# Can String Theory Explain Quantum Gravity and Fundamental Constants?

• jonmtkisco
In summary: In standard star formation, there is not a continuous influx of new material being added "from the outside" of the system. In the virialized dust scenario, this is explicitly the case. That is a HUGE difference, and it is the whole point of my question that started this entire thread.In summary, the conversation discusses two different scenarios: one involving a hypothetical region of space filled with electrons, and the other involving a dense dust cloud. The first scenario proposes that the strong electromagnetic potential of the electrons would make it impossible for them to self-collapse into a black hole, regardless of their density. The second scenario considers a region filled with dust that collapses due to gravity, but then virializes due
jonmtkisco
1. As a thought experiment, imagine a region of space which (inexplicably) is very densely filled with electrons and contains no other matter. Gravity would drive collapse towards a singularity, but electromagnetism would cause the electrons to repulse each other. Since electromagnetic potential is far stronger than gravitational potential per unit of mass, is it impossible for such a collection of electrons to self-collapse into a black hole, regardless of the density of the electron cloud? My guess is that it is impossible.

2. Now let's imagine a region of space filled very densely with (electrically neutral) dust. Gravity causes the dust cloud to collapse, but then random motions and interactions. cause the dust cloud to virialize. If dust continues to infall into this region (from "outside"), thereby increasing its density indefinitely, and the newly infalling dust also virializes, is there any density threshold at which the total gravity of dust would "overcome" the virial resistance and cause the cloud to collapse into a black hole? (No gravity waves or external perturbations are allowed in this exercise). My guess is that the dust cloud would continue to virialize more and more with ever increasing angular momentum, withstanding collapse until the virial motion reaches a significant percentage of the speed of light, at which time the energy required to further increase the angular momentum would grow (due to special relativity) to the point where the cloud collapses into a black hole rather than gaining further angular momentum.

Jon

You are describing the formation of stars, i.e. overdense regions that collapse as far as the physics of the material making up the overdensity permits. Your questions would be answered by any text dealing with stars, their formation evolution and death.

Hi Wallace,
There is no such thing as a star formed entirely of electron plasma, with no ions.

And my virial question is addressing a scenario where the dust density is far higher than in the molecular clouds where "natural" stars form.

In both cases, I'm trying to explore what would happen in an artificially created extreme environment.

Jon

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As stars collapse the density becomes large, and further collapse is prevented by the physics of the material of the cloud. This is no different in the situation you describe. Your dust cloud would either form a star, black hole or whatever depending on the mass of the cloud and the elements it is composed of in exactly the same way as standard star formation.

As for the electron only case clearly the electrostatic repulsion would prevent collapse up until the mass was large enough to overcome the electron degeneracy pressure. Look up the Chandresarkar limit, again from any text about stars.

Hi Wallace,

The Chandresarkar limit applies to electron degenerency, when electrons are confined so tightly that they impinge upon the Pauli Exclusion principle.

However, I do not believe that a cloud comprised entirely of electron plasma could ever compress itself gravitationally to the Chandresarkar limit. Total gravity increases as the mass of the plasma increases, but the electrostatic repulsion of the negatively charged plasma also increases in the same proportion. Thus I think that in principle it is impossible for gravity alone to ever collapse an electron plasma.

Regarding the ability of virial motion to stop gravitational collapse, I think that as the total mass is increased, the virial motion will be radiated away as heat, which will tend to diminish any subsequent increase in angular motion. However, if additional density is added at a fast enough rate, there may be insufficient time for the cloud to radiate away much virial energy. For that reason, it seems to me that angular motion could continue to increase. When the temperature gets hot enough, nuclear fusion will kick into add outward pressure. If we continue to add dust mass rapidly, the gas pressure will be overcome and electron degeneracy and then neutron degeneracy will occur. If more mass is added, the structure would collapse to a black hole. But we have not dealt with the possibility that the structure will continue to add virial angular motion which could prevent (not merely reduce) further collapse. As I said, my guess is that in this scenario the only thing which could prevent the angular motion from increasing indefinitely is special relativity as the rotating dust particles approach the speed of light.

