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Andrew Testa

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Getting lost at page 5. The theories regarding entropy within a black hole seem to be making some assumptions that I'm not entirely comfortable with either, although that's probably an artifact of my understanding, or rather lack thereof.
Trying to imaging alternate spacetimes is confusing, if that's what you're getting lost on. Here's a quick analogy, not really correct, but it points out the overview. Since we're all somewhat audio folks around here ('else why be reading HTF), let's examine measurements of an audio signal. We can graph it in the time domain, that is plot dB vs. time, or we can graph it in the frequency domain, plotting dB vs. frequency.

In the first, time and signal strength are 2 dimensions that sound can exist in. We can formulate theories on how sound behaves over time based on it. In the second, frequency and signal strength are 2 dimensions that sound can exist in. We can formulate theories about how sound behaves over frequency ranges based on it. Each attempts to explain the behavior of sound, but they use different dimensions to do so. formulas for time based sound are different from formulas for frequency based sound. Some aspects of sound are better described in one vs. the other. For example, a time domain measurement doesn't give you any information about whether that 6 dB spike was at 10Hz or 3000 Hz.

These different sound domains can be thought of as different spacetimes. They all attempt to describe the physical universe, but they make different assumptions about the nature of the dimensions their formulas describe. Their goal is to find a set of initial conditions that lead to physical behavior similar to what we see, but trying alternate approaches that can explain things that can't be explained by using our accepted 4D (3D + Time) spacetime. Frequently that involves postulating multiple dimensions or bizarre mathematical descriptions of basic particles. But what they are basically doing is trying alternate formulas to describe the universe. Those sets of formulas are collectively called a spacetime, since they try to describe all of space and time as we see it.

BrianW, does this work as an analogy?

As far as the entropy, don't worry. Black hole thermodynamics is truly the stuff at the bottom of the rabbit hole. There's no common sense to it, and it makes people like me need a dose of South Park to clear the head. I once tried reading one of Kip Thorne's books on black holes, and when he got to the effects of spinning, charged black holes (still in chapter one) I suddenly became illiterate.

Andy
 

BrianW

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BrianW, does this work as an analogy?
Sure!

I haven't read the article in question (so be advised that what I’m about to say may not even apply), but another way to think about it is to remember that there are two mainstream approaches to describing nature:

1. Make assumptions about nature, and derive a formula from those assumptions that passes the test of further observations.

2. Create an arbitrary formula that fits current observations, and marvel/laugh/scoff at the weirdness of the implied underlying assumptions that must be true in order for the formula to be applied.


A classic example of the first approach is Relativity Theory. Einstein assumed that the speed of light is unchanging, regardless of reference frame, and all the math fell into place based on that one assumption. Testing against further observations continues to this day.

A good example of the second approach is Super String Theory. Super string theorists are crafting a formula that describes the Universe based solely on its fit with nature, and on the formula's "appeal" (symmetry, simplicity, even beauty). The implied underlying assumption – that we must live in a ten-dimensional Universe – required for Super String Theory to be “true” is interesting, but immaterial since it cannot be tested.

And before you think that the second approach is new-fangled and inferior (after all, it doesn’t employ the Scientific Method like the first approach does), you should know that Newton’s mathematical description of gravity was also crafted using the second approach. He largely used math that worked, simply because it worked, without any prior assumption about the underlying nature or cause of gravity itself.

So it is sometimes acceptable to use a tool to describe the Universe, as long as it describes it accurately, even if the tool can't possibly exist without first turning your brain inside-out.

Again, I haven’t read the article (I plan to this weekend), but depending on context, if certain unthinkable things must be true in order for a formula or description of nature to be applied, and as long as that formula or description helps you to arrive at a valid place to be, I wouldn’t worry about it too much.

Having said that, from Andrew's first mention of the article, it does sound like a derivation of an unbelievable description of nature based on otherwise reasonable assumptions, which is pretty much the opposite of what I just described. So after I get around to reading the article, I reserve the option to come back here and delete everything in this post after the word, ”Sure!”

