Black Holes

[peter09]

I must admit that I am a bit of a lurker here, I've been following these sorts of discussions for a while.

We need to understand that mathematics is an incredibly powerful tool when in can be mapped to reality. For instance your sat nav uses mathematics to resolve your position from the GPS signal, understand the mapping and time such that it can predict how long it is going to take you to get home.

The ability of maths to predict/model physical reality forms a supreme foundation of our understanding and the use of the world about us. Almost all our technology uses an underlying infrastructure of mathemetics.

The point of this discussion is that mathematics, unlike science, is not constrained to our physical reality, it can provide solutions that to 'engineers' are not real. Mathematicians also accept that these situations occur, but maths, not being a science can still explore these 'unreal' solutions.

The difficulty for all is that sometimes it is not clear whether a 'solution' describes a physical reality or it is an unreal solution (still mathematically valid). Black Holes appear to be an example of this situation.

[mharratsc]

Let's face it- it's mercenary work. They're mathematicians, and they're paid to solve whatever their clients want them to solve. In this instance- black holes. *shrug*

Mr. Sharples doesn't have to subscribe to the concept of black holes himself, he's just solving the math that's on the table. The argument that he maintains with Stephen Crothers is purely professional- they disagree on the meaning of a symbol in an equation (or at least that is how it comes across to me). The argument isn't whether 'black holes exist in reality or not.' At least as far as I can determine from Mr. Sharples disclaimer above.

Regardless- this thread does go a good distance in showing how you're not going to reverse-engineer the Universe from E=MC2 though.

What comes out of the equations is only as good as what goes in, you know? o.O

[Aardwolf]

Oops. Incorrectly attributed the quote on my previous post (what happened to the edit button?).

I'll try again.

My point all along has been that BH's do exist as solutions to the Einstein equations (contrary to Crothers' thoughts), but this is not to say that they necessarilly correspond to a distinct physical entity.

But if they dont correspond to a distict physical entity what exactly is the point of the solutions? What do you believe theoretical physicists study?

[Nereid]

One item that's been mentioned - quite a few times - is whether there is observational evidence that is consistent with the existence of ~solar-mass black holes, and/or ~million-to-billion solar-mass black holes.

A key term here is 'black holes'; if, per JSharples, these things are valid solutions to sets of equations that are (part of) the theory of general relativity (GR), then research into the consistency (observations, with black holes of the GR kind) would seem to be both interesting and scientifically sound. If, on the other hand, per Crothers, black holes of the GR kind do not exist, then what's the point?

(Of course, showing that all relevant, objective, independently verifiable observational evidence is consistent with ~solar mass black holes of the GR kind does not - in and of itself - mean that all relevant, objective, independently verifiable observational evidence is INconsistent with plasmoids of the Lerner kind, say! The consistency tests can, and should, be done independently).

[Aristarchus]

Ok Aristarchus, we have moved off point. The mathematics behind black holes includes differential geometry and the theory of boundary value problems in differential equations. The mathematical principles underlying these topics have nothing to do with the physical world. And so I am, as I have ever been, advocating that the mathematics behind black holes has nothing to do with the scientific method.

Bottom line, the mathematics has to comport with observations, not simply ignoring scientific method in order to prop up a fallacy based upon inference. The inference is simply a geometric interpretation of geodesic motion

Let's take a look at the language, and see just how far astray in tends to ignore the process of basing something off observation. Note, my emphasis provided:

It has been claimed that the near-horizon conformal symmetry is associated with a large class of black holes in arbitrary dimensions [2, 19]. It seems plausiblethat probing the nearhorizon geometry of these black holes would lead to an operator of the form of H, possibly with a different coefficient for the inverse square term [8]. It is thus likely that the analysis presented above for the massive Schwarzschild black hole could be generalized to include other cases as well.

My point all along has been that BH's do exist as solutions to the Einstein equations (contrary to Crothers' thoughts), but this is not to say that they necessarilly correspond to a distinct physical entity.

