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

  1. #91
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    My guess is it's more true in medicine, where there must be a great deal of "on the job" training for how to cope with real situations. Physics doesn't have to mess with reality nearly that much, ironic though that might sound. But each physics textbook typically does focus on only a small set of problems, with names like "classical mechanics" or "electricity and magnetism," and in them will be found various classes of toolkits for solving various types of problems. It's still up to the user to graft this whole business together into a working understanding of how to use physics to understand the world! But in this case, it's a simple case of overstressing a single context for the degeneracy pressure idea, sort of like overstressing the connection between quantum strangeness and cats. There's actually nothing in anything I said that contradicts any textbooks, it's all a question of what they choose to tell you and what they choose to leave out because it's not within their sphere of interest. That's the extent to which it's not the full story-- simply not the application of interest. So for example, you will rarely find a quantum mechanics textbook solve the orbit of the Earth around the Sun, which might lead you to think a problem like that is "outside quantum mechanics" as we heard in this thread, but that's not true-- it's simply not the application of interest.
    Last edited by Ken G; 2018-Feb-16 at 10:27 PM.

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  3. #93
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    Ken G: A lie that I think that that gravity cannot be used with QM

    Quote Originally Posted by Ken G View Post
    No you don't, because you think one cannot use gravity with quantum mechanics.
    19 February 2018 Ken G: It is a lie that I think that that gravity cannot be used with quantum mechanics.
    You have known since 5 February 2018 that I think that is GR that cannot be included in QM.
    5 February 2018: QM is flat spacetime, GR is curved spacetime, thus GR cannot be used with quantum mechanics

    My post before the one you relied to was very clear.
    Quote Originally Posted by Reality Check View Post
    My real claims are:
    1. Textbook QM & gravity
      QM cannot include GR.
      QM can include Newtonian gravity.
      It is trivial to show that including Newtonian gravity gives a Bohr radius greater than the radius of the observable universe. That means that a gravity bound "atom" is bigger than the observable universe!
      ...
    A lie by quote mining when I did not answer a question abut gravity & QM.
    Quote Originally Posted by Reality Check View Post
    I understand "quantum mechanics ground states always require knowledge of the force or force constraints" because I was the one who first correctly named the Hamiltonian operator in the Schrodinger equation where those forces go to fix your misnaming (the energy operator is different). A university education in physics leading to an (unused) MSc. in solid state physics with a thesis involving QM means that I have known this basic physics for many years.
    My education is why I understand that quantum mechanics ground states always require knowledge of the force or force constraints. That is PHYS 101. My thesis was applying a "force constraint" in QFT to derive the transport properties of certain alloys. So we can plug in Newtonian gravitation into QM but not GR as I have been stating for a couple of weeks now.

    A lie because I was the one who found a textbook usage of Newtonian gravity in QM and that it produces unphysical ground states for bound systems - something you still have not acknowledged.
    8 sources with no G for any white dwarf "ground state" and the unphysical ground state from gravity in QM (bigger than the observed universe !)
    Last edited by Reality Check; 2018-Feb-18 at 08:37 PM.

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    All I see are questions that have been answered, and a delusion that this is the ATM forum. And quite frankly, I have no idea what you are trying to say with:
    Quote Originally Posted by Reality Check
    It is a lie that I think that that gravity cannot be used with quantum mechanics.
    You have known since 5 February 2018 that I think that is GR that cannot be included in QM.
    You can't even seem to be consistent with yourself. I think you mean you've known that since 5 February, though you won't admit it! (Even now you are trying to claim it is my knowledge about when you knew something that is what has changed! Amazing.) Your original objection was that when I said gravity causes the ground state of the white dwarf was that gravity can't be used in QM. Now you say it is only GR that can't. Why would you even think your moving the goal posts here is relevant? I don't care at all when you learned you were wrong, and what you now think is true, I care about what I've explained in this thread.

    Again: the ground state of the electrons in a white dwarf is very obviously controlled by the gravity of the white dwarf, and it is also very obvious that quantum mechanics can treat gravity, so none of your objections have any validity, they only serve to create confusion among people trying to understand degeneracy pressure. As it happens in white dwarfs, the gravity that controls the ground state of the electrons appears through their interaction with the ions, and the ions can be treated classically if one wishes to. These technical details in no way alter anything I've explained, as I already knew about them when I explained it. Anyone is free to either understand why the central concepts of degeneracy pressure usually do not require extreme conditions, or not understand that, I've done all I can.
    Last edited by Ken G; 2018-Feb-18 at 09:37 PM.

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    Quote Originally Posted by Ken G View Post
    ...(In particular, had Schroedinger predated Newton, he could have explained Kepler's laws of planetary orbits entirely within quantum mechanics, had he been able to arrive at the required potential energy function, which is actually quite easy.)
    Len Moran, Ken G goes very wrong here.
    He knows that the physics has to be known before it can be put into the Hamilton. The Hamilton contains a potential function. Had Schrödinger predated Newton, he would have needed to do what Newton did - show that an inverse square law gave Kepler's laws and thus the potential to put into the Hamiltonian. Without that all he could have done is say that an arbitrary potential would mean that orbits were quantized. Which is a bit of a problem because planets are not the only things astronomers knew about - there were also comets with their relatively irregular orbits which also orbit the Sun. Today we also know about asteroids and that we can put satellites into orbits with no sign of quantization.

