What is wrong with the Kalam Cosmological Argument?

[Magical Wand]

Wow, you seem to be scientists, I am just a layman so obviously I don’t aspire to be at your level.


But anyway let’s start with the second law of thermodynamics.

P1 If the universe is past eternal the entropy of the universe would be nearly 100%

P2 the entropy of the universe is low (far from 100%)

Therefore the universe is not past eternal.

An analogy could be if you have a glass of water with ice, you can safely conclude that the water has only been there for a limited amount of time, (otherwise the ice would melt)

This seems to be strong evidence in favor of the beginning of the universe.

What’s your opinion on this? How can you have low entropy if the universe is past eternal?

So, I actually made a post about this titled The 2nd law of thermodynamics is not evidence of God

Anyway, Meow Mix's argument is relevant, too, because entropy is always low when the field decays. Once it decays, entropy starts growing. However, given eternal inflation, there could always be low entropy fields decaying in the future. And the same may well apply to the past.

But it is important to notice this assumes eternal inflation is correct (that is, that an inflationary multiverse exists), and that this creation of bubble universes had no beginning. That's certainly a possibility (and it seems there is some evidence supporting it), but it is not necessary to refute the entropy argument.

 

[Magical Wand]

Wow, you seem to be scientists, I am just a layman so obviously I don’t aspire to be at your level.


But anyway let’s start with the second law of thermodynamics.

P1 If the universe is past eternal the entropy of the universe would be nearly 100%

P2 the entropy of the universe is low (far from 100%)

Therefore the universe is not past eternal.

An analogy could be if you have a glass of water with ice, you can safely conclude that the water has only been there for a limited amount of time, (otherwise the ice would melt)

This seems to be strong evidence in favor of the beginning of the universe.

What’s your opinion on this? How can you have low entropy if the universe is past eternal?

In my favorite cosmological model, the scalar field always existed in the past without decaying; it was inactive. The entropy only starts growing once the field decays. In other words, the entropy only starts growing when the Big Bang occurs. That's because entropy only makes sense when there is a distribution of particles in a closed system. But before the scalar field was activated, there were no particles around so that entropy could be measured. Space was empty (of real particles).

Particles only appear once the field decays. So, that's when you can talk about entropy growth.

 

[leroy]

The universe you see has an entropic gradient, but given things like inflation, the universe you see is not the entire universe (it is just where the inflaton field has decayed; which gives you a bubble where the entropic gradient clock begins, and gives local time its arrow). But elsewhere, the inflaton field has not decayed; it is a different time, a metatime.

So you can have a beginning of time (local time), but that wouldn’t be an ontological beginning.

This isn’t an exact picture, but a simple way to think of it is if you have a space in which you create universes that live and die, obviously time would “begin” in those universes, and time would end in those universes (if Penrose is onto something, which he might be). But the overall space those universes develop in has its own time. So while universe A begins and ends, perhaps universe Z begins and ends temporally after that entire process. (The point being: do you see how there is a more encompassing, and different, time than the time we know of here in our entropic gradient in this case?)

What you need to disabuse yourself of is the notion that the only time that exists is defined by the entropic gradient that we see; but there could be gradients outside of this universe’s entropic gradient.

Again, I have vastly oversimplified all of this (for one reason, I’m on a phone right now), but the general concept conveyed should still help to answer the question.

Having multiple (infinite) local universes is a hard consequence to escape from with inflation.

Well it seems to me that you are making 2 big assumptions

1 there is a vast universe outside our bubble (the universe is trilions over trillions over trilions of times larger than the observable universe)

2 the average entropy in the universe is close to 100% we simply happen to be in a relatively small and statistically insignificant bubble where the entropy is low.

This 2 assumptions seem completely adhoc and unparsimonious to me.

But the gratest objection would be the fact that our bubble is very big, (much bigger than necessary) it would have been vastly more likely that we live in a bubble say as small as our solar system.

 

[Meow Mix]

Well it seems to me that you are making 2 big assumptions

1 there is a vast universe outside our bubble (the universe is trilions over trillions over trilions of times larger than the observable universe)

2 the average entropy in the universe is close to 100% we simply happen to be in a relatively small and statistically insignificant bubble where the entropy is low.

This 2 assumptions seem completely adhoc and unparsimonious to me.