Crothers has delineated very appropriately how the positing of Schwarzschild related to the latter's correspondance with Einstein. This is not something that one could accuse Crothers as getting wrong, because Crothers cites the historical examples that provides evidence for what he proposes.

For example:

On the Gravitational Field of a Sphere of Incompressible Fluid according to Einstein’s Theory

Just as in “Mass point”, also for the sphere the general equations must be specialised to the case of rotation symmetry around the origin.

We have to determine a solution of these 5 equations that is free from singularities in the interior of the sphere. At the surface of the sphere it must be p = 0, and there the functions f together with their first derivatives must reach with continuity the values (9) that hold outside the sphere.

The integration constants must now be determined in such a way that the interior of the sphere remains free from singularities and the continuous junction to the external values of the functions f and of their derivatives at the surface of the sphere is realised.

On the road of these solutions, that are clearly not physically meaningful, since they give infinite pressure at the center, one can go over to the limit case of a mass concentrated to one point, and retrieves then the relation = 3, which, according to the previous study, holds for the mass point. It is further noticed here that one can speak of a mass point only as far as one avails of the variable r, that otherwise in a surprising way plays no rˆole for the geometry and for the motion inside our gravitational field. For an observer measuring from outside it follows from (40) that a sphere of given gravitational mass /2k2 can not have a radius measured from outside smaller than:

[JSharples]

But if they dont correspond to a distict physical entity what exactly is the point of the solutions? What do you believe theoretical physicists study?

Hi Aardwolf,

Theoretical physicists mostly study mathematical theories of physics, like GR. It is a fairly blurry boundary between mathematics and theoretical physics. The latter can be largely categorised as the application of mathematical principles to problems in physics.

Theoretical physicists will also try to develop theory to explain observations. Peter09 mentions a good example in sat nav. Initial versions of sat nav were observed to be inaccurate, the inaccuracies were fixed through the efforts of theoretical physicists who made the necessary calculations (using GR) to correct the measurements for gravitational time dilation. In fact the metric they used would probably not have been that different to the Schwarzschild metric.

If a current theory can't explain observations then a new theory is sought.

In the case of GR and black holes, there are a number of observations that are consistent with the existence of physical entities corresponding to black hole solutions...

[Aardwolf]

But if they dont correspond to a distict physical entity what exactly is the point of the solutions? What do you believe theoretical physicists study?

Hi Aardwolf,

Theoretical physicists mostly study mathematical theories of physics, like GR. It is a fairly blurry boundary between mathematics and theoretical physics. The latter can be largely categorised as the application of mathematical principles to problems in physics.

Theoretical physicists will also try to develop theory to explain observations.

Indeed. And what exactly is the point of explaining an observation with an object that doesnt correspond to a distict physical entity? It seems to me there is absolutely no logic in dissassociating a mathematical entity from a real entity if you are a theoretical physicist. It might be valid as an abstract mathematical solution but it has no place in the real world and therefore essentially useless as a solution to Einsteins real world problem.

Peter09 mentions a good example in sat nav. Initial versions of sat nav were observed to be inaccurate, the inaccuracies were fixed through the efforts of theoretical physicists who made the necessary calculations (using GR) to correct the measurements for gravitational time dilation. In fact the metric they used would probably not have been that different to the Schwarzschild metric.

What Peter09 is refering to are the mathematical calculations based on trigonometry and have nothing to do with GR. Sat navs dont make GR adjustments for gravitational time dilation. The gravitational time dilation adjusment was a one-off adjustment amending the frequencies of the clocks aboard the satellites. I'm not sure what you are refering to when you say early versions were inaccurate. The first satellite was used to determine the clock offset required and this has been incorporated into all satellites ever since. However, there is no way of knowing if this was even necessary as all satellite clocks are routinely corrected because of drift, drift rate, bias, orbital drift etc. And these are problems associated with stable clocks fixed and shielded on earth. Launching an instument like this into space can introduce it's own problems.

Of course that initial clock frequency adjustment for gravitational time dilation is offset by the smaller time dilation effect caused by fast movement. However no-one can explain how this fixed element works, considering the satellites are moving at different speeds to each other and to the observer on the ground. No further calculations are ever introduced to account for this.

