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

  1. #31
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    Quote Originally Posted by Ken G View Post
    .Yes, gravity can affect the ground state, and it can even determine when there is none.
    "affect" is not 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..."
    The English meaning of due is "caused by". The ground state of an system is quantum mechanics leading to quantum degeneracy pressure. Gravity does not cause quantum ground states or degeneracy pressure.
    Electromagnetism and gravity do affect the type and population of the states of the system.

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    Quote Originally Posted by Reality Check View Post
    That is indeed what "due to" means, but I see nothing of value in any of the rest of your interpretation of my words.
    As I've said many times, you simply don't understand. When I say that gravity determines if there is a ground state or not in those systems, then I mean that the absence of the ground state is due to gravity. Why you don't understand that is a complete mystery to me, but quite frankly, is not my problem.
    Gravity does not cause quantum ground states or degeneracy pressure.
    Here you are simply guilty of a logical fallacy. I said gravity caused there to not be a ground state. For some unknown reason, you think that's the same thing as gravity causing degeneracy pressure, because you just included both those things together in your last sentence. You are thus speaking sheer nonsense. And no, that's not an "insult," it is a logical conclusion.
    Last edited by Ken G; 2018-Jan-26 at 02:46 AM.

  3. #33
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    Quote Originally Posted by Ken G View Post
    That is indeed what "due to" means, ...usual insults...
    And thus the statement in the "ground state due to self-gravity..." post was wrong because the ground state is QM not GR.

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    I have no idea what you think you are arguing, I see no merit. I see no problem at all in saying that the ground state of a self-gravitating system (like a white dwarf) is "due to" gravity, if the ground state is controlled by gravity. What problem you imagine there simply stems from misunderstanding, of either the language, the physics, or both.

    For a particle in a box, you will find the ground state depends on the size of the box. If the box is infinite, so there's no box, there's no ground state. So the ground state is "due to" the box. This is basic simple English. Nevertheless, in this totally obvious situation, it could not be correctly claimed, as you did above, that saying the box causes the ground state implies that the box is the cause of quantum degeneracy pressure. That's like saying that if a man causes the death of another by shooting them, the man is the cause of bullets. It's total nonsense. All I can do is repeat what I have said all along, and if you still don't understand, there's just nothing more I can say:

    1) To know the ground state of any system, you need to understand the forces. And yes, one of them can be gravity, your claim above that it cannot because GR is not QM is sheer nonsense.

    2) When the system is close to its ground state, it can both quantitatively useful and conceptually powerful to imagine the system is supported in equilibrium by an effective force called "degeneracy pressure."

    3) When the force responsible for determining the ground state (yes, the force that causes the ground state, because there would be no ground state without such a force) is strong and long-range, as for electric attraction, the densities in the ground state are completely mundane and everyday, so this is actually the application of degeneracy pressure that is most common and most important in our everyday lives.

    4) When the only force on the particles is Newtonian gravity (so that one can say it is a force at all, of course it can also be done in GR in the usual way), that force is very weak and long-range, and the ground state it produces involves a very high kinetic energy and yields very high density.

    5) Unfortunately, since case (4) is the only one most people hear about, there is an amazingly widespread misconception that degeneracy effects are only important at very high density, or otherwise very extreme conditions, so they miss the everyday applications that are much more important. This misconception underlies the OP question, which is why the questioner took a system that is already pretty close to degenerate and asked about what to do to make it degenerate in the way most people think about. The light bulb came on when it was recognized that all bound systems are like particles in a box, and they can all be regarded as held up by degeneracy pressure whenever they are near their ground state.

    6) Ergo, the powerful way to think about "degeneracy pressure" is simply to understand that it is the effective force responsible for preventing the collapse of any system that is near its ground state. Now that doesn't sound like extreme conditions, does it?

    There. You either understand all that or you don't, because I have been saying all that for this whole thread.
    Last edited by Ken G; 2018-Jan-26 at 01:58 PM.

