No-Hair Theorem

The no-hair theorem postulates that all black hole solutions of the Einstein-Maxwell equations of gravitation and electromagnetism in general relativity can be completely characterized by only three externally observable classical parameters: mass, electric charge, and angular momentum.^[1] All other information (for which "hair" is a metaphor) about the matter which formed a black hole or is falling into it, "disappears" behind the black-hole event horizon and is therefore permanently inaccessible to external observers. Physicist John Archibald Wheeler expressed this idea with the phrase "black holes have no hair"^[1] which was the origin of the name. In a later interview, John Wheeler says that Jacob Bekenstein coined this phrase.^[2]

The first version of the no-hair theorem for the simplified case of the uniqueness of the Schwarzschild metric was shown by Werner Israel in 1967.^[3] The result was quickly generalized to the cases of charged or spinning black holes.^[4][5] There is still no rigorous mathematical proof of a general no-hair theorem, and mathematicians refer to it as the no-hair conjecture. Even in the case of gravity alone (i.e., zero electric fields), the conjecture has only been partially resolved by results of Stephen Hawking, Brandon Carter, and David C. Robinson, under the additional hypothesis of non-degenerate event horizons and the technical, restrictive and difficult-to-justify assumption of real analyticity of the space-time continuum.

Contents

• 1 Example
• 2 Changing the reference frame
• 3 Four-dimensional space-time
• 4 Extensions
• 5 Counterexamples
• 6 Observational results
• 7 See also
• 8 References
• 9 External links

 

Example

Suppose two black holes have the same masses, electrical charges, and angular momenta, but the first black hole is made out of ordinary matter whereas the second is made out of antimatter; nevertheless, they will be completely indistinguishable to an observer outside the event horizon. None of the special particle physics pseudo-charges (i.e., the global charges baryonic number, leptonic number, etc.) are conserved in the black hole.^{[citation needed]}

Changing the reference frame
 
Every isolated unstable black hole decays rapidly to a stable black hole; and (excepting quantum fluctuations) stable black holes can be completely described (in a Cartesian coordinate system) at any moment in time by these eleven numbers:

• mass-energy M,
• linear momentum P (three components),
• angular momentum J (three components),
• position X (three components),
• electric charge Q.

These numbers represent the conserved attributes of an object which can be determined from a distance by examining its gravitational and electromagnetic fields. All other variations in the black hole will either escape to infinity or be swallowed up by the black hole.
By changing the reference frame one can set the linear momentum and position to zero and orient the spin angular momentum along the positive z axis. This eliminates eight of the eleven numbers, leaving three which are independent of the reference frame. Thus any black hole which has been isolated for a significant period of time can be described by the Kerr–Newman metric in an appropriately chosen reference frame.

Four-dimensional space-time

The no-hair theorem was originally formulated for black holes within the context of a four-dimensional spacetime, obeying the Einstein field equation of general relativity with zero cosmological constant, in the presence of electromagnetic fields, or optionally other fields such as scalar fields and massive vector fields (Proca fields, spinor fields, etc.).^{[citation needed]}

Extensions

It has since been extended to include the case where the cosmological constant is positive (which recent observations are tending to support).^[6]
Magnetic charge, if detected as predicted by some theories, would form the fourth parameter possessed by a classical black hole.

Counterexamples

Counterexamples in which the theorem fails are known in spacetime dimensions higher than four; in the presence of non-abelian Yang-Mills fields, non-abelian Proca fields, some non-minimally coupled scalar fields, or skyrmions; or in some theories of gravity other than Einstein’s general relativity. However, these exceptions are often unstable solutions and/or do not lead to conserved quantum numbers so that "The 'spirit' of the no-hair conjecture, however, seems to be maintained".^[7] It has been proposed that "hairy" black holes may be considered to be bound states of hairless black holes and solitons.
In 2004, the exact analytical solution of a (3+1)-dimensional spherically symmetric black hole with minimally coupled self-interacting scalar field was derived.^[8] This showed that, apart from mass, electrical charge and angular momentum, black holes can carry a finite scalar charge which might be a result of interaction with cosmological scalar fields such as the inflaton. The solution is stable and does not possess any unphysical properties, however, the existence of scalar field with desired properties is only speculative.

Observational results

The LIGO results provide the first experimental observation of the uniqueness or no-hair theorem.^[9][10] This observations are consistent with Stephen Hawking theoretical work on black holes in the 1970s.^[11][12]

See also

• Black hole information paradox
• Event Horizon Telescope

References

1. 
   

