Virasoro algebra

Black hole thermodynamics

From Wikipedia, the free encyclopedia

In physics, black hole thermodynamics is the area of study that seeks to reconcile the laws of thermodynamics with the existence of black hole event horizons. Much as the study of the statistical mechanics of black body radiation led to the advent of the theory of quantum mechanics, the effort to understand the statistical mechanics of black holes has had a deep impact upon the understanding of quantum gravity, leading to the formulation of the holographic principle.

 It is important that ones is able to see the progression from abstraction to a interpretation of foundational approach.

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Andy Strominger:

This was a field theory that lived on a circle, which means it has one spatial dimension and one time dimension. We derived the fact that the quantum states of the black hole could be represented as the quantum states of this one-plus-one dimensional quantum field theory, and then we counted the states of this theory and found they exactly agreed with the Bekenstein-Hawking entropy.See:Quantum Microstates: Gas Molecules in the Presence of a Gravitational Field

See:Microscopic Origin of the Bekenstein-Hawking Entropy

Of course I am interested the mathematical framework as it might be compared to some phenomenological approach that gives substance to any theoretical thought.

For example, Tommaso Dorigo is a representative of the type of people who may affect the general distribution of "subjects" that may grow at CERN or the Fermilab in the next decade or two. And he just published a quote by Sherlock Holmes - no kidding - whose main point is that it is a "capital mistake" to work on any theory before the data are observed.See:Quantum gravity: minority report

I think you were a little harsh on Tommaso Dorigo  Lubos because he is really helping us to understand the scientific process at Cern. But you are right about theory in my mind, before the phenomenological approach can be seen. The mind need to play creatively in the abstract notions before it can be seen in it's correlations in reality.

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Virasoro algebra

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v • d • e

In mathematics, the Virasoro algebra (named after the physicist Miguel Angel Virasoro) is a complex Lie algebra, given as a central extension of the complex polynomial vector fields on the circle, and is widely used in string theory.

Contents 1 Definition 2 Representation theory 3 Generalizations 4 History 5 See also 6 References

Definition

The Virasoro algebra is spanned by elements

L_i for

and c with

L_n + L _{− n}

and c being real elements. Here the central element c is the central charge. The algebra satisfies

[c,L_n] = 0

and

The factor of 1/12 is merely a matter of convention.
The Virasoro algebra is a central extension of the (complex) Witt algebra of complex polynomial vector fields on the circle. The Lie algebra of real polynomial vector fields on the circle is a dense subalgebra of the Lie algebra of diffeomorphisms of the circle.
The Virasoro algebra is obeyed by the stress tensor in string theory, since it comprises the generators of the conformal group of the worldsheet, obeys the commutation relations of (two copies of) the Virasoro algebra. This is because the conformal group decomposes into separate diffeomorphisms of the forward and back lightcones. Diffeomorphism invariance of the worldsheet implies additionally that the stress tensor vanishes. This is known as the Virasoro constraint, and in the quantum theory, cannot be applied to all the states in the theory, but rather only on the physical states (confer Gupta-Bleuler quantization).

Representation theory

A lowest weight representation of the Virasoro algebra is a representation generated by a vector v that is killed by L_i for i ≥1 , and is an eigenvector of L₀ and c. The letters h and c are usually used for the eigenvalues of L₀ and c on v. (The same letter c is used for both the element c of the Virasoro algebra and its eigenvalue.) For every pair of complex numbers h and c there is a unique irreducible lowest weight representation with these eigenvalues.
A lowest weight representation is called unitary if it has a positive definite inner product such that the adjoint of L_n is L_−n. The irreducible lowest weight representation with eigenvalues h and c is unitary if and only if either c≥1 and h≥0, or c is one of the values

for m = 2, 3, 4, .... and h is one of the values

for r = 1, 2, 3, ..., m−1 and s= 1, 2, 3, ..., r. Daniel Friedan, Zongan Qiu, and Stephen Shenker (1984) showed that these conditions are necessary, and Peter Goddard, Adrian Kent and David Olive (1986) used the coset construction or GKO construction (identifying unitary representations of the Virasoro algebra within tensor products of unitary representations of affine Kac-Moody algebras) to show that they are sufficient. The unitary irreducible lowest weight representations with c < 1 are called the discrete series representations of the Virasoro algebra. These are special cases of the representations with m = q/(p−q), 0<r<q, 0< s<p for p and q coprime integers and r and s integers, called the minimal models and first studied in Belavin et al. (1984).
The first few discrete series representations are given by:

