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

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## Are you stating there are systems whose QM ground state is known by including gravity

Originally Posted by Ken G
1) To know the ground state of any system, you need to understand the forces. And yes, one of them can be gravity.
An implication that there are systems whose QM ground state is known by including gravity in QM. So:
1a) Are you stating there are systems whose QM ground state is known by including gravity in QM, e.g. in the Hamiltonian of the Schrodinger equation?
1b) If yes than give your sources for those systems whose QM ground state is known by including gravity in QM.
N.B. This is a request for your sources that you used to make your assertion.

However I did my own research. My suspicion was that any solution of the Schrodinger equation with a gravitational potential would lead to physically insignificant results because there is that pesky gravitational constant G with its small value. On the other hand, we have many experiments that can detect very small effects. I Googled for 'Schrödinger equation gravitational potential" and found a Q&A that cited one of the few QM textbooks that look at gravity & the Schrödinger equation and it is available online! Look for "J. J. Sakurai - Modern Quantum Mechanics". The second edition has 3 pages on Gravity in Quantum Mechanics starting on page 131. Page 132 gives an example "to appreciate the difficulty involved in seeing gravity in bound-state problems". The Bohr radius for a bound electron and neutron is around 1013 light years - much larger than the estimated size of the universe. But there is the possibility of detecting gravity-induced quantum interference.

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Originally Posted by Reality Check
Post 34 is simple stuff that I already know, mostly about particles in a box.
Excellent, then you actually don't disagree with anything I've been saying. I thought so. Yet impossibly, you then ask:
1a) Are you stating there are systems whose QM ground state is known by including gravity in QM, e.g. in the Hamiltonian of the Schrodinger equation?
Obviously yes.
1b) If yes than give your sources for those systems whose QM ground state is known by including gravity in QM.
Google "white dwarf models." Take any, they all do the same thing. The only wrinkle is that you have to use a fluid description (which treats the electrons and ions together), which simplifies having to write the separate forces on the ions and electrons. This is completely standard.

To expand on this technical detail, what is actually happening in both a white dwarf and a non-degenerate star like the Sun is that the force that keeps the electrons from expanding is an electric force that prevents charge separation from the ions. But since the electric field produces an opposite force on ions and electrons,
the net electric force adds to zero on any collection of particles with no net charge, which is what you get. So it ends up being gravity that determines the ground state of the fluid, and you can neglect the electric forces if you simply treat the fluid. The fluid pressure comes, as usual, from the kinetic energy density, and the kinetic energy is in the electrons when degenerate. The gravitational potential energy comes from the ions. In this way, gravity controls the ground state of the electrons,
via the need for no charge separation. In particular, the value of G sets the attributes of a white dwarf if you have all the other parameters.
However I did my own research. My suspicion was that any solution of the Schrodinger equation with a gravitational potential would lead to physically insignificant results because there is that pesky gravitational constant G with its small value.
Ah me, back to that again. Your research was not very good, it almost sounds like you think changing the "pesky" value of G would not change the ground state of a white dwarf! It doesn't make sense to me that you could possibly think that, yet it also doesn't make sense to me that you could claim what you just said, if you didn't. So you see my quandary, I still have absolutely no idea what you are on about. Everything I'm trying to say is nicely summarized in the post you just said you agreed with, so you are really wasting everyone's time now.
Last edited by Ken G; 2018-Feb-13 at 02:14 AM.

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Originally Posted by Reality Check
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.
No one who can actually read would ever think I said any such thing. Just ask yourself this: why did you start your quotation marks after the phrase "degeneracy pressure" and not before? Answer: because it would be ridiculous to put them before, as you would be quoting something I never said and never implied. So your entire "logic" rests on abuse of quotation. There is no need for any forces in a white dwarf other than gravity, and it would have the same structure, if collisions alone maintained the absence of separation between ions and electrons. In actual fact, it is electric forces, but there is no significant potential energy associated with those forces because something called the "deBye length" is too small to allow a significant electric potential. Hence, the only potential energy that matters in a white dwarf is gravitational potential energy, which is precisely the thing that distinguishes that application of degeneracy pressure from the more mundane everyday (and far more important) applications I have been talking about this whole thread. In everyday materials, the electric potential energy is much more important than gravitational potential energy, but in white dwarfs, it is the other way around. That is why white dwarfs have high density, they are the ground states ruled by gravity. Metals have their ground states ruled by electric forces, as do atoms and molecules themselves. This is the entire reason that density has nothing to do with the importance of degeneracy, as I have been saying all along.
Fermi gases have degeneracy pressure in any circumstances.
Wrong. What people mean by "degeneracy pressure" (and it would be much better understood if people realized this is completely mundane gas pressure, not some new or strange form of pressure) applies only when close to the ground state. Fermi gases nowhere near their ground state, such as the electrons in the Sun right now, do not exhibit "degeneracy pressure." You can tell because the formula for degeneracy pressure has nothing to do with the Sun. More to the point, and this is something I keep having to repeat, the only thing that "degeneracy pressure" means is the special case of normal gas pressure that all gases have due to their kinetic energy density that applies when the gas is near its ground state. You just don't understand degeneracy pressure, you merely vacillate between claiming that you already know everything I'm saying, and then making completely wrong claims like this one.
Last edited by Ken G; 2018-Feb-13 at 02:13 AM.

