Black Holes

[Tormod]

According to the maths, I can bring home a carpet measuring -4m by -4m to cover the floor of my 16 square metre study.

 

I can't carry it home over my shoulder.

 

So...how *would* you get the carpet home? :eek:

 

(Sorry, I just *had* to ask!) :)

[CraigD]

The negative solution is non-real when we're talking about carpets. A negative carpet is not a real thing. I can't carry it home over my shoulder.

The point I was attempting to make about negative components of vector quantities is that they simply indicate the orientation, not the scalar magnitude, of a vector. In the case of a carpet, a negative vector component indicates its direction with reference to an arbitrary coordinate system.

 

The rectangular carpet we’ve been discussing is defined by vectors [math]\lbrace 4, 0 \rbrace , \lbrace 0, 4 \rbrace[/math] or [math]\lbrace -4, 0 \rbrace , \lbrace 0, -4 \rbrace[/math] or [math]\lbrace 4, 0 \rbrace , \lbrace 0, -4 \rbrace[/math] or [math]\lbrace 2 \sqrt{2}, -2 \sqrt{2} \rbrace , \lbrace 2 \sqrt{2}, 2 \sqrt{2} \rbrace[/math] or [math]\lbrace 2 , 2 \sqrt{3} \rbrace , \lbrace 2 \sqrt{3}, -2 \rbrace[/math], or any of an infinite number of vector pairs that, put together into a square matrix, have determinant 16 or -16. We can’t just say “a carpet with edges length 4 and 4”, because that could describe a non-rectangular parallelogram carpet (not a popular model in the average home furnishings store), such as one defined by vectors [math]\lbrace 4, 0 \rbrace , \lbrace \sqrt{15}, 1 \rbrace[/math], which has an area of only 4.

 

Notice that area is actually defined as the absolute value of the determinant of the matrix, so the whimsical example I gave of a [math]\lbrace 4i, 0 \rbrace , \lbrace 0, 4i \rbrace[/math] carpet is actually a case of physically unrealistic edges but a realistic area – Never-land physics indeed.

 

The larger point at which I was hinting is that math is only as real, or unreal, as the formal system (AKA “formalism”) in which it’s used. Claiming that the formalism of, for example, Relativity, does not apply to reality because it uses math, and math can be used in formal system that don’t apply to reality, evidences I believe a naive appreciation of how formal systems are used in physics. Ignoring its technical accuracy (as discussed at some length in 9270 the square root operation is not conventionally considered to have negative values), statements such as

But mathematics tells us that if we take the square root of an area of sixteen square metres, the possible solutions are lengths of four metres and minus four metres.

that hint at revealing an underlying inappropriateness of mathematics to physical reality, are, IMHO, due to this naivety.

 

There are strong arguments that the predictions of Relativity are inapplicable to physical domains such as black holes, but they rest, I think, in that it is a classical physics theory – that is, it treats massive objects as ideal particles with perfectly knowable attributes of mass, position, and velocity. Although many theorists have combined it with the formalism of quantum mechanics, the union appears uneasy, and the elegant simplicity of Relativity compromised by it.

 

Michio Kaku captured the intuitive dissatisfaction physicist feel with Relativity and black holes, I think, in his 1994 popular physics book “Hyperspace: A Scientific Odyssey Through Parallel Universes, Time Warps, and the Tenth Dimension”, in which he used the analogy of Relativity being made of perfect marble, quantum mechanics of knotty wood.

[CraigD]

I can't carry it home over my shoulder.

So...how *would* you get the carpet home? :cup:

 

(Sorry, I just *had* to ask!) :cup:

I’ll take a crack at this one:

Flip it around and carry it on your other shoulder …

or, maybe …

role it up outside-in, then …

 

I take it back. I don’t want to think about the formalism of rolling up carpets. :eek: :)

[Farsight]

So...how *would* you get the carpet home? :eek:

 

(Sorry, I just *had* to ask!) :)

 

To get a negative carpet home I'd get down on my hands and knees in the living room with my clippers and cut a big square hole in my carpet four metres by four metres. Then I'd roll it up, put it over my shoulder, and take it to the carpet shop, walking backwards for dramatic effect. I would then hand it over to the man and accept his £100, then go home where I would crack open a bottle of wine with my guests and display to them my negative carpet on my living room floor. I will then be forcibly restrained and delivered to a safe place where people talk gently to me and ensure I take my medication.