  5. #35
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    Quote Originally Posted by Ken G View Post
    I have no idea what you think you are arguing, ....
    I am not arguing anything. I answered your question of "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". I listed your 2 posts on degeneracy pressure that I did construe doing that:
    "In systems that do not have a ground state due to self-gravity..."
    "...ground state of gases that are purely self-gravitating..."
    The replies are you writing about what I should have construed. This is redundant when I have read your later posts that make it clear that those posts do not mean what is written.

    But then you go back to asserting that gravity causes quantum degeneracy pressure when gravity is not part of QM.

    Gravity in stars allows fusion. The fusion makes stars hot. When fusion stops we get a hot white dwarf with a gas of free elections. QM states that a gas of free electrons has degeneracy pressure. Gravity has caused a set of conditions under which electron degeneracy pressure is significant.

    ETA: On second thoughts maybe this is an argument - a rather trivial one about the meaning of "cause". I go with a "direct consequence" interpretation. The quantum Pauli exclusion principle is needed for quantum degeneracy pressure to exist so the cause is quantum mechanics. You seem to want a "makes the conditions for" interpretation.
    Last edited by Reality Check; 2018-Feb-01 at 10:24 PM.

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    Quote Originally Posted by Reality Check View Post
    But then you go back to asserting that gravity causes quantum degeneracy pressure when gravity is not part of QM.
    Goodness, you are just repeating two very silly claims. These are why they are silly:
    1) You claim I said gravity causes degeneracy pressure. Anyone can see I never said any such thing. What I did say is that the ground state of a self-gravitating system (like a white dwarf) is due to gravity. Of course gravity works in concert with degeneracy pressure, like a gun works in concert with a bullet to make a hole in a target. One can certainly say that the hole is caused by a bullet without claiming that bullets cause guns, but you don't seem to understand that.
    2) You claim that gravity is not part of QM. That shows a complete lack of understanding of how QM works. QM uses something called the "energy operator," which means that any force that can be responsible for potential energy is certainly part of quantum mechanics. Although it is true that gravity can be modeled in many ways, the way it is modeled in QM is via this potential energy function. Ergo, QM does include gravity, in precisely the same way that it includes the electrostatic potential in an atom.
    So these claims you are making are false, and I keep telling you why they are false, but you cannot understand. So be it, my comments are for those who can.
    Gravity in stars allows fusion. The fusion makes stars hot.
    I see that you do not understand fusion either. Fusion does not make stars hot, for the very simple reason that you cannot get fusion unless the star is already hot. So no, you don't understand causation at all, regardless of whether you think it is "direct consequence" or "makes the conditions for." The hotness of a star is neither the "direct consequence" of fusion, nor does fusion "make the conditions for" the star to be hot, so you cannot even be consistent with your own language. But if you want to understand the role of gravity in the ground state of a white dwarf, it is this: gravity makes the ground state what it is, given the rest of the rules of QM. To anyone else, that means the ground state "is due to" gravity in the same way that the ground state of a hydrogen atom is "due to" the electric attraction between proton and electron. To anyone else, that is.
    Last edited by Ken G; 2018-Feb-02 at 10:10 PM.

  7. #37
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    Quote Originally Posted by Ken G View Post
    Goodness, you are just repeating two very silly claims. ...
    1. This is my real claim:
      Quote Originally Posted by Reality Check View Post
      I answered your question of "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". I listed your 2 posts on degeneracy pressure that I did construe doing that:
      "In systems that do not have a ground state due to self-gravity..."
      "...ground state of gases that are purely self-gravitating..."
      The replies are you writing about what I should have construed.
      Extra emphasis added.
    2. QM still does not include gravity regardless of unsupported "energy operator" assertions.
      FYI: Gravity is caused by curved space-time. QM is has no curved space-time. The operators in QM are only defined in a flat space-time.
    3. Irrelevant insult - I understand fusion. Not writing a post with an entire astrophysics textbook on stars does not make me ignorant about fusion.