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## Give your sources for those systems whose QM ground state ...

Originally Posted by Ken G
Obviously yes.
...
Now we have a confirmed assertion but still you do not give your sources.
13 February 2018 Ken G: Give your sources for those systems whose QM ground state is known by including gravity in QM.

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And I told you to do it yourself. As I said, any source at all will do, and I explained exactly how they all work just above. Look yourself and don't pretend this is the ATM forum. You said you did some research already, so I'll tell you the key thing to look for: the way the "pesky" value of G fundamentally affects the attributes of a white dwarf. That's the only hint you get from me, maybe someone else will explain it to you more completely than I did above.
Last edited by Ken G; 2018-Feb-13 at 02:37 AM.

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Originally Posted by Ken G
And I told you to do it yourself.
And I want to verify that you have read somewhere, sometime something that supports your assertion.
13 February 2018 Ken G: Give your sources for those systems whose QM ground state is known by including gravity in QM.

Originally Posted by Ken G
As I said, any source at all will do, ...
Any source at all?
The first link Google gives me (your results may vary which is another reason for you to supply your sources) is Synthetic Colors and Evolutionary Sequences of Hydrogen- and Helium-Atmosphere White Dwarfs. So "any source at all will do" is wrong. The rest of the first page is
• Comparison of White Dwarf Models with STIS Spectrophotometry ...
• Isochrones and Luminosity Functions for Old White Dwarfs
• Explosive Nucleosynthesis in Near-Chandrasekhar Mass White Dwarf ...
• Hubble's constant and exploding carbon–oxygen white dwarf models ...
• Pulsation Periods of Rotating White Dwarf Models
• White Dwarf Models of Supernovae and Cataclysmic Variables ...
• Uniform period spacings in white dwarf models
• The mode trapping properties of full DA white dwarf evolutionary models

The second link in the results is Comparison of White Dwarf Models with STIS Spectrophotometry but it is about their spectra from computer models. So "any source" is doubly wrong.

ETA: My question is about gravity as treated in QM where the textbook physics is as I stated:
Originally Posted by Reality Check
Page 132 gives an example "to appreciate the difficulty involved in seeing gravity in bound-state problems". The Bohr radius for a bound electron and neutron is around 1013 light years - much larger than the estimated size of the universe. But there is the possibility of detecting gravity-induced quantum interference.
The role of gravity outside of QM is in question. That is basic astrophysics. A stable star has to have hydrostatic equilibrium.
Last edited by Reality Check; 2018-Feb-13 at 03:17 AM.

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Originally Posted by Reality Check
Any source at all?
Question for you-- yes or no. Do all those sources use "G" in the models they refer to? Answer that.

The role of gravity outside of QM is in question.
I have no idea what you even think that sentence means. So no, that nonsense is not what is in question, anywhere but in your head.

8. Originally Posted by Ken G
Originally Posted by Reality Check
The role of gravity outside of QM is in question.
I have no idea what you even think that sentence means. So no, that nonsense is not what is in question, anywhere but in your head.
From context I'm guessing the word "not" was omitted.
But did you ever claim that gravity was part of QM?

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Originally Posted by grant hutchison
From context I'm guessing the word "not" was omitted.
But did you ever claim that gravity was part of QM?
Honestly I can't put the word "not" in that sentence anywhere to make it any better! But let me step back and clarify. There is not much point in saying what is "in" quantum mechanics and what is "outside" it, because quantum mechanics is built on the backs of other theories. The formalism of quantum mechanics uses operators, as you know, and the way these operators are built is quite manual-- there is no theory that tells us what the right operator is, we take a classical concept and just turn it into a quantum operator. For example, you can ask is energy "in" quantum mechanics, or "out" of it? Well, the Schroedinger equation takes a time derivative of a wavefunction and associates it with a Hamiltonian operator on that wavefunction. That's it, that's all it does, so there's no energy "in" the formalism. However, in situations where a system has a definite energy and the Hamiltonian is time independent, then the action of both the time derivative operator and the Hamiltonian operator is to spit out that energy. The Schroedinger equation was invented out of whole cloth to give the classical answer for a particle moving in a potential, in the spirit of quantum thinking about how these things should be framed. So does the fact that energy inspired the Schroedinger equation mean that energy is "in" quantum mechanics, or does the fact that the formalism doesn't refer to energy at all mean it is "out" of quantum mechanics? We can look at what happens when the Hamiltonian operator is time dependent, but then the situation gets very confused and even experts start having arguments about the meaning of energy. The same happens in general relativity, where global energy becomes a much different animal than the energy of a given particle in a given reference frame, so is energy "in" GR or not?

