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

Article From New York Times and More

Brookhaven National Laboratory

HOT A computer rendition of 4-trillion-degree Celsius quark-gluon plasma created in a demonstration of what scientists suspect shaped cosmic history.

In Brookhaven Collider, Scientists Briefly Break a Law of Nature

The Brookhaven scientists and their colleagues discussed their latest results from RHIC in talks and a news conference at a meeting of the American Physical Society Monday in Washington, and in a pair of papers submitted to Physical Review Letters. “This is a view of what the world was like at 2 microseconds,” said Jack Sandweiss of Yale, a member of the Brookhaven team, calling it, “a seething cauldron.”

Among other things, the group announced it had succeeded in measuring the temperature of the quark-gluon plasma as 4 trillion degrees Celsius, “by far the hottest matter ever made,” Dr. Vigdor said. That is 250,000 times hotter than the center of the Sun and well above the temperature at which theorists calculate that protons and neutrons should melt, but the quark-gluon plasma does not act the way theorists had predicted.

Instead of behaving like a perfect gas, in which every quark goes its own way independent of the others, the plasma seemed to act like a liquid. “It was a very big surprise,” Dr. Vigdor said, when it was discovered in 2005. Since then, however, theorists have revisited their calculations and found that the quark soup can be either a liquid or a gas, depending on the temperature, he explained. “This is not your father’s quark-gluon plasma,” said Barbara V. Jacak, of the State University at Stony Brook, speaking for the team that made the new measurements.

It is now thought that the plasma would have to be a million times more energetic to become a perfect gas. That is beyond the reach of any conceivable laboratory experiment, but the experiments colliding lead nuclei in the Large Hadron Collider outside Geneva next winter should reach energies high enough to see some evolution from a liquid to a gas.

See more at above link.

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Violating Parity with Quarks and Gluons
by Sean Carroll of Cosmic Variance

This new result from RHIC doesn’t change that state of affairs, but shows how quarks and gluons can violate parity spontaneously if they are in the right environment — namely, a hot plasma with a magnetic field.

So, okay, no new laws of physics. Just a much better understanding of how the existing ones work! Which is most of what science does, after all.

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Quark–gluon plasma

From Wikipedia, the free encyclopedia

A QGP is formed at the collision point of two relativistically accelerated gold ions in the center of the STAR detector at the relativistic heavy ion collider at the Brookhaven national laboratory.

A quark-gluon plasma (QGP) or quark soup^[1] is a phase of quantum chromodynamics (QCD) which exists at extremely high temperature and/or density. This phase consists of (almost) free quarks and gluons, which are the basic building blocks of matter. Experiments at CERN's Super Proton Synchrotron (SPS) first tried to create the QGP in the 1980s and 1990s: the results led CERN to announce indirect evidence for a "new state of matter"^[2] in 2000. Current experiments at Brookhaven National Laboratory's Relativistic Heavy Ion Collider (RHIC) are continuing this effort.^[3] Three new experiments running on CERN's Large Hadron Collider (LHC), ALICE,^[4] ATLAS and CMS, will continue studying properties of QGP.

Contents 1 General introduction 1.1 Why this is referred to as "plasma" 1.2 How the QGP is studied theoretically 1.3 How it is created in the lab 1.4 How the QGP fits into the general scheme of physics 2 Expected properties 2.1 Thermodynamics 2.2 Flow 2.3 Excitation spectrum 3 Experimental situation 4 Formation of quark matter 5 See also 6 References 7 External links

General introduction

The quark-gluon plasma contains quarks and gluons, just as normal (baryonic) matter does. The difference between these two phases of QCD is that in normal matter each quark either pairs up with an anti-quark to form a meson or joins with two other quarks to form a baryon (such as the proton and the neutron). In the QGP, by contrast, these mesons and baryons lose their identities and dissolve into a fluid of quarks and gluons.^[5] In normal matter quarks are confined; in the QGP quarks are deconfined.
Although the experimental high temperatures and densities predicted as producing a quark-gluon plasma have been realized in the laboratory, the resulting matter does not behave as a quasi-ideal state of free quarks and gluons, but, rather, as an almost perfect dense fluid.^[6] Actually the fact that the quark-gluon plasma will not yet be "free" at temperatures realized at present accelerators had been predicted already in 1984 ^[7] as a consequence of the remnant effects of confinement. 

