Talk:Degenerate matter/Archive 1

Please Clarify
This sentence "Therefore, even though the plasma is cold, the molecules must be moving very fast on average. This leads to the conclusion that if you want to compress an object into a very small space, you must use tremendous force to control its particles' momentum." does not make sense to me and I have a bachelors level of understanding of physics. How can something be very cold and have very fast moving particles? Are they all moving in the same direction? That would not make sense from either the standpoint of the particles being on local orbitals or uncertainty. —Preceding unsigned comment added by 72.194.124.25 (talk) 03:49, 26 July 2009 (UTC)


 * Temperature in this context is referring to excitation above the ground state, if I understand correctly. Everyday matter is usually considered to be at about 300 K despite electrons having kinetic energies of several eV to several hundred eV (tens of thousands to millions of kelvin equivalent). A less handwavy argument would probably involve measuring the entropy of the system and working back from that to temperature.--Christopher Thomas (talk) 07:04, 26 July 2009 (UTC)


 * See Fermi velocity for some explanation. Yes it goes through entropy. There is little randomness in states more than kT below the Fermi surface. Gah4 (talk) 22:13, 11 July 2019 (UTC)

Visuals
I think that a tidy picture, or animation, showing the degenerate state of electrons, along with their energy levels and perhaps their charge or something would really help make sense of this article. brithans 2008/11/05 09:06 —Preceding undated comment was added at 14:06, 5 November 2008 (UTC).

Errors
A commentator who appears to know what he's talking about has mentioned very recently that this article contains factual errors. Just FYI, since not knowing much about the subject myself I can't find or fix them. --Kizor 02:09, 15 December 2005 (UTC)

What?! Solids degenerate matter? Either it is too late or there is something wrong here....--AN 07:06 Nov 7, 2002 (UTC)


 * After one false start I have now addressed the above query (see article history). It was certainly worth doing as it provided the opportunity to point to metals, thereby linking together solid state physics as well as astrophysics and quantum mechanics.  Alan Peakall 12:13 Nov 8, 2002 (UTC)

"...then degeneracy pressure can do no more, because nothing can move faster than the speed of light." Can someone please reword this sentence? the explanation given (and quoted) makes little sense at best. I know nothing can move faster than c, but I'm unconvinced that the "degeneracy pressure" is in any way related to this restriction. Digemedi 02:09 Nov 16, 2008 (UTC)

A proposed name for white dwarf material.
I have a suggestion for a name for white dwarf material => densimetal

I've choose this name basically because white dwarf material is very, very dense, and has many similarities to metals (or should metals be considered something similar to white dwarf material? :-) ).

What do you think about this name?

Marcio Fialho 2:57 Dec 21, 2004 (UTC)

This seems to me wrong terminology - the conduction electrons alone as a degenerate, free electron gas - What!!! an electron gas? this is confusing as a gas is the most compressible state and degenerate matter is as far as one can get from compressiblity. Gepay@jaemspay@ntelos .net a gas of electrons ho ho ho I believe in Santa Claus and dark matter


 * Wouldn't that be original research, or vanity ?


 * Yes, why is neutronium, which is basically a solid, being referred to as a gas ("neutron gas") in this article? Neutronium is not compressible without losing its identity as being neutronium. --Spunionztastic (talk) 07:59, 31 October 2018 (UTC)


 * Text from 2002, three years before the creation of this article: "If we assume that a stellar core (or other object such as a white dwarf) is supported by electron gas pressure at some time after fusion stops, we can derive a relation between the mass of the core (or object) and its radius [...] Neutron Stars \ Produced when the force of gravity becomes so strong that the reaction \ e+p&rarr;n+v \ occurs \ Are supported by the pressure from a degenerate neutron gas in a manner analogous to the pressure from electrons in white dwarfs" -- emphasis added by me, from http://web.archive.org/web/20020719103457/http://ircamera.as.arizona.edu/astr_250/Lectures/Lecture_17.htm --Spunionztastic (talk) 08:17, 31 October 2018 (UTC)

Eleetism Detected
can you guys rewrite that article so that normal people can understand what you are talking of!? what is 'dominant contribution'? the article is written in a way that only people who know what degenerate matter is can recognize the meaning.it is not explanatory. if you know what that article is about you might say:"oh well". but someone without any knowledge about that matter wont get any benefit out of it. --212.202.37.226 21:03, 17 May 2005 (UTC)jangirke


 * I've glanced at this article. Certainly a person who does not know any physics could not understand it, but maybe that is because this topic can be understood only by those who know some physics.  It does not look to me as if you need to know what degenerate matter is to understand the definition given here.  The words "dominant contribution" would be understood by any normal high-school graduate.  You'd be more credible if you'd learn to spell elite and elitism. Michael Hardy 22:36, 16 Jun 2005 (UTC)