My point was that the semantics of whether gravity belongs "in" or "out" of QM is of no consequence, what matters is that we routinely calculate how a model of Newtonian gravity is responsible for the ground state of self-gravitating systems like white dwarfs. There are ways to get it into the quantum mechanics, via the way quantum mechanics treats potential energy. There is a bit of sleight of hand, but this is not at all uncommon, indeed all of physics involves a kind of sleight of hand because we always introduce simplifications into any system. The simplification introduced into a white dwarf is that the fact that the gravitational potential energy is manifested in the ions, while the kinetic energy is manifested in the electrons, is swept under the rug by simply asserting that the need to avoid charge separation requires that the electrons end up being ruled by the way gravity affects the ions. So the charge separation imposes a kind of effective gravitational potential energy on the electrons, which is then plugged into the quantum mechanics of the ground state in the way potential energy is always put into quantum mechanics-- by following the classical analog. We end up with a fluid description that balances the gradient in the kinetic energy density (related to what is often called pressure) with the gravitational force on the fluid.

Importantly, the only thing quantum mechanics does here is to allow you to associate a temperature with the kinetic energy, which relates to how the kinetic energy is apportioned among the particles and how heat gets transported. In idealized white-dwarf models, that apportionment is the ground state, which is the zero temperature state. That's it-- that's all quantum mechanics is doing in white dwarf models, it is telling you what the zero temperature state is. If you don't care about temperature, you can do the whole thing with kinetic energy, and you don't even have to care how it is apportioned because nonrelativistic pressure doesn't care how it is apportioned. This is what so few people understand about "degeneracy pressure." The only thing you need the quantum mechanics for is to be able to know when you have reached the ground state and cannot lose any more heat, that's all quantum mechanics is doing for white dwarf structure.

That's always true of the transition from classical to quantum limits-- you are doing fine classically until you've lost enough heat to get somewhere close to the ground state, and that's why you need quantum mechanics to tell you when you are getting close and how the situation is going to be changed by the fact that you are getting close. In many cases, we can go to the opposite limit of the ground state itself, using quantum mechanics to tell us what that is, and we don't even need to worry much about how we got there. This is more or less how white dwarf models work, when we idealize the white dwarf as the zero temperature state even when we know it isn't quite there yet.
Last edited by Ken G; 2018-Feb-13 at 05:36 PM.

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Originally Posted by Ken G
Question for you-- yes or no. Do all those sources use "G" in the models they refer to?
Sorry but that is a dumb question because you know that you gave a Google search with over 9,000 results - people will not read all of over 9,000 links !

Made a mistake and are honest enough to acknowledge it: "The role of gravity outside of QM is in question." is missing a not. I also HAVE to add the context explicitly since you cADID NOT UNDERSTAND IT.
The role of gravity outside of QM is not in question for stars including white dwarf . That is basic astrophysics. A stable star has to have hydrostatic equilibrium. That is gravity by itself, not included in QM and so "outside of QM" balanced by thermal and degeneracy pressure.

You seem to be trying to answer the older white dwarf specific question:
8 Feb 2018 Ken G: Give mainstream sources for the "the standard model of a white dwarf" that includes gravity in QM.
13 February 2018 Ken G: Give your sources for those systems whose QM ground state is known by including gravity in QM.

The sources that I have found do not support the assertion:
1. The Wikipedia article on QM not mention it being used for gravity.
2. Electron degeneracy pressure as in white dwarfs not include G for gravity.
3. The white dwarf article does not mention that gravity is used in the electron degeneracy pressure derivation.
4. Properties of Degenerated Fermi-Gas in Astrophysics by Hsin-Yu Chen (PDF) does bot use gravity to derive electron degeneracy pressure.
5. The Pauli exclusion principle (QM, not gravitation) is why free electrons have degeneracy pressure: Astrophysics and the Pauli principle
6. 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.
7. There is the 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).
8. The literally textbook physics that gravity in QM produces a Bohr radius bigger than the universe and induces at least 1 not detected yet quantum effect.
Originally Posted by Reality Check
Look for "J. J. Sakurai - Modern Quantum Mechanics". The second edition has 3 pages on Gravity in Quantum Mechanics starting on page 131. Page 132 gives an example "to appreciate the difficulty involved in seeing gravity in bound-state problems". The Bohr radius for a bound electron and neutron is around 1013 light years - much larger than the estimated size of the universe. But there is the possibility of detecting gravity-induced quantum interference.