But the gratest objection would be the fact that our bubble is very big, (much bigger than necessary) it would have been vastly more likely that we live in a bubble say as small as our solar system.

These points are more reasoned out than you may believe. You'll have to forgive me on some of this as, while I'm an astrophysics grad student, actual QFT classes aren't until this fall semester and next spring; so I'm responding without as much technical expertise as I would otherwise have in a year. Still, I think I can give a sufficient response based on what we've touched on under different topics, especially the cosmology courses.

With (1), whether or not there is a wider universe outside of our cosmos (if we use the term "cosmos" for our bubble), while not directly observable, is a logical consequence of inflationary theory, which is very strongly evidenced by observation. See also Phi's response in post #502, as it's relevant. If we find evidence of inflation in the cosmos that we see, then it's not just throwing our arms up and saying "maybe there's a lot more outside all of this," it's a very reasonable consequence of the observations. The way inflation works in QFT is that there is an inflaton (not a typo) field that decays not unlike a radioactive isotope might decay.

Where it decays becomes a bubble cosmos, of which ours is one. Since it doesn't decay all at once, elsewhere it continues, and it can continue eternally (and could have been happening eternally). Since inflation expands at enormously greater intervals than the cosmic expansion of the visible universe, inflation quickly dominates over bubbles; and it nicely balances with the gravity of bubble cosmoses (it is a Paul Davies-style free lunch: 1 + (-1) = 0).

So, calling (1) an assumption sort of walks a fine line. Yes, we can't directly observe a larger eternal inflation universe; but if we make observations about inflation in the cosmos we can see, the rest are consequences of that observation. And we do make observations that strongly support inflationary theory.

Regarding (2), Phi beat me to the punch in #502 again. Keep in mind that time's arrow and entropy are the same thing. The Big Bang event was an entropic minimum, but an entropic minimum is not the same thing as an ontological beginning. Even if we didn't have any evidence for inflation (and we do, I'm just saying even if we didn't) then the second premise of the Kalam Cosmological Argument would still be unjustified because there would still be another possibility.

The fact remains that there is not only another possibility than an ontological beginning, but also good reason to think there wasn't one for the cosmos (meaning, again, the local bubble universe).

So this is why Craig pulls up people like Vilenkin, Borde, and Guthe. But that doesn't work either, because all that their paper does is tell us that our metrics are singular in the realm of quantum gravity, which is a giant non-surprise. Craig doesn't really understand it.

 

[joelr]

Q1
It simply means that it's excistance is independent of time. For example if you grant that numbers or moral values excist independently of the human mind, then numbers and moral values would also be timeless objects (also called platonic objects)

Values are mental states which require time. A timeless frame of reference experience no time or space. Nothing happens.

I would not deny that possibility, maybe there was a timeless "cosmic egg" but I would argue the cosmic egg woulnt be a sufficient cause for the universe

We know a universe exists and laws of nature. No Gods exist that can be demonstrated. If the universe came from something saying it's because of a man-made mythological character instead of simply more aspects of nature and natural laws doesn't make much sense.
Right where out current cosmology ends, bang GOD! RIght there, at that spot. Wow, what a coincidence?
God is always right at the edge of science. In Newtons time the planetary orbits that couldn't quite be figured out was were God was adding a little help.

 

[TagliatelliMonster]

Wow, you seem to be scientists, I am just a layman so obviously I don’t aspire to be at your level.


But anyway let’s start with the second law of thermodynamics.

P1 If the universe is past eternal the entropy of the universe would be nearly 100%

P2 the entropy of the universe is low (far from 100%)

Therefore the universe is not past eternal.

An analogy could be if you have a glass of water with ice, you can safely conclude that the water has only been there for a limited amount of time, (otherwise the ice would melt)

This seems to be strong evidence in favor of the beginning of the universe.

What’s your opinion on this? How can you have low entropy if the universe is past eternal?

First acknowledges that the poster's scientific knowledge is vastly superior to his own.
Then proceeds to debate based on declarations about thermodynamics.


Priceless.

I also find it hilarious that you didn't actually respond or acknowledge any of his 6 points and instead jumped on something else he didn't even mention.

Absolutely priceless.

 

[leroy]

Particles only appear once the field decays. So, that's when you can talk about entropy growth.

@Meow Mix
And you Made similar points, so my responses to her also apply to you, (if you think I ignored a relevant point made by you please let me know


But if the universe is past eternal, it remains inexplicable why our fields decayed 13.8B years ago to produce our big bang.