This is definetly written in such a way as to make it unecessarily complicated. This article has an en passant definition of degenerate matter which makes a lot more sense than the gibberish laid out in here. http://en.wikipedia.org/wiki/Helium_flash
 * I got A's in two university physics classes, although it was some time ago, and I found the article to be a bit over my head. Actually, I think I understood more of the article as a result of taking Chemistry than Physics, but I digress. As I understand it, this is matter that is so dense that the electrons don't have the ability to orbit at the normal radius (quantum state) and therefore is compacted beyond a density that would normally be obtained through mere physical compression. Not enough compression for fusion, but somewhere in between a normal state and a state ready for fusion. Now, I probably have something wrong here, but it would sure be nice if this were edited to a more approachable level for the average Wikipedia reading level. This sort of material is found in brown dwarfs, so a link to there would also be nice. KellyCoinGuy
 * So far I've read a few paragraphs in, and I find the article to be excellent so far. It is written so a noob like me with no physics background can get an idea of what's being discussed. This is much better than I can say for almost any other "fancy" physics article I've read on Wikipedia. Radishes (talk) 03:17, 13 April 2008 (UTC)
 * well, it is a 100% quantum phenomenon, and you can't escape that. However, as I will write soon, it isn't only in far away stars, but is also the state of electrons in metals. It explains that one place in the article, and then forgets it for the rest. Well, electrons in a metal are close to a degenerate Fermi gas at room temperature, being so much lower than the Fermi temperature.  (Fermi energy/k.) It is a side effect of Pauli exclusion, though that is hard to explain without a lot of quantum mechanics, other than that is just the way it is. Gah4 (talk) 06:56, 16 February 2021 (UTC)
 * So far I've read a few paragraphs in, and I find the article to be excellent so far. It is written so a noob like me with no physics background can get an idea of what's being discussed. This is much better than I can say for almost any other "fancy" physics article I've read on Wikipedia. Radishes (talk) 03:17, 13 April 2008 (UTC)
 * well, it is a 100% quantum phenomenon, and you can't escape that. However, as I will write soon, it isn't only in far away stars, but is also the state of electrons in metals. It explains that one place in the article, and then forgets it for the rest. Well, electrons in a metal are close to a degenerate Fermi gas at room temperature, being so much lower than the Fermi temperature.  (Fermi energy/k.) It is a side effect of Pauli exclusion, though that is hard to explain without a lot of quantum mechanics, other than that is just the way it is. Gah4 (talk) 06:56, 16 February 2021 (UTC)
 * well, it is a 100% quantum phenomenon, and you can't escape that. However, as I will write soon, it isn't only in far away stars, but is also the state of electrons in metals. It explains that one place in the article, and then forgets it for the rest. Well, electrons in a metal are close to a degenerate Fermi gas at room temperature, being so much lower than the Fermi temperature.  (Fermi energy/k.) It is a side effect of Pauli exclusion, though that is hard to explain without a lot of quantum mechanics, other than that is just the way it is. Gah4 (talk) 06:56, 16 February 2021 (UTC)

A degenerate gas is not particularly incompressible
Contrary to what I'm reading here, an ideal degenerate gas is not particularly incompressible. A nonrelativistic degenerate gas has an adiabatic index of 5/3, the same as an ordinary monatomic gas such as helium. A relativistic ideal gas has an adiabatic index of 4/3, which is quite compressible -- more compressible than ordinary air, with an adiabatic index of 1.4.

The incompressibility of solids is not a consequence of degeneracy. It is a consequence of short-range repulsive forces between the core electrons of the atoms making up the solid. --Kgbudge 05:38, 24 July 2005 (UTC)
 * And the short range force is due to Pauli exclusion and degeneracy. Gah4 (talk) 06:58, 16 February 2021 (UTC)
 * And the short range force is due to Pauli exclusion and degeneracy. Gah4 (talk) 06:58, 16 February 2021 (UTC)

Editing pass completed
I've made minor tweaks to the neutron- and electron-degeneracy paragraphs (mostly noting mass cutoffs), and added stub content for proton-, quark-, and preon-degeneracy paragraphs. I really don't think the preon-degeneracy section belongs in this article at all, as there are presently no serious proposals that preons exist (my understanding is that they were ruled out by accelerator experiments some time in the 1990s). I've put it in its own section for now (on speculative forms of degenerate matter).

If anyone who's actually a researcher in the field could add more detail to the proton degeneracy section, it would be greatly appreciated. I dug up information on it being a useful corrective term for models of metallic hydrogen formation and equations of state during supernova explosions, but I don't know what the standard "everyone-cites-these" papers and references on the topic are. --Christopher Thomas 07:50, 24 February 2006 (UTC)

Difference between momentum and velocity.
"Because protons are much more massive than electrons, the same minimum momentum represents a much smaller velocity for protons than for electrons. As a result, in matter with approximately equal numbers of protons and electrons, proton degeneracy pressure is much smaller than electron degeneracy pressure..."

The author is apparently unaware that velocity does not figure into pressure. Pressure, especially here, is momentum per time per area. It's not velocity that matters. It's area. It's kind of hard to write an article about particle physics when you don't even understand Newtonian physics. --76.209.50.222 18:23, 15 February 2007 (UTC)


 * Velocity figures into the time element of pressure. A gas of an equal number of slower velocity particles will have fewer particle impacts per unit area per unit time, and thus lower pressure given the same particle momentum.Warren Dew 00:20, 14 November 2007 (UTC)

Yes. this article is bloated and full of loose statements. I hope to find time to work on it. Dark Formal 04:50, 17 February 2007 (UTC)

Question
i'm pretty much ignorant concerning physics yet i'm in need finding out what a degenerate crystal phase is. is this article the right place to look for an answer?--Vandreou 10:21, 10 June 2007 (UTC)

No degeneracy within the Schwarzchild radius?

 * "As far as known today, no degeneracy state can occur within the Schwarzschild radius of a black hole, thus all its energy will be located in an infinitely dense singularity."