• m = 2: c = 0, h = 0. The trivial representation.
• m = 3: c = 1/2, h = 0, 1/16, 1/2. These 3 representations are related to the Ising model
• m = 4: c = 7/10. h = 0, 3/80, 1/10, 7/16, 3/5, 3/2. These 6 representations are related to the tri critical Ising model.
• m = 5: c = 4/5. There are 10 representations, which are related to the 3-state Potts model.
• m = 6: c = 6/7. There are 15 representations, which are related to the tri critical 3-state Potts model.

The lowest weight representations that are not irreducible can be read off from the Kac determinant formula, which states that the determinant of the invariant inner product on the degree h+N piece of the lowest weight module with eigenvalues c and h is given by

which was stated by V. Kac (1978), (see also Kac and Raina 1987) and whose first published proof was given by Feigin and Fuks (1984). (The function p(N) is the partition function, and A_N is some constant.) The reducible highest weight representations are the representations with h and c given in terms of m, c, and h by the formulas above, except that m is not restricted to be an integer ≥ 2 and may be any number other than 0 and 1, and r and s may be any positive integers. This result was used by Feigin and Fuks to find the characters of all irreducible lowest weight representations.

Generalizations

There are two supersymmetric N=1 extensions of the Virasoro algebra, called the Neveu-Schwarz algebra and the Ramond algebra. Their theory is similar to that of the Virasoro algebra.
The Virasoro algebra is a central extension of the Lie algebra of meromorphic vector fields on a genus 0 Riemann surface that are holomorphic except at two fixed points. I.V. Krichever and S.P. Novikov (1987) found a central extension of the Lie algebra of meromorphic vector fields on a higher genus compact Riemann surface that are holomorphic except at two fixed points, and M. Schlichenmaier (1993) extended this to the case of more than two points.

History

The Witt algebra (the Virasoro algebra without the central extension) was discovered by E. Cartan (1909). Its analogues over finite fields were studied by E. Witt in about the 1930s. The central extension of the Witt algebra that gives the Virasoro algebra was first found (in characteristic p>0) by R. E. Block (1966, page 381) and independently rediscovered (in characteristic 0) by I. M. Gelfand and D. B. Fuks (1968). Virasoro (1970) wrote down some operators generating the Virasoso algebra while studying dual resonance models, though he did not find the central extension. The central extension giving the Virasoro algebra was rediscovered in physics shortly after by J. H. Weis, according to Brower and Thorn (1971, footnote on page 167).

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See:Quantum Gravity Summer School Also pictures by Hecaicedo Photostream

Stephen Hawking At PI Institute

Waterloo, Ontario, Canada, June 20, 2010 - In a public address before a packed audience at Perimeter Institute for Theoretical Physics (PI), Prof. Stephen Hawking, PI Distinguished Research Chair, recounted his research, life and times, saying that it has been a glorious period to contribute to our picture of the universe. Prof. Hawking is conducting private research activities at PI this summer, in what is expected to be the first of many visits.  

See: Stephen Hawking on Perimeter Institute and Special Places & Times for Scientific Progress

About TVO

TVO is Ontario's public educational media organization and a trusted source of interactive educational content that informs, inspires and stimulates curiosity and thought. TVO's vision is to empower people to be engaged citizens through educational media. The TVO signal can be found across Canada on Bell TV channel 265 or Shaw Direct channel 353. You will also find TVO on channel 2 via cable or over-the-air in most areas of Ontario.


