post
    Except that it has nothing to do with degeneracy. Look at the first words in that subsection...
    That subsection is what happens for a singularity
    At densities greater than those supported by any degeneracy, gravity overwhelms all other forces.
    This is simply a (slightly imprecise) statement that strong enough gravitation can overcome any degeneracy pressure. The previous sections go through the known sources of degeneracy pressure.

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    Quote Originally Posted by Reality Check View Post
    Yes, I know. That was my point, but John already recognized the oversight. Still, all that is of little consequence, the larger issue is what I said above: degeneracy pressure is a much broader issue than what everyone talks about, i.e., what happens at very high density. That latter context really only applies in the context of when the forces are gravity alone. When the forces include small-range electric forces, we have a far more mundane version of degeneracy that surrounds us every moment of our lives, but hardly anyone recognizes that because of how poorly the topic is generally handled. Worse, even the name "degeneracy" is quite poorly chosen-- degeneracy normally means multiple states that have the same energy, but of course that has nothing at all to do with the phenomenon of "degeneracy pressure." Frankly, what everyone is talking about should just be called what it is: the simple quantum mechanical ground state of gases that are purely self-gravitating and suffer no other interparticle forces, because that's all it is.
    Last edited by Ken G; 2018-Jan-11 at 02:53 AM.

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    Quote Originally Posted by Ken G View Post
    ...the larger issue is what I said above: degeneracy pressure is a much broader issue than what everyone talks about, i.e., what happens at very high density.
    The more physically significant or interesting cases of degeneracy pressure are at high density, e.g. white dwarf and neutron stars, so that is what is talked about.
    The "mundane" degeneracy pressures are well known and well taught but not emphasized. Solid state physics courses (at least the ones I did) mention that metals are hard to compress due to degeneracy pressure.

    Without degeneracy there is no degeneracy pressure and so degeneracy has everything to do with the phenomenon of degeneracy pressure!

    Degeneracy is a QM phenomena, i.e. the "simple quantum mechanical ground state of gases that are purely" interacting via non-gravitational forces. The "self-gravitating" stuff sounds more suitable for an ATM thread.
    ETA: Self-gravitation
    Self-gravity is the gravitational force exerted on a body, or a group of bodies, by the body(ies) that allows it/them to be held together.[2] Self-gravity (self-gravitation) has important effects in the fields of astronomy, physics, seismology, geology, and oceanography.[3][4][5]
    Last edited by Reality Check; 2018-Jan-11 at 03:34 AM.

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    Quote Originally Posted by Reality Check View Post
    The more physically significant or interesting cases of degeneracy pressure are at high density, e.g. white dwarf and neutron stars, so that is what is talked about.
    And that's what is completely wrong. The conduction electrons in a common metal are a wonderful example of degeneracy pressure, and are much closer to you right now than any white dwarf.

    What they actually mean whenever you see "degeneracy pressure" in most textbooks is actually limited to when gravity is the only force, but obviously that has nothing at all to do with either quantum mechanics or "degeneracy", it's purely an accident of how the topic is approached. Which is the problem.

    The "mundane" degeneracy pressures are well known and well taught but not emphasized.
    That claim is self-contradictory on two levels. First, it contradicts what you just said, for the reason I just explained. Second, it is essentially an oxymoron to say something is "well taught but not emphasized." If it's not emphasized, it's not well taught, because what is being well taught is precisely what is being well emphasized. Again, this is the whole point.
    Solid state physics courses (at least the ones I did) mention that metals are hard to compress due to degeneracy pressure.
    Again, notice how this contradicts the first thing you just said above!

    Degeneracy is a QM phenomena, i.e. the "simple quantum mechanical ground state of gases that are purely" interacting via non-gravitational forces. The "self-gravitating" stuff sounds more suitable for an ATM thread.
    You clearly do not understand degeneracy pressure if you think that, despite how well you believe it has been taught to you. Unless you include self-gravity, there is zero implication that degeneracy pressure involves very high density! So this clearly implies: every single time you ever saw "high density" in the same breath as "degeneracy pressure," they were always talking only about self gravity. Now notice how common it is to include with information about degeneracy pressure, including this very thread, the implication of very high density. Just read this thread, which is why I posted in the first place. I always know two things whenever I see someone talking about degeneracy pressure:
    1) they will think it requires very high density, and
    2) they will be talking only about self-gravity.
    This thread is like one example out of a hundred, and that includes physics contexts just as often as astronomy ones. Even the Wiki cited above, which will always be pretty good because it is a Wiki, says "The degenerate state of matter, insofar as it deviates from an ideal gas, arises at extraordinarily high density (in compact stars) or at extremely low temperatures in laboratories." So they get points for realizing there are non-astrophysical contexts, but give those points back for promoting the misconception that degeneracy pressure is only relevant for extreme environments. A common metal is the best everyday application of the notion, and indeed, even a single large atom is a fairly nice application from the conceptual standpoint.
    Last edited by Ken G; 2018-Jan-11 at 04:25 AM.