This can't be right. The whole universe is inside its own Schwarzschild radius. If this were true, there could be no degeneracy in the universe. --Doradus (talk) 15:49, 25 June 2009 (UTC)

Read again: the universe is not a black hole. Though I agree anyone who thinks they can say anything about what does or doesn't happen inside a black hole is getting a bit ahead of themselves 220.253.55.234 (talk) 12:57, 29 June 2009 (UTC)


 * Ah, I get it. Until this very moment, I thought anything inside its own Schwarzschild Radius was a black hole.  Thanks for clarifying.  --Doradus (talk) 15:56, 28 July 2009 (UTC)

Usually we think of black holes as high density. But even very low density matter can form a black hole if the volume is large enough. Is the volume of the universe filled with enough matter for it to be a black hole? The critical density is equivalent to about 5 hydrogen atoms per cubic metre. Ordinary matter comprises the equivalent of only 0.2 hydrogen atoms per cubic metre, but when dark matter is added in, the total is oh so close to the critical density. Current thinking is that in addition to these there is an overwhelming amount of dark energy, which prevents the universe from being a black hole.

A black hole is a region of space-time from which nothing, not even light, can escape. An event horizon is any boundary in space-time, beyond which events cannot affect an outside observer. (Event horizons are seldom absolute: a region of space-time causually cut off from one set of observers, may be able to influence other observers.) A singularity occurs when/where-ever curvature of space-time, as expressed by invariant scalars, becomes infinite. Here invariant means independent of any choice of (allowed) co-ordinate system.

Black holes have singularities associated with them. If a black hole (with no electrical charge) in a vacuum is not rotating, the singularity is a point in space (i. e. a line in space-time); if rotating, the singularity is a ring in space. Aside: You do not need to have a black hole to have a singularity. The Big Bang is an example.

Singularities can have event horizons associated with them. For example, distant observers, who are not moving relative to the non-rotating black hole discussed earlier, are not affected by any events within a sphere of the Schwarzschild radius surrounding the central singularity.

This brings up a point of frequent confusion. People often use the Schwarzschild metric to provide co-ordinates around this kind of black hole. Co-ordinates in this particular system become singular as you approach the Schwarzschild radius. But the invariant curvature has no singularity there. So the surface of the sphere is not a singularity of the kind defined earlier. From the standpoint of the distant observers, the singularity is behind the event horizon, so unobservable by them.

The situation for rotating or charged black holes is not as simple. The formulas indicate it may be possible to have black holes with singularities which are not hidden by event horizons (naked singularities,) though the conditions needed to achieve this may be too extreme to exist. —Preceding unsigned comment added by 68.145.187.67 (talk) 02:25, 2 September 2010 (UTC)

Now back to the section of the article: "At densities greater than those supported by any degeneracy, gravity causes the matter to collapse into a point of zero volume." We have seen this is true only in the most idealized (and non-rotating) case. Perhaps "collapse to infinite density" would be better.

"As far as is known today, no degeneracy state can exist within the Schwarzschild radius of a black hole, [...]" A neutron star could fall into a vast, low density, black hole and pass the Schwarzschild radius. This is an example of a degeneracy state existing within the Schwarzschild radius of a black hole. From the standpoint of the neutron star falling into a non-rotating black hole, this existence would likely be brief. Perhaps we should say "be sustained" rather than "exist". However, bringing in the Schwarzschild radius may need rethinking, since this inherently limits the discussion to idealized, non-rotating black holes in a vacuum (large enough to make the mass of degenerate stars negligible.)

"... thus all its energy (mass) will be located in an infinitely dense singularity. The reason for this is that a force of infinite magnitude would be required to sustain matter at any finite volume within the event horizon." For large enough rotating black holes, it may be possible for a piece of degenerate matter to avoid hitting the singularity altogether. See the wormhole debate. A force of infinite magnitude would be required to sustain matter at a finite volume if the trajectory ends at a singularity.

The idea of this section of the article is right - an object falling (or collapsing) into a black hole, can end up heading toward a singularity and no degeneracy (short of some degeneracy related to quantum gravity / the limits of general relativity) will stop its infinite compression. —Preceding unsigned comment added by 68.145.187.67 (talk) 04:02, 2 September 2010 (UTC)

Concept section
I very much liked that section. I'm neither a physicist or a mathematician so I kind of wish every Wikipedia physics article had a semi-layman concept section... 99.236.221.124 (talk) 19:36, 22 July 2010 (UTC)

Reifying language
The first sentence reads, "Degenerate matter is matter which has such extraordinarily high density that the dominant contribution to its pressure is attributable to the Pauli exclusion principle." The principle describes the pressure, it is not the pressure itself (or attributable to it). This is like saying that the Earth orbits the Sun because of the theory of gravitation, rather than that it orbits because of gravity. Can this be rephrased so that it does not make it sound as if the principle is the cause of the phenomena? Like, "the...pressure is attributable to the forces described by the Pauli exclusion principle?" —Preceding unsigned comment added by 24.22.166.163 (talk) 00:22, 10 December 2010 (UTC)
 * I was going to change it to "Degenerate matter is matter which has such extraordinarily high density that the dominant force contribution to its pressure is a repulsive exchange interaction as described by the Pauli exclusion principle." when I noticed that the first sentence is followed by a reference to a book that I don't own. So, I cannot check what the book says and if the reference still makes sense after that change. Someone with access to the book should check, or we should find another reference. 74.125.121.49 (talk) 08:43, 10 December 2010 (UTC)

Neutron Stars supported by degeneracy
I replaced this:
 * neutron stars, which are partially supported by the pressure from a degenerate neutron gas (more so by repulsive interactions between nucleons )

with this:
 * neutron stars, which are primarily supported by the pressure from a degenerate neutron gas.