    I have a M.Sc. on theoretic solid state physics. That is roughly 5 years of learning physics including QM and basic GR. The energy operator in QM is a partial derivative wrt time in flat space-time. The concept of partial differentiation in flat space-time cannot be applied to a curved space-time. It turns out that the concept has to be expanded to include properties of the space-time. N.B. Do not complain because I did not write a full textbook explanation. If you are interested in the details then there are plenty of sources explaining what happens in a curved space-time, e.g. Leonard Susskind's lectures on YouTube Einstein's General Theory of Relativity.
    Last edited by Reality Check; 2018-Feb-04 at 11:34 PM.

  8. #38
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    Quote Originally Posted by Reality Check View Post
    FYI: Gravity is caused by curved space-time. QM is has no curved space-time.
    Ah me. As I already explained to you, physics just doesn't work that way. Real physicists do not claim what causes gravity, they invoke models of gravity that they have good reason to expect to work in the context of interest. Seriously, this is a science forum, you should know this. Sometimes they invoke a theory called general relativity, which talks about curved spacetime. More often, they invoke a theory called Newtonian gravity, which invokes a potential energy function. When doing quantum mechanics, often gravity is treated via that second model, and we get things like the standard model of a white dwarf. Has it not even occurred to you that everything you ever heard in your life about explaining white dwarfs involved using gravity in quantum mechanics?

    Occasionally, gravity is invoked in quantum mechanics via the model of general relativity, and we get things like Hawking radiation, even though the two models are not strictly self-consistent. When that happens, physicists are trying to anticipate the elements of both theories that will continue to hold in some future theory that will attempt to unify them. This is generally regarded as irrelevant for white dwarf models, because the gravity there is weak enough that one should be able to simply use Newtonian gravity in quantum mechanics. So please stop repeating your wrong understanding of how physics works, you might confuse people who don't know better.
    [*]Irrelevant insult - I understand fusion.
    You just showed you either did not understand fusion, or cause and effect. Since you have claimed over and over that you do understand cause and effect, I was generously allowing that perhaps it is fusion you don't understand. Because by basic logic, it is one or the other, since you just said that fusion is the cause of stars being hot, and I just told you that fusion requires high temperature already.
    Not writing a post with an entire astrophysics textbook on stars does not make me ignorant about fusion.
    No one is asking you to write any textbooks, merely to cease repeating your misconceptions after they have been explained to you. Am I being a little hard on you? Yes, but it's because you insist on repeating these false claims over and over. All I can do is explain why you are wrong, and instead of making counterargument, you simply object to being told you are wrong!
    I have a M.Sc. on theoretic solid state physics.
    I have no interest in your education, it only makes your wrong statements more important to correct because people might think you know what you are talking about. And I'm sure there are many statements you could make that would indeed be correct, just not these ones. Pointing out that you have not understood something is not "insulting" you, unless you cannot separate yourself from an incorrect claim you are making.
    The energy operator in QM is a partial derivative wrt time in flat space-time.
    OK, now there are two new errors I need to correct. First of all, the energy operator is not a partial derivative in time, although people may sometimes us imprecise language along those lines. If you look up the Schroedinger equation, you will see that it equates the action of that time derivative on a wavefunction with the action of the actual energy operator. Or to make this even clearer, look up the time independent form of the Schroedinger equation, which has an energy operator and no time derivatives. Then you can understand what an energy operator actually is in quantum mechanics.

    Your second error is your insinuation that gravity cannot be treated in flat spacetime, but as I just said, there are several different models of gravity that get used in the context of quantum mechanics. The one to which I refer is the one commonly used in the context of white dwarfs, i.e., the one relevant to this thread, which is to treat gravity via a potential energy in flat spacetime. You can find references to it in almost any theoretical treatment of white dwarfs, you shouldn't have to look far.
    Do not complain because I did not write a full textbook explanation.
    Again, I am not complaining, I am correcting errors. I have no interest in making complaints, but I do want people to know the scientific truth, on a science forum. If you'd like me to cease correcting errors, then cease entering them into the forum!
    Last edited by Ken G; 2018-Feb-05 at 02:30 PM.

  9. #39
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    Ken G: Give mainstream sources for the "the standard model of a white dwarf"...