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    so degeneracy in a bit of metal, under ordinary circumstances, it due to being a solid, rather than a gas?
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    Quote Originally Posted by Mudskipper View Post
    so degeneracy in a bit of metal, under ordinary circumstances, it due to being a solid, rather than a gas?
    In a metal, some of the electrons break free of the atoms, and act like a degenerate gas. Their "degeneracy pressure" is rather low, because the density is quite mundane of course, but nevertheless it is what keeps the metal from contracting, and makes it hard to compress. The telltale sign of degeneracy is that the kinetic energy of the electrons in, say, a metal fork, are so high that if the electron gas was acting like a classical gas, it would burn you badly to touch the fork. But degeneracy greatly limits the electrons' ability to give up heat (since the electrons are near their ground state, which is the whole point), driving their temperature down to room temperature instead of the super high temperature you would otherwise expect given the electron kinetic energy. What makes the fork hard to compress is known as "degeneracy pressure," in a context not normally discussed (because the interparticle forces are not gravity). Nevertheless, this is an equally interesting, and far more important, application than white dwarfs or neutron stars.
    Last edited by Ken G; 2018-Jan-11 at 08:39 AM.

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    Quote Originally Posted by Mudskipper View Post
    so degeneracy in a bit of metal, under ordinary circumstances, it due to being a solid, rather than a gas?
    Yes. A solid has a relatively stable lattice of ions. A metal has free elections forming an electron gas. The ion lattice provides the "box" that allows the electron gas to be degenerate.

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    Quote Originally Posted by Ken G View Post
    And that's what is completely wrong. ...
    It is wrong that people (e.g. me!) are taught that "conduction electrons in a common metal are a wonderful example of degeneracy pressure" ?

    QM does not include gravity thus gravity is never the only force in degeneracy pressure examples. The solid state physics textbook example of electrons in metals do not mention gravity. The astronomy textbook example of white dwarfs tend to mention gravity because that is what holds white dwarfs together.
    Properties of Degenerated Fermi-Gas in Astrophysics by Hsin-Yu Chen (PDF) has no force of gravity in it.

    You need to read Electron degeneracy pressure
    Electron degeneracy pressure is a particular manifestation of the more general phenomenon of quantum degeneracy pressure. The Pauli exclusion principle disallows two identical half-integer spin particles (electrons and all other fermions) from simultaneously occupying the same quantum state. The result is an emergent pressure against compression of matter into smaller volumes of space. Electron degeneracy pressure results from the same underlying mechanism that defines the electron orbital structure of elemental matter. For bulk matter with no net electric charge, the attraction between electrons and nuclei exceeds (at any scale) the mutual repulsion of electrons plus the mutual repulsion of nuclei; so absent electron degeneracy pressure, the matter would collapse into a single nucleus. In 1967, Freeman Dyson showed that solid matter is stabilized by quantum degeneracy pressure rather than electrostatic repulsion.[1][2][3] Because of this, electron degeneracy creates a barrier to the gravitational collapse of dying stars and is responsible for the formation of white dwarfs.
    Degeneracy pressure is QM, not GR and is non-gravitational.

    Gravity in solid matter is ignored and we still have quantum degeneracy pressure. Gravity in stars is not the cause of quantum degeneracy pressure.

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    Quote Originally Posted by Reality Check View Post
    It is wrong that people (e.g. me!) are taught that "conduction electrons in a common metal are a wonderful example of degeneracy pressure" ?
    No.
    QM does not include gravity thus gravity is never the only force in degeneracy pressure examples.
    Wrong.

    The solid state physics textbook example of electrons in metals do not mention gravity.
    Obviously.
    The astronomy textbook example of white dwarfs tend to mention gravity because that is what holds white dwarfs together.
    Also obvious.Yes, and no mention of high density either. That's why I said I'm talking about references to high density. Like this thread. Like the 100 other threads in this forum in which you will find degeneracy pressure mentioned.
    Degeneracy pressure is QM, not GR and is non-gravitational.
    Obviously degeneracy pressure is non-gravitational, that was more or less my point from the start.