The old reference was from 1998, the new one  a review from 2011 (thus more up-to-date). On page 2 it claims:
 * the size of a neutron star mainly depends on the balance between gravity force and degenerate neutron pressure

Moreover, it references the 1998 paper (reference 115, referred to as APR in the text), and on page 11 suggests that it is only accurate in the outer core:
 * A common drawback of the above models [FPS, SLy, and APR] is the application of a Lorentz non-invariant theory to the description of hadrons. Such a description becomes a priori incorrect in the central part of the core, where the speeds of nucleons on the Fermi surface may constitute an appreciable fraction of the speed of light.

In light of this I have made the above change, although it would be nice to have confirmation from an expert. - Tim314 (talk) 10:59, 6 June 2011 (UTC)

Overcoming Degeneracy Pressure
I think this article is superb. Having said that is it possible for more elaboration to be given to the process by which degenerate pressure is overcome? My understanding is that the pressure arises from the exclusion principle which states that particles cannot be in the same quantum state, so what happens to these states to allow this pressure to be overcome? I take it the exclusion principle is not violated at this point? It was with this question in mind that I came to this article and I think it would be a valuable addition if someone qualified could answer it. (Doothedoogie (talk) 23:06, 2 January 2012 (UTC))


 * I think overcome is wrong. When you compress a Fermi gas (or liquid), you increase the Fermi velocity, until the pressure matches the external pressure. That determines the compressibility. In the case of stars, this pressure shifts the equilibrium between  p + e-  <--> n, eventually leading to neutron stars.  (Supported by neutron degeneracy pressure, instead of electron degeneracy pressure.)  Gah4 (talk) 22:23, 11 July 2019 (UTC)

I have a question about electron and neutron degeneracy pressure. Does the pressure not vary depending on location i.e. the surface, or the center of the object? If the numbers given are exceeded, presumably usually at the object's core, then collpse happens at that location. Does the same collpase also have to happen throughout the whole of the rest of the object, or is it possible to have two or more different types of degenerate matter depending on the pressure at different locations throughout the object? — Preceding unsigned comment added by 2600:8800:1701:AFD0:84CB:894B:A4CF:BF05 (talk) 16:21, 18 October 2021 (UTC)

Use of Uncertainty Principle as a means of Explanation
Hi all. I'm not a regular contributor to wikipedia so feel free to tell me to get lost if I'm barking up the wrong tree.

I have a concern about the 'Concept' section where the Uncertainty Principle (I'll abbreviate to HUP for brevity) is used to try and explain why there is a pressure. I don't think it's technically accurate. The HUP is not a driving reason in these circumstances - IIRC it's derived from the use of photons or other particles to measure position or velocity. Low energy photons have high wavelength so can't be used to measure distance particularly accurately, but low energy so do not disturb the particle's velocity very much, and vice-versa for high energy photons. Hence a limit in our ability to measure a situation which can't be broken unless we find some new kind of particle with less momentum than a photon for a given wavelength. Basically what I'm saying is HUP is a practical limit of interactions between particles rather than a fundamental law, so HUP isn't able to CAUSE anything really.I'm reminded of how Bernoulli is often used to explain lift on an aerofoil when in fact that's, again, not a driving principle and more misleading than explanatory (even though it's kind-of true and kind-of related).

Degeneracy is more about how if two particles want to share the same quantum state (perhaps position can be used more in more natural English), they can't, so they must have different spin or energy level seeing as a different position isn't possible under our extreme compression.

The beginning of the article explains this very well, but the 'Concept' section confuses rather than clarifies IMO. Perhaps a diagram of Energy Levels on the y-axis, and Position on the x-axis before and after limiting compression would be helpful? Or maybe even overlaying a couple of wave harmonics or something, to show that two waves of equal harmonic can't be distinguished, so one must pop up a harmonic to be anything other than the same particle? — Preceding unsigned comment added by 92.232.151.145 (talk) 23:12, 25 January 2014 (UTC)


 * I think you've got it right. The HUP appears to be used as a sort of hand-waving motivation to explain the raised particle momenta, but I think that it has no place being mentioned here. A better explanation of how distinct quantum states must differ is needed, resulting in a spread of momenta (and this is more the Pauli exclusion principle, not the HUP). Even the lede falls short in interpreting pressure as additional energy needed to elevate particles into more energetic states: pressure is nothing other than the rate of transfer of momentum per unit area across a surface, and thus arises directly from the particle momenta, not via some circuitous added-energy-that-would-be-required mechanism as described, even though these must be equal. —Quondum 00:02, 26 January 2014 (UTC)


 * Well, you can go directly to Fermi energy which describes the filling of quantum states. HUP is commonly used to explain why helium is liquid at absolute zero, which includes zero-point motion in the explanation. Even at absolute zero, atoms in a crystal still vibrate. For helium, the amplitude of the vibration, at usual pressure, is more than the atomic spacing. Gah4 (talk) 23:33, 11 July 2019 (UTC)

Boson condensation is degenerate gas too?
Kittel's Thermal Physics has both Fermi gases and Bose gases becoming "degenerate gases" at low temperature and high density. Reif's Fundamentals of Statistical and Thermal Physics says the same. Right now this article focusses entirely on cold Fermi gases, but is it generally recognized that Bose condensates are also degenerate matter? Nanite (talk) 08:13, 31 January 2014 (UTC). You mix bosons with Bose-Einstein condensate here. BEC= BOSE EINSTEIN CONDENSATE is extremely cold matter of overlapping fat-spread out molecules. It is more like a liquid. All atoms vibrate almost like one harmonically. Usually we use degenerate as a term for high pressures-high temperatures but yes, in a way there are similarities. We need a BEC to BEC collision to find more data, but it is hard to move a BEC and keep it a BEC.