Jon

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Again, this is all dealt with in standard texts on star formation. I strongly recommend that you look to read up on this if you are interested in this further.

Hi Wallace,

I think you already know there is no standard text on star formation that discusses the gravitational collapse of clouds comprised solely of electron plasma. That scenario does not occur naturally.

And I have yet to find one that describes a situation where a virialized dust cloud far denser than any natural molecular cloud collapses directly into a black hole.

I would greatly appreciate if you would direct me to a specific text reference, but only if it deals with the specific scenarios I mentioned. Frankly I don't think you can because I believe such a text does not exist. But I am happy to be proved wrong because I want to learn about this subject.

Jon

The 'specific scenario' you describe is no different to parts of the process of star formation. I'm not sure why you think it is any different? You've got a dense lump of stuff in which gravity is (or isn't) balanced by thermal or other sources of pressure. Such objects are called stars. Calling it 'a virilised dust cloud' doesn't change the physics, and the physics that matters is the same as what occurs in stars.

Neutron stars are pretty dense objects, and if you go much denser then you get a black hole. What happens to your dust cloud will depend on its density in a way no different to stars.

Hi Wallace,

I recognize that the virialized dust scenario is not entirely different from standard star formation. However, I'm posing a scenario where both the dust density and total mass are so extremely high that the dust cloud collapses gravitationally straight through the star phase and into the degenerate matter phases. My specific question is at what point the virial angular velocity reaches a maximum, and what specifically prevents it from increasing beyond that maximum? I suppose that if nothing else happens first, eventually the dust particles will be pressed tightly together, and at that point surface friction should prevent individual particles from gaining individual virial motion. But presumably the dominant collective virial angular momentum would be transferred to the resulting solid lump. Then will the lump continue gaining rotational angular momentum as it further collapses, or is this the end of that process?

The electron plasma scenario departs much further from any natural scenario, since as far as I know there is no known situation in which vast freestanding clouds of pure electron plasma would form naturally. My only point here is that, regardless of how much total mass increases, the electron plasma will never collapse gravitationally at all, not to the form of a star or a solid, and certainly not to the Chandresarkar limit. In this kind of scenario, electrostatic repulsion will always prevail over gravity, and the cloud must inevitably disperse.

Jon

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I think that for point 1 you are not right and the cloud should collapse into a black hole.

Consider the usual collapse steps or levels in stars. At every of the levels you have some fermions that determine a degeneracy pressure. If gravity overcomes the degeneracy pressure, the fermions become compressed too much for the exclusion principle to hold. Then, nature solves the problem by converting those fermions into other ones with a higher degeneracy pressure. This process takes place until there is no fermion anymore to convert to. Then a black hole is formed.

For the usual star scenarios with baryonic matter the last step would be some kind of quark star. If gravity is still stronger quarks will be futher compressed. To avoid a violation of the exclusion principle something must occur. Since quarks are elementary particles and since no other reaction is possible, a black hole is formed.

I would then conclude that for a cloud of elementary fermions (electrons or whatever) a black hole would be formed if gravity is strong enough.

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Wallace said:
As for the electron only case clearly the electrostatic repulsion would prevent collapse up until the mass was large enough to overcome the electron degeneracy pressure. Look up the Chandresarkar limit, again from any text about stars.

I think what jonmtkisco is saying is that the inverse beta-decay process which allows the transition from electron-degenerate to neutron-degenerate matter wouldn't be an option if all particles where electrons (no protons to capture the electrons, hence no neutrons for neutron-degenerate matter) which implies that electron-degeneracy would prevail regardless of the pressure/densities brought on by the gravitational collapse. Maybe, under extreme conditions, if the inverse beta-decay option isn't available, the electrons would form tauons and then a whole new form of degenerate matter with a new process of collapse but the end result still being a black hole (a negatively charged Newman one at that)? Speculative but I suspect that a group of electrons with a mass in excess of 3+ sol could not undergo gravitational collapse without becoming something exotic.

stevebd1, your description of my point is correct. There can be no neutron degeneracy if there are no protons for the electrons to mate with!

