Dear Lawrence,

I just read your new paper "Exceptional Black Holes" for the second time. Much of the content is in prior papers, but you did break out the 10-D transformation in more detail. I find it interesting that your J3(O) posses an SO(8) triality. Have you read my book? Section 7.2 has some potentially important SO(8) symmetries based on a simple FCC lattice.

Have Fun!

Ray Munroe

I am writing up more explicit results with this. I sent an early phase of this to you last week. The purpose is to compute a general Born-Infeld action from this, which is the cornerstone of M-theory.

Cheers LC

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Dear. Dr. Lawrence B Crowell,

The thrust of your essay depends upon the existence of, at the least, Black Holes. Before I evaluate and vote of this essay, can you please say something about the empirical evidence for the existence of Black Holes. I am not asking for a theoretical explanation. I want to know if there is empirical evidence that clearly distinguishes the existence of a black hole from an otherwise very massive object?

James

I don't know how knowledgable you are on the subject. A sort of general source can of course be found at Wikipedia:

http://en.wikipedia.org/wiki/Black_holes

The main point of evidence lies with accretion disk and quasar jets which are observed. Black holes are the only known power source which can generate these enormously high energy events. Attempts with phenomenology of hyperstars and other putative sources have failed to theoretically work, nor do they satisfy observational data.

Another source is with the motion of stars near the center or the Milky Way galaxy. The UCLA astronomy dept has their research posted at the UCLA Galactic Center Group

http://www.astro.ucla.edu/~ghezgroup/gc/

The animation of stars is from data taken by tracking the motion of galactic center stars about nothing visible, but yet based on basic calculations must be around 10 million solar masses.

My paper really discusses quantum black holes more than large astrophysical black holes. Yet quantum black holes should also exist, and amplitude signatures for them have appeared in RHIC data.

http://arxiv.org/abs/0805.3579

Yet it has to be admitted that as yet the data is not solid or conclusive.

Cheers LC

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Dr. Crowell,

Thank you for your quick response. In rereading my message just now, I think I should make it clear that my rating does not depend upon what I think about your answers. I have no intention of giving someone with your skills a poor rating. I have high respect for your knowledge. It is the case that, because of my own work which is not nearly as sophisticated as yours, I do not believe in Black Holes. I think perhaps I was not as specific as I needed to be when asking my question. I will rephrase it: Is there empirical evidence that distinguishes between equal masses one of a Newtonian view and one of an Einsteinian view? I am phrasing it this way because you responded by referring to a 'power source'. In other words, is there empirical evidence that can distinguish between two power sources of equal mass, one of which is Newtonian and one of which is Einsteinian?

James

James

I am not sure if you disbelief in black holes is due to a rejection of relativity and general relativity, or if it is due to your opinion that matter should prevent the complete implosion of stuff into a black hole.

Newtonian mechanics, without relativity, indicates that the energy of a system is given by

E = (1/2)mv^2 - GMm/r,

A body dropped from infinity with E = 0 will reach different radii from the center with velocity v^2 = 2GM/r, or equivalently that velocity is reached once the particle reaches a radius r = 2GM/v^2. So it does not take much to set v = c, the speed of light, to get r = 2GM/c^2, which is the same horizon result of general relativity for the Schwarzschild solution. This is the Newtonian black hole, though it is a bit different from that of relativity. It differs from the general relativity result in that if I send a particle towards the gravity field with E > 0 or E < 0 I can adjust the radius at which it reaches a velocity v, which includes v = c. Relativity requires that the speed of light is an invariant of the universe, so that no observer can exist on a frame where electromagnetic radiation is observed traveling at a velocity different from c = 2.99e5km/sec (approximately).

The question might refer to whether there must exist a solid surface with some gravity fields identified as black holes. There are two reasons to think it is highly unlikely this can be the case. The first reason is that bodies with a solid surface interact with in-falling material with a "slash." The stuff crashes onto the surface and there are distinct signatures for that. This is found with neutron stars and white dwarf stars. Objects identified as black holes lack this signature. The black hole at the galaxy center has been observed to tidally rip an orbiting star that gets close and rip material off of it. No splash was observed. Another reason to doubt the existence of a solid material surface is that even in the Newtonian case, where you predict a black hole of sorts, there are no known materials which can resist gravitational implosion or collapse at the radius near r = 2GM/c^2. Also for a solid surface at this radius the solid surface would have to be made of material which can resist collapse by permitting sound or pressure waves to travel through it at velocity v > c. This is not permitted within the context of relativity theory.

