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Offline angst

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Science just not prepared for the truth?
« on: 07/11/2009 13:57:24 »
I was watching the recent offering from BBC's Horizon - Who's Afraid of a Black Hole - and it got me thinking. It seems, as far as I can see, that far from Einstein's relativity not being able to explain the mathematics of a singularity, they explain it perfectly adequately. It seems, to me, that the scientists involved simply do not accept the idea of infinite density.

Am I missing something here? In fact, on a very basic level isn't such a result absolutely obvious? If you are looking to discover the density of a measureless point in space which has mass, the result will clearly be infinite?


 

Offline Vern

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« Reply #1 on: 07/11/2009 14:27:03 »
Yes; however nature has arranged itself so that we can never get to infinity by incremental steps. Every piece of mass we may add to a clump in space is only an increment. It is not possible to model the formation of a Black Hole if you include relativity phenomena in the model. The best you can do is get part way there.

Edit: So, how do black holes form? How do they avoid the arithmetic that says it can't happen?  The same arithmetic that allows the possibility of Black Hole existence forbids their creation.

« Last Edit: 07/11/2009 15:26:03 by Vern »
 

Offline LeeE

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Science just not prepared for the truth?
« Reply #2 on: 07/11/2009 15:54:16 »
You need to be very careful when you start throwing infinities around, especially in the real world/universe.

Density requires two factors; mass and volume, but the hypothetical singularities at the center of Black Holes have no volume, which isn't the same as infinitely small i.e. 0 ≠ 1/∞.  Trying to apply the concept of density to the a singularity then, is not going to produce valid answers, and working on the basis that the density is infinite is really misleading yourself.

The problem stems in part from the mathematical slight of hand that allows to to work with zero as a valid number.  For example, lets say I want to give you a gift of an apple, so I give you zero apples, tell you to take one for yourself, and then ask you to give the remainder back to me.  Mathematically, this is fine, but in real life it's nonsensical.

With a BH, all we can say for sure is that space behaves as though there were a concentration of mass acting at that point, but not that there is a mass at that point.  What we can almost certainly be sure of is that whatever is behaving as a mass at that point is not mass in any form that we know it and hence trying to apply density to it is equally invalid.
 

Offline Vern

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« Reply #3 on: 08/11/2009 02:14:32 »
From what I think we have discovered, we know that we cannot incrementally add mass to a local area of space until it becomes a gravitational singularity. I'm not sure I even know that means. Maybe I should say infinitely dense instead of gravitational singularity. Anyway we know we can't get there. So what is it that is at the centre of most galaxies?

Maybe it is an accumulation of mass that is almost as dense as our Black Hole concept. I wonder if it is a requirement of a Black Hole that it contain a singularity. Is it possible that an accumulation of mass that is not infinitely dense could still be dense enough to produce a gravitational field that would not allow light to escape?
« Last Edit: 08/11/2009 02:16:38 by Vern »
 

Offline LeeE

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« Reply #4 on: 08/11/2009 11:21:10 »
We haven't discovered anything; we've only deduced it.

The funny side to this is that the deduction also implies that the rules upon which the deduction was made are not applicable to the circumstances pertaining to the deduction ;D
 

Offline Vern

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« Reply #5 on: 08/11/2009 15:31:58 »
Yes; I agree. :)  But now I don't know what were the rules we were using.  :) I think it is GR that allows for the possibility of black holes existence. What would be the rules that don't apply to incrementally adding to a local area of space until it becomes a black hole?

My contention was that any set of equations that describe the process of black hole creation will fail to produce a black hole when relativity phenomena must be a part of the equations.
 

Offline PhysBang

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« Reply #6 on: 09/11/2009 12:45:09 »
I was watching the recent offering from BBC's Horizon - Who's Afraid of a Black Hole - and it got me thinking. It seems, as far as I can see, that far from Einstein's relativity not being able to explain the mathematics of a singularity, they explain it perfectly adequately. It seems, to me, that the scientists involved simply do not accept the idea of infinite density.

Am I missing something here? In fact, on a very basic level isn't such a result absolutely obvious? If you are looking to discover the density of a measureless point in space which has mass, the result will clearly be infinite?
The word "singularity" doesn't mean "point of infinite density" , though it is often taken to mean that (and popularly used to mean that). The word means a proposed state of a physical system where the mathematical description of the system does not make sense. For a singularity, we can derive a number of contradictory and non-sensical statements. Even in general relativity, there are singularities within the full description of a black hole. Some of them can be removed through a careful description of the objects, but not all of them. This is the real problem.
 

Offline angst

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« Reply #7 on: 09/11/2009 22:17:32 »
I was watching the recent offering from BBC's Horizon - Who's Afraid of a Black Hole - and it got me thinking. It seems, as far as I can see, that far from Einstein's relativity not being able to explain the mathematics of a singularity, they explain it perfectly adequately. It seems, to me, that the scientists involved simply do not accept the idea of infinite density.

Am I missing something here? In fact, on a very basic level isn't such a result absolutely obvious? If you are looking to discover the density of a measureless point in space which has mass, the result will clearly be infinite?
The word "singularity" doesn't mean "point of infinite density" , though it is often taken to mean that (and popularly used to mean that). The word means a proposed state of a physical system where the mathematical description of the system does not make sense. For a singularity, we can derive a number of contradictory and non-sensical statements. Even in general relativity, there are singularities within the full description of a black hole. Some of them can be removed through a careful description of the objects, but not all of them. This is the real problem.