If a current theory can't explain observations then a new theory is sought.

I agree, which is why it makes no sense for gravitational theory to still be valid. Changing the theory everytime new phenomena are discovered that don't fit the predictions is cheating. I'm sure the EU theorists wouldn't get away with that kind of manipulation.

In the case of GR and black holes, there are a number of observations that are consistent with the existence of physical entities corresponding to black hole solutions...

An unobservable infinitely limbed alien holding the stars in orbit from the centre of the galaxy is also a solution that corresponds to observation. Corresponding to observation just isn't good enough. Nails, screws, dowels, glue, brackets and tape are all valid solutions to the question "what holds my cabinet together?" Only one is correct and if you cant directly observe which it is, they are all just a guess. And you'd still be wrong because it's dovetailed.

[Aristarchus]

Indeed. And what exactly is the point of explaining an observation with an object that doesnt correspond to a distict physical entity?

JSharples is not articulating properly the role of theoretical physics. The latter is supposed to use quantitative methods for predictive measurements. If theoretical physics does not use mathematical models as predictive tools related to observed phenomena, then it is only guiding theory along the lines of conceptualizations as opposed to actuality. What is happening now is backwards of the scientific methodology. The mathematical models comport with the theories rather than the observations. Even worse, the observations must now comport with the theories, not vice versa, as it should.

One analogy I can draw is something that happens in Operations Research. Operations Research was created by the British in response to the military logistical problems confronted during WWII, as OR applied research conclusions based off mathematical models countering conventional military reasoning. One example is that the accepted military thought was based upon using few naval escort vessels for merchant ships in the assumption that this would result in far fewer target hits on merchant ships. OR methods came to the opposite conclusion, and the OR application provided for greater naval escorts for the merchant ships, which drastically reduced the number of target hits on the latter.

However, in universities today, on the PhD level of OR, there are those involved in graduate work that explore mathematical models that serve for no practical application in the real world, counter to the reason for creating the science of OR. This is not to state that this kind of graduate work serves no purpose, but let's be cleared that its only significance is for the mathematical models themselves.

In the same sense, this is what has happened in theoretical physics - string theory being a prime example. String and M theories sit in the compartmentalized inventions of beautiful mathematic and thus even proponents of the two latter theories state that it might never provide observational evidence, relegating it to a belief along the lines of a philosophy or religion. As for black holes, the CERN experiments are supposed to provide observational data, of which YTD has produce little if next to nothing, but even with that you will still have the question of scalability which will still have to be measured against the scalability solutions found in plasma cosmology.

In fact the metric they used would probably not have been that different to the Schwarzschild metric.

Probably?? Why is it that a statement like this can be posited under an assumed authority, but there is no citation or linking of materials from you that provides a concatenation for the historical use of the Schwarzschild metric?

[JohnMT]

Hi all,

This is my brief rant on the subject.

I am not a 'mathematician' by any means, nor do I pretend to be, except to say that I did study mathematics to a fairly high degree during the course of my long studies to become an qualified Aeronautical Engineer.

Be that as it may...and personal attributes aside.

This 'Black Holes' discussion seems to me to assume that a particular mathematical entity exists within an unproven formula (R-this or r-that...the Schwarzschild radius etc), which no doubt is derived from Pure Mathematics/Einsteinianism etc and that it may or may not give real substance to the apparent existence of their actually being Black Holes.

If a supposed 'Black Hole' had (or has) actually been observed (and I stress OBSERVED), then the mathematics can be applied accordingly and the results of these observations verified in their entirety.
No problem with that at all.

But it seems without question that the obverse, or the reverse of this question/supposition, is actually the case.

Whereas mathematics is a most wonderful invention and a very useful tool, how dare the so-called 'Theoretical Astrophysicists and Cosmologists' of this day declare that their wishful mathematical derivations and hence esoteric thinking, are absolute fact.
Are we deluded, or they?

