Asymptotic Freedom in QCD and...

[NotEinstein]

Don't be dishonest.

If you think I'm dishonest, feel free to get the moderators involved.

1.
Your immediate objection/claim is that if y > kx then dy/dx > k is incorrect.
This has been resolved. I have clarified that for first quadrant operation (where x,y and k are +ive), this holds.

Right, because you apparently don't understand my point, let's plug in some dummy numbers:
y = x + 5
k = 1
x > 0 (actually not needed in this case)

Then always: y > kx
dy/dx = 1
k = 1
dy/dx > k
1 > 1
But 1 is not larger than 1.

QED.

Do you admit that your this objection is removed?

I have just proved it wrong once again.

No, drama and no word games, simple yes or no, pl.

No, I do not admit that your obviously wrong derivation is correct, obviously.

2.
Once you acknowledge above, then we will move over to next objection. One by one.

OK, one by one.

 

[RajeshTrivedi]

Right, because you apparently don't understand my point,

I have understood your point. You have forgotten your basics, you are just playing word games.

y = x + 5
k = 1
x > 0 (actually not needed in this case)
Then always: y > kx
dy/dx = 1
k = 1
dy/dx > k
1 > 1
But 1 is not larger than 1.

QED.

There is a mistake in your proof, which will be difficult for you to figure out. [Hint : You are using dy/dx of y = x, for dy/dx of y > x. Both are different numbers.]

I will guide you through..

1. Consider the first quadrant (YOX) of Cartesian coordinates.
2. Draw a line OP such that angle POX is Arctan(k)
3. This line will be y = kx, all the points (x,y) on this line will satisfy y = kx.
4. All the points between OP and OY will satisfy the inequality y > kx.
5. Take an arbitrary point P' between OP and OY, this will satisfy y > kx.
6. Now

for y > kx
Angle (P'OX) > Angle (POX)
tan(P'OX) > tan(POX)
dy/dx > k.

(tan(POX) is k, and tan(P'OX) is dy/dx of y>kx.)

I have just proved it wrong once again.
No, I do not admit that your obviously wrong derivation is correct, obviously.

No, you have just proved that you are ill equipped even to handle basics maths.


[As far as involving moderator is concern, then I will leave it to James R and his team. It is a forum rule that if a person persists with mistaken argument despite a direct and clear proof is shown to him, then it tantamount to intellectual dishonesty and trolling. Lets see what they do]. If they can decide to shift this thread to pseudo, then surely they can see through your persistent mistaken argument, despite proof of contrary.

 

[NotEinstein]

I have understood your point. You have forgotten your basics, you are just playing word games.

If you think I'm playing word games, please involve the moderators.

There is a mistake in your proof, which will be difficult for you to figure out. [Hint : You are using dy/dx of y = x, for dy/dx of y > x. Both are different numbers.]

I will guide you through..

1. Consider the first quadrant (YOX) of Cartesian coordinates.
2. Draw a line OP such that angle POX is Arctan(k)
3. This line will be y = kx, all the points (x,y) on this line will satisfy y = kx.
4. All the points between OP and OY will satisfy the inequality y > kx.
5. Take an arbitrary point P' between OP and OY, this will satisfy y > kx.

Agreed so far.

6. Now

for y > kx
Angle (P'OX) > Angle (POX)
tan(P'OX) > tan(POX)
dy/dx > k.

(tan(POX) is k, and tan(P'OX) is dy/dx of y>kx.)

But that if I draw my line through P' parallel to OP, and use k=1? That's what I've done with my numerical example. y > kx, but dy/dx = 1, per construction.

You are measuring your angle(P'OX), but that's doesn't give dy/dx if the line through P' doesn't go through the origin O.

No, you have just proved that you are ill equipped even to handle basics maths.

Well, at least one of us is unable to do even basic maths, I agree.

[As far as involving moderator is concern, then I will leave it to James R and his team. It is a forum rule that if a person persists with mistaken argument despite a direct and clear proof is shown to him, then it tantamount to intellectual dishonesty and trolling.

I am aware of this.

Lets see what they do].

Yes, let's.

If they can decide to shift this thread to pseudo, then surely they can see through your persistent mistaken argument, despite proof of contrary.

I'm confident they will indeed be able to see through someone's persistent mistaken argument(s), yes.

 

[RajeshTrivedi]

But that if I draw my line through P' parallel to OP, and use k=1? That's what I've done with my numerical example. y > kx, but dy/dx = 1, per construction.