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    Quote Originally Posted by Ken G View Post
    ... Wrong
    Wrong: Solid state physics textbooks exist and have degeneracy pressure examples. You should know that gravity does not appear at all for the example of metals and their degeneracy pressure. Thus gravity is never the ONLY force in degeneracy pressure examples.

    Quote Originally Posted by Ken G View Post
    ... Obviously degeneracy pressure is non-gravitational, that was more or less my point from the start.
    My point was that the self-gravitating term you have been using is inappropriate to the definition of quantum degeneracy pressure (as you now seem to agree).
    Gravitation and electromagnetism are forces that allow significant degeneracy pressure to exist as in white dwarfs and metals respectively.

    Properties of Degenerated Fermi-Gas in Astrophysics by Hsin-Yu Chen (PDF) does "mention of high density", i.e. that of white dwarfs:
    In previous part, we consider all particle as perfect gas, which means that there is not interaction between particles. However, in the interior of white dwarf, the density is so high that the particle seperation are compressed
    High density is implicit in the introduction:
    The degenerated fermi-gas is a dominated component in a highly dense region in Astronomy, such as the center of a white dwarf.
    (the center of a white dwarf has high density)
    Last edited by Reality Check; 2018-Jan-12 at 02:10 AM.

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    Quote Originally Posted by Reality Check View Post
    My point was that the self-gravitating term you have been using is inappropriate to the definition of quantum degeneracy pressure (as you now seem to agree).
    You apparently have not understood anything I said, so let me summarize. Of course degeneracy pressure does not directly involve gravity. Neither does it necessarily involve high density. This is what I have been saying. What you have missed is what I also said: the only time high density is relevant for degeneracy pressure is when the sole force involved is gravity, which is what most people don't know. The more common, relevant, and important applications of degeneracy pressure involve contexts with forces much stronger than gravity, and then the densities involved are completely mundane, as with everyday metals, and even single large atoms. I'm sorry if you didn't get all that the first time, but there it is. Your pretense that I have somehow changed what I have been saying is tiresome.

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    Quote Originally Posted by BigDon View Post
    Line 1, Would the rock get intensely hot? Yes.
    Not necessarily.

    But in cold, high-density matter of fermions, constituent particles in their ground state with zero point movement only do have large momenta.

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    Quote Originally Posted by Ken G View Post
    You apparently have not understood anything I said, so let me summarize. ...
    This does not change the meaning of self-gravitating. A metal with a degenerate electron gas is not a self-gravitating body.
    The popular (because astronomy is popular) and thus the most common example on the Internet is electron degeneracy pressure in white dwarfs. People who learn about the less popular (How many "Carl Sagans" of solids can you think of ) solid state physics learn about electron degeneracy pressure in solids. People who use Wikipedia learn about both.
    Electron degeneracy pressure
    Electron degeneracy pressure is a particular manifestation of the more general phenomenon of quantum degeneracy pressure. The Pauli exclusion principle disallows two identical half-integer spin particles (electrons and all other fermions) from simultaneously occupying the same quantum state. The result is an emergent pressure against compression of matter into smaller volumes of space. Electron degeneracy pressure results from the same underlying mechanism that defines the electron orbital structure of elemental matter. For bulk matter with no net electric charge, the attraction between electrons and nuclei exceeds (at any scale) the mutual repulsion of electrons plus the mutual repulsion of nuclei; so absent electron degeneracy pressure, the matter would collapse into a single nucleus. In 1967, Freeman Dyson showed that solid matter is stabilized by quantum degeneracy pressure rather than electrostatic repulsion.[1][2][3] Because of this, electron degeneracy creates a barrier to the gravitational collapse of dying stars and is responsible for the formation of white dwarfs.
    So what is the problem?