    Quote Originally Posted by Ken G View Post
    Ah me. As I already explained to you, physics just doesn't work that way. Real physicists do not claim what causes gravity,...
    Real physicists read textbooks where GR states that gravity is caused by the curvature of spacetime. Real physicists learn about the enormous success of GR which confirms that GR is correct (as far as we know) and thus gravity is caused by the curvature of spacetime. Real physicists (like I was) attribute the cause of gravity to the model that best describes gravity - that is GR where gravity is caused by the curvature of spacetime. What real physicists conclude is that QM with its flat spacetime cannot include gravity caused by a curved spacetime and a different quantum gravity theory is needed.

    Unsupported claims and insults is not valid debate so:
    Ken G: Give mainstream sources for the "the standard model of a white dwarf" that includes gravity in QM.

    The standard model of white dwarfs certainly includes gravity. That gravity would be the Newtonian approximation (i.e. gravity in a flat spacetime). Otherwise the electron pressure would make them explode and not exist!
    This is a white dwarf
    ...The material in a white dwarf no longer undergoes fusion reactions, so the star has no source of energy. As a result, it cannot support itself by the heat generated by fusion against gravitational collapse, but is supported only by electron degeneracy pressure, causing it to be extremely dense
    Gravity and QM are separate in that article contrary to your claim.

    This is quantum mechanics
    Quantum mechanics (QM; also known as quantum physics or quantum theory), including quantum field theory, is a fundamental theory in physics which describes nature at the smallest scales of energy levels of atoms and subatomic particles.[2]
    Gravity is only mentioned in the context of there being no viable unification of QM and gravity yet.

    This is electron degeneracy pressure - note that there no G thus no gravity involved.

    Properties of Degenerated Fermi-Gas in Astrophysics by Hsin-Yu Chen (PDF) is an explanation of the physics behind the standard model of a white dwarf.
    Part 1 is Degeneracy of Electrons for a non-interacting electron gas. This is the derivation of electron degeneracy pressure. No gravity there. Part II (Pressure Ionization) also has no G for gravity but gravity plays a role - the ionization is a result of the high density in the center of a white dwarf.
    Last edited by Reality Check; 2018-Feb-08 at 09:02 PM.

  10. #40
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    This is the definition of the energy operator. That ∂/∂t is a partial derivative with respect to time.

    If you look up the Schrödinger equation you will see the textbook energy operator with its partial derivative with respect to time on the LHS of the equation.
    the symbol ∂/∂t indicates a partial derivative with respect to time t
    On the RHS you will see the Hamiltonian operator
    Ĥ is the Hamiltonian operator (which characterises the total energy of the system under consideration).
    ETA: A fuller explanation of the Schrödinger Hamiltonian.

    The physics of the system being considered appears on the other side of the equation as the Hamiltonian operator. Look down the page at the solution for a hydrogen atom and see that the Coulomb interaction is part of the Hamiltonian operator and that the energy operator does not change. Thus when you answer
    Ken G: Give mainstream sources for the "the standard model of a white dwarf" that includes gravity in QM.
    there should be a gravitational potential in the Hamiltonian operator.
    Last edited by Reality Check; 2018-Feb-09 at 01:02 AM.

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    Quote Originally Posted by Reality Check View Post
    Real physicists read textbooks where GR states that gravity is caused by the curvature of spacetime.
    But the point that you are obviously missing, and that I have labored to correct for you (or to help avoid your confusing others reading this), is this fact does not imply they need to believe, or do believe, that gravity is really caused by the curvature of spacetime, as you seem to maintain. In point of fact, the vast majority of theoretical physicists don't think gravity is caused by curvature of spacetime, they expect a quantum theory of gravity which doesn't look like that at all. This is widely known, you should know this. But it doesn't matter if most physicists are right about this or not-- what matters is what everyone on a science forum should already know: physics invokes models that are tailored to the desired application. That's it, that's what physics does. Most of the time, that's Newtonian gravity. Sometimes, as with GPS satellites, it is general relativity. And rarely, it is neither, but instead an anticipated marriage of GR and quantum field theory, which produces ideas like Hawking radiation. You will find many threads on this forum about Hawking radiation, and all of them combine gravity and quantum mechanics in a much more speculative (and even somewhat controversial) way than the simple marriage of Newtonian gravity and quantum mechanics that is white dwarf theory. But the point is, we use whatever models we need for the situation, so your claim that one cannot talk about quantum mechanics along with the effects of gravity on a ground state is just plain wrong.
    Last edited by Ken G; 2018-Feb-09 at 02:53 PM.