You have done many things to sustain your objection. You brought in square function, inverse function, outside object, vacuum inside the object and now the parallel line.
Why dont you simply prove that if y > kx then dy/dx > k is false (dont change the goal post, by introducing y =1 /x or x^2 or kx+5 etc).

 

[exchemist]

I have understood your point. You have forgotten your basics, you are just playing word games.




No, you have just proved that you are ill equipped even to handle basics maths.


[As far as involving moderator is concern, then I will leave it to James R and his team. It is a forum rule that if a person persists with mistaken argument despite a direct and clear proof is shown to him, then it tantamount to intellectual dishonesty and trolling. Lets see what they do]. If they can decide to shift this thread to pseudo, then surely they can see through your persistent mistaken argument, despite proof of contrary.

It is in Pseudo, and has been for a while, hasn't it?

 

[NotEinstein]

You have done many things to sustain your objection. You brought in square function, inverse function, outside object, vacuum inside the object and now the parallel line.
Why dont you simply prove that if y > kx then dy/dx > k is false

Which I have done using "square function, inverse function, outside object, vacuum inside the object and now the parallel line".

(dont change the goal post, by introducing y =1 /x or x^2 or kx+5 etc).

If you think I'm changing the goalposts, then you haven't defined them properly in the first place. If you don't specify any specifics for "y" except that it has to be "+ive" and linear, then $$y=x+5$$ for the $$x>0$$ domain is a valid choice.

But let's fix that. Please list all requirements on x, y, and k.​

 

[RajeshTrivedi]

If you think I'm changing the goalposts, then you haven't defined them properly in the first place. If you don't specify any specifics for "y" except that it has to be "+ive" and linear, then $$y=x+5$$ for the $$x>0$$ domain is a valid choice.

But let's fix that. Please list all requirements on x, y, and k.​

It is just that you have not understood properly. Let me rephrase,

1. When an object of mass M is just at EH.
2. Then for outer most surface r = Rs and m = M.
3. At this instant, all the inner fraction sphere (of mass m where m<M and radius r) will be out of their (m) respective schwarzschild radius.

for this to be true for any given fraction of mass m (m<M) of radius r, following condition should meet

m > rc^2/2G

this leads to

dm/dr > c^2/2G

Your objection is that dm/dr > c^2/2G is false even if m > rc^2/2G. Prove your claim or retract.

 

[NotEinstein]

It is just that you have not understood properly. Let me rephrase,

1. When an object of mass M is just at EH.
2. Then for outer most surface r = Rs and m = M.

Agreed.

3. At this instant, all the inner fraction sphere (of mass m where m<M and radius r) will be out of their (m) respective schwarzschild radius.

False. I can give a density distribution where that two main components: a inner core, which has a mass $$m_1$$ such that there's an event horizon at $$r_1$$, and a spherical shell at some $$r_\text{shell}>r_1$$ that has mass $$m_2$$ such that at some $$r_2>r_\text{shell}$$ the Schwarzschild condition holds ($$m_1+m_2$$ is $$M$$).

This object thus has two event horizons. But note how it still conforms to your point #1 and point #2. In other words, point #3 does not follow; you are making assumptions/imposing restrictions without naming them. Please also post these additional assumptions/restrictions.

for this to be true for any given fraction of mass m (m<M) of radius r, following condition should meet

m > rc^2/2G

this leads to

dm/dr > c^2/2G

Which is proved to be false in general under your stated conditions by my example above, as $$\frac{dm}{dr}$$ in that example is zero between $$r_1$$ and $$r_\text{shell}$$.

Your objection is that dm/dr > c^2/2G is false even if m > rc^2/2G. Prove your claim or retract.

I've given multiple examples now where your logic fails. I've thus already proven my claim multiple times. You are the one that keeps repeating a claim without proof. Please prove your claim or retract it.

 

[RajeshTrivedi]

3. At this instant, all the inner fraction sphere (of mass m where m<M and radius r) will be out of their (m) respective schwarzschild radius.

Agreed.

False. I can give a density distribution where that two main components: a inner core, which has a mass $$m_1$$ such that there's an event horizon at $$r_1$$, and a spherical shell at some $$r_\text{shell}>r_1$$ that has mass $$m_2$$ such that at some $$r_2>r_\text{shell}$$ the Schwarzschild condition holds ($$m_1+m_2$$ is $$M$$).

This object thus has two event horizons. But note how it still conforms to your point #1 and point #2. In other words, point #3 does not follow; you are making assumptions/imposing restrictions without naming them. Please also post these additional assumptions/restrictions.