Why this is referred to as "plasma"

A plasma is matter in which charges are screened due to the presence of other mobile charges; for example: Coulomb's Law is modified to yield a distance-dependent charge. In a QGP, the color charge of the quarks and gluons is screened. The QGP has other analogies with a normal plasma. There are also dissimilarities because the color charge is non-abelian, whereas the electric charge is abelian. Outside a finite volume of QGP the color electric field is not screened, so that volume of QGP must still be color-neutral. It will therefore, like a nucleus, have integer electric charge.

How the QGP is studied theoretically

One consequence of this difference is that the color charge is too large for perturbative computations which are the mainstay of QED. As a result, the main theoretical tools to explore the theory of the QGP is lattice gauge theory. The transition temperature (approximately 175 MeV) was first predicted by lattice gauge theory. Since then lattice gauge theory has been used to predict many other properties of this kind of matter. The AdS/CFT correspondence is a new interesting conjecture allowing insights in QGP.

How it is created in the lab

The QGP can be created by heating matter up to a temperature of 2×10¹² kelvin, which amounts to 175 MeV per particle. This can be accomplished by colliding two large nuclei at high energy (note that 175 MeV is not the energy of the colliding beam). Lead and gold nuclei have been used for such collisions at CERN SPS and BNL RHIC, respectively. The nuclei are accelerated to ultrarelativistic speeds and slammed into each other while Lorentz contracted. They largely pass through each other, but a resulting hot volume called a fireball is created after the collision. Once created, this fireball is expected to expand under its own pressure, and cool while expanding. By carefully studying this flow, experimentalists hope to put the theory to test.

How the QGP fits into the general scheme of physics

QCD is one part of the modern theory of particle physics called the Standard Model. Other parts of this theory deal with electroweak interactions and neutrinos. The theory of electrodynamics has been tested and found correct to a few parts in a trillion. The theory of weak interactions has been tested and found correct to a few parts in a thousand. Perturbative aspects of QCD have been tested to a few percent. In contrast, non-perturbative aspects of QCD have barely been tested. The study of the QGP is part of this effort to consolidate the grand theory of particle physics.
The study of the QGP is also a testing ground for finite temperature field theory, a branch of theoretical physics which seeks to understand particle physics under conditions of high temperature. Such studies are important to understand the early evolution of our universe: the first hundred microseconds or so. While this may seem esoteric, this is crucial to the physics goals of a new generation of observations of the universe (WMAP and its successors). It is also of relevance to Grand Unification Theories or 'GUTS' which seek to unify the four fundamental forces of nature.

Expected properties

Thermodynamics

The cross-over temperature from the normal hadronic to the QGP phase is about 175 MeV, corresponding to an energy density of a little less than 1 GeV/fm³. For relativistic matter, pressure and temperature are not independent variables, so the equation of state is a relation between the energy density and the pressure. This has been found through lattice computations, and compared to both perturbation theory and string theory. This is still a matter of active research. Response functions such as the specific heat and various quark number susceptibilities are currently being computed.

Flow

The equation of state is an important input into the flow equations. The speed of sound is currently under investigation in lattice computations. The mean free path of quarks and gluons has been computed using perturbation theory as well as string theory. Lattice computations have been slower here, although the first computations of transport coefficients have recently been concluded. These indicate that the mean free time of quarks and gluons in the QGP may be comparable to the average interparticle spacing: hence the QGP is a liquid as far as its flow properties go. This is very much an active field of research, and these conclusions may evolve rapidly. The incorporation of dissipative phenomena into hydrodynamics is another recent development that is still in an active stage.

Excitation spectrum

Does the QGP really contain (almost) free quarks and gluons? The study of thermodynamic and flow properties would indicate that this is an over-simplification. Many ideas are currently being evolved and will be put to test in the near future. It has been hypothesized recently that some mesons built from heavy quarks (such as the charm quark) do not dissolve until the temperature reaches about 350 MeV. This has led to speculation that many other kinds of bound states may exist in the plasma. Some static properties of the plasma (similar to the Debye screening length) constrain the excitation spectrum.