Prof. Hawking's lecture will air on TVO on:
     - Sunday, June 20 at 8:00 pm and
       12:30 am EDT
     - Saturday, June 26 at 6:00 pm EDT
     - Sunday, June 27 at 5:00 pm EDT
     - Tuesday, July 6 at 10:00 pm EDT
TVO is viewable across Canada on Bell TV channel 265, Shaw Direct channel 353, and channel 2 in most areas of Ontario. 

Einstein Tower

Just wondering when the Einstein Tower was built?

See:Science Park "Albert Einstein" Potsdam

The connection to the design of the tower and the comment on pueblo design sparked familiarity with a image of a tower on the edge of the grand canyon and my posting on the Old One. 13.7 blog just recently had a blog posting on the religiosity of Einstein.

Desert View Watchtower was built in 1932 and is one of Mary Colter's best-known works. Situated at the far eastern end of the South Rim, 27 miles (43 km) from Grand Canyon Village, the tower sits on a 7,400 foot (2,256 m) promontory. It offers one of the few views of the bottom of the Canyon and the Colorado River. It is designed to mimic an Anasazi watchtower though it is larger than existing ones.[18]

I was wondering if there was some correlation that inspired Einstein with the Einstein Tower with that architectural design of the native culture?

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It is designed to mimic an Anasazi watchtower though it is larger than existing ones

Picture of Einstein was in 1931 while tower was 1932?

Anyway, I thought this picture important from a mandalic understanding of giving a historical example of what can be embedded in the very soul of an individual, as if this is an example of the foundations of mathematics depicted even historically cast in design and what is common among human beings today in their foundational search for meaning.

Fred Kabotie (c.1900 - 1986) was a famous Hopi artist. Born Nakayoma (Day After Day) into the Bluebird Clan at Songo`opavi, Second Mesa, Arizona, Kabotie attended the Santa Fe Indian School, and learned to paint. In 1920, he entered Santa Fe High School, and commenced a long association with Edgar Lee Hewett, a local archaeologist, working at such excavations as Jemez Springs, New Mexico and Gran Quivira. He also sold paintings for spending money.

In 1926, Kabotie moved to Grand Canyon, Arizona, working for the Fred Harvey Company as a guide. After various other jobs and travel, he was hired in 1932 by Mary Colter to paint his first murals at her new Desert View Watchtower.

Kabotie went on to a distinguished career as a painter, muralist, illustrator, silversmith, teacher and writer of Hopi Indian life. He continued to live at Second Mesa. Kabotie was instrumental in establishing the Hopi Cultural Center and served as its first president.

Fred's son Michael Kabotie (born 1942) is also a well-known artist.

Source: Jessica Welton, The Watchtower Murals, Plateau (Museum of Northern Arizona), Fall/Winter 2005. ISBN 0897341325

Quasicrystal and Information

Consequently, a universe where time is real must be loveless. I don't like that idea.Impressions from the PI workshop on the Laws of Nature

Quasicrystals are structural forms that are both ordered and nonperiodic. They form patterns that fill all the space but lack translational symmetry. Classical theory of crystals allows only 2, 3, 4, and 6-fold rotational symmetries, but quasicrystals display symmetry of other orders (folds). They can be said to be in a state intermediate between crystal and glass. Just like crystals, quasicrystals produce modified Bragg diffraction, but where crystals have a simple repeating structure, quasicrystals are more complex.

Aperiodic tilings were discovered by mathematicians in the early 1960s, but some twenty years later they were found to apply to the study of quasicrystals. The discovery of these aperiodic forms in nature has produced a paradigm shift in the fields of crystallography and solid state physics. Quasicrystals had been investigated and observed earlier^[1] but until the 80s they were disregarded in favor of the prevailing views about the atomic structure of matter.