Gravity (Newtonian, not GR) can be treated within QM which I have not disagreed with. But it is trivial to show that this gives no practical ground state for bound systems (I suspected this from my 8 years experience of using QM). I did not know about gravity-induced quantum interference.
Last edited by Reality Check; 2018-Feb-13 at 08:20 PM.

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Originally Posted by Ken G
My point was that the semantics of whether gravity belongs "in" or "out" of QM is of no consequence, what matters is that we routinely calculate how a model of Newtonian gravity is responsible for the ground state of self-gravitating systems like white dwarfs.
My point for many days is that there is no evidence for "we" doing that routine calculation - there is you making unsupported assertions. If it was routine then you would have given your sources immediately. But you had to resort to e Google search with > 9,000 results as a source !

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.

The we who do the actual calculations see that Newtonian gravity gives physically impractical QM ground states, e.g. a Bohr radius magnitudes greater than the radius of the universe. The we that write about degeneracy pressure and white dwarfs (admittedly on Wikipedia so far) do not include gravity in QM calculations - almost as if they had read QM textbooks!

7 sources about degeneracy pressure, white dwarfs and a rare textbook section Gravity in Quantum Mechanics.

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Originally Posted by Reality Check
Sorry but that is a dumb question because you know that you gave a Google search with over 9,000 results - people will not read all of over 9,000 links !
Actually, I think that's a dumb answer to a very good question. The answer you ducked is, yes, G appears in white dwarf models, so your claims that gravity can't be used in quantum mechanics, or doesn't affect the solution, are just wrong. But go on believing you are right. It appears neither of us are going to learn anything from the other, though fortunately I already understand degeneracy pressure. For anyone else still reading this, my takeaway message for you is that degeneracy pressure is not in any way restricted to extreme conditions, it happens in completely mundane and everyday situations as well. What unifies white dwarfs with everyday systems, despite the dramatic differences in density, is simply that both deal with systems near their ground state. That's when "degeneracy" matters, and that's what I wanted to say.
Last edited by Ken G; 2018-Feb-14 at 04:50 AM.

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Originally Posted by Reality Check

Gravity (Newtonian, not GR) can be treated within QM which I have not disagreed with. But it is trivial to show that this gives no practical ground state for bound systems (I suspected this from my 8 years experience of using QM). I did not know about gravity-induced quantum interference.
So can I ask you again, would you expect a testable outcome from the predictive model you advocate (i.e. a predictive model that is discerned by you to be "mainstream") to differ if gravity is included in the said model in the sense that has been suggested by Ken?

Or is this discussion about interpretations and descriptive models rather than the nuts and bolts of a predictive model?
Last edited by Len Moran; 2018-Feb-14 at 03:04 PM.

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Originally Posted by Len Moran
So can I ask you again, would you expect a testable outcome from the predictive model you advocate...
I am not advocating any predictive model. I am advocating the expectation that someone making an unsupported assertion needs to give evidence to support the assertion. Thus my questions.

I am advocating textbook physics. Gravity in quantum mechanics leads to a Bohr radius magnitudes greater then the known radius of the universe. Textbook astrophysics balances Newtonian gravity against thermal pressure and degeneracy pressure (that is the separate consideration of QM).

ETA: The textbook I found gives an answer to your original "do you consider we would get different predictive outcomes" question.
If we have Newtonian gravity + thermal pressure + degeneracy pressure + gravity in quantum mechanics then we will obviously get different predictive outcomes from having just the first 3. However the difference should not be measurable and maybe not ever measurable in this universe. Astrophysicists neglect degeneracy pressure in mainstream stars because it is negligible. Astrophysicists neglect thermal pressure in white dwarfs because it is negligible. Astrophysicists neglect gravity in QM for all stars because it is negligible.

The last point is easy to understand for me because I had years working with QM. Electron degeneracy pressure is basically that elections have to occupy high energy states because they are excluded from lower energy states. Gravity should only produce a tiny shift in the energy levels of an degenerate electron gas- maybe on the order of its relative strength (a shift of 1 in 1039?) or maybe there is a square root in there (a shift of 1 in 1010?). N.B. this is an educated guess not a scientific source!
Last edited by Reality Check; 2018-Feb-14 at 09:31 PM.

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## Ken G: How many of the > 9000 results did you read

Originally Posted by Ken G
Actually, I think that's a dumb answer to a very good question. ....
What was dumb was a question seeming to ask me to read over 9000 Google results to see if all of them contain G. On the other hand, you may have meant just the first 10 results that I list. But that implies that you ignored the list and ignored the Google results so:
15 February 2018 Ken G: How many of the > 9000 results did you read to get your exception that every one has G?