Singularity ???
At densities greater than those supported by any degeneracy, gravity overwhelms all other forces. To the best of our current understanding, the body collapses to form a black hole. In the frame of reference that is co-moving with the collapsing matter, all the matter ends up in an infinitely dense singularity at the center of the event horizon. In the frame of reference of an observer at infinity, the collapse asymptotically approaches the event horizon.

As a consequence of relativity, the extreme gravitational field and orbital velocity experienced by infalling matter around a black hole would "slow" time for that matter relative to a distant observer. Einstein's theories though predict, that only the relativistic inner clock of particles slows down. Einsteins theory of relativistic inner clocks, never mentioned collision rates. In the very perturbed fields of the vicinity of a black hole, the relativistic inner perception of slow particles plays no major role. Countless collisions reshape new particles, so the relativistic slow down does not appear to the beholder. All we see outside a black hole, is not something slowing down, just a body that follows the general swirl pattern and slowly disintegrates. In the vicinity of a black hole, particles even collide with fields themselves. All particles are field excitements. In the vicinity of a black hole, the virtual particles of the fields have so huge energy, they can become real and collide if another particle falls over. Many science book depictions cause confusion to readers. The "falling astronaut" does not follow the swirling pattern, but falls straight inside the core, because it is more dramatic, but not accurate also. In many video depictions in popular science, the artists show "the falling astronaut" getting spaghettified in a straight line, and not in a swirl. Also many artists do not consider that during spaghettification "the swirling victim's" atoms, collide with other atoms, even fields. If the black hole is huge, at the beginning, there is almost no spaghettification. When serious spaghetificattion starts, it is a swirling explosion of plasma matter, not an artistic spaghettification. Many serious scientists, focus on mislead artistic misperceptions, just because are more dramatic than a long swirling degradation of the entering object. Also they focus so much in inner relativistic time perception of objects, they forget that all laws of physics are active at the same time, so we have field collision, and plasma collision. Quantum mechanical collisions do not follow the inner clock relativistic time of a single particle, because it produces new particles with new born inner times, also particles during birth have relativistic inner time noise, because gravity takes time, to force a particle follow the relativistic inner time of the black hole. Gravity is the relativistic tuning of inner times among objects. In order we have gravity, we need virtual particles among the small object and the surrounding be exchanged many times in order the new particles obtain a low inner time level, like the massive body. If we have constant micro collisions, we disturb the virtual particles exchanging to normalize our inner times. Therefore we will not observe (if we could) "the falling astronaut" entering the black hole horizon for bilions of years. He would follow a swirl pattern, and when he approaches stronger regions of the black hole's field, he would explode in a swirl, not spaghettified in a line, but in a swirl of random particles, products of his genuine particles but not his original ones. Also Einstein's relativistic types, predict that only the perception of time inside a particle, therefore the series of it's componental data oscillation will slow relativistically to the flow of time of the big object like a black hole. Einstein's relativity DEMANDS high speeds, in order the inner time of a particle slow down. Even great scientists claim that "the falling astronaut" will move slower, because of popular artistic videos. Einstein's inner perception of time, demands extremely high external speed in order an object maintain it's inner relativistic speed almost frozen, but even that cannot happen when we have countless collisions that reform our particles before they echange vitural particles to tune their inner clock to the black holes core. The mathematical types, demand "the falling astronaut" to die fast in a swirl of plasma, except if our black hole is huge, and he is far away from killing fields - then he will become a satellite of the black hole, or he will be expeled by the black hole. Another option is a degrading satellite orbit, but then he will die when his oxygen ends, or until radiation kills him. Also if the "inner relativistic time" of the astronaut is slow, he will perceive his death as very fast, and we will still behold a very fast death if the astronaut is very close to the black hole center, because in order to keep a low orbit, bodies have to move faster and faster. The truth is that the astronaut when he approaches huge fields, he would die instantly, far away from the event horizon. Stephen Hawking claims there is no absolute spherical event horison, and that is true, because quantum mechanics allow energy streams, brobabilistically break off and release that energy into new particles, from any region of the black hole, even the central region's degenerate hyper-preon. Even solar flares are fields that break off and form new particles, and the source of energy might be even deep inside the sun. In the black hole, black hole flares are more extreme, but because of the condensational tray pressure, so fields break off into particles easily at the poles of the black hole.

Mathematics fail to support a pure single pointed singularity. Modern theories predict that the black hole core is a degenerate particle, a weird form of preon that consists a single particle, not a quark soup. The term particle is not acceptable by all scientists for the black hole core, because it has not an absolute harmonic chart with standardized energy levels. The black hole preon is a particle with no inner harmony or standard oscillation modes. We can derscribe it only probabilistically, because it is unstable, even though it has a constant average energy level.