Yes, you can give a density profile, please refer to my post #126

#126 part

Your objection and your implied claim that inner fractions will also be beneath their respective schwarzschild radius in general will be true only if density profile of the object follows:

d(r) > c^2/(8piGr^2)
(It is actually greater than or equal to) d(r) is the radial density at r radius.
on putting values of c and G, the above density profile becomes:
d(r) > (5.3 * 10^25)/r^2 kg/m3.
Need I elaborate further how unrealistic this density profile is?

if you calculate values and see then your this m1, m2 example supports this view only. Subject to if you understand a very basic thing, that if a density profile d(r) = f(r) gives all the points of an object just at their inner part EH, then all the points will be beneath their EH if density profile d(r) > f(r). Where will you get a density profile of the order d(r) > 10^25/r^2 kg/m3 when the core is just at EH?

Which is proved to be false in general under your stated conditions by my example above, as $$\frac{dm}{dr}$$ in that example is zero between $$r_1$$ and $$r_\text{shell}$$.

I've given multiple examples now where your logic fails. I've thus already proven my claim multiple times. You are the one that keeps repeating a claim without proof. Please prove your claim or retract it.

No it is not proved false, it is just that you have forgotten your basics and you are incapable of recalling even when reminded.
You could not prove that if m>rc^2/2G then why dm/dr > c^2/2G is false? The point is it cannot be proved wrong, you are just playing with all the other functions but not with this.

 

[NotEinstein]

(There's a slight misquote in your post: the "agreed" was not to point #3.)

Yes, you can give a density profile, please refer to my post #126

if you calculate values

What values?

and see then your this m1, m2 example supports this view only.

The grammar here appears broken. What are you trying to say?

Subject to if you understand a very basic thing, that if a density profile d(r) = f(r)

Why are you introducing a non-specified function to replace another non-specified function? This doesn't do anything.

gives all the points of an object just at their inner part EH, then all the points will be beneath their EH if density profile d(r) > f(r).

Why must this be true? Why must the density be larger inside the object than on its outer surface? You are claiming here that a spherical shell is an invalid matter configuration; in other words, you are saying that a spherical shell cannot form an event horizon.

More interesting is that you are saying it cannot have a constant density, thereby disproving your own assertions in your texts.

Where will you get a density profile of the order d(r) > 10^25/r^2 kg/m3 when the core is just at EH?

In my post #132, I gave you a Fermi-style estimate, indicating that the outer regions of neutron stars can reach these densities just fine.

No it is not proved false, it is just that you have forgotten your basics and you are incapable of recalling even when reminded.

Last time I checked, zero is not larger than amy positive number, and you haven't pointed out any mistakes in my math.

You could not prove that if m>rc^2/2G then why dm/dr > c^2/2G is false?

I have already done so multiple times. That you apparently fail to understand that isn't my fault.

The point is it cannot be proved wrong,

Except it already has been multiple times; you just stubbornly refuse to accept this.

you are just playing with all the other functions but not with this.

At least several of the functions I've used in some of the examples I've provided comply perfectly with the requirements you've given, so you are either wrong or making an irrelevant point.

 

[RajeshTrivedi]

For any given spherical object (not reduced to BH singulairty), all the points including interior points will lie on respective Event Horizon (an interior point respective EH is by considering the mass inner to this point), then to satisfy this condition,

r = 2Gm/c^2

(where m is the mass of the inner sphere of radius r).

This will give us: m = rc^2/2G
from this dm/dr = c^2/2G
This will give the density profile as

d(r) = c^2/(8piGr^2) or of the order (5.3* 10^25)/r^2 kg/m3.

[This density profile is for all the points (surface+interior) to be on their respective EH], but for all the points to be beneath their respective EH, the density must be higher than above

that is d(r) > 5.3*10^25/r^2 kg/m3.

[No, realistic object when at EH will satisfy this density profile and hence it can be easily deduced that when the object is at EH, it is not necessary that all the inner shell points will also lie on their respective EHs.]

NotEinstein is not able to produce any credible objection to this, he has been trolling. But since this observation of mine, is coupled with some kind of alternative proposal, and people like NotEinstein are supporters of mainstream, so the moderator team is also keeping a blind eye to his persistent incorrect objection.

 

[Xelasnave.1947]

NotEinstein is not able to produce any credible objection to this, he has been trolling.