It must be understood of course that in science we never really prove things, but only support theories and their predictions with a body of evidence. So in some sense we have not proven that black holes exist. It is however the case that astronomic evidence presents growing support for the existence of black holes.

Cheers LC

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Dr. Lawrence B Crowell,

Thank you for that response. It is helping me reform my question. With regard to what I think about relativity theory: No I don't accept it as real. Even the proofs put forward appear to me to miss their mark. Its not my own opinion that I am trying to get at. However, the definition of a black hole does rely upon relativity theory. It is that distinction that I wish to isolate and question.

I have no question with regard to what happens physically to matter when it is that dense. You wrote about strings, their curvature of spacetime, and the effects upon them when they reach a black hole. Speaking about space and time, it seems to me that those are the properties that relativity theory uses to establish when a black hole forms. You gave a helpful response in your last message; however, you did not refer directly to space or time.

It seems to me that determining whether or not the super massive object is a black hole depends upon some evidence that includes effects upon space and time. I wanted to avoid taking your time by discussing relativity theory in general. I also was hoping to avoid an answer of the type: Time is relative or GPS work not work. That kind of answer appears to me to miss its mark. So, when I asked if there was empirical evidence to distinguish a black hole from an equally massive object of matter, I was wondering if there is any evidence that can be put forward that does not depend upon a prior belief in relativity theory. For example: If a traveler, who knew nothing about Einstein's theory, came upon a black hole, is there anything empirically known about black holes that would help him to determine that something extroardinary has happened to space and time.

I'm sorry, but I don't feel that I am succeeding in making my point. I think it sounds as if I am asking for more explanations about the details of relativity theory and the standard proofs put forward in defense of it. I am not. I am asking about empirical knowledge that clarifies the existence of a black hole without referring back to relativity theory itself. If you believe that I am lacking the understanding necessary to appreciate the reality of black holes, you can say so without offending me. There is no need to write a lengthy lesson type response. I think I have taken enough of your time on this question. I appreciate the responses you gave.

James

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Dear James,

I used to work with NASA, and later taught College-level Astronomy. I understand that many people don't believe in Black Holes.

The concept of a Black Hole does not require General Relativity. It only requires that we can define a speed of light, c, and an

escape velocity, and that we can determine a mass and radius such that the escape velocity is greater than c.

Black Holes are a strange phenomena in that their properties make them impossible to directly observe. We infer the existance of Black Holes based on indirect observations such as the rotation speeds of stars near a galactic center. If a star is orbiting the center of a galaxy at a much faster speed than what we expect from counting bright stars within its orbit, then we know there is invisible mass present. Is this Dark Matter or a Black Hole? The normal assumption is that Black Holes exist at galactic centers. You may want to check out these

NASA

LINKS.

If String theory/ M-theory is correct, we should expect strings to be distorted by intense gravitational fields, and follow these gravitational field lines. If a Black Hole is a quantum phenomena, we might expect an abrupt quantum break in these strings, and thus closed string loops become open strings. If a Black Hole is a non-quantum event, then we should expect these field lines to asymptotically approach infinity as an infinite collection of parallel (but never quite touching) lines.

Have Fun!

Dr. Cosmic Ray

I have to say that relativity theory has been confirmed to extraordinary levels. Special relativity is well understood and more used than researched. The patching together of local regions of space that are flat enough for special relativity is what gives general relativity. General relativity has also passed all the experimental tests put to it. The last test was the Gravity Probe B, which was sent to detect the frame dragging effects of a rotating gravitating body. The rotation drags space around with it. The Gravity Probe B is documented in:

http://en.wikipedia.org/wiki/Gravity_Probe_B

The data analysis is ongoing, due to the fact the measurement was of a very small effect due to the small curvatures induced by Earth's weak gravity field. Another test is the Rebka-Pound experiment which demonstrated Doppler shift of light be gravity, as predicted by general relativity. The Taylor-Hulst observation of two neutron stars in a mutual orbit indicated how the orbit is decaying at a rate exactly predicted by the general relativistic emission of gravity waves.

So relativity is pretty well substantiated. Virtually everybody in physics accepts it as the realistic theory of spacetime and gravitation. The matter is not hotly disputed. So I can only leave the relativity issue at this point. It is a bit like Darwinian evolution. Again scientists regard it as the unifying theory for the relatedness and structure of life. Yet there are those who adamantly call it a falsehood in favor of creationist ideas.