 

The thing about all this is that a mathematical solution is sometimes crazy, but it's not always plain, and people just don't spot it. I've got that book, Craig, I used to think it was really good. I used to think Michiu Kaku was a great guy, somebody to really admire. Now I think he has bought some of those crazy solutions. Parallel Universes. Time Warps. Other scientists talk about Time Travel, and they are totally serious. Getting back to the point of the thread, most physicists talk about black hole singularities in a very familiar fashion, as if they were common objects, one in every lab.

 

But they really, really, do not exist. And they never ever will.

 

 

PS: Don't think I'm disparaging of General Relativity, I'm not. I just think there's something wrong with the mathematical formalism or the interpretation of it. There are no black hole singularities because time dilation goes infinite at the event horizon, so there's no singularities to cause a blow-up. I don't like to tout, but see RELATIVITY+ for details. If anybody can give me some considered feedback to it, I'd be grateful.

[Qfwfq]

I will then be forcibly restrained and delivered to a safe place where people talk gently to me and ensure I take my medication.

I don't see why. Actually, you gave a perfect example, just like how one may have -1000 bucks in the bank...

[Farsight]

I don't see why. Actually, you gave a perfect example, just like how one may have -1000 bucks in the bank...

 

Where in the bank? Read this: MONEY EXPLAINED

[Qfwfq]

In the same "place" as when you have a positive balance.

 

I don't need an explanation of what money is and, if the example troubled you, imagine you have 7 tonnes of grain ripening in your field but you owe some trader a total of twelve, in exchange for cattle that was already delivered. Ya gotta come up with those 5 tonnes, before the cattle gets seized.

[Farsight]

That money isn't actually anywhere. If you bothered to read MONEY EXPLAINED you'd understand what I meant by that. And that -5 tons of grain that you've "got" isn't anywhere either. It's in the same "place" as my negative carpet. And the same "place" as the black hole singularity. Nowhere, because it isn't real, it doesn't actually exist. The black hole singularity will only exist in the future, and it's always in the future for all time.

[Qfwfq]

I did read that thread and gave my own reply.

 

And a debt is as real as your creditor's club! :shrug:

[Farsight]

Show me some of this "real" debt. Weigh it, measure it, package it. Grind the Universe down to a powder then show me an atom of it. You can't, because debt is only a concept. A type of agreement. We can agree that IOU one carpet. The agreement is binding, we call it "real" by convention, even though we know it's intangible and is not a measurable property of any real system. And that carpet I owe you, my negative carpet, that's definitely not a real thing. It's just a concept. Just like the black hole singularity that will only exist in the future for the rest of time.

[Jay-qu]

Popular I think you have to get straight the difference in definitions between 'real' and mathematically real. By definition a real number is anywhere (but not including) from negative to positive infinity. While the real you refer to is that of a tangible object, yes I agree with you, you certainly cannot hold a negative quantity like a positive one but you have to be carefull how you throw around and define the word real.

[Qfwfq]

Weigh it, measure it

-5 tonnes!

 

Obviously it isn't a specific part of all the grain that exists or will exist, this is simply because we're talking about a fungible asset. I disagree that it's just the mathematical definition of [math]\norm\mathbb{R}[/math], the fact that an obligation can be enforced is a real, practical fact that makes the debt as real as the collateral it is backed by. Having your house mortgaged is very much like only owning part of it, although it works differently.

 

For comparison, suppose the situation about the grain arose not because you had misjudged the crop but because some of the grain was stolen just at the time of harvest, bringing the total down from the margin you were counting on when dealing for the cattle to 5 tonnes less than the total debt. Of your 12 tonne debt, 7 are still in your possession and 5 are not. This time you can associate your -5 tonnes with 5 of those stolen ones, wherever they are now.