The very first result I got says that "all of them contain G" is wrong. The web page Synthetic Colors and Evolutionary Sequences of Hydrogen- and Helium-Atmosphere White Dwarfs only has g (note the lower case).

I have no doubt that models of all stars contain G for the simple reason that they balance Newtonian gravity against thermal and degeneracy pressure. A difference between main sequence stars and white dwarfs is that thermal pressure dominates in the former and degernacy pressure in the latter.

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.

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Originally Posted by Reality Check
I am not advocating any predictive model. I am advocating the expectation that someone making an unsupported assertion needs to give evidence to support the assertion. Thus my questions.

I am advocating textbook physics. Gravity in quantum mechanics leads to a Bohr radius magnitudes greater then the known radius of the universe. Textbook astrophysics balances Newtonian gravity against thermal pressure and degeneracy pressure (that is the separate consideration of QM).
Ok, thanks.

I am just trying to get a "feel" of what this discussion/conflict actually relates to in terms of verified models. It would be perfectly valid for you to tell me to go and find out for myself the degree to which the text book physics has been applied experimentally to this question of degeneracy, but I'm taking a short cut and simply asking you if it is the case that all that you expound in this thread can be related to actual verified models. I'm more than happy to take your word on this, my question simply relates to how I should compare Ken's take on this with the text book physics. If we are talking about a straightforward comparison between "unsupported" assertions from Ken and verified models, then the verified model would win out obviously. But if we are talking about assertions from textbook physics verses assertions from Ken, then I for one will always be very interested in what he has to say because very often he gets to the root of fundamental misconceptions within physics.

So could you clarify for me (if you wish to do so) what the nature of the playing field here is - does the playing field on your side consist of unverified assertions mixed in with best fit models or does it consist of solid verified predictive models in its entirety? If it is the former then I think we all would do well to take seriously Ken's thoughts on this, if it is the latter then perhaps it should be a ATM matter.

That's all that interests me here, I want to know the context within which Ken and yourself are at loggerheads, I am happy to accept that you are properly citing text book physics, but I would like to be happier about understanding the context of applying that text book physics to the issue in question, I would be happier knowing the degree to which (if any) the textbook physics is making assumptions of its own.

As I said, you would be entirely correct in telling me to go and find out for myself, so I'm certainly not setting up any scenario in which to challenge what you say in this thread by asking you this question. I am simply interested in understanding the nature of the playing field we are on here because as I have said, I always have a great respect for the insight that Ken often brings to issues within physics, not a kind of ATM insight, more of an insight into how mainstream physics arrives at things and the pitfalls that often accompanies mainstream physics, insight that is often glossed over by many (and I am not saying you are doing this).

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Originally Posted by Reality Check
I have no doubt that models of all stars contain G for the simple reason that they balance Newtonian gravity against thermal and degeneracy pressure.
Excellent, then we can all finally understand my statement that gravity causes white dwarf electrons to have the ground state they do. I'm glad this could be resolved so easily.

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## Ken G: What force acts to compress a star, etc.

Originally Posted by Ken G
Excellent, then we can all finally understand my statement that gravity causes white dwarf electrons to have the ground state they do. I'm glad this could be resolved so easily.
Still not understanding textbook astrophysics is not a resolution. I will make it clearer with some questions and their textbook answers.
Ken G: What force acts to compress a star?
Ken G: What forces act to expand a star?
Ken G: What do we have to do with the compression and opposition forces to have a stable star?

On one side is the force of gravity compressing a star and the factor of G.
On the other side there is the force from thermal pressure (no G) and electron degeneracy pressure (no G) which unfortunately is not listed in that hydrostatic equilibrium article.

I do not expect answers from you given the still unanswered questions and an ignored question.
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?

Correct answers also seem unlikely since you still show no signs of understanding a QM textbook section on gravity in QM.
7 sources about degeneracy pressure, white dwarfs and a rare textbook section Gravity in Quantum Mechanics.
That hints that you will not understand the fact that gravity is on a separate side of equilibrium from pressures. Maybe you will surprise me though!

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Originally Posted by Len Moran
Ok, thanks.

I am just trying to get a "feel" of what this discussion/conflict actually relates to in terms of verified models.
The "feel" you should get is that there is no evidence that gravity in QM has a role in verified models of white dwarfs and plenty of evidence that it is not in any models of white dwarfs.
See my list which includes the textbook reason why gravity in QM is ignored by almost every area of science. The Bohr radius of a gravitationally bound election and neutron is larger than the known radius of the universe. The ground state of this "atom" is an "atom" larger than the universe. Excited states are even larger. So we can neglect this for bound systems.