Roughly, an ordering is non-periodic if it lacks translational symmetry, which means that a shifted copy will never match exactly with its original. The more precise mathematical definition is that there is never translational symmetry in more than n – 1 linearly independent directions, where n is the dimension of the space filled; i.e. the three-dimensional tiling displayed in a quasicrystal may have translational symmetry in two dimensions. The ability to diffract comes from the existence of an indefinitely large number of elements with a regular spacing, a property loosely described as long-range order. Experimentally the aperiodicity is revealed in the unusual symmetry of the diffraction pattern, that is, symmetry of orders other than 2, 3, 4, or 6. The first officially reported case of what came to be known as quasicrystals was made by Dan Shechtman and coworkers in 1984.^[2] The distinction between quasicrystals and their corresponding mathematical models (e.g. the three-dimensional version of the Penrose tiling) need not be emphasized.

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What Is Information? by Stuart Kauffman

Put briefly — and Schrodinger did not say so guessing his intuition is up to us — I think his intuition was that an aperiodic crystal breaks a lot of symmetries, therefore contains a lot of (micro) constraints that can enable an enormous diversity of real and organized processes to happen physically. This idea of organized processes seems to be hinted at in his statement that the aperiodic crystal would contain a microcode for (generating) the organism. I have inserted “generating”, and this is the set of specific processes aspect of information that I think we need to incorporate into our idea of what information IS.  I think Schrodinger is telling us both a deeper meaning of what information “is”, and part of how the universe got complex — by repeatedly breaking symmetries that enabled organized processes to happen that both provided new sources of free energy and enabled the breaking of further symmetries.

There Be Dragons on the Dark Matter Issue?

 I have been intrigued by the comparison of the latest reporting by Bee of Backreaction at a workshop at Perimeter Institute about the Laws of Nature: Their Nature and Knowability.

Bee writes, "Yesterday, we had a talk by Marcelo Gleiser titled “What can we know of the world?”."

I look at this from a historical position as it has been outplayed from the beginning as to the understanding that gravity in the universe can have it's counterpart revealed the action of a phenomenology search for the dark matter constituents while describing the state of the uinverse.

The type of detective work described by Sherlock Holmes has been used by astronomers for a long time to deepen our understanding of the universe. Ever since the phenomenal success of Isaac Newton in explaining the motion of the planets with his theory of gravity and laws of motion in 1687, unseen matter has been invoked to explain puzzling observations of cosmic bodies.

Sirius A & B

For example, the anomalous motion of Uranus led astronomers to suggest that an unseen planet existed, and a few years later, in 1846, Neptune was discovered. This procedure is still the primary method used to discover planets orbiting stars.
A similar line of reasoning led to the detection in 1862, of the faint white dwarf Sirius B in orbit around the bright star Sirius.

In contrast, the attempt to explain the anomalies in the motion of Mercury as due to the existence of a new planet, called Vulcan, did not succeed. The solution turned out to be Einstein's theory of general of relativity, which modified Newton's theory.

Today, astronomers are faced with a similar, though much more severe, problem. Unlike the case of Uranus, where the gravity of Neptune adds a fraction of a percent to the gravitational force acting of Uranus, the extra force needed in the cases described below is several hundred percent! It is no exaggeration to say that solving the dark matter problem will require a profound change in our understanding of the universe. See:Field Guide to Dark Matter

So given the outlay of experiential work to the subject there would be those that counter the proposal to support such research because they believe that such an exercise if fruitless to solving the nature of the cosmos and the way the universe could be expanding according to some speeding up of a gravitational consideration ?

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Update:
Impressions from the PI workshop on the Laws of Nature


See Also:
There Be Dragons?
Map of North America from 1566 showing both Terra In Cognita and Mare In Cognito.
Sounding Off on the Dark Matter Issue
Dark Matter Discovery Announced by Nasa

The Total Field

Conclusion:The state of mind of the observer plays a crucial role in the perception of time.Einstein

SPOILER ALERT:

To make a very, very long story short we discovered via Christian Shephard aka Jack’s dead father that all of the people on Oceanic 815 including Desmond, Daniel, Charlotte, Kate, Sawyer, Miles, Lapidus, Claire, Sayid, Sun, Jin, Richard, Michael, Walt, Miles, Ana Lucia, Locke, Hurley and Benjamin did really live on the island but when they died they moved on to L.A for their afterlife where they had the life that they always dreamed off. In The End we learned that those who did eventually find a way to forgive the people who hurt them , and forgave themselves were reunited with the people who meant something to them an went to heaven.See:Lost Finale Explanation:Lost Purgatory Ending Theories

Lost as in the emotive experience, as the "physiological and mental connection of being" winds down.