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    Quote Originally Posted by Reality Check View Post
    This is the definition of the energy operator. That ∂/∂t is a partial derivative with respect to time.
    All right, you have the semantics correct here, but not the point. I should have used the term "Hamiltonian operator" in place of "energy operator" above, but since the usual way we apply the Schroedinger equation has them equated to each other, the difference is hardly important. What is important is what I said above: the Hamiltonian operator used in quantum mechanics requires a potential energy function, and quantum physicists just plug in whatever potential energy function they want there-- including gravity. The potential energy function is never itself part of quantum mechanics, it is always borrowed from classical mechanics and simply turned into an operator to plug it into the Hamiltonian operator. That's always done, everywhere in quantum mechanics, so to think that this is somehow not allowed with gravity but is allowed the electric or magnetic forces is just plain wrong.
    The physics of the system being considered appears on the other side of the equation as the Hamiltonian operator.
    Yes, your irrelevant semantic point is indeed correct, I was mistaken to correct the semantics but I was certainly right to correct what matters: your wrong claim that any of that refutes in any way the use of the gravitational potential energy function in the Hamiltonian of quantum mechanics, which is all I need for what I said: gravity controls the ground state of the electrons in a white dwarf (in any model that treats the electrons and ions together as a fluid-- a technicality appears that electric forces are needed to convert the effects of gravity on the fluid into individual effects on the particles, but this technicality is of no consequence in the fluid picture you will always see).
    Ken G: Give mainstream sources for the "the standard model of a white dwarf" that includes gravity in QM.
    there should be a gravitational potential in the Hamiltonian operator.
    Obviously that is my whole point.
    Last edited by Ken G; 2018-Feb-09 at 02:56 PM.

  13. #43
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    Quote Originally Posted by Ken G View Post
    But the point that you are obviously missing,....
    I maintain that scientists take as the cause of gravity the cause in the best modal available (GR and the curvature of spacetime). A still unknown quantum gravity theory does not change that.

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    Quote Originally Posted by Reality Check View Post
    I maintain that scientists take as the cause of gravity the cause in the best modal available (GR and the curvature of spacetime). A still unknown quantum gravity theory does not change that.
    Which is why it's misleading to talk about a "cause" of gravity. These "causes" are merely mathematical theories that can be used to make predictions about gravity.

    Grant Hutchison

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    Souurces that shoud but do not mention gravity in QM

    Quote Originally Posted by Ken G View Post
    All right, you have the semantics correct here, but not the point.
    Scientific definitions are not semantics. You made a mistake. The energy operator does have a ∂/∂t which you denied. But at least we are talking about the correct part of the Schrodinger equation now.
    Repeating unsupported assertions do not answer the question I asked.

    Ken G: Give mainstream sources for the "the standard model of a white dwarf" that includes gravity in QM.


    The Wikipedia article on QM not mention it being used for gravity.
    Electron degeneracy pressure as in white dwarfs not include G for gravity.
    The white dwarf article does not mention that gravity is used in the electron degeneracy pressure derivation.
    Properties of Degenerated Fermi-Gas in Astrophysics by Hsin-Yu Chen (PDF) does bot use gravity to derive electron degeneracy pressure.
    The Pauli exclusion principle (QM, not gravitation) is why free electrons have degeneracy pressure: Astrophysics and the Pauli principle
    The Pauli exclusion principle which gives us degeneracy pressure is a consequence of the properties of wave functions and is not part of or derived from the Schrodinger equation.

    There is the pesky fact that electron degeneracy pressure is a specific case of the more general quantum degeneracy (however the article doesn't look at the pressure caused by degeneracy).