    With Newtonian gravity and its potential function, Schrödinger would have derived that the Earth orbiting the Sun has the Bohr radius = (h bar^2)/GNmEMs. See J. J. Sakurai, Modern Quantum Mechanics second edition page 133, equation 2.7.15 for the simple case of an electron "orbiting" a neutron (in that case the ground state "orbit" is bigger than the universe). A look at the magnitudes involved suggests a ground state Earth orbiting inside an atomic nucleus !
    h bar = 10 -14 J.s/rad
    G = 6.67408 × 10-11 m3 kg-1 s-2
    mE = 5.97237×10^24 kg
    mS = 1.989 × 10^30 kg
    a0 ~ 10-95 meters.

    He repeats: 19 February 2018 Ken G: It is a lie that I think that that gravity cannot be used with quantum mechanics.
    Last edited by Reality Check; 2018-Feb-19 at 03:08 AM.

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    Ken G: A lie that the questions I asked have been answered

    Quote Originally Posted by Ken G View Post
    All I see are questions that have been answered, ...
    19 February 2018 Ken G: A lie that the questions I asked have been answered.
    I have asked him for the sources he had to back up his assertions. He not cited any of his sources at all to back up his assertions. The closest he has come is Google "white dwarf models" with an later implication that all of the results contain G when the very first result does not !
    Whoops misread the Google results - 29,000, not 9,000:
    1 of 29,600 results: Synthetic Colors and Evolutionary Sequences of Hydrogen- and Helium-Atmosphere White Dwarfs has no G or gravity in the model.
    2 of 29,600 results: Explosive Nucleosynthesis in Near-Chandrasekhar Mass White Dwarf Models for Type Ia Supernovae: Dependence on Model Parameters no gravity, a scan thru gives no G but I an sure Ken G can correct me.
    29,000 more results to be looked at and posted here for Ken G's education ?

    He repeats: 19 February 2018 Ken G: It is a lie that I think that that gravity cannot be used with quantum mechanics.
    I was clear on 5 February 2018 that it was GR that cannot be included in QM.
    Last edited by Reality Check; 2018-Feb-18 at 09:49 PM.

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    Citing sources is not a question, it's a self-delusion that this is the ATM forum. If you need sources to understand my explanation, you can find them yourself. I explained every point I made, if you don't know the physics behind it, look it up. When you need clarification, I've already given it. The questions you are posing now are irrelevant hijacks. At some point it is no longer worth my time.

    And please don't try to confuse people with your wrong analysis of solar system orbits. Anyone who knows quantum mechanics well knows it is straightforward to solve any classical mechanics problems with quantum mechanics, it's merely unnecessary to do so. Since you like references, here's a video that explains why all F=ma problems (like Kepler's laws) can be arrived at entirely with quantum mechanics: https://www.youtube.com/watch?v=Ofg4tDmyVvM
    (Your analysis is utterly wrong for two reasons:
    1) it has the wrong units, you should have squared the mass of the Earth, but more importantly
    2) you implied that the Earth's orbit should be treated as being in its ground state orbiting the Sun, but that's waaay wrong.)

    So Len, don't pay any attention, there is no problem using quantum mechanics to understand the orbit of the Earth. This is Bohr's "correspondence principle." The fact that the Earth is nowhere near its ground state orbit is merely the reason we would never want to use the concept of degeneracy pressure to understand the orbit of the Earth, but we very well can use it to understand the density of the Earth, to order of magnitude anyway. The electrons in the interior of the Earth do act to a rough approximation as being in a ground state controlled by gravity, which is why I answered the original OP by saying it is odd to take rock and crush it in order to make the degeneracy pressure concept relevant-- it already is, to a very rough approximation. In my view, this was all out there by post #7 in the thread, and the length of this thread is mostly pure hijack by one person who refused to understand this.
    Last edited by Ken G; 2018-Feb-18 at 10:09 PM.

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    I seem to recall that Reality Check saw GR as the best fit model of gravity and pointed out that unless we could incorporate this into the QM calculations then the predictive model was going to give a very flawed prediction if we start off with a premise that gravity has to be part of the predictive model. I think he agreed that Newtonian gravity could be plugged into the QM calculations, but presumably considered that this would not give an accurate prediction.

    It does seem to be the case that the gravitational aspect of the predictive model for a white dwarf can be worked out classically in terms of ions, so we may not even have to worry about how to plug gravity directly into the QM model, it can be done indirectly.

    So perhaps there shouldn't be the need to discuss the application of the correspondence principle if we can separate the classical from QM in doing the calculations for a white dwarf. But this doesn't seem to have been especially picked up, so maybe that's a bit of a simplistic understanding on my part. But putting to one side the possibility of being able to combine classical with QM indirectly, I am still left with the feeling that if GR could be seamlessly incorporated into QM in a manner that would suit Reality Check then all would be well. But apparently it cannot because QM can only deal with flat space, not curved space. But I'm left wondering, why not live with a less accurate Newtonian model if that can be plugged into QM? Just because GR cannot be plugged into QM doesn't mean that's the end of the story surely? If we find that a predictive model concerning this issue of degenerate pressure gives the best results when gravity is included in those instances where gravity is very dominant then couldn't we be satisfied with using the Newtonian model? I mean to say, couldn't the fact that GR can't be used with QM be indicative of a deeper problem with GR and QM that just doesn't show up with Newtonian gravity?