Well is that such a bad thing the thread keeps going and most entertain ing it is.
Good to see you here and hope all is going well.
Alex

 

[NotEinstein]

For any given spherical object (not reduced to BH singulairty), all the points including interior points will lie on respective Event Horizon (an interior point respective EH is by considering the mass inner to this point), then to satisfy this condition,

r = 2Gm/c^2

(where m is the mass of the inner sphere of radius r).

Incorrect; they must lie on or within their Schwarzschild radius.

This will give us: m = rc^2/2G
from this dm/dr = c^2/2G

This is the change with respect to the Schwarzschild radius of the minimum mass necessary to satisfy the Schwarzschild condition.

This will give the density profile as

d(r) = c^2/(8piGr^2) or of the order (5.3* 10^25)/r^2 kg/m3.

By setting "the minimum mass necessary to satisfy the Schwarzschild condition" equal to "the encompassed mass" and the "Schwarzschild radius" equal to the "radial coordinate" you have derived a density profile that will be exactly at the Schwarzschild condition for all points including interior points.

[This density profile is for all the points (surface+interior) to be on their respective EH], but for all the points to be beneath their respective EH, the density must be higher than above

that is d(r) > 5.3*10^25/r^2 kg/m3.

Incorrect. I can build a density profile that has a large mass in its center, with an event horizon extending far beyond it, and with a spherical shell at the outer edge of this region. Or formulated the other way around: I can have a spherical shell that's at the edge of the event horizon of the inner core. Such a density distribution has d(r)=0 between the inner core and the outer shell, thus proving that your condition on a minimum density is not necessary in general.

[No, realistic object when at EH will satisfy this density profile

Which is, as just proven (again) not necessary. Additionally, neutron stars can reach that density in their outer regions.

and hence it can be easily deduced that when the object is at EH, it is not necessary that all the inner shell points will also lie on their respective EHs.]

This conclusion I do not disagree with; it's the derivation leading up to it that's the problem.

NotEinstein is not able to produce any credible objection to this,

Or: "RajeshTrivedi has been unable to understand all the credible objections to this". One of the two.

he has been trolling.

If you think I have been trolling, please contact the moderation and have them deal with it.

But since this observation of mine, is coupled with some kind of alternative proposal,

No, it's coupled with high school level math that contains many mistakes, unspoken assumption, and a fundamental lack of understanding of GR.

and people like NotEinstein are supporters of mainstream,

I'm a supporter of truth, mostly. Your derivation is wrong.

so the moderator team is also keeping a blind eye to his persistent incorrect objection.

Is this a "it's a conspiracy" claim?
But if you don't like the members of this forum, if you don't like the premise of this forum ("science forums"), and you don't like the moderation of this forum, might I suggest you find another place where you feel more accepted? You're only hurting yourself more by staying here.

 

[NotEinstein]

Well is that such a bad thing the thread keeps going and most entertain ing it is.

I have a feeling the thread is going to end soon, seeing as RajeshTrivedi is just repeating him-/herself without actually addressing (or even acknowledging) all the credible objections I've brought forth so far.

 

[Xelasnave.1947]

I have a feeling the thread is going to end soon, seeing as RajeshTrivedi is just repeating him-/herself without actually addressing (or even acknowledging) all the credible objections I've brought forth so far.

Please don't let it end.
Alex

 

[NotEinstein]

Please don't let it end.

I'm not planning on it, but in my experience, when one side of a discussion gets stuck just repeating themselves, the discussion ends soon afterwards.

 

[RajeshTrivedi]

and hence it can be easily deduced that when the object is at EH, it is not necessary that all the inner shell points will also lie on their respective EHs.]

This conclusion I do not disagree with;

Thank you.
This is what all along I have been saying,
and the result of this is that if a photon is produced at any such inner point then it need not travel towards the center, if it is directed radially outward, it can very well travel outward, till it encounters a point (on the collapsing core) which brings the point inside the now changed inner part's Schwarzschild radius..

 

[RajeshTrivedi]

I have a feeling the thread is going to end soon, seeing as RajeshTrivedi is just repeating him-/herself without actually addressing (or even acknowledging) all the credible objections I've brought forth so far.

This is another dishonest attempt.
You are just playing with the words, you have not produced any credible objection. In your previous post you agreed to whatever I was saying.
If you further play with words, you will be humbled that even the simple mathematical proof and my claim of unrealistic density profile >5.3*10^25/r^2 is also correct.

 

[NotEinstein]

Thank you.

Not sure why you are thanking me?

This is what all along I have been saying,

No, it's not. What you've been saying all along is a mess of incorrect calculations and derivations, missing definitions and conditions, dodging questions, and failing to explain yourself.