I thought what was very special was the recognition of all the memories traveling one path, all the fabrications of six years of Lost, to realize that they all could had been traveling in the after death consciousness. I mean, the fabrications of the island was a mass illusion, to support experience,  while all the emotions are played out with each of the persons involved "until they finally recognized each other enough" to gather one more time in the church.

What was special is that as each person is awakened to the reality of where they are, by thefinal  touch of love that connects the souls to that deeper level of recognition, while the memories of all that the had gone before was moved through flashes of realization that brought the experience together, culminating in the chance to go through the final gate to the light.




The island was hell. To burn out the light was to extinguish any hope of the light to support the illusions of the island and of the life of those in the after death consciousness.

I mean there are a lot of discrepancies once you realize that not all the people are there. A plane did escape, yet, there is no record of those people, while the focus was on a core group. The main actors I guess.

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I think the journey to understanding the whole thing is to understand the "heaviness that supports the contention as gravity" is to evolve through the scientific understanding, as the ancients did,  looking toward cosmology.

CARL JUNG by Dr. C. George Boeree

The most important archetype of all is the self. The self is the ultimate unity of the personality and is symbolized by the circle, the cross, and the mandala figures that Jung was fond of painting. A mandala is a drawing that is used in meditation because it tends to draw your focus back to the center, and it can be as simple as a geometric figure or as complicated as a stained glass window. The personifications that best represent self are Christ and Buddha, two people who many believe achieved perfection. But Jung felt that perfection of the personality is only truly achieved in death

That the continued evolution toward GR, is to solidify our understanding of the inverse square law of our positions in context of the life experience? Not just of the planets and galaxies held to the fabric of spacetime in the universe?

The general theory of relativity is as yet incomplete insofar as it has been able to apply the general principle of relativity satisfactorily only to gravitational fields, but not to the total field. We do not yet know with certainty by what mathematical mechanism the total field in space is to be described and what the general invariant laws are to which this total field is subject. One thing, however, seems certain: namely, that the general principal of relativity will prove a necessary and effective tool for the solution of the problem for the total field.Out of My Later Years, Pg 48, Albert Einstein

If you were to believe that the "books of the dead" Tibetan or Egyptian were really about books of life, then in the case of the Tibetan, the "clear light" was preceded "by the lost in reliving experiences, as in the fog  of not understanding, or smoke, as in the show Lost. It is about moving toward that Clear light. That we could be lost for a time, and why, beside the death beds practitioners would help the soul travel through the ether of being of the experienced that they gained in life.

If the heart was free from the impurities of sin, and therefore lighter than the feather, then the dead person could enter the eternal afterlife.

If you take this last ancient plate and the wording below as to the experience one can have, it does not seem to unlikely that our way in the after death world can be constructed according too, the heaviness with which we can experience life emotively. If you understanding Einstein's conclusion,  as to the pretty girl and the hot stove,  then you understand that experience can have it's durations too.

Hubble Takes a Close-up View of a Reflection Nebula in Orion

Image Credit: NASA and The Hubble Heritage Team (STScI) 

ABOUT THIS IMAGE:

Just weeks after NASA astronauts repaired the Hubble Space Telescope in December 1999, the Hubble Heritage Project snapped this picture of NGC 1999, a nebula in the constellation Orion. The Heritage astronomers, in collaboration with scientists in Texas and Ireland, used Hubble's Wide Field Planetary Camera 2 (WFPC2) to obtain the color image.


NGC 1999 is an example of a reflection nebula. Like fog around a street lamp, a reflection nebula shines only because the light from an embedded source illuminates its dust; the nebula does not emit any visible light of its own. NGC 1999 lies close to the famous Orion Nebula, about 1,500 light-years from Earth, in a region of our Milky Way galaxy where new stars are being formed actively. The nebula is famous in astronomical history because the first Herbig-Haro object was discovered immediately adjacent to it (it lies just outside the new Hubble image). Herbig-Haro objects are now known to be jets of gas ejected from very young stars. 