According to all of the sources I have found, the electron degeneracy pressure in white dwarf models is derived from a free (noninteracting) electron gas. Forces such are gravity are thus explicitly excluded. The degeneracy pressure comes from the fact that electrons are fermions.
Another source: A slideshow (PDF) DEGENERATE EQUATIONS OF STATE & WHITE DWARFS

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If you need answers to those questions, you can always start your own thread, maybe someone will have interest in them. They're too trivial for me to bother. What I intended to say in this thread, I have spelled out quite clearly. Those who wish to understand, may, and those who wish to misunderstand, well that's up to them.

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Originally Posted by Ken G
If you need answers to those questions, you can always start your own thread, maybe someone will have interest in them.
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?

These are the latest questions for you about the physics being discussed in this thread (white dwarf models start with the balance of gravity against pressures (electron degeneracy pressure dominating)):
15 February 2018 Ken G: What force acts to compress a star?
15 February 2018 Ken G: What forces act to expand a star?
15 February 2018 Ken G: What do we have to do with the compression and opposition forces to have a stable star?
I know and gave the textbook answers to these questions. The hope is that by answering them for yourself you will learn that gravity appears on one side by itself and QM is on the other side with no gravity included.

I assume you know what thermal pressure is and that the gas laws do not include G. Maybe you still do not know what electron degeneracy pressure is and how it is derived despite the several times sources have been given to you, so the next questions will be:
Does the equation for electron degeneracy pressure include G? [Textbook answer = no]
What does the word "free" mean for the free electron gas used to derive electron degeneracy pressure? [Textbook answer = not interacting by any forces]
Is the Schrodinger equation used to derive electron degeneracy pressure? [Textbook answer = no]
Look up the answers for yourself and see if I am wrong. Or agree with the sources I have given you that have textbook answers.
Last edited by Reality Check; 2018-Feb-15 at 09:03 PM.

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I'm sorry you still have questions, I've aready done my best to explain to you how degeneracy pressure works. Let's peruse some of the false claims you have made so far:
Originally Posted by Reality Check
The more physically significant or interesting cases of degeneracy pressure are at high density, e.g. white dwarf and neutron stars, so that is what is talked about.
Do you still not understand that this is not the most physically significant or interesting cases of degeneracy pressure, for the reasons I explained?

Originally Posted by Reality Check
Degeneracy is a QM phenomena, i.e. the "simple quantum mechanical ground state of gases that are purely" interacting via non-gravitational forces.
Do you still think it is possible to understand the ground state of the electrons in a white dwarf without understanding the role of gravity in that ground state? (As I explained, the role of gravity appears via the need to avoid charge separation with the ions, but in a fluid picture there is no need to include electric fields, so the crucial force is gravity. This is made obvious by the fact that G appears prominently in the ground state structure of a white dwarf.)

Originally Posted by Reality Check
QM does not include gravity.
Do you still believe that utter baloney?

Originally Posted by Reality Check
The ground state of an system is quantum mechanics leading to quantum degeneracy pressure.
Do you still not understand that quantum mechanics ground states always require knowledge of the force or force constraints? It's almost like you think ground states pop right out of quantum mechanics with no other inputs from the situation.

Originally Posted by Reality Check
And thus the statement in the "ground state due to self-gravity..." post was wrong because the ground state is QM not GR.
Do you still not understand that the ground state of white dwarf electrons is very much due to the self-gravity of the star? I mean, where else do you think the G in the ground state equation for a white dwarf comes from?

Originally Posted by Reality Check
Real physicists read textbooks where GR states that gravity is caused by the curvature of spacetime.
Do you still not understand that there are plenty of physics textbooks that say gravity is caused by an inverse-square force? And do you still not understand that most theoretical physicists expect for the textbooks to some day say that gravity is mediated by a particle called a graviton, rather than spacetime curvature? And do you still not understand how physics works, where we use whatever model of gravity we need for the situation?

So the only question I have is, given all the misconceptions you have sown into this thread, are you still laboring under all of them, or have you actually learned something? Because if you haven't, I certainly hope the others reading the thread have, so that my efforts have not been completely wasted.

For those with the capability to understand, let me repeat the crucial point. The only reason (yes, only) that people think degeneracy pressure is associated with very high density is because they are only aware of the application of degeneracy pressure in which the self-gravity of the system is the confining force, and self-gravity is such a weak force that it only dominates for very massive systems, leading to very high densities for the ground state. When electric forces are the confining force, degeneracy pressure appears in systems with quite mundane everyday density, because everyday materials are often close to their ground states.

The crucial takeaway is that exactly the situations where degeneracy pressure matters are exactly the situations where the system in question is somewhere close to its ground state. For a white dwarf, the system in question involves electrons and ions, and the force of gravity is decisive in establishing the ground state for the fluid as a whole. Anyone is to be forgiven for not already knowing this, because almost nobody already knows this, which is why I'm telling you.
Last edited by Ken G; 2018-Feb-15 at 10:27 PM.