Many say a BEC to BEC collision (Bose-Einstein Condensate) would bring light to weird matter, but no lab has managed to maintain a BEC during motion, via magnets of moving focus. — Preceding

=Einstein in the train, sees the external speed of the train to be fast, and inner data=people of the particle train be slow, but here EVEN PHOTONS STRETCH but because of gravity==

Singularity[edit] At densities greater than those supported by any degeneracy, gravity overwhelms all other forces. To the best of our current understanding, the body collapses to form a black hole. In the frame of reference that is co-moving with the collapsing matter, all the matter ends up in an infinitely dense singularity at the center of the event horizon. In the frame of reference of an observer at infinity, the collapse asymptotically approaches the event horizon. As a consequence of relativity, the extreme gravitational field and orbital velocity experienced by infalling matter around a black hole would "slow" inner time of particles for that matter relative to a distant observer, but also the observable speed they move, because huge gravity elongates photons and their rate of transfering information. The speed of light is a constant, so that elongation of photonal periods, does slow the rate of informational transmition as long as the period becomes bigger. The higher the observable motion of an object, the lower the inner time of it's particles, but here gravity causes photons to stretch, therefore also information of the image of the objects close to the black hole. High gravity would add more doppler shifting on photons, except the doppler effect of different parts of the black holes twirl.

Numbers, where are the numbers?
The article is remarkably lacking in numbers -- densities (in mass and in particles per volume), pressures, temperatures, etc.. --187.106.62.53 (talk) 19:03, 17 June 2014 (UTC)

Reference for Chandrasekhar limit
I realize that the currently accepted best value of the Chandrasekhar limit is slightly different. If someone can conveniently provide a reference to the latest accepted value, that would be an improvement. Fartherred (talk) 21:25, 31 January 2015 (UTC)

"Awkward" spectrum neutron stars?
> "neutron stars with awkward spectrums have been used in arguments [for quark degenerate matter existing]

Pardon the reverse-pun, but what on Earth does this mean? Jimw338 (talk) 16:04, 11 February 2018 (UTC)
 * thanks for pointing that out. --MaoGo (talk) 09:16, 31 May 2018 (UTC)
 * As you can see the article has a lot of issues. --MaoGo (talk) 10:52, 31 May 2018 (UTC)

superconductivity and superfluidity
The article seems to mostly mention stars for its examples of degenerate matter. As well as I know, though, superconductivity and superfluidity are also examples of degenerate matter, and could be included. Gah4 (talk) 23:35, 11 July 2019 (UTC)

The 9/8 Schwarzschild radius limit
Reportedly, any object of radius smaller than $$\frac{9}{8}$$ of its Schwarzschild radius will undergo gravitational collapse, no matter what type of degeneracy is trying to generate a counterpressure; this seems worth mentioning in this article. It does not depend on quantum effects, but is a consequence of well-understood phenomena in general relativity. (Unfortunately I don't have a good source on the matter, so I'm hoping someone else can help out once the issue has been raised. I haven't encountered any mention of it elsewhere on Wikipedia either. 🙁)

What it's all about, in more detail
Given the mass distribution in an object (for example a white dwarf), it is a straightforward application of general relativity to work out what internal pressure is needed to balance the gravity. For a non-rotating but rotationally symmetric object, the density and pressure both end up being functions of radial position alone, so once past the tensor algebra part of the calculations, the equations end up being elementary ODEs. They are not the same as for Newtonian gravity however, since in general relativity pressure itself is a source of gravity, so in order to maintain a steady state the counterpressure needs to balance not only the gravity from the actual mass but also the gravity contribution from the pressure. Under "usual" conditions this is only a minor correction, but in very compact objects it can become dominant.

When I took general relativity, it was a hand-in problem to compute the pressure (as a function of radial position) for a constant density ball (with total mass and radius as parameters); we were then asked to examine what happens if the radius is shrunk (density is increased). It turns out that as the ball radius approaches $$\tfrac{9}{8}$$ of the Schwarzschild radius for this mass, the pressure in the center of the ball tends to infinity! Beyond this limit, no amount of pressure (regardless of what domain of physics might be generating it) can balance gravity, so the ball will collapse. Concretely I suppose there would form an event horizon inside the ball, meaning the pressure outwards at that radial position vanishes, so that the ball starts collapsing, but that gets trickier to do the math for. What is straightforward to see is that there is no static solution to Einstein's equations when the ball gets that compact.

Some follow-up problems called for doing the same calculation with other density distributions, resulting in the same outcome. Our teacher mentioned that although this conjecture hadn't been proved, it was generally believed that no stable body with a radius less than $$\tfrac{9}{8}$$ of the Schwarzschild radius could exist, since noone had been able to come up with a mass distribution that attained such compactness while avoiding infinite pressure. But this is obviously a claim that needs a reputable source. 95.199.30.253 (talk) 20:19, 17 September 2019 (UTC)