    At the end of the day, we hypothesize using a mix of models and we make predictions based upon that mix. The models may not be perfect, but we know that models are not some kind of absolute truth of anything, they relate only to what comes out of them when tested. So if a model of degenerate pressure shows a dependency on gravity, then lets model that in any way that works even if it means we have to use Newtonian gravity instead of GR. The fact that GR doesn't fit with QM should not I think be taken as indicating the hypothesis concerning gravity and degenerate pressure is wrong necessarily, there could be other reasons why it doesn't fit. No model is a holy grail of the physical world.

    So we seem to have competing models being argued over, but I am a bit uneasy over rejection of one model occurring because a particular model of gravity doesn't fit with QM, it would be different if the model couldn't use any model of gravity, that surely would be a non starter, but that's not the case here, the model in question works with Newtonian gravity. That doesn't mean it is a true picture of what "really is" any more than it would if GR could be plugged into QM, rather it gives us a working predictive model incorporating descriptive mechanisms and nothing more than that.

    But I will concede that I am having difficulty in following the twists and turns of this thread, so it is entirely conceivable that I have missed crucial areas of discussion, so the above needs to viewed in that context.

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    Quote Originally Posted by Ken G View Post
    Citing sources is not a question, it's a self-delusion that this is the ATM forum.
    No one who can read thinks this is the ATM forum because " Forum -> Science and Space -> Science and Technology" is at the top of the page. Part of the expectation in mainstream science and in the real world is that a person who makes an unsupported assertion needs to support it. The best support for an unsupported scientific assertion in science is citations of the scientific literature. It is unreasonable to demand that people look for something that might not exist. Especially when the evidence so far is that it does not exist. Thus:
    8 Feb 2018 Ken G: Give mainstream sources for the "the standard model of a white dwarf" that includes gravity in QM.
    13 Feb 2018 Ken G: Give your sources for those systems whose QM ground state is known by including gravity in QM.
    15 February 2018 Ken G: How many of the > 9000 results did you read to get your exception that everyone has G?

  10. #100
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    Quote Originally Posted by Len Moran View Post
    I seem to recall that Reality Check saw GR as the best fit model of gravity and pointed out that unless we could incorporate this into the QM calculations then the predictive model was going to give a very flawed prediction if we start off with a premise that gravity has to be part of the predictive model. I think he agreed that Newtonian gravity could be plugged into the QM calculations, but presumably considered that this would not give an accurate prediction.
    That is close to what I have been saying for the last couple of weeks, Len Moran. The only thing is that my point about GR is that it is impossible to include it within QM, especially n the simplistic way Ken G wants (plug it into the Hamiltonian in the Schrödinger equation). There are fundamental mathematical issues with that. Theorists have been struggling with including GR in QM or vice versa for many decades and have not succeeded yet.

    The textbook physics is that we can neglect Newtonian gravity in QM except for what look like rare circumstances. J. J. Sakurai, Modern Quantum Mechanics second edition covers "Gravity in Quantum Mechanics" in less than 3 pages. Page 133 gives the example of gravity-induced quantum interference first seen in 1975. J. J. Sakurai was an expert in QM rather than astrophysics however we would expect him and later editors to mention if gravity in QM was known to be used in astrophysics.

    I did a calculation for the Earth orbiting the Sun and that gave a ground state "orbit" with a Bohr radius of a0 ~ 10-95 meters. The Bohr radius is the most probable distance or "position of maximum probability density".
    Last edited by Reality Check; 2018-Feb-19 at 02:23 AM.

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    Ken G : Ignorance that F=ma is "like Kepler's laws"

    Quote Originally Posted by Ken G View Post
    Since you like references, here's a video that explains why all F=ma problems (like Kepler's laws) can be arrived at entirely with quantum mechanics: https://www.youtube.com/watch?v=Ofg4tDmyVvM
    19 February 2018 Ken G: Ignorance that F=ma is "like Kepler's laws".
    Kepler's laws of planetary motion were later summarized by Newton's law for gravitation only. F=ma is Newton's second law for any force. These are two different laws. The forces in these Newtonian laws can be put equal but that is not "like Kepler's laws"., e.g. we can do this for freely falling bodies.
    Last edited by Reality Check; 2018-Feb-19 at 02:44 AM.

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    Question Ken G: Are you just guessing about gravity in QM for the Earth or do you have sources

    Quote Originally Posted by Ken G View Post
    (Your analysis is utterly wrong for two reasons:
    1) it has the wrong units, you should have squared the mass of the Earth, but more importantly
    2) you implied that the Earth's orbit should be treated as being in its ground state orbiting the Sun, but that's waaay wrong.)
    Actually read my post. mE is the mass of the Earth, not the squared mass of the Earth. Squaring it is part of what gives the low value of radius of the explicitly stated ground state of the Earths orbit. This is the state that you have been going on about for weeks now for white dwarfs so I gave the result for it. But now we have a new question!

    You assert that the Earth is not in a ground state. But could the first excited state be too high for the Earth to occupy it? This implies that you know the energy of that first excited state and maybe the other excited states.
    19 February 2018 Ken G: Are you just guessing about gravity in QM for the Earth or do you have sources? If you have sources give an example.
    The track record in this thread says you are guessing but you may surprise me.

