Phase Transitions and the Unparticles

Another Odd Thing About Unparticle PhysicsHoward Georgi

The peculiar propagator of scale invariant unparticles has phases that produce unusual patterns of interference with standard model processes. We illustrate some of these effects in e+e− → µ+µ−.

To be a bit more precise, every space that feels "real" has associated with it a sense of distance between any two points. On a line segment like the Koch coastline, we arbitrarily chose the length of one side of the first iterate as a unit length. On the Euclidean coordinate plane the distance between any two points is given by the Pythagorean theorem

Fractals have a special property that underpins the odd features of unparticles. They are patterns that are "scale invariant". In the case of Britain, the ins and outs of the coastline contain smaller jagged features that in turn contain smaller ins and outs and so on. This characteristic means that these unparticles don't change appearance when viewed at different scales- which is very different from objects we're familiar with.

Wrapping the Energetic Particles to the Cosmos

The Origin of the Highest Energy Particles
Date: 2008-01-09 14:00:00

Abstract:

After almost a century of observations, the ultra-high energy sky has finally displayed an anisotropic distribution. A significant correlation between the arrival directions of ultra-high cosmic rays measured by the Pierre Auger Observatory and the distribution of nearby active galactic nuclei signals the dawn of particle astronomy. These historic results have important implications to both astrophysics and particle physics.

See:http://pirsa.org/08010000/

Ueber die Hypothesen, welche der Geometrie zu Grunde liegen.

As I pounder the very basis of my thoughts about geometry based on the very fabric of our thinking minds, it has alway been a reductionist one in my mind, that the truth of the reality would a geometrical one.



The emergence of Maxwell's equations had to be included in the development of GR? Any Gaussian interpretation necessary, so that the the UV coordinates were well understood from that perspective as well. This would be inclusive in the approach to the developments of GR. As a hobbyist myself of the history of science, along with the developments of today, I might seem less then adequate in the adventure, I persevere.




On the Hypotheses which lie at the Bases of Geometry.
Bernhard Riemann
Translated by William Kingdon Clifford

[Nature, Vol. VIII. Nos. 183, 184, pp. 14--17, 36, 37.]

It is known that geometry assumes, as things given, both the notion of space and the first principles of constructions in space. She gives definitions of them which are merely nominal, while the true determinations appear in the form of axioms. The relation of these assumptions remains consequently in darkness; we neither perceive whether and how far their connection is necessary, nor a priori, whether it is possible.

From Euclid to Legendre (to name the most famous of modern reforming geometers) this darkness was cleared up neither by mathematicians nor by such philosophers as concerned themselves with it. The reason of this is doubtless that the general notion of multiply extended magnitudes (in which space-magnitudes are included) remained entirely unworked. I have in the first place, therefore, set myself the task of constructing the notion of a multiply extended magnitude out of general notions of magnitude. It will follow from this that a multiply extended magnitude is capable of different measure-relations, and consequently that space is only a particular case of a triply extended magnitude. But hence flows as a necessary consequence that the propositions of geometry cannot be derived from general notions of magnitude, but that the properties which distinguish space from other conceivable triply extended magnitudes are only to be deduced from experience. Thus arises the problem, to discover the simplest matters of fact from which the measure-relations of space may be determined; a problem which from the nature of the case is not completely determinate, since there may be several systems of matters of fact which suffice to determine the measure-relations of space - the most important system for our present purpose being that which Euclid has laid down as a foundation. These matters of fact are - like all matters of fact - not necessary, but only of empirical certainty; they are hypotheses. We may therefore investigate their probability, which within the limits of observation is of course very great, and inquire about the justice of their extension beyond the limits of observation, on the side both of the infinitely great and of the infinitely small.

For me the education comes, when I myself am lured by interest into a history spoken to by Stefan and Bee of Backreaction. The "way of thought" that preceded the advent of General Relativity.


Einstein urged astronomers to measure the effect of gravity on starlight, as in this 1913 letter to the American G.E. Hale. They could not respond until the First World War ended.

Translation of letter from Einstein's to the American G.E. Hale by Stefan of BACKREACTION

Zurich, 14 October 1913

Highly esteemed colleague,

a simple theoretical consideration makes it plausible to assume that light rays will experience a deviation in a gravitational field.