metals
The article in one tiny place mentions that the electrons in metals can be considered a degenerate Fermi gas, but then the rest of the article seems to indicate that it exist in far away stars under rare conditions. Well, I suppose that at room temperature it is a little away from degenerate, but still pretty close. It would seem, though, that with metals being something we commonly run into, and neutron stars not so often, that it could be more prominent. Gah4 (talk) 07:05, 16 February 2021 (UTC)
 * Sure but when people discuss degenerate matter, they are mostly talking about star stuff. When discussing metals, it is mostly to discuss electron degeneracy pressure.--ReyHahn (talk) 07:19, 16 February 2021 (UTC)
 * OK, that is it. I got to this page from degeneracy pressure and was surprised that it didn't include all that I thought it should.  I didn't think about a separate article.  Should there be a note at the top mentioning that one?  Gah4 (talk) 09:13, 16 February 2021 (UTC)
 * Perhaps the articles should be merged, and the scope of this article expanded from astrophysics to also include degeneracy pressure in ordinary matter? This article includes most of the text from Electron degeneracy pressure anyway, divided between the sections Concept (main article Fermi gas) and Electron degeneracy. Would there be any negative effects from this? Jähmefyysikko (talk) 18:35, 26 July 2023 (UTC)
 * I am partially against, do you have some references that "degegenerate matter" is commonly used to refer to metals? I added the definition from an astronomy dictionary. I am aware that electrons in a metal and nucleons have a similar description but the whole article already is based on describing extreme cases. How often do people use the term for metals and nucleons? Maybe the title could be changed into "degeneracy pressure" and that way we could have both, but extra effort is required. Note that Fermi gas already covers many cases.--ReyHahn (talk) 05:21, 27 July 2023 (UTC)
 * On the other hand, the article already states many times that the concept of degeneracy pressure explains metals.--ReyHahn (talk) 05:24, 27 July 2023 (UTC)
 * Thanks for the answer. I agree that degenerate matter is not a label normally used for ordinary metals, so the title should be changed if a merge is done. But degeneracy pressure seems common enough term to qualify for a title. I will start a larger discussion on merging only when I know that I actually have time to work on the article. Jähmefyysikko (talk) 07:24, 27 July 2023 (UTC)
 * On the other hand, the article already states many times that the concept of degeneracy pressure explains metals.--ReyHahn (talk) 05:24, 27 July 2023 (UTC)
 * Thanks for the answer. I agree that degenerate matter is not a label normally used for ordinary metals, so the title should be changed if a merge is done. But degeneracy pressure seems common enough term to qualify for a title. I will start a larger discussion on merging only when I know that I actually have time to work on the article. Jähmefyysikko (talk) 07:24, 27 July 2023 (UTC)

Lead sentence dramatically incomplete.
C class indeed. The article content is not terrible but how do we know?

I don't believe the lead sentence is correct. As far as I can tell almost all ordinary matter is "degenerate" in that the the term seems to mean the ground state of a fermion system. Density is not a consequence or cause of degeneracy. The reference cited has two definitions, the first does not say ground state of ordinary matter, but does describe it:

''degenerate matter Physics. a dense matter in which fermions (electrons, neutrons, protons) must occupy states of high kinetic energy in order to satisfy the Pauli exclusion principle''.

(Even this definition is a bit bogus since the fermions occupy the lowest possible states consistent with the Pauli principle, not ones of "high kinetic energy").

The Fowler and the Lieb refs make the point that the Pauli role in the stability of ordinary matter is the same effect as the stability of white dwarf stars. Johnjbarton (talk) 14:08, 27 July 2023 (UTC)
 * I am glad to help here. I did not create the article but I cleaned it up from even a worse shape before. I would not call all ordinary matter degenerate matter. I agree that ordinary matter is always degenerate in some sense, but here we refer to the idea of have a sea of fermions occupying most of the low energy states even in the presence of temperature. The same principle with the atomic nuclei, it can be degenerate, but just because of that we are not calling all matter degenerate matter. Do Fowler or Lieb ever use the term "degenerate matter"? therein lies the whole nuance of this article. — Preceding unsigned comment added by ReyHahn (talk • contribs)


 * Such description applies well to ordinary metals. Typical values of Fermi energy are about 2-10 eV and 1 eV corresponds to 10000K, so the typical Fermi energy for metals is much larger than room temperature. Bruus & Flensberg's textbook (draft versoion) says the following: Jähmefyysikko (talk) 18:11, 27 July 2023 (UTC)
 * Yes, thanks that helps. That is the modern understanding for a Fermi electron gas. Which is to say, a type of ordinary matter.
 * I started a History section based on some articles I found. I've traced down "degenerate/degeneracy". Nothing at all to do with quantum state degeneracy! Rather it was a name Nernst invented to describe ideal gas behavior at T->0 no longer being ideal.
 * This makes the phrase "degeneracy pressure" quite bizarre. Degenerate matter is kinda ok because it can mean a state of matter at effectively T->0 (as the kT << Ef implies). Johnjbarton (talk) 18:45, 27 July 2023 (UTC)
 * I'm beginning to think that my history source may not be clear. In various other places I read that Nernst was ahead of pack on the transition to quantum. I wonder if it is possible that his use of the word "degeneration" was in fact related to quantum degeneracy. I've found no article that mentions any confusion between degenerate gas and quantum degeneracy. I did find one reference on degeneracy pressure. Johnjbarton (talk) 04:36, 28 July 2023 (UTC)
 * I am bit lost on your purpose. Are you saying that for example glass is degenerate matter? What about polar materials? Clearly the electrons in metals under standard pressure and temperature can be considered like a degenerate gas and degeneracy pressure plays a role in their bulk modulus, but maybe one would not call the whole metal as degenerate matter because, for example, the ions are not degenerate gas (even if the ion nuclei is again degenerate gas).--ReyHahn (talk) 10:49, 28 July 2023 (UTC)
 * At least I am trying to get some understanding whether there is anything fundamentally different between metals and degenerate matter in stars, before forming an opinion on what should happen with the article. I still do not see the difference between metals and white dwarves. If I understand correctly, the ions in a white dwarf are not degenerate, in the sense that it is the electron degeneracy which provides the internal pressure, not the ionic one. (But with white dwarves I only know the physics from Wikipedia, so I might be wrong.) Jähmefyysikko (talk) 12:55, 28 July 2023 (UTC)
 * You have a point there, the ions in the white dwarf are not degenerate (as in metals). That was my first argument so I will desist on that. My second argument as of now, it's that I tracked "degenerate matter" in condensed matter book and could not find any mention. It seems to be discussed mostly in astrophysics books.--ReyHahn (talk) 17:13, 28 July 2023 (UTC)
 * The electron degeneracy pressure article is the source of my confusion. The refs are about stability of bulk matter and they are also applied to white dwarf stars. I believe all of these cases are similar in the sense of being fermion systems in the ground state: the electrons seek the lowest level compatible with Pauli.
 * I believe the combination of Thomas-Fermi density theory and Pauli principle is used for all the cases. However, obviously does not make sense to ask about marginal (differential) properties in bulk. So "why stable" but not "specific heat".
 * The "degeneracy" part is a different aspect in that special effects only occur for T->0. That is what separates "ordinary stable bulk matter" from Fermi metals and white dwarfs. In this regime, electrons dominate bulk properties. Thus I don't think that the type of matter alone dictates "degenerate".
 * I still think the "degeneracy pressure" aspect needs solid references. The only way it makes sense is as an explanation for pressure at T->0. It has to be a bulk property, it has to be a kind of hand wave reaction force to gravity. White dwarf stars can't have surface pressure due to electrons, they would simply escape.
 * In any case I assert that our collective uncertainty based on these articles suggest further work. Johnjbarton (talk) 17:44, 28 July 2023 (UTC)
 * There are sources of "electron degeneracy pressure", I will add some if that helps.--ReyHahn (talk) 08:47, 29 July 2023 (UTC)