Experimental situation

Those aspects of the QGP which are easiest to compute are not the ones which are the easiest to probe in experiments. While the balance of evidence points towards the QGP being the origin of the detailed properties of the fireball produced in the RHIC, this is the main barrier which prevents experimentalists from declaring a sighting of the QGP. For a summary see 2005 RHIC Assessment.
The important classes of experimental observations are

• Single particle spectra (photons and dileptons)
• Strangeness production
• Photon and muon rates (and J/ψ melting)
• Elliptic flow
• Jet quenching
• Fluctuations
• Hanbury-Brown and Twiss effect and Bose-Einstein correlations

Formation of quark matter

In April 2005, formation of quark matter was tentatively confirmed by results obtained at Brookhaven National Laboratory's Relativistic Heavy Ion Collider (RHIC). The consensus of the four RHIC research groups was that they had created a quark-gluon liquid of very low viscosity. However, contrary to what was at that time still the widespread assumption, it is yet unknown from theoretical predictions whether the QCD "plasma", especially close to the transition temperature, should behave like a gas or liquid^[8]. Authors favoring the weakly interacting interpretation derive their assumptions from the lattice QCD calculation, where the entropy density of quark-gluon plasma approaches the weakly interacting limit. However, since both energy density and correlation shows significant deviation from the weakly interacting limit, it has been pointed out by many authors that there is in fact no reason to assume a QCD "plasma" close to the transition point should be weakly interacting, like electromagnetic plasma (see, e.g., ^[9]).

See also

• Hadrons (that is mesons and baryons) and confinement
• Hadronization
• Neutron stars
• Plasma physics
• QCD matter Quantum Chromodynamics matter
• Quantum electrodynamics
• Quantum chromodynamics
• Quantum hydrodynamics
• Relativistic plasma
• Strangeness production
• Strange matter

References

1. ^ Hadron production from a boiling quark soup: A thermodynamical quark model predicting particle ratios in hadronic collisions
2. ^ A New State of Matter - Experiments
3. ^ Relativistic Heavy Ion Collider, RHIC
4. ^ Alice Experiment: Welcome to ALICE Portal
5. ^ The Indian Lattice Gauge Theory Initiative
6. ^ WA Zajc (2008). "The fluid nature of quark-gluon plasma". Nuclear Physics A 805: 283c-294c. doi:10.1016/j.nuclphysa.2008.02.285. http://arxiv.org/PS_cache/arxiv/pdf/0802/0802.3552v1.pdf. 
7. ^ "How free is the quark-gluon plasma", M. Plümer, S. Raha and R. M. Weiner, Nucl. Phys. A 418 (1984) 549c; Phys. Lett. B139 (1984) 198
8. ^ Color-singlet clustering of partons and recombination model for hadronization of quark-gluon plasma
9. ^ arXiv:nucl-th/0403032v1

External links

• The Relativistic Heavy Ion Collider at Brookhaven National Laboratory
• The Alice Experiment at CERN
• The Indian Lattice Gauge Theory Initiative
• Quark matter reviews: 2004 theory, 2004 experiment
• Lattice reviews: 2003, 2005
• BBC article mentioning Brookhaven results
• Physics News Update article on the quark-gluon liquid, with links to preprints
• Read for free : "Hadrons and Quark-Gluon Plasma" by Jean Letessier and Johann Rafelski Cambridge University Pres (2002) ISBN 0 521 38536 9 , Cambridge, UK;

Historical Figures Lead Us to the Topic of Entanglement

Einstein Exhibit

We regard quantum mechanics as a complete theory for which the fundamental physical and mathematical hypotheses are no longer susceptible of modification.

--Heisenberg and Max Born, paper delivered to Solvay Congress of 1927

You know I have watched the long drawn out conversation on Backreaction about what was once already debated, to have advanced to current status in the world represented as a logic orientated process with regard to entanglement.

What are it's current status in terms of its expression experimentally to know what it is we are doing with something that had been debated long ago?