 

Of course what you mean is that it isn't 5 tonnes of material. That's a different thing. Something needn't be material in order to be real. Actually the notion of material is something we take for granted in everyday experience but it gets a bit hazy down in particle physics, a particle and the corresponding antiparticle can each be somewhat regarded as the lack of the other. A sufficent amount of energy can even become the pair, each being the lack from which the other came out. Even with less than enough energy, it can happen virtually. Unlike the thieve's loot and your missing grain, either particle or antiparticle can be the lack and either can be the presence; it's both ways. Freakin' wierd, but that's how it is.

[Eilizsia]

I didn't know where to put this.

 

Nothing reaches the center of a black hole.

 

 

As an object enters a black hole it becomes smaller in volume and more condensed and heavier. So it might stay the same in mass but it still becomes smaller, and the closer it gets to the center of the black hole, the smaller it gets, this process goes on forever, the object never hits the center.

 

Black Holes Dont Have a Centre. They Have a Core, The Core Itself Collects Energy, When Energy surounding the black hole reduces, so does the lenght of the vortex, The vortex can only exist if the core exists, Usually the Core Is at the centre of a A Star. But sometime, It coulb be at the centre of a quasar

[CraigD]

Show me some of this "real" debt. Weigh it, measure it, package it. Grind the Universe down to a powder then show me an atom of it. You can't, because debt is only a concept.

Debt, carpets defined by distance vectors with negative components, carpets with negative or imaginary areas, or any other concept of which a human being is aware, exist symbolically as complicated material objects consisting of the cells, chemicals, and ions that allow a human being to be aware of the concept. Although I collect such an object (along with a lot of extra tissue), dry and grind it into a power, and show the result to Popular, if ground into a powder or otherwise damaged, such an object ceases to allow a human being to be aware of a concept – in a material sense, that particular instance of the concept ceases to exist.

Just like the black hole singularity that will only exist in the future for the rest of time.

Like an ordinary carpet, or any objectively real object, a black hole, which may, like the concept of an imaginary object, exist symbolically as objects in a human brain, has an objective reality. Nearly every black hole has a profound, dramatic, observable effect on both fermionic matter and bosonic energy, regardless of whether any human being is aware of it. In terms of the amount of matter and energy affected by a black hole, it is much more real than a carpet.

 

Precisely what a black hole is is much less certain than that they exists. Some theories predict that much of the matter and energy of a black hole is located at a point – a singularity – and that the singularity forms only at infinite time relative to a distant observer. They’re not very satisfying predictions, relying on a combination of quantum physics to explain the degeneracy involved in very high or infinitely high density matter, and classical gravity or General Relativity to explain gravity. Quantum mechanics has outstanding problems explaining gravity. Classical gravity and General Relativity fail to realistically explain the small scale behavior of matter and energy.

 

The defining characteristic of a black hole is that, for some distance from its center of mass, its escape velocity is greater than the speed of light in vacuum. It’s not an essential characteristic that its gravitating body have an infinitely great density – although the minimum density of stellar-mass black holes (about 10[math]^{31}[/math] kg) is very high (about 10[math]^{18}[/math] kg/m[math]^3[/math]), for a super-massive one (about 10[math]^{40}[/math] kg) , it’s only about 0.73 kg/m[math]^3[/math] – about the same as the air on Earth at an altitude of 10,000 m.

 

Although it’s questionable that supermassive black holes consisting of low-density materials can form naturally, the idea is not entirely far-fetched. By my calculations, a globular cluster star formation of about 10[math]^9[/math] (a billion) solar masses could, in the normal course of its orbital dynamics, “fall into” black hole status. Note, however, that such a globular cluster would be several hundred times more massive (contain several hundred times more stars) than the largest observed, such as Omega Centauri or Mayall II.

 

Although the detailed physics of black holes are uncertain, their existence is not. Although they produce counterintuitive theoretical predictions (such as infinite time dilation), they are not prohibited by, nor do they invalidate, best current theories. Although they are not well described by current theories, they place important constraints on them: for example, for the Standard Model to be extended to include gravity (via the inclusion of the graviton), and General Relativity to be accurate concerning black holes, the graviton cannot interact with itself.

[Farsight]

Craig: can I make it clear that I'm asserting that the singularity does not exist. Black holes are out there.