Misner, Charles W.; Thorne, Kip S.; Wheeler, John Archibald (1973). Gravitation. San Francisco: W. H. Freeman. pp. 875–876. ISBN 0716703343. Retrieved 24 January 2013.

https://www.youtube.com/watch?v=BIHPWKXvGkE&feature=youtu.be&t=6m

Israel, Werner (1967). "Event Horizons in Static Vacuum Space-Times". Phys. Rev. 164 (5): 1776–1779. Bibcode:1967PhRv..164.1776I. doi:10.1103/PhysRev.164.1776.

Israel, Werner (1968). "Event horizons in static electrovac space-times". Commun. Math. Phys. 8 (3): 245–260. Bibcode:1968CMaPh...8..245I. doi:10.1007/BF01645859.

Carter, Brandon (1971). "Axisymmetric Black Hole Has Only Two Degrees of Freedom". Phys. Rev. Lett. 26 (6): 331–333. Bibcode:1971PhRvL..26..331C. doi:10.1103/PhysRevLett.26.331.

Bhattacharya, Sourav; Lahiri, Amitabha (2007). "No hair theorems for positive Λ". arXiv:gr-qc/0702006v2.

Mavromatos, N. E. (1996). "Eluding the No-Hair Conjecture for Black Holes". arXiv:gr-qc/9606008v1.

Zloshchastiev, Konstantin G. (2005). "Coexistence of Black Holes and a Long-Range Scalar Field in Cosmology". Phys. Rev. Lett. 94 (12): 121101. arXiv:hep-th/0408163. Bibcode:2005PhRvL..94l1101Z. doi:10.1103/PhysRevLett.94.121101.

"Gravitational waves from black holes detected". BBC News. 11 February 2016.

"Gravitational waves detected 100 years after Einstein's prediction" (PDF). LIGO. February 11, 2016. Retrieved 11 February 2016.

https://www.facebook.com/stephenhawking/posts/965377523549345 Stephen Hawking

1. http://www.bbc.com/news/science-environment-35551144 Stephen Hawking celebrates gravitational wave discovery

External links

• Hawking, S. W. (2005). "Information Loss in Black Holes". arXiv:hep-th/0507171v2., Stephen Hawking’s purported solution to the black hole unitarity paradox, first reported in July 2004.

Categories
 

Black holes

Theorems in general relativity

Is Gravity Now part of the Standard Model?

I leave this as a open question as I will be compiling information in this regard. If the initial configuration of the source is being transmitted as gravitational waves then this is also part of "other information" being traversed through space and space-time?

Image Credit: NASA Goddard Space Flight Center.

This in affect pertains to recent events regarding the detection of gravitational waves recent. So I have ideas about this now.

***

See:

• When Black Holes Collide. 
• Everything you need to know about gravitational waves
• Dear Dr Bee: Can LIGO’s gravitational wave detection tell us something about quantum gravity?
•  Can LIGO Test Quantum Gravity?

Homodyne detection

Optical Homodyne Detection.

Homodyne detection is a method of detecting frequency-modulated radiation by non-linear mixing with radiation of a reference frequency, the same principle as for heterodyne detection.

In optical interferometry, homodyne signifies that the reference radiation (i.e. the local oscillator) is derived from the same source as the signal before the modulating process. For example, in a laser scattering measurement, the laser beam is split into two parts. One is the local oscillator and the other is sent to the system to be probed. The scattered light is then mixed with the local oscillator on the detector. This arrangement has the advantage of being insensitive to fluctuations in the frequency of the laser. Usually the scattered beam will be weak, in which case the (nearly) steady component of the detector output is a good measure of the instantaneous local oscillator intensity and therefore can be used to compensate for any fluctuations in the intensity of the laser.

Homodyne and heterodyne techniques are commonly used in thermoreflectance techniques.

Homodyne detection was one of the key techniques in demonstrating spooky action at a distance.^[1]

Contents

• 1 Radio technology
• 2 See also
• 3 References
• 4 External links
•  

Radio technology

In radio technology, the distinction is not the source of the local oscillator, but the frequency used. In heterodyne detection, the local oscillator is frequency-shifted, while in homodyne detection it has the same frequency as the radiation to be detected. See direct conversion receiver.

See also

• Optical heterodyne detection
• Heterodyne detection
• Heterodyne

References

1. Maria Fuwa, Shuntaro Takeda, Marcin Zwierz, Howard M. Wiseman & Akira Furusawa (24 March 2015). "Experimental proof of nonlocal wavefunction collapse for a single particle using homodyne measurements". Nature Communications 6 (6665): 6665. doi:10.1038/ncomms7665.