:)
 

chris_everett

Second Unit
Joined
Jul 20, 2003
Messages
403
Andy,
I like your analogy, and I would say that it does apply, at least to a point. I don't have any problems with multiple spacetimes, and after a couple more reads of the article, the last couple of pages do add up, more or less, (I was getting lost in the Using anti-de Sitter spacetime, theorists have devised a concrete example of the holographic principle at work: a universe described by superstring theory functioning in an anti-de Sitter spacetime is completely equivalent to a quantum field theory operating on the boundary of that spacetime) but they are relient of the entropy of a black hole being a "mirror" of sorts to the rest of the universe, and that seems like a big jump to me. They seem to be making assumptions about black holes, that we don't have any data to support. Again, I may not be following their logic correctly, but that's my take after a few reads.

Brian,
I've always liked superstring thery for the reasons that you mentioned, (although for practical purposes, relativity seems more useful).
 

Andrew Testa

Second Unit
Joined
Mar 22, 2002
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The data we actually have about black holes is very small. Most of their work is theoretical, deriving the consequences of an event based solely on the relativistic equations. The link to reality is that so far, everything we've been able to measure about black holes, including their existence, was already predicted by relativity. The assumption is that other properties that are predicted will also eventually be found to be true. If not, then we get to shake up physics and make more accurate models, and all the neat conjecture is wrong. Heh, it's happened plenty of times before.

The use of black holes isn't so much as a mirror as it is an upper bound. And since this theory came from black hole research, it's a logical place to start. So they aren't saying that a black hole can be used to determine how much information your body can store, they're saying that your body cannot store any more information than could a black hole with an event horizon that physically surrounds your body, and that the maximum amount of that informations cannot exceed an amount that's proportional to the surface area of the event horizon. It is merely an upper bound to the information that can be stored within that volume of space.

The extrapolation to the universe at large is that all the information in the universe cannot exceed the information storage capacity of an event horizon that encompasses the volume of all the universe's matter clumped together. In other words, the total amount of information contained in the universe has an upper bound that can be completely described by a surface area. If that's the upper bound, then at any given time, like now, the universe could be completely described by far less than the surface are of an encompassing event horizon.

The black hole itself isn't important. What's important is that it's event horizon surface area completely describes it's information content, and that it's surface area is an upper bound to what anything else could store. Therefore everything 3D can be stored on a 2D medium. Since our universe is actually 4D and may not have a boundary, it's really hard to conceptualize that. So they used the other spacetimes as examples since they have simple, predictable properties and the physics is much easier. The triumph of their theory is that a set of formulas (a 'physics') describing a universe (the anti-de Sitter), are completely equivalent to a physics that only exists on the boundary of that universe. In other words, all the information in the de Sitter universe can be stored in the surface area of its boundary. In the hologram analogy, the boundary of the universe is the film that creates an illusion of more dimensions.

I hope that didn't just restate what you already know, or just stir the confusion. Let me know if it's any clearer.

Andy
 

chris_everett

Second Unit
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Jul 20, 2003
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Andy,
Thanks, that does help. That's mostly what I understood the article to be saying as well, but I'm glad to see i wasn't misinterpreting it. And it makes it a lot easier to explain my problems with it. Even when I typed "mirror" I wasn't comfortable with it, but I could not think of a clear description.
The triumph of their theory is that a set of formulas (a 'physics') describing a universe (the anti-de Sitter), are completely equivalent to a physics that only exists on the boundary of that universe. In other words, all the information in the de Sitter universe can be stored in the surface area of its boundary. In the hologram analogy, the boundary of the universe is the film that creates an illusion of more dimensions.
I was still getting a bit lost here, but It seems to be they have an "if my theory is accurate, than my theory is accurate". I'm waffling on that, but, well..... Again, my standard disclaimer applies.

I'm getting a headache....
 

BrianW

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Brian
Okay, I'm on the same page, now. Please disregard my previous post, as it has absolutely nothing to do with anything going on here.

Or anywhere else, for that matter.