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    Quote Originally Posted by Reality Check View Post
    That is close to what I have been saying for the last couple of weeks, Len Moran. The only thing is that my point about GR is that it is impossible to include it within QM, especially n the simplistic way Ken G wants (plug it into the Hamiltonian in the Schrödinger equation). There are fundamental mathematical issues with that. Theorists have been struggling with including GR in QM or vice versa for many decades and have not succeeded yet.

    The textbook physics is that we can neglect Newtonian gravity in QM except for what look like rare circumstances.
    So, presumably you are saying that if there is no mathematical route that would connect GR with QM then it poses a severe problem for any hypothesis that models the forces required for degenerate pressure as being gravitational in those circumstances where gravity is a very dominating force, a problem in the sense that it will not be possible to form a quantitative predictive model using our best model of gravity. The hypothesis could only build a descriptive model with a less than vigorous (you might not agree that there is any) mathematical underpinning.

    But whereas I was suggesting that perhaps we could accept an approximate predictive model using Newtonian gravity being plugged into QM, you would say that such a suggestion would not even give us an approximate predictive model because there is no classical model of gravity that can be plugged into QM in order to give a quantitative predictive model of degenerate pressure and gravity combined.

    So it does seem (to me at any rate) that the disagreement concerns the degree (if any) to which a quantative model can be established that is able to combine gravity and QM with respect to the effect/cause/influence that gravity has on degenerate pressure. Ken clearly considers that it is possible to have such a model, you consider that you cannot. Your view is based upon textbook physics, Ken looks to the way physics is practiced in order to pragmatically construct working models.

    I'm not sure how this thread can bridge that divide.
    Last edited by Len Moran; 2018-Feb-19 at 09:38 AM.

  14. #104
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    Quote Originally Posted by Len Moran View Post
    I seem to recall that Reality Check saw GR as the best fit model of gravity and pointed out that unless we could incorporate this into the QM calculations then the predictive model was going to give a very flawed prediction if we start off with a premise that gravity has to be part of the predictive model. I think he agreed that Newtonian gravity could be plugged into the QM calculations, but presumably considered that this would not give an accurate prediction.
    Yes, that is indeed what he seemed to think, in which case he should take that bad physics to ATM. Mainstream white dwarf models routinely use Newtonian gravity to set the ground state of the white dwarf electrons, via the need to avoid charge separation from the ions, and get excellent results.
    It does seem to be the case that the gravitational aspect of the predictive model for a white dwarf can be worked out classically in terms of ions, so we may not even have to worry about how to plug gravity directly into the QM model, it can be done indirectly.
    Yes, we can indirectly solve for the ground state of white dwarf electrons. That's why I said gravity causes the ground state of white dwarf electrons to be what it is, and the ATM proponent blew a gasket.

    So perhaps there shouldn't be the need to discuss the application of the correspondence principle if we can separate the classical from QM in doing the calculations for a white dwarf.
    We don't need the correspondence principle here, but we have it all the same. Claims that it doesn't apply here are a hijack of what matters.
    But this doesn't seem to have been especially picked up, so maybe that's a bit of a simplistic understanding on my part. But putting to one side the possibility of being able to combine classical with QM indirectly, I am still left with the feeling that if GR could be seamlessly incorporated into QM in a manner that would suit Reality Check then all would be well.
    All is already well, just use Newtonian gravity and don't care if it bothers Reality Check.
    But apparently it cannot because QM can only deal with flat space, not curved space.
    Well you can certainly do quantum field theory in curved spacetime, that's why you have heard of "Hawking radiation." But really, who cares, one needs neither GR nor quantum field theory to understand white dwarfs.
    But I'm left wondering, why not live with a less accurate Newtonian model if that can be plugged into QM?
    Of course.
    At the end of the day, we hypothesize using a mix of models and we make predictions based upon that mix.
    Bingo.
    Last edited by Ken G; 2018-Feb-19 at 04:24 PM.

  15. #105
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    Quote Originally Posted by Reality Check View Post
    Actually read my post. mE is the mass of the Earth, not the squared mass of the Earth.
    Yes I know, but it should have been the squared mass, so your answer is nonsense. If you can't even see your answer has the wrong units, the situation is obviously hopeless. But that error is essentially typographic, the real problem is that the Earth isn't orbiting in its ground state, so your entire calculation that assumes it is is irrelevant. Impossibly, you seem to think that because I am correctly arguing that white dwarfs are near their ground state, that this somehow requires the Earth's orbital ground state should apply too! And I can't even begin to understand how you got from my statement that F=ma can be used to understand Kepler's laws to thinking I said the reverse. All you are proving is that you cannot follow basic logic, and your only device for argumentation is misquotation.
    Last edited by Ken G; 2018-Feb-19 at 04:28 PM.