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    Quote Originally Posted by Reality Check View Post
    This does not change the meaning of self-gravitating. A metal with a degenerate electron gas is not a self-gravitating body.
    Why on Earth do you think I ever said anything different? I'm mystified, but as I said, you just don't understand. I said that many of the most important degenerate systems are not self-gravitating, and I mentioned common metals as a supporting example, and now you are telling me that common metals are not self-gravitating. It's pretty unbelievable.
    The popular (because astronomy is popular) and thus the most common example on the Internet is electron degeneracy pressure in white dwarfs.[
    And I'm equally mystified why you think I don't know that either. Reread everything I said and try again, because everything I said is entirely consistent with all of that obvious stuff.
    So what is the problem?
    The problem, as I said many times, is how many people, and how many sources (even the Wiki, by the way, as I also pointed out above) associate degeneracy (and "degeneracy pressure") with extreme conditions, especially high density. Just read the OP, for crying out loud-- indeed the very first answer to the OP stated "Can't have degenerate matter without the compression, lack of compression forces causes degenerate matter to turn back into normal matter", which is a very common kind of thing to hear. The Wiki said you get it in very dense systems or systems so cold you only find them in laboratories. The OPer seemed to have quite a light bulb come on when he/she asked "so, are you saying that the atoms in a rock are like particles in a box?". So they came to understand the point, which was my goal.
    Last edited by Ken G; 2018-Jan-18 at 11:40 PM.

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    Quote Originally Posted by Ken G View Post
    ...The problem, as I said many times, is how many people,...
    Election degeneracy pressure has both solid matter and white dwarfs.
    The OP has solid matter and neutron stars.
    Degenerate matter mentions degeneracy pressure in solid matter
    Degeneracy pressure contributes to the pressure of conventional solids, but these are not usually considered to be degenerate matter because a significant contribution to their pressure is provided by electrical repulsion of atomic nuclei and the screening of nuclei from each other by electrons. In metals it is useful to treat the conduction electrons alone as a degenerate, free electron gas while the majority of the electrons are regarded as occupying bound quantum states. This contrasts with degenerate matter that forms the body of a white dwarf, where all the electrons would be treated as occupying free particle momentum states.
    Last edited by Reality Check; 2018-Jan-19 at 12:19 AM.

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    All true, but apparently you don't understand much of it.
    Frankly, the last sentence is what is wrong Even for white dwarfs which are not " purely self-gravitating " and do "suffer" other interparticle forces.
    White dwarfs are purely self-gravitating, in the same sense that they are spherical (those are the approximations we use to treat them). So you're wrong again. I get it: you cannot understand what I am saying.

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    Quote Originally Posted by Ken G View Post
    dwarfs are purely self-gravitating, ...
    Anyone can understand what you wrote in those 2 posts - that quantum degeneracy pressure is due to self-gravitation which you should know. However "You apparently have not understood anything " insults tend to hide this.

    Still not purely true because there is electron degeneracy pressure without which white dwarfs would be neutron stars !
    Properties of Degenerated Fermi-Gas in Astrophysics by Hsin-Yu Chen (PDF)
    Part 1: Degeneracy of Electrons (non-interacting electron gas)
    Part II: Pressure ionization (add in interactions as in metals)

    Quantum degeneracy is "the simple quantum mechanical ground state of gases that are purely self-gravitating and suffer no other interparticle forces". A gas of non-interacting even by gravity Fermi particles can be degenerate.
    Last edited by Reality Check; 2018-Jan-23 at 11:23 PM.

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    Quote Originally Posted by Reality Check View Post
    Anyone can understand what you wrote in those 2 posts - that quantum degeneracy pressure is due to self-gravitation which you know is incorrect.
    As I said before, how you could construe my posts as saying that degeneracy pressure (it's always quantum, that's redundant) is due to self-gravitation is completely beyond me. Needless to say, I never said anything like that, nor does anyone else seem to think I did. I suggest you read it all over again, slowly.
    Not purely true because there is electron degeneracy pressure without which they would be neutron stars !
    Yeah, no one has any idea what you are trying to say there, but it doesn't even sound remotely close to correct.

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    Quote Originally Posted by Ken G View Post
    As I said before, ...
    Because that is what you wrote.
    "In systems that do not have a ground state due to self-gravity..."
    "...ground state of gases that are purely self-gravitating..."
    That is simple enough to understand. You are stating that there is exists a ground state and that it is due to self gravitation. Insults still do not make this English mean anything different.
    Last edited by Reality Check; 2018-Jan-23 at 11:38 PM.

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    Yes, I know what I wrote. I guess because I understand what those words mean.
    That is simple enough to understand. You are stating that there is exists a ground state and that it is due to self gravitation.
    Yes, gravity can affect the ground state, and it can even determine when there is none. This is what I have been talking about, and it's still just as true as when I said it.
    Last edited by Ken G; 2018-Jan-25 at 03:36 AM.

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