  16. #46
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    Quote Originally Posted by grant hutchison View Post
    Which is why it's misleading to talk about a "cause" of gravity. These "causes" are merely mathematical theories that can be used to make predictions about gravity.
    I did not make my point clear enough so thanks for pointing it out.
    It is the match of a theory to the real world that is vitally important. Einstein did not just write GR and declare that curvature of spacetime is the cause of gravity! He showed that GR explained what Newtonian gravitation could not and made testable, falsifiable predictions that Newtonian gravitation could bot make.

    We believed that gravity was caused by a force with an inverse square law because that matched the data. Until we got data that did not match. We believe now that gravity is caused by the curvature of spacetime because there is enormous evidence that GR is correct. Tomorrow we may believe that gravity is caused by something else.

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    Quote Originally Posted by Reality Check View Post
    I did not make my point clear enough so thanks for pointing it out.
    It is the match of a theory to the real world that is vitally important. Einstein did not just write GR and declare that curvature of spacetime is the cause of gravity! He showed that GR explained what Newtonian gravitation could not and made testable, falsifiable predictions that Newtonian gravitation could bot make.

    We believed that gravity was caused by a force with an inverse square law because that matched the data. Until we got data that did not match. We believe now that gravity is caused by the curvature of spacetime because there is enormous evidence that GR is correct. Tomorrow we may believe that gravity is caused by something else.
    I don't think we believe that gravity is "caused" by any of these things, even though people (sometimes scientists) have been known to use the word loosely. A set of mathematical equations can't cause anything. Gravity is best described by curved spacetime, until a better description comes along.

    I wouldn't normally belabour this point, but it's relevant to the way you and Ken are talking past each other so eloquently.

    Grant Hutchison

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    Quote Originally Posted by grant hutchison View Post
    I don't think we believe that gravity is "caused" by any of these things, even though people (sometimes scientists) have been known to use the word loosely. A set of mathematical equations can't cause anything. Gravity is best described by curved spacetime, until a better description comes along.
    I agree: A set of equations alone cannot cause anything. It is the match to the real world that turns a description into a cause which is a standard term in science for ""best description until something better comes along". It is correct usage for the context but not general English.

    This is not what Ken G and I am discussing. He has the assertion that the standard model of white dwarfs include putting gravity into QM. I pointed out that this is impossible for GR because as you write "Gravity is best described by curved spacetime". His response was that it is classical gravitation that is plugged into QM. There is no sign of this in any of the sources I have cited to him. A couple of sources explicitly exclude gravity in derivations. I do not recall any example of gravity being treated in QM from my short stint as a physicist. On the other hand, may area was solid state physics so I could have missed it. Thus my question for him.

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    Quote Originally Posted by Reality Check View Post
    I agree: A set of equations alone cannot cause anything. It is the match to the real world that turns a description into a cause which is a standard term in science for ""best description until something better comes along". It is correct usage for the context but not general English.

    This is not what Ken G and I am discussing. He has the assertion that the standard model of white dwarfs include putting gravity into QM. I pointed out that this is impossible for GR because as you write "Gravity is best described by curved spacetime". His response was that it is classical gravitation that is plugged into QM. There is no sign of this in any of the sources I have cited to him. A couple of sources explicitly exclude gravity in derivations. I do not recall any example of gravity being treated in QM from my short stint as a physicist. On the other hand, may area was solid state physics so I could have missed it. Thus my question for him.
    You seem to be misunderstanding the replies, however. And the misunderstanding seems to me to be because of this idea that separate theories create separate causes for different phenomena, which can't be mixed together.
    I may be wrong in my perception. Perhaps Ken will say if it makes any sense to him.

    Grant Hutchison

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    Quote Originally Posted by grant hutchison View Post
    You seem to be misunderstanding the replies, however.
    The English is clear in Ken G's posts, e.g. "quantum physicists just plug in whatever potential energy function they want there-- including gravity" from this recent post.

    My question is about this post:
    often, they invoke a theory called Newtonian gravity, which invokes a potential energy function. When doing quantum mechanics, often gravity is treated via that second model, and we get things like the standard model of a white dwarf.
    That "When doing quantum mechanics" is the mistake that I see.