When Black Holes Collide

See also: What Happens When Black Holes Collide? - Kip Thorne

 

Inside Einstein's Mind

See Also: Inside Einstein's Mind | NOVA - PBS Documentary 

Heaven, is a State of Mind

The idea about heaven in the regard with which you ponder, is it not very far away then? Meaning, that heaven is really right next door to you all the time. Heaven then, could be a state of mind, consciousness where we can move in time in very interesting ways. Heaven literally then, could sit in the very same space that you are standing in? So this idea then rests on how one may interpret geometric dimensional attributes as facets and degrees with which we access not only the future, but about how that future affects the past.

 I see a clock, but I cannot envision the clockmaker. The human mind is unable to conceive of the four dimensions, so how can it conceive of a God, before whom a thousand years and a thousand dimensions are as one?

• From Cosmic religion: with other opinions and aphorisms (1931), Albert Einstein, pub. Covici-Friede. Quoted in The Expanded Quotable Einstein, Princeton University Press; 2nd edition (May 30, 2000); Page 208, ISBN 0691070210

While in the film we see physical manifestations as gravitational waves,  as a bar code and a distribution of dust according to those patterns, these are derivatives of some higher dimensional thinking being communicated from the Tesseract, as books falling to the floor. So the gravitational waves have "a source" from which information is attained. The watch,  as time being communicated in the second hand. We use time as a means of representing a fourth physical dimension.

Penrose's Influence on Escher
During the later half of the 1950’s, Maurits Cornelius Escher received a letter from Lionel and Roger Penrose. This letter consisted of a report by the father and son team that focused on impossible figures. By this time, Escher had begun exploring impossible worlds. He had recently produced the lithograph Belvedere based on the “rib-cube,” an impossible cuboid named by Escher (Teuber 161). However, the letter by the Penroses, which would later appear in the British Journal of Psychology, enlightened Escher to two new impossible objects; the Penrose triangle and the Penrose stairs. With these figures, Escher went on to create further impossible worlds that break the laws of three-dimensional space, mystify one’s mind, and give a window to the artist heart.

I think artists in some way explore these limitations of how such a thought construct could have been realized and in regards to Dali (are such dimensional attributes really inaccessible to the mind?), while we may make comments on his character, this does not limit one to realize how the Tesseractbecomes the measure that heaven can be seen in the construct of such thoughts you are engaged in.

The implied idea of symmetry(the God Particle),  possibly, as to perfection in the way one may look at heaven and in Plato's case regardless of how old the philosophy is, it helps to point to some ideas about how the Catholic religion in Rome grabbed hold of Plato by a finger, as pointing up in relation to Aristotle in the School of Athen's fresco done by Raphael in the Signatore's rooms at the Vatican.

Its All a Wave

The bizarre nature of reality as laid out by quantum theory has survived another test, with scientists performing a famous experiment and proving that reality does not exist until it is measured.

Physicists at The Australian National University (ANU) have conducted John Wheeler's delayed-choice thought experiment, which involves a moving object that is given the choice to act like a particle or a wave. Wheeler's experiment then asks - at which point does the object decide?

Common sense says the object is either wave-like or particle-like, independent of how we measure it. But quantum physics predicts that whether you observe wave like behavior (interference) or particle behavior (no interference) depends only on how it is actually measured at the end of its journey. This is exactly what the ANU team found. See:
Experiment confirms quantum theory weirdness

if and when......just for clarification.

Oddly enough, Shechtman has one complaint about the field that he originated: use of the word quasicrystal. "I do not like the term, since it implies that quasi-periodic crystals are not crystals, and according to the new International Union of Crystallographers definition, they are. But the term is widely used. I prefer to call them quasi-periodic materials. The term quasicrystal, in fact, does not appear in the article ranked eighth on our list of the ten most-cited Physical Review Letters.2011 Chemistry Nobel for . . . Quasicrystal Physics!

Is a quasi-crystal, just a diffraction pattern? If and when......we observe it?  So we can say that everything is a diffraction pattern/wave? As an observer, we collapse the wave function?

 We want to simplify it......all else is added to the simplicity to say.....you have this theory of everything to suggest......by comparison a virtual reality is a tool with which we collapse the wave function? See, it just become much more complicated? We are working on a wave function machine, not just a computer.

 Oh for sure, you want to get "a hold" of yourself. Then there is this causal connection to the beliefs that you form? You become much more responsible about the way in which you choose to do things, yes?