I am tired of listening to these brainwashed so-called 'experts' who seem to 'know it all', waffling on with gay abandon and almost absolute assertion about the apparent/real existence Black holes and the such, when all they do in reality is purely to regurgitate their University training under the guise of being a 'Doctor' (which is to say, a much more highly-brainwashed individual, who cannot think sideways, because of the intense indoctrination suffered during those long years of self inflicted purgatory...such I think, are so deluded, that they no hope left...but that is only my opinion.)

For just one example (and there are many others):

The deluded Dr. Phil Plait (the next professed Carl Sagan?) wrote a book some years ago entitled 'Bad Astronomy' and I have a copy and have read it several times.

Much of what he says in his book is quite simplistic and verifyably true (except perhaps for his Chapter on Velikovsky, Chap 18 ... 'Worlds in Derision'...'Velikovsky vs. Modern Science', which does not impress me one bit...other than his complete ignorance of the subect).
Fortunately, Phil Plait doesn't say anything in his book about 'black holes' and other weired entities and for that I am glad.
The book no doubt was intended for the 'layman' and for that he has done a good service and I give him due credit (excepting also a couple of other chapters on UFO's and planetary alignments etc...which no doubt all such books must contain in order to fill spaces).

As for this 'layman' aspect (which I mentioned above), the rest of his deliberations speak precisely as to how much we currently know about Astronomy and Cosmology.
THAT in my understanding is precisely, IT!
Phil Plait got it right... We know Nothing much at all, other than what we actually observe!
(As Manuel said in an episode of 'Fawlty Towers'..."I know nothing...nothing I know"...Ha, ha

More seriously and Conventionally speaking, our so-called 'experts' really have nothing much more to offer than what Manuel has said, other than their rather stupid assumptions and most ridiculous suppositions concerning unproven entities.

One might therefore ask:
'Wherein lies the most honoured and accepted 'Scientific Method' in these cases?

Further, such simplistic declarations and teachings a Phil Plait, regurgitated from his many years of learning, can also be learned from any basic textbooks on these subjects.

Seems to me that the entire study of our celestial realms over the past hundred years and more, has become so stagnant and disturbingly irrelevant (there being no true explanations), that we have been 'stuck in the mire' for a very, very long time and hence have advanced virtually nowhere.

'Black Holes' and all their unproven mathematical derivatives it seems to me, are purposely 'planted' in order to 'save the day'...and I for one (and no doubt many others too), just cannot buy this utter nonsense.

Ah well, said my bit,

Cheers,

John

[StevenJay]

Wherein lies the most honoured and accepted 'Scientific Method' in these cases?

Probably in a jar of formaldehyde - on a shelf in a museum-like setting, deep within the bowels of the "Church," under 24/7 armed guard for. . . posterity.

[KuhnKat]

Mathematics grew out of the Sumerian system of weights and measures 8000 years ago, according to this website: http://en.wikipedia.org/wiki/Ancient_Me ... easurement

Respectfully submitted,
Dotini

Your link only goes back to 6000BCE (4000BC). Couldn't find that 8000 number. The 6000 was in reference to coinage so would probably be reasonable for your statement. Here is an interesting quote:

"In Early Dynastic Sumer (c 3500-2300 BCE) metrology and mathematics were indistinguishable and treated as a single scribal discipline."

[webolife]

Kuhnkat,
What're you saying? That BCE isn't just another name for BC?

[klypp]

1. Many animals are cats.
2. Dogs are animals.
"1 and 2 taken together still admit the possibility that" dogs may be cats.

Inconsistency in your reasoning? No...
Now it looks more like there is no reasoning at all. Your "basic logic" simply sucks!

Sorry Klypp, but you're the one whose basic logic needs some work. The more correct (but still imperfect) analogy would have been:
1. Many animals are not cats.
2. Dogs are animals.
1 and 2 taken together still admit the possibility that dogs may not be cats.

A direct analogy would have been:
1. Many animals are not quadrupeds.
2. Humans are animals.
1 and 2 taken together still admit the possibility that humans may not be quadrupeds.