Concept? How does uncertainty lead to energy?
There is not a single reference in the entire concept section.

The article claims that: Since the locations of the particles of a highly compressed plasma have very low uncertainty, their momentum is extremely uncertain. Then displays the uncertainty relation with Planck's constant. So here we have objects of astronomical dimensions, say half the diameter of the Earth and an equation typically important on the scale one half the diameter of an atom. Something does not add up, or maybe multiple up is more correct in this case.

Suppose we let this slide: how then does an uncertainty in momentum lead to an energy? I'm sure there is a completely rational explanation, but I assert that even a trained physicist would need to puzzle out why this can be. Johnjbarton (talk) 14:18, 27 July 2023 (UTC)
 * Modern physics teaching is filled with this kind of heuristic derivations, but I agree that if there is not a source, it is worth peanuts. I think the equation is not being applied on the whole gas but in the idea that fermions are so densely packed that their position is very localized. Anyway I would recommend just dropping the whole idea unless somebody can source it. I am also missing how to go from the uncertainty principle to a pressure but maybe with enough mental acrobatics one can arrive to a dimensional analysis correct expression. A look into some introductory books might help but I have none in mind right now (or at least none with this heuristics).--ReyHahn (talk) 15:28, 27 July 2023 (UTC)
 * I’d say its more about dimensional analysis. Typical momentum has to be something like p ~ hbar*n^(1/3), where n is the number density. The original argument sounds dubious: I see no reason why the states sould be localized, as in the Fermi gas they are plane waves at any pressure. As for the pressure, here the dimensional analysis is actually rather easy: pressure has the dimension of energy density, so we take fermi energy times the number density. But in my opinion, the Fermi gas model is easy enough so that one can use it to justify the story instead of resorting to dimensional analysis. Jähmefyysikko (talk) 20:42, 27 July 2023 (UTC)
 * I did find some slightly less handwavy versions of this argument but not one I would reference (Physics stack exchange).
 * I cut this section. We can do better with Taylor and with Ashcroft and Mermin.
 * Johnjbarton (talk) 23:08, 31 July 2023 (UTC)

Degenerate matter is not a state of matter
The lead sentence starts: but no example or reference is given. The examples are all models: electron gas in stars or metals, neutrons in metals or hypothetical (quarks).
 * Degenerate matter is a highly dense state of fermionic matter...

Is there something I'm missing? Johnjbarton (talk) 17:53, 31 July 2023 (UTC)


 * I changed the lead paragraph. The article is in a odd place, its not about something specific -- eg white dwarf stars -- nor about a model -- eg Fermi gas, but some intersection. Johnjbarton (talk) 22:37, 31 July 2023 (UTC)
 * Johnjbarton (talk) 22:38, 31 July 2023 (UTC)

Merge history in lead into History section
The lead contains a history paragraph that can be merged into the history section now that we have one. This would reduce the size of the lead. ReyHahn (talk) 18:15, 31 July 2023 (UTC)


 * Works for me, I'd prefer a single clean sentence in the lead about history: make the lead a definition and a summary. Johnjbarton (talk) 18:38, 31 July 2023 (UTC)

New concept
I started a rewrite of the Concept section. Not really happy with the result so I'll try again later. Nevertheless better than the previous content. I would like this section to be less handwavy and a bit deep than the lead but not mathy. Feedback and edits welcome. Johnjbarton (talk) 22:41, 31 July 2023 (UTC)


 * The second (and third) paragraph of the intro should be merged with the Concept section. Then the intro can just be a summary, including a sentence on degenerate pressure and gas. Johnjbarton (talk) 23:05, 31 July 2023 (UTC)
 * So are we merging electron degeneracy pressure here? --ReyHahn (talk) 08:55, 1 August 2023 (UTC)
 * If this article were better I don't think we need the other one. "Degeneracy pressure" redirects here. But that's another topic IMO. Johnjbarton (talk) 14:17, 1 August 2023 (UTC)