Solvay Physics Conference 1927 02:55 - 2 years ago

The most known people who participated in the conference were Ervin Schrodinger, Niels Bohr, Werner Heisenberg, Auguste Piccard, Paul Dirac, Max Born, Wolfgang Pauli, Louis de Broglie, Marie Curie, Hendrik Lorentz, Albert Einstein and others. The film opens with quick shots of Erwin Schrodinger and Niels Bohr. Auguste Piccard of the University of Brussels follows and then the camera re-focuses on Schrodinger and Bohr. Schrodinger who developed wave mechanics never agreed with Bohr on quantum mechanics. Solvay gave Heisenberg an opportunity to discuss his new uncertainty principle theory. Max Born's statistical interpretation of the wave function ended determinism in atomic world. These men - Bohr, Heisenberg, Kramers, Dirac and Born together with Born represent the founding fathers of quantum mechanics. Louis de Broglie wrote his dissertation on the wave nature of matter which Schrodinger used as basis for wave mechanics. Albert Einstein whose famous response to Born's statistical interpretation of wave function was "God does not play dice." Twenty-nine physicists, the main quantum theorists of the day, came together to discuss the topic "Electrons and Photons". Seventeen of the 29 attendees were or became Nobel Prize winners. Following is a "home movie" shot by Irving Langmuir, (the 1932 Nobel Prize winner in chemistry). It captures 2 minutes of an intermission in the proceedings. Twenty-one of the 29 attendees are on the film. --- It's Never too Late to Study: http://www.freesciencelectures.com/ --- Notice: This video is copyright by its respectful owners. The website address on the video does not mean anything. ---

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The Einstein-Podolsky-Rosen Argument in Quantum Theory

First published Mon May 10, 2004; substantive revision Wed Aug 5, 2009

In the May 15, 1935 issue of Physical Review Albert Einstein co-authored a paper with his two postdoctoral research associates at the Institute for Advanced Study, Boris Podolsky and Nathan Rosen. The article was entitled “Can Quantum Mechanical Description of Physical Reality Be Considered Complete?” (Einstein et al. 1935). Generally referred to as “EPR”, this paper quickly became a centerpiece in the debate over the interpretation of the quantum theory, a debate that continues today. The paper features a striking case where two quantum systems interact in such a way as to link both their spatial coordinates in a certain direction and also their linear momenta (in the same direction). As a result of this “entanglement”, determining either position or momentum for one system would fix (respectively) the position or the momentum of the other. EPR use this case to argue that one cannot maintain both an intuitive condition of local action and the completeness of the quantum description by means of the wave function. This entry describes the argument of that 1935 paper, considers several different versions and reactions, and explores the ongoing significance of the issues they raise.

Might I confuse you then to see that their is nothing mystical about what our emotive states implore, that we might not also consider the purpose of Venn Logic, or, a correlation to Fuzzy logic to prepare the way for how we can become emotive entangled in our psychology, are ways "biologically mixed with our multilevel perspective" about how photons interact, to see that such a color of debate could have amounted to a distinction that arises from within. Which can manifest itself on a real world stage that is psychological forced out of the confines of human emotion, to be presented as a real world force "bridle or unbridled" with regard to the human condition?

See :

Entanglement Interpretation of Black Hole Entropy 

See Also:Backreaction: Testing the foundations of quantum mechanics

What the "i" represents, is Natural?

A Conformal Diagram of a Minkowski Spacetime
John D. Norton

First, here is the conformal diagram of a Minkowski spacetime. This is the complete spacetime. It includes all of the infinity of space and the infinity of time through which things persist.

This diagram gives the simplest case in which we consider just one dimension of space.

Note the three types of infinities: timelike, lightlike and spacelike. They correspond to the different vanishing points in an ordinary perspective drawing.

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The Quantum Theory of the Electron



Paul Dirac

Projective Geometry

When one is doing mathematical work, there are essentially two different ways of thinking about the subject: the algebraic way, and the geometric way. With the algebraic way, one is all the time writing down equations and following rules of deduction, and interpreting these equations to get more equations. 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. Now, a good mathematician has to be a master of both ways of those ways of thinking, but even so, he will have a preference for one or the other; I don't think he can avoid it. In my own case, my own preference is especially for the geometrical way.