I'll be back when I get more time. Right now, I've got an impossibly unachievable artificial deadline to meet. (The deadline was determined by a trade show date, not by anything having to do with reality. Ugh.)
 

Andrew Testa

Second Unit
Joined
Mar 22, 2002
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263
"if my theory is accurate, than my theory is accurate".
Yeah, I can see how you'd come to that. In general terms, what they're saying is "this is my hypothesis, and this well known tool (alternate spacetimes) can be used to demonstrate that my hypothesis is valid in the limited case of this particular tool."

A simpler analogy that does the same thing is the following:

1) I hypothesize that the curvature of the universe can be determined by measuring the angles of an equilateral triangle that spans a large portion of the known universe.

We can't test this directly because we can't construct a triangle large enough to measure the angles with enough accuracy to see any curvature. But to prove that the hypothesis is sound (not that it's true, but that it's sound) we will apply it to two alternate spacetimes where the physics is simpler: a 2D flat rubber sheet, and a 2D rubber sheet curved in 3D.

2) We apply the hypothesis to the alternate spacetime.

A rubber sheet serves as an alternate spacetime by reducing physics to 2 dimensions. All physics still applies, but you only have to calculate two dimensions. much simpler calculations. To apply the hypothesis, draw an equilateral triangle on the rubber sheet. With the sheet flat, measure the angles. they are all 30 degrees.

Now stretch the sheet over a large bowling ball so that it takes a curved shape. This is alternate spacetime number 2. Measure the angles again; they are all greater than 30 degrees.

3) Does our hypothesis fit the physics of the test spacetime?

Well, on a flat 2D sheet the angles are 30 degrees, and if we curve the sheet the angles increase with the curvature. So in limited case of our 2D spacetimes, the hypothesis is correct; angles of 30 degrees indicate a flat universe, and angles greater than 30 degrees indicate a curved universe. Furthermore, the angles increase with increasing curvature, a result not part of the hypothesis, but one that follows by investigating the alternate spactime.

4) Generalize to the known universe.

We know that spacetime can curve, that's been measured. Is the universe as a whole curved, or is it flat? Our alternate spacetime calculation leads us to believe that if we could construct an equilateral triangle that spanned a significant region of the universe, then measuring the angles would indeed be a valid test to tell us if the universe was curved or flat.

The alternate spacetime serves as a microcosm in which to test difficult theories. It doesn't prove that the theory is correct, but it can prove that the theory is valid under some limited conditions.

Is that helpful?

Andy
 

chris_everett

Second Unit
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Jul 20, 2003
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403
Thanks Andy.

His premise is that the missing entropy is reflected in an increase in the surface area of the horizon.
And if this is accurate, everything else falls into place, but that seems to be one hell of a big if. To large of one for me to take at face value. I'm afraid that I'm going to have to research their work further to see what their support for this claim is.

Two of my 'always remember' bits are being challanged here.

1. "Extraordanary claims require extraordinary proof"
2. "A wise man does not build his house upon the sand"
 

Andrew Testa

Second Unit
Joined
Mar 22, 2002
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263
Black Hole Horizon Area Quantization
A variety of examples support the conjecture that the horizon area of a near-equilibrium black hole is an adiabatic invariant in the sense that slow perturbations of the hole leave the area invariant. In physics the quantum operators corresponding to adiabatic invariants often have a discrete spectrum. By analogy the Kerr black hole mass M might have a discrete spectrum provided the classical relation between horizon area, mass and angular momentum goes over into the quantum theory. Semiclassical evidence is presented that there exists a quantum of horizon area independent of black hole scale so that the black hole horizon area eigenvalues are uniformly spaced, or equivalently, the spacings between black hole mass levels go roughly like 1/M. Black hole entropy can then be interpreted, as first done by Mukhanov, as quantifying the degeneracy of these levels. Quantization of horizon area suggests that the area operator is part of an algebra of black hole observables and other operators. I describe such an algebra, delineated by Mukhanov and myself, which, based on a few assumptions, leads to the uniformly spaced area eigenvalues. It is crudely reminiscent of Pauli's algebraic quantization of the H atom, so that the black hole seems to play the same role in gravitation that the atom played in the nascent quantum mechanics.
I can assure you that the actual lecture will be completely unintelligible beyond that point to the likes of you and me. When these guys talk to each other it's worse than trying to decode rap lyrics. Good luck in your research, and I really mean that. I'm content to trust his peer review so that MY brain doesn't have to turn to Jello.