It is widely accepted that consciousness or, more generally, mental activity is in some way correlated to the behavior of the material brain. Since quantum theory is the most fundamental theory of matter that is currently available, it is a legitimate question to ask whether quantum theory can help us to understand consciousness. Several programmatic approaches answering this question affirmatively, proposed in recent decades, will be surveyed. It will be pointed out that they make different epistemological assumptions, refer to different neurophysiological levels of description, and use quantum theory in different ways. For each of the approaches discussed, problematic and promising features will be equally highlighted.Quantum Approaches to Consciousness -

The quantum mind or quantum consciousness[1] hypothesis proposes that classical mechanics cannot explain consciousness. It posits that quantum mechanical phenomena, such as quantum entanglement and superposition, may play an important part in the brain's function and could form the basis of an explanation of consciousness. It is not a single theory, but a collection of hypotheses.

So, Experiment confirms quantum theory weirdness and we are having problems with a classical interpretation of a quantum process in this thread? Help.

Quantum cognition is an emerging field which applies the mathematical formalism of quantum theory to model cognitive phenomena such as information processing by the human brain, decision making, human memory, concepts and conceptual reasoning, human judgment, and perception.[1][2] [3][4] The field clearly distinguishes itself from the quantum mind as it is not reliant on the hypothesis that there is something micro-physical quantum mechanical about the brain. Quantum cognition is based on the quantum-like paradigm[5][6] or generalized quantum paradigm [7] or quantum structure paradigm [8] that information processing by complex systems such as the brain, taking into account contextual dependence of information and probabilistic reasoning, can be mathematically described in the framework of quantum information and quantum probability theory.

Quantum cognition uses the mathematical formalism of quantum theory to inspire and formalize models of cognition that aim to be an advance over models based on traditional classical probability theory. The field focuses on modeling phenomena in cognitive science that have resisted traditional techniques or where traditional models seem to have reached a barrier (e.g., human memory [9] ), and modeling preferences in decision theory that seem paradoxical from a traditional rational point of view (e.g., preference reversals [10]). Since the use of a quantum-theoretic framework is for modeling purposes, the identification of quantum structures in cognitive phenomena does not presuppose the existence of microscopic quantum processes in the human brain.[11]

Maybe look at quantum erasure experiment first and draw your conclusion. Then, take in the experimental process being cited in the article link above.

. Setup of the delayed choice quantum eraser experiment of Kim et al. Detector D₀ is movable

 A delayed choice quantum eraser experiment, first performed by Yoon-Ho Kim, R. Yu, S.P. Kulik, Y.H. Shih and Marlan O. Scully,^[1] and reported in early 1999, is an elaboration on the quantum eraser experiment that incorporates concepts considered in Wheeler's delayed choice experiment. The experiment was designed to investigate peculiar consequences of the well-known double slit experiment in quantum mechanics as well as the consequences of quantum entanglement.

Shall I be so bold then to announce that "everything," is a wave?

  The QL model developed in this article has a temporal basis, based on a (hypothetical) argument that cognitive processes are based on at least two time scales: a (very fine) subcognitive one and a (much coarser) cognitive one.  See: The quantum-like brain on the cognitive and subcognitive time scales

Who is observing? If everything is a wave, then "who" is observing? Look around you there is all these waves.......who is observing all these waves? Who, is observing this screen in front of you? Who is manipulating the components(waves) of this wave function box in order to make "waves" on your screen?

 When they observed it as to how it was measured? Again, should I be so bold to say it all is a wave?

Image in form of the Biology of Belief

With the geometric way, one is thinking in terms of pictures; pictures which one imagines in space in some way, and one just tries to get a feeling for the relationships between the quantities occurring in those pictures. Paul Dirac

I always used these geometrical ideas for getting clear notions about relationships in relativity although I didn’t refer to them in my published works.Oral History Transcript — Dr. P. A. M. Dirac

I am presently incubating thoughts about information as an image as it first received in this form. Any thoughts about this?

In the biology of belief, such a reception of the image first, allows us to see the form of the possibility, as a complete whole. What this means is that one has to be receptive first. That "an idea" can exist and you are the device that can receive information. You are a antenna, as a expression of the biological device in being able to receive.

One does not deny the research that goes on and the effort tried to piece together what is currently a known, and that all that is known is the entirety of the subject, as much as your resource allows you to gather. Even still, even if, the entirety of the subject is not complete given the depth of others to have knowledge about this subject, the next step, is to have garnered a step in that right direction. This serves as a correlate of one's consciousness and awareness, to see, the next step in the attainment of that knowledge, can be verified.