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Originally Posted by Ken G
I'm sorry you still have questions, I've aready done my best to explain to you how degeneracy pressure works ....
I do not want your "explanations" yet again because the growing list of sources I find tells me that they are wrong. But Wikipedia, a QM textbook, etc. may be also wrong. Thus I still want the mainstream scientific literature that you read to base your assertions on.

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?

These are the latest questions for you about the physics being discussed in this thread (white dwarf models start with the balance of gravity against pressures (electron degeneracy pressure dominating)):
15 February 2018 Ken G: What force acts to compress a star?
15 February 2018 Ken G: What forces act to expand a star?
15 February 2018 Ken G: What do we have to do with the compression and opposition forces to have a stable star?

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!
2. That textbook QM & gravity makes it absurd to talk about the ground state of a white dwarf having measurable physical effects unless you can give sources.
The expectation from the Bohr radius alone is that the most probable location of particles in the ground state of a white dwarf is outside of the observable universe ! However an N-particle treatment may give different results.
3. Textbook QM degeneracy.
This is quantum degeneracy thus degeneracy is a QM phenomena ! The reality is that degeneracy pressure is derived from Pauli exclusion not the Schrodinger equation and its Hamiltonian that has the potential of forces.
Last edited by Reality Check; 2018-Feb-15 at 11:52 PM.

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## 8 sources with no G for any white dwarf "ground state"

The sources that I have found do not support the assertion that white dwarf models include any "ground state from a gravitating body", e.g. plug gravity into QM (Schrodinger's equation).
1. The Wikipedia article on QM not mention QM being used for gravity.
If it was common to do this, e.g. for stellar models (it is not only white dwarfs that have gravity!), then it is possible that the authors of the article would know and write that. However the article needs to explain why gravity is not commonly used in QM - see below.
2. Electron degeneracy pressure as in white dwarfs not include G for gravity.
3. The white dwarf article does not mention that gravity is used in the electron degeneracy pressure derivation.
4. Properties of Degenerated Fermi-Gas in Astrophysics by Hsin-Yu Chen (PDF) does bot use gravity to derive electron degeneracy pressure.
5. The Pauli exclusion principle (QM, not gravitation) is why free electrons have degeneracy pressure: Astrophysics and the Pauli principle
6. 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.
7. There is the 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).
8. No gravity in a slideshow (PDF) DEGENERATE EQUATIONS OF STATE & WHITE DWARFS
9. The literally textbook physics that gravity in QM produces a Bohr radius bigger than the universe and induces at least 1 not detected yet quantum effect.
J. J. Sakurai - Modern Quantum Mechanics. second edition has 3 pages on Gravity in Quantum Mechanics starting on page 131. Page 132 gives an example "to appreciate the difficulty involved in seeing gravity in bound-state problems". The Bohr radius for a bound electron and neutron is around 1013 light years - much larger than the estimated size of the universe. But there is the possibility of detecting gravity-induced quantum interference.
Last edited by Reality Check; 2018-Feb-15 at 11:48 PM.

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Then I was right, you still have all those misconceptions I listed. Oh well, it's nothing to me. For the rest, again:

The only reason that people think degeneracy pressure is associated with very high density is because they are only aware of the application of degeneracy pressure in which the self-gravity of the system is the confining force, and self-gravity is such a weak force that it only dominates for very massive systems, leading to very high densities for the ground state. When electric forces are the confining force, degeneracy pressure appears in systems with quite mundane everyday density, because everyday materials are often close to their ground states.

The crucial takeaway is that exactly the situations where degeneracy pressure matters are exactly the situations where the system in question is somewhere close to its ground state.

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Originally Posted by Ken G
Then I was right, you still have all those misconceptions I listed. ...
You are wrong. I did not address an attempt to derail from your still supported assertions at all. But since you insist.

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.

I understand that endlessly repeating an unsupported assertion reflects badly on you ("ground state of white dwarf electrons is very much due to the self-gravity of the star").
The ground state of any election gas is due to the interaction between the electrons which is electromagnetism because electrons are charged and "quantum mechanics ground states always require knowledge of the force or force constraints" . Unless you are denying that electrons are charged ?
But if we ignore all interactions then we get the textbook derivation for pressure in a free electron gas. Fowler (below) gives reasons to ignore the electrostatic interaction. It is mainstream physics that we can neglect gravity between the elections - see the mainstream textbook I cited. Which is what every derivation of electron degeneracy pressure I have seen does. The sources including gravity are what you are incapable of producing.
As for an election gas in a potential well from the star as a whole, that would need a source.