Lets break down my original arguments about BHs: let M be the set of mathematical entities and let P be the set of physical entities.

The statement
"1. There are many things that exist as mathetical entitites without any corresponding physical entity."
means that M is not a subset of P.

The statement
"2. That BH's exist as mathematical entities is a derivable fact."
means that BHs are in M, but since M is not a subset of P, you can't conclude that BHs are also in P.

Really Klypp, this is how I would have to explain the logic to a kid in primary school...! (You're not a kid in primary school are you???)

Sorry, I haven't had time to deal with this before and maybe I should just leave it. On the other hand, fearing that someone out there might swallow this shallow nonsense, I'll try to round it up.

So, what was my cat and dog example about?
It is what is called a counterexample. Aristotle used it, and it has been in common use by logicians every since. The point is that all it takes to prove that the form of an argument is invalid is a single instance of that form where the premises are true and the conclusion is false. Or, as in this case, just nonsense.
Everyone that ever opened a book on basic logic, knows this. JSharples does not. And thus he embarks on the hopeless mission of creating counterexamples to the counterexamples! It’s just hilarious!

Now, some might come to think that there is no false conclusion in these examples. So maybe JSharples come out all right after all?
Not so. Because this is the glaring mistake JSharples should have spotted in the first place. The reason why there is no false conclusion is that there is no conclusion at all! That something “may be” or “may not be” is as inconclusive as can be.
The general form of an argument in basic logic is two or more premises followed by a conclusion. Both the premises and the conclusion must be propositions, i.e. they have to be either true or false. JSharples “conclusions” are neither.

To make this clear, “dogs are cats” is a valid term in formal logic. It can be either true or false. Terms like “dogs may be cats”, “dogs may not be cats”, humans may not be quadrupeds” are not valid. These terms can not be false. They are always true.
And thus, you don’t need premises for such “conclusions”. You can’t use formal logic to validate them. In fact, they have nothing to do with formal logic.

Have a look at what happens when he “breaks down” his argument. He “concludes”, or rather “can’t conclude” that
“BHs are in M, but since M is not a subset of P, you can't conclude that BHs are in P.”
Note that it doesn’t matter whether BHs are in M or not. You still “can’t conclude that BHs are in P”.

Constructs like this has nothing to do with logic. The proper term is nonsense.

[jjohnson]

The escape velocity at the distance of the event horizon from the center of mass of the black hole to which that event horizon belongs, is posited to be c, the speed of light.
Matter cannot be accelerated to the speed of light.
Therefore matter cannot be accelerated beyond the event horizon from within.

Light travels at only one velocity, its "local" speed in whatever medium it finds itself.
Therefore light reaching the event horizon from inside a black hole has, by definition, escape velocity, and therefore... escapes.

(A) So why can we not see into a black hole? Or at least see light departing its event horizon, whether it forms a usable image or not? Why is a black hole supposed to be black?

Are black holes suspected of being at the center of nearly all galaxies drawing in Cold Dark Matter, which is supposed to be preferentially "clumped" around the central galactic bulge and halo? Why is the effect of all that CDM's gravity on a galaxy not gradually decreasing with time as the black hole sucks that in, too? If the black hole exerts gravity, it must do so because the source of its gravity is the mass residing inside its event horizon.

(B) So the force of gravity can be exerted through the event horizon, and that force will increase as more matter is drawn into the black hole? How can a gravity field be projected to the exterior of an event horizon/black hole, when electromagnetic fields allegedly cannot?

[JSharples]

Sorry, I haven't had time to deal with this before and maybe I should just leave it. On the other hand, fearing that someone out there might swallow this shallow nonsense, I'll try to round it up. [Followed by a bunch of nonsense about cats, dogs and counterexamples....]

Yes, you should have just left it Klypp. I appreciate the lecture, but you should know that we did cover basic logic, set theory and methods of proof as part of our undergraduate mathematics course. We even had to pass an exam!

Consider the following proposition: "This proposition is false".
Is it true or false? If we are to take your word for it then it must be one or the other...

Please let me know when you're having your next tea party...