If the universe is past ethernal then any field that existed would have decayed an infinite amout of time ago.

An analogy would be imagine that you are playing poker since infinite past, given this I would conclude that you got your first “full house” and infinite amount of time ago, it makes no sense that you got your first “full house” 13.8 billions years ago (nor at any point in the finite past)

@Meow Mix With (1), whether or not there is a wider universe outside of our cosmos (if we use the term "cosmos" for our bubble), while not directly observable, is a logical consequence of inflationary theory, which is very strongly evidenced by observation. See also Phi's response in post #502, as it's relevant. If we find evidence of inflation in the cosmos that we see, then it's not just throwing our arms up and saying "maybe there's a lot more outside all of this," it's a very reasonable consequence of the observations. The way inflation works in QFT is that there is an inflaton (not a typo) field that decays not unlike a radioactive isotope might decay.

My problem is not the claim that inflation (or even eternal inflation is true) for the sake of this discussion we can assume that such model is true.

The issue is that all the observable universe seems to have low entropy while your model of “infinite past” predicts high entropy (nearly 100% entropy) even in eternal inflation entropy on average always increases so low entropy is not expected to be seen.

Given that our observations contradict your predictions you have to go beyond science and speculate a lot……. For example under your view our observable universe should be just a small grain of sand compared to the whole universe, such that the observed low entropy would be just a statistically insignificant exception.

But talking about the second law my biggest objection to an infinite past would be that the universe would be dominated by Boltzmann brains, Boltzmann brains would be the most typical and abundant type of observer…. So your world view forces you to conclude that you are a Boltzmann Brain. You must conclude that all your observations your memories and even this conversations are just an illusion. Paradoxically all your evidence for “inflation” would also be an illusion.

So the way I see it ether

1 you are a Boltzmann brain

2 the universe is not past eternal

Honestly I see this as a devastating objection to any godless model that includes infinite past and/or infinite (or many) worlds , any opinion on that?

So this is why Craig pulls up people like Vilenkin, Borde, and Guthe. But that doesn't work either, because all that their paper does is tell us that our metrics are singular in the realm of quantum gravity, which is a giant non-surprise. Craig doesn't really understand it.

well quote from Guth

Although inflation is generically eternal into the future, it is not eternal into the past: it can be proven under reasonable assumptions that the inflating region must be incomplete in past directions
Eternal inflation and its implications

quote from Vilenkin
eternal infation, cyclic evolution, and the emergent universe. The first two of these scenarios are geodesically incomplete to the past, and thus cannot describe a universe without a beginning
Did the universe have a beginning?

I might be wrong but at least as a layman it seems obvious to me that these scientists are claiming and concluding that eternal inflation can’t be “past eternal” am I missing something?

 

[leroy]

First acknowledges that the poster's scientific knowledge is vastly superior to his own.
Then proceeds to debate based on declarations about thermodynamics.

You might find it impressive and hard to believe but sometimes people debate with better informed people just for the sake of learning

I know this is something that goes beyond your comprehension because you are at another level, you already made your view, and you don’t need to learn anything else because you already know that anything that contradicts your view must be wrong,

But I am not at your level I am still trying to learn.

Priceless.

I also find it hilarious that you didn't actually respond or acknowledge any of his 6 points and instead jumped on something else he didn't even mention.

Absolutely priceless.

Of the 6 points I decided to start with point 1 and with thermodynamics that he did mentioned…………so what are you talking about?

 

[TagliatelliMonster]

You might find it impressive and hard to believe but sometimes people debate with better informed people just for the sake of learning

I know this is something that goes beyond your comprehension because you are at another level, you already made your view, and you don’t need to learn anything else because you already know that anything that contradicts your view must be wrong,

But I am not at your level I am still trying to learn.

The difference is that I don't try to argue about things I have no knowledge off.
You have been touting your fallacious god arguments like kalam and fine tuning for years. Many before @Meow Mix etc, including actual physicists, have schooled you on the many problems with these arguments and your mistakes and misunderstandings.

Like all those, I predict you will ignore these as well.
I predict that if you are still on this forum in 6 months, you'll still be making the exact same arguments, virtually unchanged.

Don't accuse me of "having made up my mind" and assuming that anyone that doesn't agree "must be wrong". That is in fact exactly what you do.