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    Quote Originally Posted by Ken G View Post
    Yes I know, but it should have been the squared mass, ....
    You are right, I missed out the squared term in the textbook that you are still denying. The corrected equation to plug those constants into
    Quote Originally Posted by Reality Check View Post
    Bohr radius = (h bar^2)/GNmE^2Ms. See J. J. Sakurai, Modern Quantum Mechanics second edition page 133, equation 2.7.15 for the simple case of an electron "orbiting" a neutron (in that case the ground state "orbit" is bigger than the universe).
    Do a magnitude only calculation: h bar = 10^-14, G = 10^-11, mE squared ~10^49, mS ~ 10^30 = -14 + 11 - 49 - 30 = 82.
    a0 ~ 10-82 meters

    The calculation still gives the QM "ground state" of the Earth with a radius still inside an atomic nucleus !
    Last edited by Reality Check; 2018-Feb-19 at 08:16 PM.

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    So what? The Earth's orbit is not in its ground state. You can boldface whatever you want, your posts are still irrelevant. Stop hijacking the thread, some readers are still trying to understand degeneracy pressure.

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    Exclamation Ken G: A lie that I an "ATM proponent" when I have been citing mainstream science

    Quote Originally Posted by Ken G View Post
    Yes, that is indeed what he seemed to think, in which case he should take that bad physics to ATM.
    Fantasy or ignorance from Ken G.
    It is mainstream science that GR is the best fit model of gravity. That is what the physical evidence matching GR says, e.g. test of general relativity.

    An actual lie needs to be recorded.
    20 February 2018 Ken G: A lie that I an "ATM proponent" when I have been citing mainstream science.
    8 mainstream sources with no G for any white dwarf "ground state" and the unphysical ground state from gravity in QM (bigger than the observed universe !)
    Last edited by Reality Check; 2018-Feb-19 at 08:42 PM.

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    Ignoring the absurd hijack, here is the point of relevance:
    When self-gravity is the containment force that is responsible for the ground state of a system of electrons embedded in ions, as for a star, the density will be very high. This is because gravity is so weak relative to other forces that it only controls the ground state for very massive objects, and then the ground-state density will be very high because gravity can get quite strong for large masses (since it is always an attraction, unlike electric forces). For electric forces, ground states typically appear at mundane everyday densities, like the near-ground-states all around us right now. Now, since the concept of "degeneracy pressure" is valid any time we have electrons near their ground state, we should not associate degeneracy pressure with high density, unless we are interested in systems that are contained by gravity and are near their ground states. Like white dwarfs. Unfortunately, so many people have only heard of that specific (and relatively unimportant) application of degeneracy pressure, they are often under the misconception that degeneracy pressure always involves very high density. I hope I've clarified why that is not true, and if so, ignore the posts that are trying to sow confusion by claiming I said a bunch of things I did not. Goodness, who really cares how Reality Check imagines general relativity is related to quantum mechanics? I certainly don't, nor did it have anything to do with the above point.
    Last edited by Ken G; 2018-Feb-19 at 08:45 PM.

  21. #111
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    Quote Originally Posted by Ken G View Post
    When self-gravity is the containment force that is responsible for the ground state of a system of electrons embedded in ions, as for a star, the density will be very high......
    Repeated, unsupported "ground state" assertions and ignorance.

    For others:
    This is the mainstream science for a white dwarf.
    This paradox was resolved by R. H. Fowler in 1926 by an application of the newly devised quantum mechanics. Since electrons obey the Pauli exclusion principle, no two electrons can occupy the same state, and they must obey Fermi–Dirac statistics, also introduced in 1926 to determine the statistical distribution of particles which satisfy the Pauli exclusion principle.[39] At zero temperature, therefore, electrons can not all occupy the lowest-energy, or ground, state; some of them would have to occupy higher-energy states, forming a band of lowest-available energy states, the Fermi sea. This state of the electrons, called degenerate, meant that a white dwarf could cool to zero temperature and still possess high energy.[38][40]

    Compression of a white dwarf will increase the number of electrons in a given volume. Applying the Pauli exclusion principle, this will increase the kinetic energy of the electrons, thereby increasing the pressure.[38][41] This electron degeneracy pressure supports a white dwarf against gravitational collapse. The pressure depends only on density and not on temperature. Degenerate matter is relatively compressible; this means that the density of a high-mass white dwarf is much greater than that of a low-mass white dwarf and that the radius of a white dwarf decreases as its mass increases.[1]
    Gravity causes matter to be compressed and produces the density of free electrons in all stars. The Fermi statistics of the occupation of all states in this free electron gas gives an electron degeneracy pressure. There is also thermal pressure. The Sun is stable because the compression from gravity is balanced by the pressure from thermal and election degeneracy pressure. A white dwarf is stable because the compression from gravity is balanced by the pressure from thermal and election degeneracy pressure. The difference is the balance between the 2 pressures. As gravity increases, free electron density gets higher and electron degeneracy pressure increases. If gravity is string enough then electron degeneracy pressure dominates.

    The derivation of electron degeneracy pressure does not involve gravity, just the ground state of the free electron gas or even the ions!
    8 sources with no G for any white dwarf "ground state" and the unphysical ground state from gravity in QM (bigger than the observed universe !)

    As anyone can read the concept of electron degeneracy pressure is valid any time we have free electrons! The only time electron degeneracy pressure is zero is when the free electron density is zero.
    Last edited by Reality Check; 2018-Feb-19 at 09:08 PM.