I understand that there are "plenty of physics textbooks that say gravity is caused by an inverse-square force". It would be a lie to say that I do not know this since I have mentioned Newtonian gravity many times previously in this thread.

For others (not you Ken G): The dominating electron degernacy pressure in white dwarfs
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]
is related to the population of the ground and higher energy states of the electron gas.
On Dense Matter by R. H. Fowler, F.R.S. (PDF). Fowler describes Eddington's reasoning that stars like Sirius B should not exist. Fowler resolves the paradox by noting that the paradox is for classical statistical mechanics but the new quantum statistical mechanics actually applies for these high densities.
Last edited by Reality Check; 2018-Feb-16 at 03:38 AM.

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Originally Posted by Reality Check
I understand "quantum mechanics ground states always require knowledge of the force or force constraints"
No you don't, because you think one cannot use gravity with quantum mechanics. So just think about this a little more.

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Originally Posted by Ken G

Do you still not understand that quantum mechanics ground states always require knowledge of the force or force constraints? It's almost like you think ground states pop right out of quantum mechanics with no other inputs from the situation.
Just for my benefit and nothing to do with any kind of contribution on my part to this argument, could you clarify the above for me.

Do you mean that in order for us to model and hence quantitatively predict when a ground state will occur we have to have a quantifiable knowledge of of the force or force constraints. So in the case of a white dwarf, because this force is going to be overwhelmingly gravitational, we have to feed into the model this parameter in order to obtain a reasonable quantative prediction from the model. But if we were talking about a more mundane object where the gravitational force was minute, then the model would not require this parameter to be fed into it in order to obtain a reasonable quantitative prediction concerning the ground state.

Or are you not really talking about quantitative predictions as such here, more a descriptive account of what you consider is going on with gravity, white dwarfs and ground states.

Or am I missing the proper context of that quote?

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Originally Posted by Len Moran
Do you mean that in order for us to model and hence quantitatively predict when a ground state will occur we have to have a quantifiable knowledge of of the force or force constraints.
Yes, and the way we do that is via some classical potential energy function that we borrow for the quantum Hamiltonian. So what this means is, every force that exists in classical mechanics also exists "in" quantum mechanics. Put differently, quantum mechanics is not some "separate theory" that must avoid gravity, while classical mechanics embraces gravity. The most general way to say this is, it is well known from the early days of quantum mechanics (and summarized by Bohr in his "correspondence principle") that any problem you can solve using classical mechanics you can also solve using quantum mechanics. You just probably wouldn't. (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.)
So in the case of a white dwarf, because this force is going to be overwhelmingly gravitational, we have to feed into the model this parameter in order to obtain a reasonable quantative prediction from the model. But if we were talking about a more mundane object where the gravitational force was minute, then the model would not require this parameter to be fed into it in order to obtain a reasonable quantitative prediction concerning the ground state.
Exactly. And even more importantly, there will be other forces that are much stronger than gravity, and they will yield mundane everyday densities for the electron ground states. But those kinds of forces (generally electric) tend to cancel out in high-mass objects, leaving gravity as the confinement force in those objects, and the high mass is what leads to the high density-- high density is not a requirement of degeneracy pressure as many people are told and as the OP question appears to imagine.

So you need to understand your system, and that generally means have some classically inspired handle on it, before you can even begin to analyze it with quantum mechanics. Much of Reality Check's most confused language centers on some apparent idea he has that quantum mechanics is some kind of self-contained analysis program that does not use classical ideas and cannot be applied to gravity. But I was mostly just correcting his misconception about gravity before it infected any unsuspecting reader-- if white dwarf models are the only interest, then it suffices to treat the electrons quantum mechanically and the ions classically, and impose the connection by requiring no charge separation within the fluid model. But regardless of the approach one takes to arriving at the solution, here are the two truths to bear in mind:
1) the white dwarf electrons are reasonably close to their ground state, and are often treated as being in their ground state in simplified models of white dwarfs, and that's why degeneracy pressure is relevant, and
2) this ground state I have been talking about is controlled by the gravity of the ions in the white dwarf. Ergo, the defining characteristic of applications of degeneracy pressure that involve super high densities are precisely the situations where the ground states are controlled by the gravity in very massive objects.

So if anything Reality Check said sounded like something different from that, then ignore it.
Or are you not really talking about quantitative predictions as such here, more a descriptive account of what you consider is going on with gravity, white dwarfs and ground states.
I'm talking about the full Monte-- both quantitative predictions and qualitative understanding to go with it.
Last edited by Ken G; 2018-Feb-16 at 07:59 PM.

30. In my job, the phrase "standard textbook explanation" was generally considered to be synonymous with "not the full story". And "You'll certainly find that in the textbooks" was a polite way of saying, "You don't really understand this."
Was that just medicine?

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