More fundamentally, I don't see how an electron plasma could collapse even the slightest amount, let alone to the point of inverse beta-decay. The strong electrostatic repulsion would cause the cloud to spontaneously disperse from the very start.

Here's an esoteric question: Why is the Pauli Exclusion Principle not considered to be a fifth "fundamental force", along with the strong and weak nuclear forces, gravity and electromagnetism? It's not a manifestation of any of the four forces. Maybe effects can be characterized as forces only if they have an "attraction" component, which Pauli doesn't have (?)

Jon

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Here's a related question about virialization:

Galaxies tend to virialize extensively, with only a small percentage of their baryonic matter condensing in the center (as a supermassive black hole). On the other hand, stars tend to virialize very little, with only a tiny percentage of their matter avoiding collapse into the center (forming the star). Why the difference?

Superficially, one might expect a galaxy to be more prone to extensive central collapse, due to the huge gravity well caused by its dark matter halo. Stars on the other hand do not seem to have dark matter halos.

If stars virialized as much as galaxies do, we'd be hearing about star-mass "dust devils" that look like miniature galaxies. But of course we don't.

Does the difference between galaxies and stars result from the sheer scale difference between them, the different collapse durations, the different angular momenta, or perhaps the different particle sizes?

Jon

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Damn you guys are hella smart. Can anyone of you explain String theory to me?

Hi NYSportsguy,
I can't. String theory makes no sense to me so I mostly ignore it.

Jon

jonmtkisco said:
Here's a related question about virialization...Does the difference between galaxies and stars result from the sheer scale difference between them, the different collapse durations, the different angular momenta, or perhaps the different particle sizes?

I'm stepping pretty far out of what I actually know here, but I would speculate that it has to do with the large amount of dark matter that appears present in galaxies. If you consider the http://en.wikipedia.org/wiki/Galaxy_rotation_problem" , you could conclude that what's keeping all that mass from infalling is the same thing that's keeping the rotation curve from falling off as expected.

Following from that it would make sense that it would not occur on the star formation level because there is no large amount of dark matter at the edges of our solar system to counteract the natural gravitational attraction.

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Hi quisquis,
Quisquis said:
I would speculate that it has to do with the large amount of dark matter that appears present in galaxies.

That's an interesting idea, but I do not think it's the explanation. The Newtonian Shell Theorem says that if matter is distributed spherically around a centerpoint, the shells of matter outside of the object in question have no gravitational effect on the object. Thus only the matter (both dark and baryonic) which is closer to the center than the object would affect it, and the resulting gravity would be entirely inwards towards the center.

I found a recent star formation paper http://arxiv.org/PS_cache/astro-ph/pdf/0604/0604615v1.pdf" which may shed some light on my question. It says that virial velocities caused by turbulence in a molecular cloud tend to increase with scale, following the formula:

(well my laTex isn't working, but the formula is:) v is equiv to R^1/2

If that formula holds up to the very large scales of galaxies, it would be easy to see why they have more virial angular momentum and thus are less prone to collapse to the center.

Jon

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jonmtkisco said:
stevebd1, your description of my point is correct. There can be no neutron degeneracy if there are no protons for the electrons to mate with!
jonmtkisco, how do you explain the formation of a black hole from the collapse of a neutron star or a quark star? The same mechanism would apply for your electron cloud.

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Jonmtkisco -

My professor at Stanford was one of the founders of String theory.

I know it has something to do with linking quantum field theory and general relativity equations on a sub-atomic scale.

Hi Hellfire,

hellfire said:
jonmtkisco, how do you explain the formation of a black hole from the collapse of a neutron star or a quark star? The same mechanism would apply for your electron cloud.

Here's how Wikipedia describes collapse of a neutron star into a black hole (bold added):
The Tolman-Oppenheimer-Volkoff (TOV) limit is an upper bound to the mass of stars composed of neutron-degenerate matter (neutron stars). It is analogous to the Chandrasekhar limit for white dwarf stars. ...