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In mathematical physics, the gamma matrices, {γ⁰,γ¹,γ²,γ³}, also known as the Dirac matrices, are a set of conventional matrices with specific anticommutation relations that ensure they generate a matrix representation of the Clifford algebra Cℓ(1,3). It is also possible to define higher-dimensional Gamma matrices. When interpreted as the matrices of the action of a set of orthogonal basis vectors for contravariant vectors in Minkowski space, the column vectors on which the matrices act become a space of spinors, on which the Clifford algebra of space time acts. This in turn makes it possible to represent infinitesimal spatial rotations and Lorentz boosts. Spinors facilitate space-time computations in general, and in particular are fundamental to the Dirac equation for relativistic spin-½ particles.

In Dirac representation, the four contravariant gamma matrices are

Analogue sets of gamma matrices can be defined in any dimension and signature of the metric. For example the Pauli matrices are a set of "gamma" matrices in dimension 3 with metric of Euclidean signature (3,0).

*** 

www.mcescher.com

Can we hope to use antimatter as a source of energy? Do you feel antimatter could power vehicles in the future, or would it just be used for major power sources?

There is no possibility to use antimatter as energy "source". Unlike solar energy, coal or oil, antimatter does not occur in nature: we have to make every particle at the expense of much more energy than it can give back during annihilation.

You might imagine antimatter as a possible temporary storage medium for energy, much like you store electricity in rechargeable batteries. The process of charging the battery is reversible with relatively small loss. Still, it takes more energy to charge the battery than what you get back out of it. For antimatter the loss factors are so enormous that it will never be practical.

If we could assemble all the antimatter we've ever made at CERN and annihilate it with matter, we would have enough energy to light a single electric light bulb for a few minutes.

***

Thoughts on Angel and Demons Plot

``For me, the most attractive way ... would be to capture the antihydrogen in a neutral particle trap ... The objective would be to then study the properties of a small number of [antihydrogen] atoms confined in the neutral trap for a long time."Gerald Gabrielse, 1986 Erice Lecture (shortly after first trapping of antiprotons)
"Penning Traps, Masses and Antiprotons", in Fundamental Symmetries,
edited by P. Bloch, P. Paulopoulos and R. Klapisch, p. 59 (Plenum, New York, 1987). See:Goals for ATRAP

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Physics at this high energy scale describes the universe as it existed during the first moments of the Big Bang. These high energy scales are completely beyond the range which can be created in the particle accelerators we currently have (or will have in the foreseeable future.) Most of the physical theories that we use to understand the universe that we live in also break down at the Planck scale. However, string theory shows unique promise in being able to describe the physics of the Planck scale and the Big Bang.

Fear and Ignorance

This is a very significant physical result because it tells us that the energy of a system described by a harmonic oscillator potential cannot have zero energy. Physical systems such as atoms in a solid lattice or in polyatomic molecules in a gas cannot have zero energy even at absolute zero temperature. The energy of the ground vibrational state is often referred to as "zero point vibration". The zero point energy is sufficient to prevent liquid helium-4 from freezing at atmospheric pressure, no matter how low the temperature.

See:Quantum Harmonic Oscillator: Energy Minimum from Uncertainty Principle

It would be hard here to explain the way I see these things. In the way one can shift perspective, to think, that this measure of any "systemic reason" would ask that one consider the state of equilibrium?

It would be foolish to me for any science process to discount the value on how one can measure storms in space not to think that "such resonances" could have not found suitable actions as being represented in sociological correspondence.

Let us see how these great physicists used harmonic oscillators to establish beachheads to new physics.

Albert Einstein used harmonic oscillators to understand specific heats of solids and found that energy levels are quantized. This formed one of the key bridges between classical and quantum mechanics.

Werner Heisenberg and Erwin Schrödinger formulated quantum mechanics. The role of harmonic oscillators in this process is well known.

Paul A. M. Dirac was quite fond of harmonic oscillators. He used oscillator states to construct Fock space. He was the first one to consider harmonic oscillator wave functions normalizable in the time variable. In 1963, Dirac used coupled harmonic oscillators to construct a representation of the O(3,2) de Sitter group which is the basic scientific language for two-mode squeezed states.

Hediki Yukawa was the first one to consider a Lorentz-invariant differential equation, with momentum-dependent solutions which are Lorentz-covariant but not Lorentz-invariant. He proposed harmonic oscillators for relativistic extended particles five years before Hofstadter observed that protons are not point particles in 1955. Some people say he invented a string-model approach to particle physics.