Andy
 

BrianW

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Would that be Jell-O pudding, or gelatin?

Here’s my take on the quote above. (And please understand, I mean no disrespect. This is all in good fun.) What follows is each sentence in the quote, followed by a simple translation:

A variety of examples support the conjecture that the horizon area of a near-equilibrium black hole is an adiabatic invariant in the sense that slow perturbations of the hole leave the area invariant.
It is my suggestion that the area of the event horizon of a steady-state black hole remains constant, even if some energy/mass transfer may appear to be taking place.

In physics the quantum operators corresponding to adiabatic invariants often have a discrete spectrum.
Quantum physics doesn’t allow things to happen all higgledy-piggledy.

By analogy the Kerr black hole mass M might have a discrete spectrum provided the classical relation between horizon area, mass and angular momentum goes over into the quantum theory.
Black holes might actually be great big quantum particles with discrete states of existence. No, really!! It could happen!

Semiclassical evidence is presented that there exists a quantum of horizon area independent of black hole scale so that the black hole horizon area eigenvalues are uniformly spaced, or equivalently, the spacings between black hole mass levels go roughly like 1/M.
Black holes are best described using algebraic analysis, but by using a fancy word like “eigenvalue,” I can introduce the concept of applying quantum analysis.

Black hole entropy can then be interpreted, as first done by Mukhanov, as quantifying the degeneracy of these levels.
This is the part where I wave my hands. Trust me.

Quantization of horizon area suggests that the area operator is part of an algebra of black hole observables and other operators.
Stuff is related to other stuff. Well, DUH!

I describe such an algebra, delineated by Mukhanov and myself, which, based on a few assumptions, leads to the uniformly spaced area eigenvalues.
Presto!

It is crudely reminiscent of Pauli's algebraic quantization of the H atom, so that the black hole seems to play the same role in gravitation that the atom played in the nascent quantum mechanics.
My work is like this other guy’s crappy theory, only better, because it has this really cosmic, mind-boggling implication associated with it!

-or-

If things pan out, I'll be considered just as brilliant as this other guy, since my work will lead to the development of quantum gravity, just like his work led to the development of quantum mechanics.


See? That wasn’t so bad. ;)
 

Andrew Testa

Second Unit
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Mar 22, 2002
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Brian's analysis is pretty darn good, especially

if I can't follow something, it's usually because it's not valid.
Chris, man, you're killing me here! Seriously, I'm almost peeing my pants trying to juxtapose that statement with a discussion of quantum mechanics! And in a friendly way, mind you, if that's possible, because I've had to DO quantum mechanics, and it's so anti-common sense when you get into the nitty-gritty of it. There are major portions of it where I could do the math but STILL couldn't tell you what the hell it means in the real world. There're many things in life I can't follow. Hell, there were many things just in school I couldn't follow. Never could understand Spanish grammar. No logic there. But I could understand, even enjoy, complex analysis and partial differential equations, classes that some of my peers couldn't for the life of them understand. Doesn't affect the validity of any of it.

I seriously look forward to hearing your opinion of the references if you decide to read them. But I absolutely won't do any math in any discussions. Not without free beer, and plenty of it. Good luck!

Andy
 

chris_everett

Second Unit
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Jul 20, 2003
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hehe...
I probably should have defined "follow". Certinly not understand, maybe not even comprehend, and certinly not following common sense, but if there isn't at least SOME level of logical thinking behind a scientific process, even just within itself, as a discussion of this nature is bound to be, then, well, your just making stuff up, no matter how many big words you use.