In a neutron star lighter than the limit, the weight of the star is supported by short-range repulsive neutron-neutron interactions mediated by the strong force and also by the quantum degeneracy pressure of neutrons. If a neutron star is heavier than the limit, it will collapse to some denser form. It could form a black hole, or change composition and be supported in some other way (for example, by quark degeneracy pressure if it becomes a quark star). Because the properties of hypothetical more exotic forms of degenerate matter are even more poorly known than those of neutron-degenerate matter, most astrophysicists assume, in the absence of evidence to the contrary, that a neutron star above the limit collapses directly into a black hole.

One would need to examine the TOV equation and the Equation of State (which is poorly understood) to try to figure out how much degeneracy pressure a pure degenerate neutron gas produces to resist further compression.

On the other hand, I assume that a pure degenerate electron gas also has an equation of state which would further resist compression after the Pauli Exclusion Principle has been completely overcome. I have no idea whether it has a "stiffer" or "softer" equation of state, more or less resistant to compression, than a degenerate neutron gas. I haven't seen anything written on this specific subject, e.g. no electron equivalent to the TOV equation. (To be clear, I'm not talking about the Chandrasarkar limit, because that's the stage where electrons combine with protons, and as we've said this scenario includes no protons.)

Certainly there is some mass and density limit beyond which a degenerate electron plasma could be externally forced to collapse into a black hole. One can readily imagine a scenario where the electron plasma is entirely enclosed within a dense spherical shell of electrically neutral matter, and this outer shell supplies enough gravity to collapse the whole structure into a black hole.

In any event, as I said I think the most important point here is that a pure electron plasma is entirely incapable of compressing itself to the point of testing the Pauli Exclusion Principle, because the strong electrostatic self-repulsion should avoid ANY initial gravitational collapse.

Jon

jonmtkisco said:
I found a recent star formation paper http://arxiv.org/PS_cache/astro-ph/pdf/0604/0604615v1.pdf" which may shed some light on my question. It says that virial velocities caused by turbulence in a molecular cloud tend to increase with scale, following the formula:
Now that LaTex is back, the formula is:

$$v \propto R^{1/2}$$

(I meant "proportional to" when I said "equivalent to").

So anyway, I guess the best technique to utilize virial motion to prevent collapse into a black hole is to start with a supersized and superdense dust cloud. Galaxy scale is better than star scale, and galaxy cluster scale is even better. I surmise that at these larger scales, virial motion is defeated slowly over time only by random collisions (and near-collisions) between stars, and by the perturbative influence of gravity waves. What I don't know is how dense a galaxy cluster must become in order to spontaneously collapse almost 100% of its matter into a black hole within a reasonable timeframe, say 20 million years. There is no indication that such high densities occur naturally.

Jon

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Jon. It does not matter if there are only electrons present. If you have an overdense clump of them (say you prepared it somehow), they will undergo the exact same stellar formation process as any other lump of matter.

The only difference is they will have a lower mass threshold (TOV limit) to form a bh than say a bunch of protons, since they will not phase transition into a neutron degeneracy state and instead promptly become a bh.. Also they carry extra EM energy, so that will further reduce the threshold if you properly take GR into account.

What is true (at least I think), is that no such object can ever exist naturally (barring something extreme), since one of the simple assumptions of stellar formation is isotropy of the dust. The electrons will never form an overdense system.

Hi Haelfix,

1. Why will an electron plasma have a lower mass threshold to form a black hole? Don't they still have a resistance to quantum degeneracy? In other words, even if the electrons are pushed tightly together, won't they still will resist being further crushed into an amorphous blob? Just as neutrons do.

2. You say that the electromagnetic energy carried by electrons causes them to have higher gravity per unit mass than, say, neutrons or protons?

3. Of course I agree that a "large" electron plasma cloud is not a natural occurrence in nature. I said that in my first post. My point is that if one could be artificially created (not farfetched) it would never self-collapse at all. True or false?