    I will also emphasis for Ken G's sake that he may be talking about a separate treatment of gravity and QM in the standard model of a white dwarf and if so he just needs to say so.
    Quote Originally Posted by Reality Check View Post
    This is a white dwarf
    ...
    Gravity and QM are separate in that article contrary to your claim.
    For main sequence stars we have
    All main-sequence stars are in hydrostatic equilibrium, where outward thermal pressure from the hot core is balanced by the inward pressure of gravitational collapse from the overlying layers.
    The equations for hydrostatic equilibrium have weight on one side and pressure on the other.

    There is a similar situation for white dwarfs. The weight from gravity has to be balanced by a pressure. In this case, the pressure is dominated by electron degeneracy pressure. There is classical weight on one side of the balance and quantum pressure on the other side. This is not inclusion of gravity in QM.

    The degeneracy pressure comes from that electrons are fermions, not any solution of the Schrodinger equation.
    Properties of Degenerated Fermi-Gas in Astrophysics by Hsin-Yu Chen (PDF)
    The density of electrons is described by Fermi-Dirac statistics as electrons have half-integral spin.
    ...
    If the density of electrons increases, the electrons will be force to higher momentum states. The high momentum electrons contribute to the pressure, and the restriction on number density at each states is the souce of degeneracy pressure.

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    Well, I see people nit-picking each other's language unproductively and fruitlessly, each of you working from different terms of reference. If you're enjoying it you should of course carry on, but it's just never going to reach a resolution.

    Grant Hutchison

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    Quote Originally Posted by grant hutchison View Post
    Well, I see people nit-picking each other's language unproductively and fruitlessly, each of you working from different terms of reference. If you're enjoying it you should of course carry on, but it's just never going to reach a resolution.
    Once again, it is not language or nitpicking. The language in Ken G's post is clear as explained in my post . The physics he clearly states is wrong as suggested by the physics I have cited, correct when he supports it or not what he meant to write.
    The "terms of reference" we (just me so far but I have hopes for Ken G ) are using is credible sources for physics to support the physics we are talking about.
    Last edited by Reality Check; 2018-Feb-12 at 03:42 AM.

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    Quote Originally Posted by Reality Check View Post
    Once again, it is not language or nitpicking. The language in Ken G's post is clear as explained in my post . The physics he clearly states is wrong as suggested by the physics I have cited, correct when he supports it or not what he meant to write.
    The "terms of reference" we (just me so far but I have hopes for Ken G ) are using is credible sources for physics to support the physics we are talking about.

    The different physics you cite as being used by both of you - do you consider we would get different predictive outcomes from applying both explanations to a testable scenario? Or are we only talking about descriptive explanations rather than predictive models?

    .

  24. #54
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    Quote Originally Posted by Reality Check View Post
    Scientific definitions are not semantics. You made a mistake. The energy operator does have a ∂/∂t which you denied.
    Again, your effort to take this thread down a completely irrelevant rabbit hole is not going to hide your basic confusion. Just reread post #34, that lays out in complete detail everything that I am saying in this thread, that is actually relevant to this thread. No point in my repeating it all, it's right there in post #34.

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    Quote Originally Posted by grant hutchison View Post
    You seem to be misunderstanding the replies, however. And the misunderstanding seems to me to be because of this idea that separate theories create separate causes for different phenomena, which can't be mixed together.
    I may be wrong in my perception. Perhaps Ken will say if it makes any sense to him.
    It is very hard to figure out what Reality Check is actually claiming that is relevant to this thread. He apparently thinks I said that gravity causes degeneracy pressure, but that is a figment of his imagination. He also appears to object to the idea that gravity causes the ground state of a white dwarf. I could have said it "is responsible for", instead of "causes," but to me those are synonymous, and in any event he might have the same confusion because he seems to object to using a model of gravity in quantum mechanics at all. This is of course an absurd objection. But more importantly, everything I am trying to say in this thread is clearly laid out in post #34, so there's little point in any other aspect of the discussion. To avoid having to look back, here is what I'm saying:

    1) To know the ground state of any system, you need to understand the forces. And yes, one of them can be gravity.