Richard Feynman was also fond of harmonic oscillators. When he gave a talk at the 1970 Washington meeting of the American Physical Society, he stunned the audience by telling us not to use Feynman diagrams, but harmonic oscillators for quantum bound states. This figure illustrates what he said in 1970.


We are still allowed to use Feynman diagrams for running waves. Feynman diagrams applicable to running waves in Einstein's Lorentz-covariant world. Are Feynman's oscillators Lorentz-covariant? Yes in spirit, but there are many technical problems. Then can those problems be fixed. This is the question. You may be interested in reading about this subject: Lorentz group in Feynman's world.

Can harmonic oscillators serve as a bridge between quantum mechanics and special relativity

?

To consider such geometrical form "as the sphere," to have encouraged collapse, and find a resulting behaviour as signalling a change overwrought by influences that will insight idealizations to division and the idea that "no" global consideration is present.

While one may debate the idea of the classification of democracies in the 167 countries around the world, a consensus to quality control of information is insinuated. So now moving beyond "the border" to lesser degrees of, while there is no offering of what the idea of democratic institutions in the free countries of the world could be related too. It's measure in the degrees thereof.

While I had offered "in bold" the understanding, they( should I offer by name?) are quick to point out in rebuttal, by an offering to discount the very source of this consideration. I am all for further dialogue, but it looks like that won't happen.

See:Central Theme is the Sun

So how does it look, as a spherical realization, that SOHO measure in terms of predicting an "outcome of weather" could not have found "early warnings" to possible outcomes in the evolution of the planet it's electrical grids and power usage, telecommunications, and the events thereof?

You had to know that Plato "saw further" by understanding the examples of the sun, as a source of "seeing beyond the shadows of the cave." Of knowing, that one could be "free of the chains that bind."

No where does this say it is easy to overcome. The sociological and psychological behaviour that evolves in that "spherical engage", but that it is always the life struggle to get back to the light. One had to be fully aware of the topological translation of the relationship between the inner/outer and the reductionist move to what is self evident. There is no way for one to be aware of the analysis and the final outcome without knowing the way in which one could move to such a result, without knowing the wider perspective that is held about life.

Turtles and Elephants

There is this notion that to work with different species and incorporate them, it some how makes it more natural an explanation?(guilty):) I guess I am guilty of same and more, by using geometrical progressiveness in place of the propensity for nature to be revealing itself in varying degrees. It was always there for inspection?

So anyway this clip I took from a previous post on, "Who said it?" charts the example I give currently in line with Bee's Backreaction: Turtles all the way up I did not go beyond the introduction, and assume it was not Davies talk. I was cut off at 14 meg while the whole talk is much longer. I'll have to try again tonight(08 sep 2008).

I still have yet to download Davies talk, given the constraints the work schedule limits with regard to the "intranet."

But just reading briefly Dr. Who's position and Markk suggestion that Dr. Who is confusing model with reality.

Bold and italicized were added by me.

The Coleman-Mandula theorem, named after Sidney Coleman and Jeffrey Mandula, is a no-go theorem in theoretical physics. It states that the only conserved quantities in a "realistic" theory with a mass gap, apart from the generators of the Poincaré group, must be Lorentz scalars.

In other words, every quantum field theory satisfying certain technical assumptions about its S-matrix that has non-trivial interactions can only have a symmetry Lie algebra which is always a direct product of the Poincare group and an internal group if there is a mass gap: no mixing between these two is possible. As the authors say in their introduction, "We prove a new theorem on the impossibility of combining space-time and internal symmetries in any but a trivial way."[1]

First off let me give you an example and you tell me how the idea of any bulk perspective given to graviton understanding will not have it's examples in terms of Lagrangian in space? Serve to help one graduate in terms of gravities when looking at the universe?

Are there no other mechanism that details the Coleman Mandula action other then a multiversity idea in terms of the false vacuum to the true?

I encourage such topological understanding given to a larger format when looking at WMAP of the global perspective. Incidences within the universe give way to a larger depiction of the anomalies generated in perceived examples of monopoles generated in Sean Carroll's group think.

That such concentrations in graviton densities would have an impact on our perceptions in terms of Lagrangian.