When it comes to black holes and the direct detection of spacetime curvature near them, the data is somewhat sparse. There are Doppler shift measurements on radiation emitted by accretion disks around black holes, which conform to a general relativistic understanding of gravity. The problem is that telescope resolution is not sufficient at this time to image the region right around the black hole. There are some "super-scopes" in the works which might be able to do just this. The optical characteristics of spacetime around the galactic black hole at the Milky Way center might be directly observed. It will take another 15 years for that data to come forth.

I will say that I wonder why it is that people with an interest in science will end up rejecting some of its central pillars. Yet there are those who elect to do this. I can only suggest that you do some of the reading and research required on basic relativity. General relativity is of course incomplete, and that problably occurs with quantum physics of black holes or maybe with the very large scale structure of the universe. Yet to be honest if you reject relativity in favor of a purely Newtonian idea of things then you will simply fail to understand things properly.

Cheers LC

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Dr. Cosmic Ray,

Thank you for your response. So may I conclude that when NASA reports finding black holes that they are not offering them as evidence of General Relativity. It may or may not be interpreted that way depending upon the belief system of the scientist? I have found that it is very difficult to discuss black holes without getting into debates about the correctness of relativity theory. I would like to think that black holes are being evaluated without the prejudice of existing theory. They may teach us a great deal if we allow the door to open.

James

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Dr. Lawrence B Crowell,

Thank you your response. Quoting you:

"Yet to be honest if you reject relativity in favor of a purely Newtonian idea of things then you will simply fail to understand things properly."

I do not agree that relativity theory has been confirmed. I do agree that it has been mathematically designed to fit empirical evidence. Relativity theory is not the only way to mathematically model that empirical evidence. Newton's work did need some refinement. Rejecting relativity theory actually results in new equations that also accurately model empirical evidence and that return us to a universe of three spatial dimensions and the independence of time. I will leave this subject alone now. I just was interested in what you had to say in support of your essay. I'll leave my opinions for my forum. Thank you for your time.

James

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Dear James,

The original concept of a "Black Hole" was conceived by John Michell in 1783 - way before Einstein, although the terminology Black Hole was coined by John Archibald Wheeler.

The only "problem" I personally have with General Relativity is that it is not Quantum General Relativity. But Lawrence is talking about Quantum Black Holes, and Lawrence and I are both interested in String Theory/ quantum gravity applications. Even though my essay dropped out of the top 16 last night, I still have hope for a unified theory.

Have Fun!

Ray Munroe

Certainly special relativity works. The time delay of muon decay was an early measurement of this. Particles which are acclerated to enormous energy would surpass the speed of light by a thousand fold if the world were completely Newtonian with Galilean transformation properties.

Cheers LC

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Dr. Lawrence B Crowell,

I didn't say that relativity theory did not work. I said that I do not agree that it has been confirmed. The equations that replace those of relativity theory do not accelerate particles passed the speed of light. Newton's work did need to be refined to take into account the properties of light. That refinement does not lead to relativity theory unless the theorist makes it happen that way as Einstein did. I understand that relativity theory is a successful pillar of today's theoretical physics. I understand why it would be believed. I just happen to think that throughout the development of physics theory decisions had to be made. I think that each of those decisions should be challenged for the purpose of rooting out misdirections. I find that pursuit rewarding. I do not insist that others should agree with me.

James

I would suspect that if you patch worked Newtonian mechanics in a way to make it fit with data which supports special relativity that you would end up in fact with special relativity --- of sorts. As for general relativity and gravitation, that might be harder or problematic.

Science never proves theories. All that science does is to measure and observe things in nature to determine if these are consistent with the implications or predictions of a certain theory. So theories are falsifiable, and a bad theory is falified right away if it has no domain of prediction. A good theory might also be falisified if it begins to fail outside some domain of observation where it really applies. This in fact happened with Newtonian physics. It began to fail to account for physically observed phenomenon. On a small scale it was supplanted by quantum mechanics and for large velocities and large gravity fields it was replaced with general relativity. General relativity is likely to be incomplete when quantum physics enters the picture. This is the problem of quantum gravity.

I will just say that special relativity states that in order for the speed of light to be an invariant, or is always measured to be the same in all frames of reference, that space and time must transform into each other. Just as the x and y coordinates in ordinary space transform into x' and y' under a rotation, it turns out that time and spatial variables also transform into each other in this more general setting. This is why you get some of the odd results of relativity, such as time dilation. This "rule" is extended for gravitation where spacetime curvature is on a small region sufficiently flat that special relativity holds. The curved spacetime then results by patching together these flat region, with connection coefficients and a calculus limit. This part gets a bit abstract and requires Riemannian geometry to address.