    2) When the system is close to its ground state, it can both quantitatively useful and conceptually powerful to imagine the system is supported in equilibrium by an effective force called "degeneracy pressure."

    3) When the force responsible for determining the ground state (yes, the force that causes the ground state, because there would be no ground state without such a force) is strong and long-range, as for electric attraction, the densities in the ground state are completely mundane and everyday, so this is actually the application of degeneracy pressure that is most common and most important in our everyday lives.

    4) When the only force in a fluid description of the particles is Newtonian gravity, treated in quantum mechanics with no problem by using its potential energy function, that force is very weak and long-range, and the ground state it produces involves a very high kinetic energy and yields very high density.

    5) Unfortunately, since case (4) is the only one most people hear about, there is an amazingly widespread misconception that degeneracy effects are only important at very high density, or otherwise very extreme conditions, so they miss the everyday applications that are much more important. This misconception underlies the OP question, which is why the questioner took a system that is already pretty close to degenerate and asked about what to do to make it degenerate in the way most people think about. The light bulb came on when it was recognized that all bound systems are like particles in a box, and they can all be regarded as held up by degeneracy pressure whenever they are near their ground state.

    6) Ergo, the powerful way to think about "degeneracy pressure" is simply to understand that it is the effective force responsible for preventing the collapse of any system that is near its ground state. Now that doesn't sound like extreme conditions, does it?
    Last edited by Ken G; 2018-Feb-12 at 07:40 PM.

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    Quote Originally Posted by Len Moran View Post
    The different physics you cite as being used by both of you - do you consider we would get different predictive outcomes from applying both explanations to a testable scenario? Or are we only talking about descriptive explanations rather than predictive models?
    Everything I'm saying is in my last post, and that's all the physics required to get all the predictions correct. I don't believe Reality Check has made any points about any physics, so it's hard to say what physics he is talking about that could be different.

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    Quote Originally Posted by Ken G View Post
    It is very hard to figure out what Reality Check is actually claiming that is relevant to this thread. He apparently thinks I said that gravity causes degeneracy pressure, but that is a figment of his imagination.
    That was what I had in mind with my remark about "nit-picking language".

    Grant Hutchison

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    Yes, the discussion should center on those six points, that's what matters here. The rest is nitpicking.

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    Quote Originally Posted by Ken G View Post
    No point in my repeating it all, it's right there in post #34.
    Post 34 is simple stuff that I already know, mostly about particles in a box. There are no sources in that post. Point "1)" suggests the inclusion of gravity in QM. That land later posts lead to my question.
    Ken G: Give mainstream sources for the "the standard model of a white dwarf" that includes gravity in QM.

  30. #60
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    Quote Originally Posted by Ken G View Post
    He apparently thinks I said that gravity causes degeneracy pressure, but that is a figment of his imagination. ...
    Read what you wrote in 11 January 2018:
    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.
    The English is clear. Up to the "Worse", you are taking about context. Then we get to degeneracy and degeneracy pressure. A complaint about naming because you assert that that degeneracy has nothing to do with degeneracy pressure. Followed by an statement that degeneracy pressure is a QM ground state of gases interacting only by gravity. Lastly you emphasize that with "because that's all it is".

    Anyone reading that post will conclude that you are asserting that degeneracy pressure is "the simple quantum mechanical ground state of gases that are purely self-gravitating and suffer no other interparticle forces", i.er. due to gravity.
    I know that you have just made an omission and an irrelevant restriction. Fermi gases have degeneracy pressure in any circumstances. Any electron gas anywhere exerts degeneracy pressure (see below). For example the free electrons in the Sun exert degeneracy pressure. That degeneracy pressure is physically significant in at least 2 cases - solids and white dwarfs.

    P.S. I do agree that degeneracy pressure might be better named because it is more an "exclusion" 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.
    ...
    This degeneracy pressure is omnipresent and is in addition to the normal gas pressure P = NkT/V. At commonly encountered densities, this pressure is so low that it can be neglected. Matter is electron degenerate when the density (n/V) is high enough, and the temperature low enough, that the sum is dominated by the degeneracy pressure.

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