Of the 6 points I decided to start with point 1 and with thermodynamics that he did mentioned…………so what are you talking about?

He mentions it, but point 1 isn't about that.

But whatevs.

 

[leroy]

The difference is that I don't try to argue about things I have no knowledge off.
You have been touting your fallacious god arguments like kalam and fine tuning for years. Many before @Meow Mix etc, including actual physicists, have schooled you on the many problems with these arguments and your mistakes and misunderstandings.

Ok then allow me to repeat the same challenge that you have ignored dozens of times.

1 Quote a comment made by me where I made a claim

2 quote a comment where my claims is proven wrong or fallacious

3 quote me repeating that claim.

I predict that if you are still on this forum in 6 months, you'll still be making the exact same arguments, virtually unchanged.

No, if any of my claims are proven wrong I will change the argument accordingly.

If I only get replies such as “I am an atheist therefore I don’t have to prove my assertions” then I would interpret that as a good sign that the argument is good and I will keep using it.






Don't accuse me of "having made up my mind" and assuming that anyone that doesn't agree "must be wrong". That is in fact exactly what you do.

He mentions it, but point 1 isn't about that.

But whatevs.

So I repeat my question… what is your point?

Yes instead of responding to every single point, I decided to start with a specific point if disagreement …. Do you see anything wrong with that?

But don’t worry I have learned a lot from you, if I ever get cornered and unable to answer I can always change the topic and try to respond to some of the other 5 points.

 

[leroy]

Right where out current cosmology ends, bang GOD! RIght there, at that spot. Wow, what a coincidence?
God is always right at the edge of science. In Newtons time the planetary orbits that couldn't quite be figured out was were God was adding a little help.

That is a strawman.

The reason why we invoke “God” is because the laws of nature (and logic) strongly suggest that the universe had a begging and a cause.

Once you accept that the universe has a cause………..God follows deductible.

 

[Magical Wand]

You have been touting your fallacious god arguments like kalam and fine tuning for years. Many before @Meow Mix etc, including actual physicists, have schooled you on the many problems with these arguments and your mistakes and misunderstandings.

Like all those, I predict you will ignore these as well.
I predict that if you are still on this forum in 6 months, you'll still be making the exact same arguments, virtually unchanged.

Wow, it is good to know that.

 

[Magical Wand]

if the universe is past eternal, it remains inexplicable why our fields decayed 13.8B [sic] years ago to produce our big bang.

If the universe is past ethernal [sic] then any field that existed would have decayed an infinite amout [sic] of time ago.

An analogy would be imagine that you are playing poker since infinite past, given this I would conclude that you got your first “full house” and infinite amount of time ago, it makes no sense that you got your first “full house” 13.8 billions years ago (nor at any point in the finite past)

The reason why it decayed at a finite time in the past is that the field was only activated once the bounce occurred (and the bounce occurred at a finite time in the past because the contraction of space ends as the radius reaches a minimal point). Physicist Petar Pavlovic from the University of Hamburg in Germany explained: "The important question could be what triggers the activation of production of matter from the scalar field – and why this mechanism is not efficient today nor before the bounce. One possibility could for instance be that the potential of this field is dependent on temperature or curvature in a proper way to enable it, or perhaps that the production of matter is determined via the non-minimal coupling of the field and curvature scalar (so, when the curvature scalar decreases from the maximal value at the bounce this term becomes negligible)."

So, in my favorite model (which Dr. Pavlovic discussed above) the field only decays at the bounce. Just to clarify; this is not a cyclical model. The universe will not re-collapse in the future in this model.

So, the response to your claim "If the universe is past ethernal [sic] then any field that existed would have decayed an infinite amout [sic] of time ago" should be that this is only true if there is a non-zero probability of the field decaying before time zero (t=0). But that's not the case. It was determined from eternity that it should only decay at t=0. Ergo, we have a undercutting defeater of your argument. Your poker analogy is a false analogy, therefore.

The issue is that all the observable universe seems to have low entropy while your model of “infinite past” predicts high entropy (nearly 100% entropy) even in eternal inflation entropy on average always increases so low entropy is not expected to be seen.

The entropy always increases in new inflationary regions (or "bubble universes"), but since new regions with low entropy are always being created, the whole system never reaches equilibrium. In other words, while Bubble A already reached equilibrium because it has existed for trillions of years, Bubble X still has low entropy since it is very new (i.e., the scalar field recently decayed, thus producing low entropy particles). So, contrary to what you asserted, we have no reason to predict the entropy of our bubble universe to be "nearly 100%".