The NGC 1999 nebula is illuminated by a bright, recently formed star, visible in the Hubble photo just to the left of center. This star is cataloged as V380 Orionis, and its white color is due to its high surface temperature of about 10,000 degrees Celsius (nearly twice that of our own Sun). Its mass is estimated to be 3.5 times that of the Sun. The star is so young that it is still surrounded by a cloud of material left over from its formation, here seen as the NGC 1999 reflection nebula.

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Hole in Space Found by Orbiting Telescope

Image courtesy ESA/HOPS Consortium

 

An orbiting European telescope looking for young stars recently found an unexpected surprise: a truly empty hole in space.

The hole lies in a nebula called NGC 1999, a bright cloud of dust and gas in the constellation Orion. The nebula glows with light from a nearby star.

The Hubble Space Telescope first snapped a picture of the nebula in December 1999. Astronomers assumed that an inky spot in the cloud was a blob of cooler gas and dust that's so dense it blocks visible light from passing through. (See a Hubble picture that shows dark globs in another nebula.)

Quark Gluon Plasma (QGP)

Blackhole substances are perhaps the most-perfect fluids in existence because they have ultra-low viscosity.

No matter what you call it, though, that substance and others similar to it could be the most-perfect fluids in existence because they have ultra-low viscosity, or resistance to flow, said Dam Thanh Son, an associate physics professor in the Institute for Nuclear Theory at the University of Washington.

Son and two colleagues used a string theory method called the gauge/gravity duality to determine that a black hole in 10 dimensions - or the holographic image of a black hole, a quark-gluon plasma, in three spatial dimensions - behaves as if it has a viscosity near zero, the lowest yet measured.

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2. A quark-gluon plasma, with the same quarks, but with "bags" disappeared and gluons flying around in their place. See: Just in case anyone forgot...

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One of the things I worked a lot on in earlier months this year (and late ones of last year) was the lead article in a cluster of articles that has appeared in the last few days in May’s special edition of Physics Today. They are sort of departmental-colloquium-level articles, so for a general physics audience, more or less. It’s about some of the things I’ve told you about here in the past (see e.g. here and here), concerning exciting and interesting applications of string theory to various experiments in nuclear physics, as well as atomic and condensed matter physics (although we do not have an article on the latter in this cluster). I had a fun time working with Peter Steinberg on the article and remain grateful to him for getting us all together in the first place to talk about this topic way back in that AAAS symposium of 2009. It was there that Steven Blau of Physics Today got the excellent idea to approach us all to do an article, which resulted in this special issue....See: The Search For Perfection…

Clifford gives a link to the PDF version of the online article "What black holes teach about strongly coupled particles" I am not sure the article is free anymore as it now requires registry. Clifford has adjusted to this by giving "his" pdf link.

Cover: In contrast with everyday liquids such as the oil and water shown on the cover, a so-called perfect fluid has exceedingly low shear viscosity. But unlike a superfluid, the perfect fluid is not in a single quantum state. Three articles in this issue explore the connection to string theory (beginning on page 29) and the possible existence of perfect fluids in two very different regimes: ultracold fermionic atoms (page 34) and ultrahot nuclear matter (page 39). (Photo by Stefan Kaben.)

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See Also:

Physics Bits and Bites

The quest for Quantum Ideal liquids

Who Has Forgotten the Child's Question?

Physicists theorize that the omnipresent Higgs field slows some particles to below light speed, and thus imbues them with mass. Are we there yet?

How many of you with children have not heard our own children speak with impatience of wanting to be "there" and having to sit a long time before this is even possible?

Well, can you imagine the patience it took to materialize the experiments at Cern, in asking fundamental question about nature? It took a lot of patience and careful planning. There is no doubt about this.