If one were to say that any manifold generated at the perception of microscopic views were indicative of a larger topological suggestion in the WMAP, would this then not account for an impression of 10 sup-500-/sup(only written this way because comment section will not allow "sup" html discription)?

Gravities had to be inclusive at all stages and manifold expressions part of this cosmological view?

Best,

Valuing Negativity by Mark Trodden

The basic point is that if one assumes that the generators of the internal symmetry group are commuting operators (and that their commutation relations define the group - i.e. that they comprise a Lie algebra), then the only possible total symmetry is a direct product of the space-time symmetries (the Poincaré group) and the internal symmetry group. This is what they meant by trivial in the abstract.

If this had been the end of the story, then bosons and fermions (and therefore force carriers and matter) would be destined to forever remain distinct. But here comes the loophole. The 1975 Haag-Lopuszanski-Sohnius theorem (after Rudolf Haag, Jan Lopuszanski, and Martin Sohnius) pointed out that if one relaxes one of the assumptions, and allows anticommuting operators as generators of the symmetry group, then there is a possible non-trivial unification of internal and space-time symmetries. Such a symmetry is called supersymmetry and, as you know, constitutes a large part of current research into particle physics.

No-go theorems are fun in physics because they formalize where the important barriers lie and provide guidance about the directions of future attacks on the problem in question. Negative results in general, although not quite as glamorous or exciting, are still great stuff. We should celebrate them. Plus, we don’t want to be like the medical community do we?

Identify the early universe in the QGP perspective needed some way in which to limit reductionism points of view and by incorporating relativity at that level, such an expression then are imparted to a more global manifold detail based on a larger progressive geometry perspective of the universe.

Universe speeding up? From the inside/out this details such a connection in my view.

Best,

This was done to verify the statements made in two comments there and to show a comment made at cosmic variance's "Lopsided Universe" were related exactly to the points I am currently making in regard to a point of view shared by Dr. Who and a consequential statement by Markk in terms of the multiverse and bubble nucleations.

Sean Carroll:But if you peer closely, you will see that the bottom one is the lopsided one — the overall contrast (representing temperature fluctuations) is a bit higher on the left than on the right, while in the untilted image at the top they are (statistically) equal. (The lower image exaggerates the claimed effect in the real universe by a factor of two, just to make it easier to see by eye.)

See The Lopsided Universe-. Basically the comments I have made in this post by Sean have remained intact although toward the end I think it was thought I might have gone to far?

Observables of Quantum Gravity

Scientists should be bold. They are expected to think out of the box, and to pursue their ideas until these either trickle down into a new stream, or dry out in the sand. Of course, not everybody can be a genuine “seer”: the progress of science requires few seers and many good soldiers who do the lower-level, dirty work. Even soldiers, however, are expected to put their own creativity in the process now and then -and that is why doing science is appealing even to us mortals.

To Be Bold

One possible way the Higgs boson might be produced at the Large Hadron Collider.


"Observables of Quantum Gravity," is a strange title to me, since we are looking at perspectives that are, how would one say, limited?

Where is such a focus located that we make talk of observables? Can such an abstraction be made then and used here, that we may call it, "mathematics of abstraction" and can arise from a "foundational basis" other then all the standard model distributed in particle attributes?

Observables of Quantum Gravity at the LHC
Sabine Hossenfelder

Perimeter Institute, Ontario, Canada

The search for a satisfying theory that unifies general relativity with quantum field theory is one of the major tasks for physicists in the 21st century. Within the last decade, the phenomenology of quantum gravity and string theory has been examined from various points of view, providing new perspectives and testable predictions. I will give a short introduction into these effective models which allow to extend the standard model and include the expected effects of the underlying fundamental theory. I will talk about models with extra dimensions, models with a minimal length scale and those with a deformation of Lorentz-invariance. The focus is on observable consequences, such as graviton and black hole production, black hole decays, and modifications of standard-model cross-sections.

So while we have created the conditions for an experimental framework, is this what is happening in nature? We are simulating the cosmos in it's interactions, so how is it that we can bring the cosmos down to earth? How is it that we can bring the cosmos down to the level of mind in it's abstractions that we do not just call it a flight of fancy, but of one that arises in mind based on the very foundations on the formation of this universe?