Jon

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Gah reply was eaten.. Semi brief version
1) If there are only electrons present by hypothesis, they have no parameter space known in current physics with which to fall back on, since they are stable fundamental particles. Since they cannot undergo inverse beta decay (as with regular dust) they will presumably form a BH right at the Chandreskhar limit (the cutoff equilibrium point between electron degeneracy pressure and gravitational forces), and not at the TOV limit.

2) I wouldn't put it that way, since protons also carry charge. However there is not necessarily the same EM stress energy content, since there are global EM fields present in the electron case. I do not know if this is significant or not to effect things that much in the hydrodynamic equations typical of stellar collapse models or not, but I think maybe yes.

3) False. Although amusingly it occurs to me that to even bring an electron plasma into a small enough volume with sufficient mass would require a ton of work. You would probably collapse yourself into a bh, long before you would reach the desired configuration.

On your point #1, present physics may not have an answer, OK. But I don't understand what basis there is for rejecting the expectation that individual electrons will resist quantum degeneracy (obliteration) just as protons do. Is there a specific justification for denigrating leptons as second class quantum citizens? Are we "quark/gluon bigots" here?

On your point #3, I agree completely that an electron plasma could never be configured so that it would even begin to collapse gravitationally. I was the one who said that such a cloud would disperse from the start.

Jon

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Hi folks, here's some more info comparing gravity and electrostatic force potentials.

From Wikipedia "Coulomb's Law" http://en.wikipedia.org/wiki/Coulomb%27s_law" (bold added):
When measured in units that people commonly use (such as SI...), the electrostatic force constant, is numerically much much larger than the universal gravitational constant. This means that for objects with charge that is of the order of a unit charge (C) and mass of the order of a unit mass (kg), the electrostatic forces will be so much larger than the gravitational forces that the latter force can be ignored. This is not the case when Planck units are used and both charge and mass are of the order of the unit charge and unit mass. However, charged elementary particles have mass that is far less than the Planck mass while their charge is about the Planck charge so that, again, gravitational forces can be ignored. For example, the electrostatic force between an electron and a proton, which constitute a hydrogen atom, is almost 40 orders of magnitude greater than the gravitational force between them.

From Univ of Texas Lecture Notes http://farside.ph.utexas.edu/teaching/em/lectures/node28.html" (bold added):
[The ratio of electrical force to gravitational force per unit mass is $$4.17 X 10^{47}$$ ]

This is a colossal number! Suppose we are studying a physics problem involving the motion of particles in a box under the action of two forces with the same range, but differing in magnitude by a factor . It would seem a plausible approximation (to say the least) to start the investgation by neglecting the weaker force. Applying this reasoning to the motion of particles in the Universe, we would expect the Universe to be governed entirely by electrical forces. However, this is not the case. The force which holds us to the surface of the Earth, and prevents us from floating off into space, is gravity. The force which causes the Earth to orbit the Sun is also gravity. In fact, on astronomical length-scales gravity is the dominant force, and electrical forces are largely irrelevant. The key to understanding this paradox is that there are both positive and negative electric charges, whereas there are only positive gravitational "charges.'' This means that gravitational forces are always cumulative, whereas electrical forces can cancel one another out. Suppose, for the sake of argument, that the Universe starts out with randomly distributed electric charges. Initially, we expect electrical forces to completely dominate gravity. These forces try to make every positive charge get as far away as possible from the other positive charges, and as close as possible to the other negative charges. After a while, we expect the positive and negative charges to form close pairs. Just how close is determined by quantum mechanics, but, in general, it is pretty close: i.e., about m. The electrical forces due to the charges in each pair effectively cancel one another out on length-scales much larger than the mutual spacing of the pair. It is only possible for gravity to be the dominant long-range force if the number of positive charges in the Universe is almost equal to the number of negative charges. In this situation, every positive change can find a negative charge to team up with, and there are virtually no charges left over. In order for the cancellation of long-range electrical forces to be effective, the relative difference in the number of positive and negative charges in the Universe must be incredibly small. In fact, positive and negative charges have to cancel each other out to such accuracy that most physicists believe that the net charge of the universe is exactly zero.