The biology then is the effort to get to the point to listen, to see, and not in the exchange of the eye of the physical world around us, but to the information that can be gathered by being receptive.

Now, receptive in the biological sense, what does that mean? Here we have a physical expression of "a state of belief," that what is possible is beyond matter, as we know biology is not. It means, information has a different form, then of what is exchanged by mediums of mass expression? Electrical signals as those measured by, the control and delivery of the medium to what current expressions have been adapted.

So a word, can have a vibratory basis that is much like an image, which can have a medium of expression, that is not understood other then what we can physically see, or physically can hear. Vibration then, can change the mass configuration of the brain, as a word by definition holds the mind to the concrete form as a judgement of belief. So a word, is on the way to being a concrete form of an expression of belief? A word is on the way to becoming an ideal.

This combination of three wavelengths of light from NASA's Solar Dynamics Observatory shows one of the multiple jets that led to a series of slow coronal puffs on Jan. 17, 2013. The light has been colorized in red, green and blue.

Image Credit: Alzate/SDO

If we convert current expressions of information as united in the matters, what conversion processes allow us to see "other information" that would not had been possible without a conversion process? So sonification may be an example as exemplified in helio-seismology of the sun. We want to know on earth when information is coming our way regarding the earth and the way the sun affects the earth. Disrupts communication.

Information Access

Why Physicists are Saying Consciousness is a State of Matter, Like a Solid, a Liquid, or a Gas.

........of “fundamental” range from the inexplicability of mentality in other, and non-mentalistic, terms to the idealist view that in some sense everything that exists is, and is only, a mental entity. Panpsychism -http://plato.stanford.edu/entries/panpsychism/

Curious as to what Tegmark sees in correlation to the three states of matter as consciousness of experience specific. Not sure of the relationship to Chalmers.  Maybe all that junk DNA is tuned specific, for what we are able to gather in terms of the unifying whole and our access to information. Sort of like Seth Cohen finding the underlying signal attenuation that gives access to frequencies specific.......his relationship to Mandelbrot.

“This leaves us with an integration paradox: why does the information content of our conscious experience appear to be vastly larger than 37 bits?” asks Tegmark.

The power generated in the junk DNA that is able to move aside all the noise and receive all that information depends on the individual and how finely tuned they are to the information process? So inexplicably junk DNA can be arranged according to the individual who accesses information? Can matter be changed by a mental outlook? Whatever you contrive to be, may have used mental attributes to accommodate any platform for creating anything.....so where did it begin.......and we arrive at you. What came first?

The Law of Attraction

The law of attraction is the name given to the maxim "like attracts like" which in New Thought philosophy is used to sum up the idea that by focusing on positive or negative thoughts a person brings positive or negative experiences into their life.[1][2] This belief is based upon the idea that people and their thoughts are both made from "pure energy", and the belief that like energy attracts like energy Law of Attraction

I do believe there is an organizing principle here( the breaking of symmetry triggers the Higgs mechanism , and of late, [Positive energy theorem] as organizing principle)......some analogies come to mind.  While materialistic of mind as mass), one has to begin to understand how and where this all begins?

“You don’t see what you’re seeing until you see it,” Dr. Thurston said, “but when you do see it, it lets you see many other things. Elusive Proof, Elusive Prover: A New Mathematical Mystery

Quickly,  what came to view was the dung beetle and how elephant shit is rolled into a ball, while this ball becomes the  food for a new generation. Not the best analogy, but one might get the abstraction of a point in a circle.

The fish is "soul food." The water the unconscious, all possible facets of the sensorium. The hook and worm, aspects of the "focus held" while you are fishing.

 Versus..........

The Principle of Finite Imagination II

While one is out fishing.....you drop your line into the water......you use bait to attract the fish......and wait for a bite? Complexity,  of getting fish from a large body of water.

So while analogies, these represent an action we are quite amenable too, given environment and the bait as an attractive,  can bring things to a point.

I too read Napoleon Hill many years ago, and this did form part of my developing perspective about what and how I think now. Positive thoughts versus negative ones which serve as a precursor to environmental change. This can be psychological in affect, as to relationships with people and what is predominant in mind. How we say things to our selves and how things become bleak in our outlook, from our constant underlying breath and from what we can say to ourselves and how we think.

Ideas drawn from vast reservoir of information has to have an attractor, so you set the stage? Thoughts? Incubation? AHA!