I've just begun reading some of the authors other work, and yes, the vast majority of it does nothing but give me a headache, but there is some logic to his statements, from what I can tell so far. Unfortunantly, I'm not going to have much time to read them until the weekend.

And remeber, this is all your fault, with that whole "False authority" and "Don't trust the Ph.D." thing :D
 

chris_everett

Second Unit
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I love google. I found what appears to be the authors original published paper on the subject, entitled "Black holes and Entropy" Published in Physical Review D on April 16 1973. Unlike his more recent works, this one is understandable to anyone with a solid knowledge of relativity and thermodynamics, as he intentionally avoids quantum mechanics whenever possible. I understood nearly all of the narrative, and even most of the math on the first read. What did I think of it? It's very good. Although it still leaves unanswered questions in the Sci Am article, it clearly establishes a solid foundation for all of it's conclusions. Particular detail is given to showing the effect of entropy on the area of a black hole, using classical thermodynamics, and supporting data is given for a number of scenarios documenting the increase in entropy that the theory demands. The Generalized Second Law, which is poorly defined in the Sci Am article, is clearly defined in the paper, the similarities between thermodynamics and black hole physics are explained in an easy to understand manner, and the tie-in to information theory is well documented. The author acknowledges the limitations of the theory (another thing missing in the Sci-Am article), and throws up what would be the most common questions to insure that his theory stands up to them as well.

After reading this paper, I'm much more inclined to take his other work that is based largely on it at face value, although I hope that some further research on my part will help answer my remaining questions.

Thanks for your encouragement to research this further Andy. It's been an enjoyable experience.
 

Andrew Testa

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Chris,

Excellent! Great job. Would you care to share that link with us?
Thanks for your encouragement to research this further Andy. It's been an enjoyable experience.
You are very welcome. Actually, I was a little worried you might be offended by my last post. On reread it does seem to be a bit of a discouragement. But it looks like you're in good shape, and that you could follow his paper is great. Sometimes they are readable, it depends on the publication. Physical Review is actually one of the worst, usually more equation than text. Again, I'm pleased I could help!

Andy
 

chris_everett

Second Unit
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Jul 20, 2003
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403
This is the Link

This is the abstract,

There are a number of similarities between black-hole physics and thermodynamics. Most striking is the similarity in the behaviors of black-hole area and of entropy: Both quantities tend to increase irreversibly. In this paper we make this similarity the basis of a thermodynamic approach to black-hole physics. After a brief review of the elements of the theory of information, we discuss black-hole physics from the point of view of information theory. We show that it is natural to introduce the concept of black-hole entropy as the measure of information about a black-hole interior which is inaccessible to an exterior observer. Considerations of simplicity and consistency, and dimensional arguments indicate that the black-hole entropy is equal to the ratio of the black-hole area to the square of the Planck length times a dimensionless constant of order unity. A different approach making use of the specific properties of Kerr black holes and of concepts from information theory leads to the same conclusion, and suggests a definite value for the constant. The physical content of the concept of black-hole entropy derives from the following generalized version of the second law: When common entropy goes down a black hole, the common entropy in the black-hole exterior plus the black-hole entropy never decreases. The validity of this version of the second law is supported by an argument from information theory as well as by several examples.
Unfortunately, you have to pay $20 to get the full text. Well worth it if you have any interest in his work, and well worth it for me just so I could sleep without dreaming about black hole horizon area.

As it relates to my question, to paraphrase, if the entropy of the visible universe only increases, than the entropy must be reflected in the horizon area, as the volume beyond the horizon area is, of course, no longer in the visible universe, and no longer can have any information. When a particle falls into a black hole, even if we assume that the particle has only the minimum possible information (it exists) once it falls into the black hole, we can know longer know if it exists or if it was destroyed, hence an increase in entropy, which must be reflected at the event horizon. The most useful proof, in plain English, is that even thought under certain circumstances black hole mass may decrease, horizon area does not.

I really was getting discouraged with some of his more recent work on information theory. It seems fascinating, but way over my head.
 

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