I also note that the self-repulsive behavior of a pure proton plasma should be essentially the same as for a pure electron plasma, despite the fact that protons are much more massive than electrons. The electrostatic repulsion is so much stronger that gravitational attraction simply is insignificant.

Jon

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Do you expect this arguments to hold at very short distances regardless of the running of the coupling constants? I expect they will not hold. In any case, I still think that the formation of a black hole is possible in principle if gravity is strong enough. Whether gravity is strong enough or not wrt the electromagnetic repulsion may be scope of discussion actually, but I don't think that you will be able to conclude anything without a detailed analysis. Without this detailed analysis I would expect that the formation of a black hole from the collapse of a quark star would be a good analogy to extrapolate the behavior of an electron cloud.

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Hi hellfire,

I don't see any basis in the straightforward physics here for your expectation.

The material I cited makes it very clear that an electron plasma's self-gravity could never cause it to spontaneously collapse even a little bit. Instead, it would spontaneously fly apart at very high acceleration due to its electrostatic self-repulsion. The aggregate electrostatic force is vastly stronger than the aggregate gravity for ANY quantity of pure electrons.

Thus self-gravitation can never cause the electrons to come within "very short distances" of each other.

If an EXTERNAL gravity source is added to the structure (such as the dense exterior electrically neutral shell I mentioned), then of course the gravity added by that external source could cause the entire structure to collapse into a black hole. As I said in an earlier post, there must be some amount of external force which can overcome the electrostatic repulsion of a finite number of electrons, and cause such a collapse. In that case, perhaps an electron would be broken up into smaller particles, such as preons. I don't think anyone knows. If individual electrons break apart then the situation is somewhat analagous to the theorized (but not generally accepted) idea of a quark star. If an electron is broken up into preons or whatever, will it lose its negative charge? I suppose it's possible.

I think you are asking whether, if electrons are externally squeezed to "very short distances" from each other, will the self-gravity of the electrons ever overcome their electrostatic repulsion? My answer is, OF COURSE NOT. As you squeeze more electrons into a given unit of volume, each newly added electron adds both gravity AND electrostatic repulsion. So the greater the electron density, the more the aggregate repulsion force exceeds the aggregate gravity. Such squeezing gives the electron plasma MORE net expansion force per unit volume than if they were allowed to move farther apart. That's assuming that the electrons are not squeezed closer than "very short distances apart."

Jon

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Those articles are talking about completely different things

In a semi realistic example with n electrons in a gas, what would happen is the charge would tend to fall into a configuration of minimized energy (i'll save you the trouble and simply tell you the answer.. all the electrons will arrange themselves in a spherically symmetric pattern along the outer radius of the center of charge). The em field actually will cancel at the center, and gravity will go through unhindered until you start reaching radius scales where electron collisions start occurring (this will cause a sort of friction and create an outward thermodynamic pressure effect) and then quantum mechanics eventually pushes them into a degenerate state, just as in ordinary stellar collapse.

You realize of course why this is no different than any regular star formation scenario with normal dust. During the initial phase of collapse, you will have some thermodynamic pressure caused by electrostatics, but this is unable to support the weight of gravity. However it will reach a point where the temperature is so large, that nuclear fusion will kick in. This can (depending on the aggregate mass) stop the collapse, and a star is born.

Hi Haelfix,
Haelfix said:
... all the electrons will arrange themselves in a spherically symmetric pattern along the outer radius of the center of charge). The em field actually will cancel at the center, and gravity will go through unhindered until you start reaching radius scales where electron collisions start occurring...

I don't know exactly what scenario you are describing, because you don't put enough context around it.

If you are describing what an (artificially assembled) freestanding spherical cloud of pure electron plasma will do in empty space, I agree that the electrons will immediately spontaneously move AWAY from the center. However I see know reason why the expanding cloud would take on the shape of a hollow ball. I think the electron cloud will retain approximately homogeneous distribution and simply retain the shape of an expanding solid ball of electrons. I don't see anything that would cause the electrons that started at the center of the sphere to accelerate away from the center faster than the electrons that started towards the outer edge. Thus the sphere will not evacuate itself.