Cheers LC

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Dr. Lawrence B Crowell,

Quoting you:

"I would suspect that if you patch worked Newtonian mechanics in a way to make it fit with data which supports special relativity that you would end up in fact with special relativity --- of sorts. As for general relativity and gravitation, that might be harder or problematic."

Why would you use the word patchwork? I presume you are intent on demonstrating my lack of understanding about the reality of relativity theory. Actually, I don't use patchwork. I move step by step from fundamentals upward toward more comples theory. I choose not to use patchwork. In my opinion, that is something similar to what Einstein did. For example, why were transform equations necessary? They are what forces results. They are not safe mathematics, because the theorist can use them to patch things together.

"As for general relativity and gravitation, that might be harder or problematic."

Actually they fall into place very easily.

"Science never proves theories."

Nor does it confirm them.

"This in fact happened with Newtonian physics. It began to fail to account for physically observed phenomenon. On a small scale it was supplanted by quantum mechanics and for large velocities and large gravity fields it was replaced with general relativity. General relativity is likely to be incomplete when quantum physics enters the picture. This is the problem of quantum gravity."

Yes Newtonian physics failed at high speed and small dimansions. He did not have the empirical evidence of these two regions available to him or he would, I think, have known what to do very quickly. I think he might have helped us avoid adopting two very different theories and spending a great many years trying to force theoretical unity onto them. Of course, they can't be brought together, but they can be replaced by a new theory, perhaps string theory, that has free access to unlimited hidden dimensions and control of space and time. That God-like combination ought to be successful at forcing unity so long as the nature of that unity is kept out of our sight. With regard to quantum gravity, I think that is an example of trying to force two incompatible theories together. It seems, for now, a safe practice. It will be a long while before that one can be tested. However, theory is very flexible and can move in just about any direction required.

"I will just say that special relativity states that in order for the speed of light to be an invariant, or is always measured to be the same in all frames of reference, that space and time must transform into each other."

Yes it does and I think that is evidence of its failure to represent reality.

"... it turns out that time and spatial variables also transform into each other in this more general setting."

Yes that is one of the really weird results of trusting in transforms.

"... time dilation."

No one has ever conducted an experiment on time.

"This "rule" is extended for gravitation where spacetime curvature is on a small region sufficiently flat that special relativity holds. The curved spacetime then results by patching together these flat region, with connection coefficients and a calculus limit."

Like I said, I am not the one doing the patching.

"This part gets a bit abstract and requires Riemannian geometry to address."

So what am I to conclude from this: That reality is an abstraction?

James

James Putnam wrote, "No one has ever conducted an experiment on time."

Of course we perform experiments on time. Atomic clocks at different floor levels at NIST will measure different time intervals due to gravitational time dilation. You mentioned GPS and relativity. That was something I worked on for a while in connection with Lageos. Again time synchorization involves experiments with time and applies general relativity. These count as experiments in time because clocks measure time.

Experiments don't prove theories, but they will confirm the predictions of a theory and support it with a preponderance of evidence.

I suppose the problem is that if you are adamant in rejecting special relativity then things are at an impass. Some years ago I ended up having a web argument with someone who ardently upheld geocentrism --- the Earth is the center of the universe or solar system. Of course this individual rejects virtually all of physics since Copernicus, Galileo and Kepler. You don't go that far back in time, but you are rejecting something which is pretty canonical in physics. You are not likely to get many physicists to agree with you on this, but I suppose you are not likely to be pursuaded by physicist either.

Cheers LC

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Dr. Lawrence B Crowell,

"Of course we perform experiments on time. Atomic clocks at different floor levels at NIST will measure different time intervals due to gravitational time dilation. You mentioned GPS and relativity. That was something I worked on for a while in connection with Lageos. Again time synchorization involves experiments with time and applies general relativity. These count as experiments in time because clocks measure time."

Yes clocks will measure different intervals due to distance from mass. They are not intervals of time; they are intervals in time. Everything occurs durring time. This is not evidence that time controls everything. It is evidence that the cause of a particular activity is changing. Are you saying that time is a cause of activity or that time controls the rate of activity? To prove either of those possibilities you need to perform experiments on time? Experiments on clock's of any type is no more informative that experiments on any other activity in the vicinity of the measurements. GPS adds only more additional information about how physical activity varies with respect to distance from mass. Unless time is established as the cause of all of this activity, then time is not the subject of measurements.

"Experiments don't prove theories, but they will confirm the predictions of a theory and support it with a preponderance of evidence."