I never suggested, or certainly didn't intend to suggest, that singularity meant that.

Another poster here touched upon what I see as the error here. The implication seems to be; that Einstein's theories 'break down' at the critical point - ie at the value of a singularity. Now, and truly, what am I missing here?; If you introduce into the equations a dimensionless point (r=0), ie an infinitely small, immeasurable singularity it follows - as inexorably as a x 0=0 -  that the density (given that the mass to be crammed into this dimensionless, infinitely small 'point' is given a definitive value) will be infinite.

This isn't Einstein's theories 'breaking down', this is a simple case of BIMBO - surely?

Is it that the smallest possible size of all this mass cannot be deduced?

I'm not trying to be 'clever' or funny here, I really can't see what I am missing. If you can't accept the inevitable result of a singularity, then don't introduce the model into the equations. Certainly don't introduce what you consider a fallacious model into the equations and then declare that the equations don't work, because the answer they give are fallacious.
« Last Edit: 09/11/2009 22:21:25 by angst »
 

Offline angst

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Science just not prepared for the truth?
« Reply #8 on: 09/11/2009 22:26:41 »
You need to be very careful when you start throwing infinities around, especially in the real world/universe.

Density requires two factors; mass and volume, but the hypothetical singularities at the center of Black Holes have no volume, which isn't the same as infinitely small i.e. 0 ≠ 1/∞.  Trying to apply the concept of density to the a singularity then, is not going to produce valid answers, and working on the basis that the density is infinite is really misleading yourself.

The problem stems in part from the mathematical slight of hand that allows to to work with zero as a valid number.  For example, lets say I want to give you a gift of an apple, so I give you zero apples, tell you to take one for yourself, and then ask you to give the remainder back to me.  Mathematically, this is fine, but in real life it's nonsensical.

With a BH, all we can say for sure is that space behaves as though there were a concentration of mass acting at that point, but not that there is a mass at that point.  What we can almost certainly be sure of is that whatever is behaving as a mass at that point is not mass in any form that we know it and hence trying to apply density to it is equally invalid.

So, in what way is zero volume NOT the same as infinitely small? If, as the starting point of your equation is r=0 then that is infinitely small. It has zero dimensions. 0, zero, has no value. It is valueless.

Working with zero as a valid number is not, as I see it, a mathematical slight of hand, it is downright bad math.

And, what is the 'form' of mass as we understand it?

Again, not trying to be 'clever' or funny.
« Last Edit: 09/11/2009 22:33:34 by angst »
 

Offline angst

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Science just not prepared for the truth?
« Reply #9 on: 12/11/2009 21:07:49 »
I was watching the recent offering from BBC's Horizon - Who's Afraid of a Black Hole - and it got me thinking. It seems, as far as I can see, that far from Einstein's relativity not being able to explain the mathematics of a singularity, they explain it perfectly adequately. It seems, to me, that the scientists involved simply do not accept the idea of infinite density.

Am I missing something here? In fact, on a very basic level isn't such a result absolutely obvious? If you are looking to discover the density of a measureless point in space which has mass, the result will clearly be infinite?
The word "singularity" doesn't mean "point of infinite density" , though it is often taken to mean that (and popularly used to mean that). The word means a proposed state of a physical system where the mathematical description of the system does not make sense. For a singularity, we can derive a number of contradictory and non-sensical statements. Even in general relativity, there are singularities within the full description of a black hole. Some of them can be removed through a careful description of the objects, but not all of them. This is the real problem.

Thank you for this response; as I have re-read it I have understood it a little more. However, this still describes what I see as the basic problem for science here, and there are hints of this within some of the responses here.

Surely one of the reasons that science is so interested in black holes is because of the singularities, because of what they can tell us about the big bang. But then, it seems, that science wants to deny what a singularity really is, and indeed must be in order to be considered to describe the 'moment' of creation.

To read that a singularity has zero volume, but that that is not infinitely small..?? This is a notional slight of hand which is as meaningful as using 0 as a real number - and, if true, surely removes any meaning of the concept in terms of the 'moment' of creation.

By the very nature of the 'moment' of creation this singularity must have come into existence within nothing. It is, by definition, a dimensionless point.

And, if we cannot believe in a singularity (in other words, cannot bring ourselves to deal with the dirty concept of infinity) then 'creation' becomes less than creation - and we then have to face the concept of the eternal.
 

Offline Vern

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« Reply #10 on: 12/11/2009 21:32:50 »
I suspect that the interest in Black Holes is because General Relativity theory does not forbid them. The arithmetic that allows Black Hole formation is lacking a control that dampens the affect of gravity as gravity increases. However, there is such a control in the general theory itself.

The control is this: Consider that the affect of gravity is acceleration. The equation for acceleration contains time as a multiplier to determine its value. Time is affected by gravity; the greater the gravity, the slower is time. Slower time means less acceleration. So gravity is affected by gravity. Gravity is self limiting.
« Last Edit: 13/11/2009 23:25:47 by Vern »
 

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