  22. #112
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    Quote Originally Posted by Len Moran View Post
    So, presumably you are saying that if there is no mathematical route that would connect GR with QM...
    I am saying that Ken G's assertion that gravity can be included in Schrodinger's equation totally fails with GR. That is obvious. Which leaves his assertion as that Newtonian gravity is included in QM for white dwarfs which he has failed to support for a couple of weeks now and counting.
    I am saying that there is no current "mathematical route that would connect GR with QM".
    I am stating the mainstream science that degeneracy pressure is a quantum phenomena originating from the Pauli exclusion principle in QM. Degeneracy pressure is not gravitational in the sense of gravity being plugged into QM. Electron degeneracy pressure is related to the density of free electrons. The density of free electrons is related to the density of matter, e.g. in a star. The density of matter in a star is related to gravity.

    I have said several times that we can plug Newtonian gravity into QM. But there is no evidence that this is used anywhere in astrophysics, especially for white dwarfs. That makes sense. Stars are very macroscopic bodies. QM for macroscopic bodies reduces to classical mechanics. Fire bullets through in a double slit experiment and they should act like particles, not waves (we can detect interference for particles up to the size of large molecules). A calculation for the Earth and Sun suggests that the Earth is a free "particle. That was done by replacing the electrostatic potential with a gravitational potential in the derivation for a hydrogen atom. The difference between energy levels still goes as 1/n^2 (n is the principal quantum number). A ground state Bohr radius ~10-82 meters implies an enormous quantum number n for the Earth's actual orbit. That is an infinitesimal energy difference between energy states and a region where maybe even a single photon would free the Earth.

  23. #113
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    Quote Originally Posted by Reality Check View Post
    I am saying that Ken G's assertion that gravity can be included in Schrodinger's equation totally fails with GR.
    Nonsensical logic. If I said gravity can be included in Newton's laws, you could equally say my obviously true statement "totally fails with GR," and it would be just as irrelevant to this thread.
    Which leaves his assertion as that Newtonian gravity is included in QM for white dwarfs which he has failed to support for a couple of weeks now and counting.
    I said Newtonian gravity controls the ground state in a white dwarf, which it does. I told you how you can tell, which is that G appears in the ground state structure of a white dwarf, making the point quite obvious. I also said gravity can be included in QM, which it can. All the rest is just in your imagination, no one else should care and no one else thinks this is the ATM forum.
    Repeated, unsupported "ground state" assertions and ignorance.
    I don't mind if you cannot understand why a white dwarf is near its ground state, and how that is used to understand its structure, but please don't undermine other people's attempts to understand this. Fortunately, Len Moran's last few posts show he has escaped confusion from your failure to follow my logic, so I guess I needn't worry. Len, you have it now, so don't let anyone get you confused. You have followed the logic perfectly, is there anything else you are still unclear about? Do you now understand where there is no direct connection between degeneracy pressure and high density?
    Last edited by Ken G; 2018-Feb-19 at 10:15 PM.

  24. #114
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    Quote Originally Posted by Ken G View Post
    Nonsensical logic...
    Basic English: You asserted that gravity (any gravity at all not specifically Newtonian) can be included in QM, specifically the Schrodinger equation.
    Basic science: The best fitting model for gravity is GR which cannot be included in QM.
    Basic logic: Thus you could not be talking about GR being included in QM. The "gravity" is Newtonian gravity.

    What is becoming a persistent fantasy of "G appears in the ground state structure of a white dwarf".
    8 Feb 2018 Ken G: Give mainstream sources for the "the standard model of a white dwarf" that includes gravity in QM.
    13 Feb 2018 Ken G: Give your sources for those systems whose QM ground state is known by including gravity in QM.
    15 February 2018 Ken G: How many of the > 9000 29,000 results did you read to get your expectation that every one has G?

    Lee Moran: Here is the mainstream science that Ken G is denying. Electron degeneracy pressure is derived using the Fermi statistics of a non-interacting electron gas (not using gravity or any ground state or even the Schrodinger equation).
    Properties of Degenerated Fermi-Gas in Astrophysics by Hsin-Yu Chen (PDF)
    What we have is the quantum version of a ideal gas. In an ideal gas the particles have a continuous distribution of energies. At T = 0, a classical ideal gas would have no energy and no pressure. For a quantum gas the energy distribution is quantized. For a Fermi gas, there is also the Pauli Exclusion principle that fermions cannot have the same state. At T = 0, a free electron gas fills its energy states up to the Fermi surface (the article is about condensed matter but applies to any Fermi gas). A Fermi gas has energy and so pressure even at T = 0. For T > 0 electrons get promoted to above the Fermi surface. This is what the Wikipedia article on white dwarfs is describing with citations to the published scientific literature.
    Such densities are possible because white dwarf material is not composed of atoms joined by chemical bonds, but rather consists of a plasma of unbound nuclei and electrons. There is therefore no obstacle to placing nuclei closer than normally allowed by electron orbitals limited by normal matter.[23] Eddington wondered what would happen when this plasma cooled and the energy to keep the atoms ionized was no longer sufficient.[38] This paradox was resolved by R. H. Fowler in 1926 by an application of the newly devised quantum mechanics. Since electrons obey the Pauli exclusion principle, no two electrons can occupy the same state, and they must obey Fermi–Dirac statistics, also introduced in 1926 to determine the statistical distribution of particles which satisfy the Pauli exclusion principle.[39] At zero temperature, therefore, electrons can not all occupy the lowest-energy, or ground, state; some of them would have to occupy higher-energy states, forming a band of lowest-available energy states, the Fermi sea. This state of the electrons, called degenerate, meant that a white dwarf could cool to zero temperature and still possess high energy.[38][40]