And I've never denied the possible correctness of that statement. It's just that you've come to a conclusion for all the wrong reasons. In other words, your stated conclusion might be correct, but you've made elementary math mistakes in coming to it. It might be true, but it is invalid logically speaking. You cannot back up your conclusion.

and the result of this is that if a photon is produced at any such inner point then it need not travel towards the center, if it is directed radially outward, it can very well travel outward, till it encounters a point (on the collapsing core) which brings the point inside the now changed inner part's Schwarzschild radius..

Only for certain density distributions, which probably are unstable.

And perhaps you could be so intellectually honest as to respond to the rest of that post too?

This is another dishonest attempt.

If you feel I'm being dishonest, feel free to involve the moderators.

I could argue that it is you that's being dishonest right now, by misrepresenting my acknowledgement of the possibility that your concluding statement may hold truth as agreeing with your derivation to reach it.

You are just playing with the words,

If you think I'm just playing with the words, feel free to involve the moderators.

you have not produced any credible objection.

Except that I have, multiple times. You repeating this accusation over and over again without backing it up is starting to look more and more like trolling.

In your previous post you agreed to whatever I was saying.

I have done no such thing, as I just explained.

If you further play with words, you will be humbled that even the simple mathematical proof and my claim of unrealistic density profile >5.3*10^25/r^2 is also correct.

Indeed, at least one of us indeed needs to be humbled.

 

[RajeshTrivedi]

Not sure why you are thanking me?


No, it's not. What you've been saying all along is a mess of incorrect calculations and derivations, missing definitions and conditions, dodging questions, and failing to explain yourself.

And I've never denied the possible correctness of that statement. It's just that you've come to a conclusion for all the wrong reasons. In other words, your stated conclusion might be correct, but you've made elementary math mistakes in coming to it. It might be true, but it is invalid logically speaking. You cannot back up your conclusion.


Only for certain density distributions, which probably are unstable.

And perhaps you could be so intellectually honest as to respond to the rest of that post too?


If you feel I'm being dishonest, feel free to involve the moderators.

I could argue that it is you that's being dishonest right now, by misrepresenting my acknowledgement of the possibility that your concluding statement may hold truth as agreeing with your derivation to reach it.


If you think I'm just playing with the words, feel free to involve the moderators.


Except that I have, multiple times. You repeating this accusation over and over again without backing it up is starting to look more and more like trolling.


I have done no such thing, as I just explained.


Indeed, at least one of us indeed needs to be humbled.

All noise, no quality at all.
I checked few other threads and shocked to see how you trolled Schmelzer, he also had to give up on you. You even just short of boasted that you may have some peer reviewed papers published in your name, while questioning his paper as decade old with few citations, why not come forward and say what you have. This thread doubly proves (along with Schmelzer thread) that you have no basic knowledge of maths and physics and just trolling around.

let us take few example,

3 Solar Mass object just at EH:
Rs = 8905 Meters.
d = 2.02 * 10^18 kg/m3
Rs (of 90% core) = 8015 Meters
R (of 90% core) = 8598 Meters.

So R(90% of core) > Rs (of 90% core), Suggesting that inner 90% fraction is out of inner fraction EH.

Density calculations when the core was just of its EH size and not yet collapsed to form BH, and calculations are done for inner fraction 90%, but any fraction can be considered and will give the same conclusion.

10 Solar Mass object just at EH:
Rs = 29685 Meters.
d = 1.82 * 10^17 kg/m3
Rs (of 90% core) = 26719 Meters
R (of 90% core) = 28661 Meters.

So R(90% of core) > Rs (of 90% core), Suggesting that inner 90% fraction is out of inner fraction EH.

30 Solar Mass object just at EH:
Rs = 89056 Meters.
d = 2.02 * 10^16 kg/m3
Rs (of 90% core) = 80150 Meters
R (of 90% core) = 85983 Meters.

So R(90% of core) > Rs (of 90% core), Suggesting that inner 90% fraction is out of inner fraction EH.


None of these density profiles are unrealistically dense or whatever as NE is handwaving, they are nuclear level or rarer.
All these clearly prove that inner fractions will be out of their respective Schwarzschild radius, this calculation is done with uniform density, I call upon this poster NotEinstein to come forward and give his non uniform density profile (within < 5.3*10^25/r^2) to disprove this, or if he has some civility he should retract his objection.

In general (not exception) when an "object is just at EH", except the outer surface points all other inner points will be out of their respective schwarzschild radius. This condition will be false only for very high unrealistic density profiles.