But talking about the second law my biggest objection to an infinite past would be that the universe would be dominated by Boltzmann brains, Boltzmann brains would be the most typical and abundant type of observer…. So your world view forces you to conclude that you are a Boltzmann Brain. You must conclude that all your observations your memories and even this conversations are just an illusion. Paradoxically all your evidence for “inflation” would also be an illusion.

So the way I see it ether

1 you are a Boltzmann brain

2 the universe is not past eternal

Honestly I see this as a devastating objection to any godless model that includes infinite past and/or infinite (or many) worlds

I'm not sure why you said this applies to an infinite past in general. In my favorite model, there was no matter prior to the first Big Bang. As a consequence, there couldn't exist Boltzmann brains produced by particles in a matter soup. In addition, the fields were not activated yet, so there were no quantum fluctuations in the vacuum to form brains. So, this isn't a problem to my model. In other words, no quantum fluctuations + no ordinary matter fluctuations = no formation of Boltzmann brains.

And it is not a problem for eternal inflation as well:

Watch at 40:31:

Watch at 27:09:

 

[Magical Wand]

Although inflation is generically eternal into the future, it is not eternal into the past: it can be proven under reasonable assumptions that the inflating region must be incomplete in past directions
Eternal inflation and its implications

Sorry, I forgot this one!

Not all cosmologists agree inflation can't be past-eternal! This is controversial.

In the paper "Inflationary Cosmology" (pp.16-17), Andrei Linde, Professor of Physics at Stanford University, wrote: "There is still an ongoing debate of whether eternal inflation is eternal only in the future or also in the past. In order to understand what is going on, let us consider any particular time-like geodesic line at the stage of inflation. One can show that for any given observer following this geodesic, the duration τᵢ of the stage of inflation on this geodesic will be finite. On the other hand, eternal inflation implies that if one takes all such geodesics and calculate the time τᵢ for each of them, then there will be no upper bound for τᵢ , i.e. for each time T there will be such geodesic which experience inflation for the time τᵢ > T. Even though the relative number of long geodesics can be very small, exponential expansion of space surrounding them will lead to an eternal exponential growth of the total volume of inflationary parts of the universe. Similarly, if one concentrates on any particular geodesic in the past time direction, one can prove that it has finite length [Ref. 59 - BGV], i.e. inflation in any particular point of the universe should have a beginning at some time τᵢ. However, there is no reason to expect that there is an upper bound for all τᵢ on all geodesics. If this upper bound does not exist, then eternal inflation is eternal not only in the future but also in the past. In other words, there was a beginning for each part of the universe, and there will be an end for inflation at any particular point. But there will be no end for the evolution of the universe as a whole in the eternal inflation scenario, and at present we do not have any reason to believe that there was a single beginning of the evolution of the whole universe at some moment t = 0, which was traditionally associated with the Big Bang."


In the book Universe in Creation (pp. 79-80), Roy R. Gould stated: “Even when some portion of space transitioned to a “big bang,” there would always be another portion that was expanding exponentially fast. In this multiverse, big bangs would take place at random locations and times, like flashbulbs lighting up an inconceivably large sports arena. The process would never stop. … The multiverse is an extraordinary prediction of continuous creation at a grand scale, with universes bubbling up from a primordial background of space and energy. It is believed that each one of the baby universes must have had an origin in time but that the whole assemblage – the multiverse – need not have had an origin and instead may be eternal.”

In the book "Impossibility" (pp. 171-172), physicist John Barrow agreed with Gould. He wrote: "Andrei Linde has discovered that inflation has a tendency to be self-reproducing. Remarkably, it appears that the fluctuations that inflation produces have form that inevitably induces further inflation to occur from small subregions of the bubbles that are already inflating. Inflation appears to be a potentially unending, self-reproducing process: in short, it is an epidemic... Probably the whole self-reproducing network of inflating bubble universes need have no beginning, but particular bubbles may have beginnings when their histories are traced backwards. These beginnings would correspond to the quantum-mechanical fluctuations in the energy of the Universe from place to place, and would appear spontaneously, with some probability, from time to time.”