    Compression of a white dwarf will increase the number of electrons in a given volume. Applying the Pauli exclusion principle, this will increase the kinetic energy of the electrons, thereby increasing the pressure.[38][41] This electron degeneracy pressure supports a white dwarf against gravitational collapse. The pressure depends only on density and not on temperature. Degenerate matter is relatively compressible; this means that the density of a high-mass white dwarf is much greater than that of a low-mass white dwarf and that the radius of a white dwarf decreases as its mass increases.[1]
    An important point is that not all fermions are in the ground state or even in a vague "near ground state".
    Last edited by Reality Check; 2018-Feb-19 at 11:40 PM.

  25. #115
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    Quote Originally Posted by Reality Check View Post
    I am stating the mainstream science that degeneracy pressure is a quantum phenomena originating from the Pauli exclusion principle in QM. Degeneracy pressure is not gravitational in the sense of gravity being plugged into QM. Electron degeneracy pressure is related to the density of free electrons. The density of free electrons is related to the density of matter, e.g. in a star. The density of matter in a star is related to gravity.

    I have said several times that we can plug Newtonian gravity into QM. But there is no evidence that this is used anywhere in astrophysics, especially for white dwarfs. That makes sense. Stars are very macroscopic bodies. QM for macroscopic bodies reduces to classical mechanics. Fire bullets through in a double slit experiment and they should act like particles, not waves (we can detect interference for particles up to the size of large molecules). A calculation for the Earth and Sun suggests that the Earth is a free "particle. That was done by replacing the electrostatic potential with a gravitational potential in the derivation for a hydrogen atom. The difference between energy levels still goes as 1/n^2 (n is the principal quantum number). A ground state Bohr radius ~10-82 meters implies an enormous quantum number n for the Earth's actual orbit. That is an infinitesimal energy difference between energy states and a region where maybe even a single photon would free the Earth.
    Ok, I misunderstood your context of Newtonian gravity in relation to QM. What you actually said (as you quote above) was that although Newtonian gravity can be plugged into QM, you know of no evidence that this is used anywhere in astrophysics. I misconstrued your post in that I thought you were implying that Newtonian gravity could not be plugged into QM and thus, far from giving my suggested approximate (an approximation I suggested as an acceptable best given the impossibility of plugging our best model (GR) into QM) predictive model of degeneracy pressure and gravity, it would in fact yield no predictive model.

    I'm not quite sure where that leaves me because I am wondering now if in fact Newtonian gravity could provide an acceptable predictive model of degenerate pressure and gravity by being plugged into QM. I entirely accept your statement that you know of no evidence to show that Newtonian gravity has ever been used in this way, but although that in itself is an indicator that suggests physicists have never seen the need to include it, it doesn't preclude the utility of using it in that way in particular circumstances. And maybe, white dwarf stars could make use of it if we hypothesise that gravity acts as a constraining force at the quantum level of degenerate pressure. That begs the question of what status we give to such an hypothesis, but I'm not going there - the fact is that a physicist on this board has chosen to offer his insight into what might be a better model of degeneracy and gravity. I don't know if that's ATM or not - but its worth listening to I think (and of course questioning as you are doing).

    What bothers me more than the ATM (or not) issue is the legitimacy of plugging Newtonian gravity into QM and thus the legitimacy of the resultant model - you have mentioned some extreme quantitative outcomes from doing just that. If it could be shown that it is a legitimate exercise to plug Newtonian gravity into QM (accepting that there will be shortcomings because we are not plugging our best model of gravity into QM) then that seems to me to be a legitimate scientific endevour that awaits testing. Should we reject this approach just because it is impossible to plug GR into QM? I know that we generally expect new models to be able to assimilate all of the predictions of older models, so I suppose you could argue that if Newtonian gravity can be plugged into QM, then GR should be able to accommodate that fact and more, but it seems it can't accommodate it. I'm not sure about that - Newtonian gravity seems to be such a good model, it seems to me to be wrong to reject its use within QM simply because GR doesn't work with QM, but I'm no authority on that aspect and never will be.

    But of course it's a different matter entirely to reject the plugging in of Newtonian gravity into QM if what we get out of it is nonsensical, but I'm not sure that we actually have arrived at that particular place.

    Just for reference, I think it is useful to place together the two competing descriptive accounts of degeneracy and white dwarf stars.

    Ken:

    When self-gravity is the containment force that is responsible for the ground state of a system of electrons embedded in ions, as for a star, the density will be very high. This is because gravity is so weak relative to other forces that it only controls the ground state for very massive objects, and then the ground-state density will be very high because gravity can get quite strong for large masses (since it is always an attraction, unlike electric forces). For electric forces, ground states typically appear at mundane everyday densities, like the near-ground-states all around us right now. Now, since the concept of "degeneracy pressure" is valid any time we have electrons near their ground state, we should not associate degeneracy pressure with high density, unless we are interested in systems that are contained by gravity and are near their ground states. Like white dwarfs. Unfortunately, so many people have only heard of that specific (and relatively unimportant) application of degeneracy pressure, they are often under the misconception that degeneracy pressure always involves very high density.