I would also ask that those that visit this blog examine the picture below, as to the nature of "First Principle," in terms of computerized data, so that you understand this in context of an algorithm written, it is but the very essence of how something could have arisen in nature, had to be written into the "data accumulation" in order for us to recognize what is at the frontier of this experiment/knowledge in question.

The question of symmetry placed in this idea of computerized data, raises the idea of the types of formations that we will used to describe data gathered by Fermi as a descriptor of cosmos events in their unfolding.

Are we there yet?

Source of Q&A from linked article above.

Q&A with the Universe From the quest for the most fundamental particles of matter to the mysteries of dark matter, supersymmetry, and extra dimensions, many of nature’s greatest puzzles are being probed at the Large Hadron Collider.
What is the form of the universe? Physicists created the Standard Model to explain the form of the universe—the fundamental particles, their properties, and the forces that govern them. The predictions of this tried-and-true model have repeatedly proven accurate over the years. However, there are still questions left unanswered. For this reason, physicists have theorized many possible extensions to the Standard Model. Several of these predict that at higher collision energies, like those at the LHC, we will encounter new particles like the Z', pronounced " Z prime." It is a theoretical heavy boson whose discovery could be useful in developing new physics models. Depending on when and how we find a Z' boson, we will be able to draw more conclusions about the models it supports, whether they involve superstrings, extra dimensions, or a grand unified theory that explains everything in the universe. Whatever physicists discover beyond the Standard Model will open new frontiers for exploring the nature of the universe. What is the universe made of? Since the 1930s, scientists have been aware that the universe contains more than just regular matter. In fact, only a little over 4 percent of the universe is made of the matter that we can see.Of the remaining 96 percent, about 23 percent is dark matter and everything else is dark energy, a mysterious substance that creates a gravitational repulsion responsible for the universe’s accelerating expansion. One theory regarding dark matter is that it is made up of the as-yet-unseen partners of the particles that make up regular matter. In a supersymmetric universe, every ordinary particle has one of these superpartners. Experiments at the LHC may find evidence to support or reject their existence.	Are there extra dimensions? We experience three dime nsions of space. However, the theory of relativity states that spacecan expand, contract, and bend. It’s possible, therefore, that we encounter only three spatial dimensions because they’re the only ones our size enables us to see, while other dimensions are so tiny that they are effectively hidden. Extra dimensions are integral to several theoretical models of the universe; string theory, for example, suggests as many as seven extra dimensions of space. The LHC is sensitive enough to detect extra dimensions ten billion times smaller than an atom. Experiments like ATLAS and CMS are hoping to gather information about how many other dimensions exist, what particles are associated with them, and how they are hidden. What are the most basic building blocks of matter? Particle physicists hope to explain the makeup of the universe by understanding it from its smallest, most basic parts. Today, the fundamental building blocks of the universe are believed to be quarks and leptons; however, some theorists believe that these particles are not fundamental after all. The theory of compositeness, for example, suggests that quarks are composed of even smaller particles. Efforts to look closely at quarks and leptons have been difficult. Quarks are especially challenging, as they are never found in isolation but instead join with other particles to form hadrons, such as the protons that collide in the LHC. With the LHC’s high energy levels, scientists hope to collect enough data about quarks to reveal whether anything smaller is hidden inside.
Why do some particles have mass? Through the theory of relativity, we know that particles moving at the speed of light have no mass, while particles moving slower than light speed do have mass. Physicists theorize that the omnipresent Higgs field slows some particles to below light speed, and thus imbues them with mass. We can’t study the Higgs field directly, but it is possible that an accelerator could excite this field enough to "shake loose" Higgs boson particles, which physicists should be able to detect. After decades of searching, physicists believe that they are close to producing collisions at the energy level needed to detect Higgs bosons.

Boundaries are what divide us

Change your thoughts and you change your world. Norman Vincent Peale

The words seem a wise choice.

This is not to support the religious right, or left,  nor to induce fear(contentions of Peale in the article,) but to support the idea of thoughts actually changing the ownership of the property we have paid for when we come to our conclusions.  What is the cost(belief) and one comes quickly to realizing the outcome has been provided for.