 

[leroy]

The reason why it decayed at a finite time in the past is that the field was only activated once the bounce occurred (and the bounce occurred at a finite time in the past because the contraction of space ends as the radius reaches a minimal point). Physicist Petar Pavlovic from the University of Hamburg in Germany explained: "The important question could be what triggers the activation of production of matter from the scalar field – and why this mechanism is not efficient today nor before the bounce. One possibility could for instance be that the potential of this field is dependent on temperature or curvature in a proper way to enable it, or perhaps that the production of matter is determined via the non-minimal coupling of the field and curvature scalar (so, when the curvature scalar decreases from the maximal value at the bounce this term becomes negligible)."

So, in my favorite model (which Dr. Pavlovic discussed above) the field only decays at the bounce. Just to clarify; this is not a cyclical model. The universe will not re-collapse in the future in this model.

So, the response to your claim "If the universe is past ethernal [sic] then any field that existed would have decayed an infinite amout [sic] of time ago" should be that this is only true if there is a non-zero probability of the field decaying before time zero (t=0). But that's not the case. It was determined from eternity that it should only decay at t=0. Ergo, we have a undercutting defeater of your argument. Your poker analogy is a false analogy, therefore.

Haven’t seen the videos.

However I have a question



The entropy always increases in new inflationary regions (or "bubble universes"), but since new regions with low entropy are always being created, the whole system never reaches equilibrium. In other words, while Bubble A already reached equilibrium because it has existed for trillions of years, Bubble X still has low entropy since it is very new (i.e., the scalar field recently decayed, thus producing low entropy particles). So, contrary to what you asserted, we have no reason to predict the entropy of our bubble universe to be "nearly 100%".



I'm not sure why you said this applies to an infinite past in general. In my favorite model, there was no matter prior to the first Big Bang. As a consequence, there couldn't exist Boltzmann brains produced by particles in a matter soup. In addition, the fields were not activated yet, so there were no quantum fluctuations in the vacuum to form brains. So, this isn't a problem to my model. In other words, no quantum fluctuations + no ordinary matter fluctuations = no formation of Boltzmann brains.

And it is not a problem for eternal inflation as well:

Watch at 40:31:

Watch at 27:09:

--havent seen the videos yet

prior to the first Big Bang

So just to understand your view, there was a first big bang? And what was there before the big bang? Some sort of Quantum Sea?

 

[Magical Wand]

--havent seen the videos yet

Yeah, you don't have to watch the whole video. It is only important to watch the time-stamps I marked.

there was a first big bang? And what was there before the big bang? Some sort of Quantum Sea?

Yes, there was, and the first Big Bang is the result of the contraction of the whole space-time manifold (so, my favorite model doesn't actually involve past-eternal inflation). Before the bounce, there was a contracting phase empty of relativistic matter. And no, there was no quantum sea in the contraction phase. The quantum decay only starts at the bounce for the reasons Pavlovic explained above.

 

[leroy]

Yeah, you don't have to watch the whole video. It is only important to watch the time-stamps I marked.



Yes, there was, and the first Big Bang is the result of the contraction of the whole space-time manifold (so, my favorite model doesn't actually involve past-eternal inflation). Before the bounce, there was a contracting phase empty of relativistic matter. And no, there was no quantum sea in the contraction phase. The quantum decay only starts at the bounce for the reasons Pavlovic explained above.

And that contracting phase lasted for an infinite amount of time?

Would you share a source that explains your view? (if possible a news article or something that a lay man like me can understand) if not I´ll do my best in understanding the technical source.

 

[Valjean]

That is a strawman.

The reason why we invoke “God” is because the laws of nature (and logic) strongly suggest that the universe had a begging and a cause.

Once you accept that the universe has a cause………..God follows deductible.

These don't follow.

 

[leroy]

These don't follow.

Well in that case you would have to explain which step fails

 

[Magical Wand]

And that contracting phase lasted for an infinite amount of time?

Correct.

Would you share a source that explains your view? (if possible a news article or something that a lay man like me can understand) if not I´ll do my best in understanding the technical source.

Of course. The first article where this very simple and elegant idea was proposed is this one: http://legacy.adsabs.harvard.edu/pdf/1991A&A...250...43B

Now, it is important to notice that I changed some of its assumptions (and mechanisms) in order to deal with objections. But I can substantiate my potential modifications using recent physics, so there is no problem in trying to first understand this paper above.