It makes sense to me that in accordance with Gauss' Law, the strength of the electrostatic field inside the expanding sphere would decrease towards the center of the sphere. EM field strength is directly proportional to distance (not the square of the distance) from the center. This is precisely analagous to the gravity field, which decreases in the same way towards the center of the sphere. Thus the electrons' own self-gravity can never exceed their electrostatic self-repulsion at the center or at any other location in the expanding sphere. (Of course at a single point at the very center, both fields are exactly zero).

Haelfix said:
You realize of course why this is no different than any regular star formation scenario with normal dust.
I disagree Haelfix, for all the reasons I have mentioned.

Haelfix said:
However it will reach a point where the temperature is so large, that nuclear fusion will kick in. This can (depending on the aggregate mass) stop the collapse, and a star is born.
Uhhh... what? How can a cloud comprised of nothing but electrons undergo nuclear fusion?

Jon

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Jon, the last point was referring ot regular dust. Electrons won't undergo fusion, so they go straight to the white dwarf stage.

Actually, the white dwarf is still very much the same problem. You have mostly all electrons there as well, concentrated in a spherical configuration. The more mass you stick in, the more electrons you get and the smaller the radius becomes. Yet gravity still wins as you increase the mass (actually its not the electrostatic field that causes the supporting outward pressure, but rather quantum mechanics).

Hi Haelfix,

Haelfix said:
Actually, the white dwarf is still very much the same problem. You have mostly all electrons there as well, concentrated in a spherical configuration.

No I'm sorry, that isn't correct. White dwarfs are comprised of matter that contains an equal complement of protons and electrons. As a star undergoes collapse to become a white dwarf, its electrons separate from the nuclei, and both the electrons and nuclei are squeezed into a space that is smaller than the normal low-energy electron orbitals. This state of matter is called "electron degenerate matter." Perhaps that name is the source of confusion here.

With even further squeezing, the particles are compressed beyond the Chandrasekhar limit, and the electrons combine with the protons to form a soup that is mostly all neutrons. This neutron soup can be squeezed further to surpass the TOV limit, in which case the individual neutrons presumably are "crushed" and the structure may collapse into a black hole.

None of the above is directly relevant to a pure electron plasma. Since there are no nuclei, there are no electron orbitals at stake. And no neutrons can form.

I have repeated this description enough times that I hope by now I've made my point. An electron plasma is a different animal, end of story.

Jon

jonmtkisco said:
The material I cited makes it very clear that an electron plasma's self-gravity could never cause it to spontaneously collapse even a little bit.
Sorry but I do not see that the material you cited is a rigorous treatment of this topic. At least I am reluctant to accept it as a proof.

Typically a white dwarf has a bunch of carbon and oxygen when it forms, however as you increase the mass of the star, the extra compression forces electrons to be stripped from the remaining nuclei, and you end up with a sea of electrons floating around the place.

So actually what you normally have is a thin outer strip around the White dwarf of mostly nondegenerate matter (read much of the nuclei), and the bulk is degenerate matter where the density of electrons is much, much higher than protons and neutrons and so forth.

If you look at the system from the interior, as I said, you have very much the same sort of thing. The more mass you put it, creates more electrons in the bulk and contrary to what you would think, actually *shrinks* the star.

Hi hellfire,
hellfire said:
Sorry but I do not see that the material you cited is a rigorous treatment of this topic. At least I am reluctant to accept it as a proof.
Fair enough, I have not found any rigorous treatment of this specific subject. If you find one please let me know; of course it would supersede our non-rigorous discussion here. I am eager to learn if there are subtle effects we haven't accounted for.

At the non-rigorous level of our discussion, the logic in favor of the behavior I've advocated is far stronger than the logic against it. It is common knowledge that the electromagnetic potential of electrons and protons far exceeds their gravitational potential.

Jon

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