    Reality check:

    This paradox was resolved by R. H. Fowler in 1926 by an application of the newly devised quantum mechanics. Since electrons obey the Pauli exclusion principle, no two electrons can occupy the same state, and they must obey Fermi–Dirac statistics, also introduced in 1926 to determine the statistical distribution of particles which satisfy the Pauli exclusion principle.[39] At zero temperature, therefore, electrons can not all occupy the lowest-energy, or ground, state; some of them would have to occupy higher-energy states, forming a band of lowest-available energy states, the Fermi sea. This state of the electrons, called degenerate, meant that a white dwarf could cool to zero temperature and still possess high energy.[38][40]

    Compression of a white dwarf will increase the number of electrons in a given volume. Applying the Pauli exclusion principle, this will increase the kinetic energy of the electrons, thereby increasing the pressure.[38][41] This electron degeneracy pressure supports a white dwarf against gravitational collapse. The pressure depends only on density and not on temperature. Degenerate matter is relatively compressible; this means that the density of a high-mass white dwarf is much greater than that of a low-mass white dwarf and that the radius of a white dwarf decreases as its mass increases.
    [1]

    Quote Originally Posted by Reality Check
    I am stating the mainstream science that degeneracy pressure is a quantum phenomena originating from the Pauli exclusion principle in QM. Degeneracy pressure is not gravitational in the sense of gravity being plugged into QM. Electron degeneracy pressure is related to the density of free electrons. The density of free electrons is related to the density of matter, e.g. in a star. The density of matter in a star is related to gravity.
    Last edited by Len Moran; 2018-Feb-20 at 01:13 AM.

  26. #116
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    Quote Originally Posted by Len Moran View Post
    I'm not quite sure where that leaves me because I am wondering now if in fact Newtonian gravity could provide an acceptable predictive model of degenerate pressure and gravity by being plugged into QM. I entirely accept your statement that you know of no evidence to show that Newtonian gravity has ever been used in this way, ...
    Where this leaves us is that in mainstream science, Newtonian gravity in QM has nothing to do with degeneracy pressure. Degeneracy pressure has its origin in the quantum mechanics of fermions. Take a free electron gas and it has pressure because the quantum Pauli exclusion principle means the electrons fill up different energy levels from the ground state up to a certain level. Do the math and we find that electron degeneracy pressure depends only on the free electron density.

    What Newtonian gravity outside of QM does is confine matter to give that free electron density.

    Plugging Newtonian gravity into QM is not that nonsensical. There are seemingly rare circumstances where it gives a measurable effect, e.g. gravity-induced quantum interferences was measured in free-falling neutron beams in 1975. But stars are a lot bigger than neutrons ! QM reduces to classical mechanics for macroscopic objects.

    What you quote from me is what I quoted from the Wikipedia white dwarf article which is textbook physics (but it is wise to check the citations). The R. H. Fowler paper from 1926 is available.
    Ken G is competing with the "textbook" physics in Wikipedia, mainstream science from a couple of papers and an actual QM textbook.

    You may also want to look at the definition of Self-gravitating Bodies
    A self-gravitating body is one that is held together by the gravitational attraction of its constituent parts. For example, the gravitational attraction between the atoms that make up a star counteract the high temperatures and pressures that would otherwise expand and dissipate it. Self-gravity is also responsible for the continued existence of objects such as gas clouds, stellar clusters, galaxy groups and clusters, and even the Universe as a whole.
    A star such as the Sun does not have very high density. Its average density is a quarter that of Earth. Models show that the low density at the photosphere rises to about 150 times the density of water at the center (12.4 × Earth).

    It is white dwarfs that are measured to have very high densities of many thousands of times greater than the Sun. This was measured soon after their discovery which lead to the exchange between Eddington and Fowler that gave us the first derivation of electron degeneracy pressure.
    Last edited by Reality Check; 2018-Feb-20 at 02:24 AM.

  27. #117
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    Quote Originally Posted by Len Moran View Post
    I'm not quite sure where that leaves me because I am wondering now if in fact Newtonian gravity could provide an acceptable predictive model of degenerate pressure and gravity by being plugged into QM.
    It can-- consider a first approximation of a neutron star.
    I entirely accept your statement that you know of no evidence to show that Newtonian gravity has ever been used in this way,
    What Reality Check doesn't know is a lot. Don't let that lead you to his misconceptions.

  28. #118
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    Quote Originally Posted by Len Moran View Post
    Just for reference, I think it is useful to place together the two competing descriptive accounts of degeneracy and white dwarf stars.
    There is nothing "competing" in those two accounts, that's all how Reality Check has confused you, exactly as I feared. Those two accounts are entirely consistent with each other. If you tell me where you see any tension between them, I will be happy to clarify why there is none. I understand both accounts, Reality Check, only one, so he does not realize they are saying the same thing. I do, and would be happy to help you get there too if you tell me why you think there is any conflict between them.

    ETA: Above all, don't get roped into his absurd claim that I ever said degeneracy pressure comes from gravity. I have no idea where he got that, but not from me.
    Last edited by Ken G; 2018-Feb-20 at 06:55 AM.

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    Okay and that is a good place to end this squabble.
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