Predictions confirm that the equations formed to define a theory were very carefully constructed to imitate the patterns observed in empirical evidence. The interpretation of the properties contained in those equations is a function of the belief system of the theorist who puts those equations forward as part of a theory. The equations, in their pure empirical form are not, at first, captive to theoretical restraints. Theory is what is added on as interpretation by theorists.

"I suppose the problem is that if you are adamant in rejecting special relativity then things are at an impass."

No, my objections are not that shortsighted. I do not agree with any of relativity theory, nor extra dimensions, nor membranes, nor strings.

"Some years ago I ended up having a web argument with someone who ardently upheld geocentrism --- the Earth is the center of the universe or solar system. Of course this individual rejects virtually all of physics since Copernicus, Galileo and Kepler. You don't go that far back in time, but you are rejecting something which is pretty canonical in physics."

Of course most of this quote has absolutely nothing to do with me. Also, I am not debating from back in time. As for my rejecting something canonical to physics, yes I am doing that. My heresy goes beyond relativity theory.

"You are not likely to get many physicists to agree with you on this, but I suppose you are not likely to be pursuaded by physicist either."

I understand that physicists will not agree with me. You may have noticed that I ask questions, but try to avoid putting my own views forward. That is because I am interested in what others think, but I also recognize that challenging belief systems is difficult. By the way, I value very highly the information shared by experimental physicists.

James

Saying a measurement of time intervals is not of time but in time can be applied to everything in a sense. A ruler could be argued to not measure units of spatial distance but units of distance in space. The same can be applied to any measurement. It can well enough be said we don't measure electric charge, or an electric field, but rather motion in putative ideas of such. There are those inclined to the philosophy of science who get tied into knots over these things. I tend to avoid these matters honestly for I think they lead nowhere.

It can be said that in special relativity everything is moving at the speed of light. Even if you are sitting still relative to a frame on Earth you are moving at the speed of light. You are moving along a fourth dimension at the speed of light, with x_4 = ct, where t is time of course and c the speed of light. Now if a particle is moving along some spatial direction with respect to some frame this distance becomes a general distance or interval

s^2 = (ct)^2 - x^2 - y^2 - z^2

At the coordinate origin with x = y = z = 0 the distance is s = ct. If the particle is moving along x = vt then this gives

s^2 = (ct)^2 - (vt)^2 = (c^2 - v^2)t^2

= c^2(1 - (v/c)^2)t^2.

We instantly have the time dilation result! That is all there really is to all of this. Of course a more general frame transformation is really needed, but this will suffice.

I can understand being skeptical of string theory or membranes. Extra dimensions are pretty canonical, for it is well enough understood since the work of Hermann Weyl back in the 1930s that a gauge potential is something which defines a transformation on an internal bundle of vector spaces. In the case of electromagnetism this internal space is a circle. So that does give, at least in a model perspective, an internal extra dimension.

At any rate, relativity theory (particularly special relativity) is well buttressed by experimental evidence. The situation is much the same for biological evolution, yet clearly there are millions how reject that science. Of course there are some theological issues involved with this rejection. Yet anyone familiar with the scientific community knows that biology is effectively unified through evolution. Much the same occurs with relativity theory. I am aware there are people out there who think it is all wrong and the like. Yet frankly I think they have just removed themselves from the intellectual process.

Cheers LC

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Dr. Lawrence B Crowell,

I will have to return and write a second message in response to time dilation. Here are some quick thoughts about your last paragraph:

"At any rate, relativity theory (particularly special relativity) is well buttressed by experimental evidence."

Yes it is.

"The situation is much the same for biological evolution, yet clearly there are millions how reject that science. Of course there are some theological issues involved with this rejection. Yet anyone familiar with the scientific community knows that biology is effectively unified through evolution."

I think it depends upon the speakers's meaning. If the meaning is that no form of intelligence potential or existing, simple or complex was involved in inanimate matter combining together to become highly intelligent life, then I think the speaker as a lot of work to do to explain how that is possible. That state of affairs is not a given, it is not an intellectually defendable position, regardless of the determination of the speaker to insist that it is.

"Much the same occurs with relativity theory. I am aware there are people out there who think it is all wrong and the like. Yet frankly I think they have just removed themselves from the intellectual process."

I understand the strength of your commitment to relativity theory. However, relativity theory is not the standard for intellectual analysis and inquiry. I say that it is the prudent scientific and intelligent thing to do to challenge it and any other theoretical invention that is forced onto the otherwise clean equations that model the patterns observed in empirical evidence.

James