[Grav. field] [Light ray]

At the rim of the Sun, this deflection should amount to 0.84" and decrease as 1/R (R = [strike]Sonnenradius[/strike] distance from the centre of the Sun).

[Earth] [Sun]

Thus, it would be of utter interest to know up to which proximity to the Sun bright fixed stars can be seen using the strongest magnification in plain daylight (without eclipse).

Fast Forward to an Effect

Bending light around a massive object from a distant source. The orange arrows show the apparent position of the background source. The white arrows show the path of the light from the true position of the source.

The fact that this does not happen when gravitational lensing applies is due to the distinction between the straight lines imagined by Euclidean intuition and the geodesics of space-time. In fact, just as distances and lengths in special relativity can be defined in terms of the motion of electromagnetic radiation in a vacuum, so can the notion of a straight geodesic in general relativity.

To me, gravitational lensing is a cumulative affair that such a geometry borne into mind, could have passed the postulates of Euclid, and found their way to leaving a "indelible impression" that the resources of the mind in a simple system intuits.

Einstein, in the paragraph below makes this clear as he ponders his relationship with Newton and the move to thinking about Poincaré.

The move to non-euclidean geometries assumes where Euclid leaves off, the basis of Spacetime begins. So such a statement as, where there is no gravitational field, the spacetime is flat should be followed by, an euclidean, physical constant of a straight line=C?

Einstein:

I attach special importance to the view of geometry which I have just set forth, because without it I should have been unable to formulate the theory of relativity. ... In a system of reference rotating relatively to an inert system, the laws of disposition of rigid bodies do not correspond to the rules of Euclidean geometry on account of the Lorentz contraction; thus if we admit non-inert systems we must abandon Euclidean geometry. ... If we deny the relation between the body of axiomatic Euclidean geometry and the practically-rigid body of reality, we readily arrive at the following view, which was entertained by that acute and profound thinker, H. Poincare:--Euclidean geometry is distinguished above all other imaginable axiomatic geometries by its simplicity. Now since axiomatic geometry by itself contains no assertions as to the reality which can be experienced, but can do so only in combination with physical laws, it should be possible and reasonable ... to retain Euclidean geometry. For if contradictions between theory and experience manifest themselves, we should rather decide to change physical laws than to change axiomatic Euclidean geometry. If we deny the relation between the practically-rigid body and geometry, we shall indeed not easily free ourselves from the convention that Euclidean geometry is to be retained as the simplest. (33-4)

It is never easy for me to see how I could have moved from what was Euclid's postulates, to have graduated to my "sense of things" to have adopted this, "new way of seeing" that is also accumulative to the inclusion of gravity as a concept relevant to all aspects of the way in which one can see reality.

See:

On the Hypothese at the foundations of Geometry

Gravity and Electromagnetism?

"The Confrontation between General Relativity and Experiment" by Clifford M. Will

The Founder of Probabilty Theory?

I want to understand what makes the world tick. Einstein said he wanted to know what was on God's mind when he made the world. I don't think he was a religious man, but I know what he means.Lenny Susskind

Pierre de Fermat IPA: [pjɛːʁ dəfɛʁ'ma] (August 17, 1601 – January 12, 1665)

With Blaise Pascal, Pierre de Fermat became the founders of the theory of probability.

A Short History of Probability

"A gambler's dispute in 1654 led to the creation of a mathematical theory of probability by two famous French mathematicians, Blaise Pascal and Pierre de Fermat. Antoine Gombaud, Chevalier de Méré, a French nobleman with an interest in gaming and gambling questions, called Pascal's attention to an apparent contradiction concerning a popular dice game. The game consisted in throwing a pair of dice 24 times; the problem was to decide whether or not to bet even money on the occurrence of at least one "double six" during the 24 throws. A seemingly well-established gambling rule led de Méré to believe that betting on a double six in 24 throws would be profitable, but his own calculations indicated just the opposite.

MESSENGER Reveals Mercury’s Geological History

Stefan of Backreaction posted a blog entry called,"Mercury looks like the Moon, nearly... that brought me up to speed on what the planet actually looks like.

His article provides for the links here in this entry, as well sets the stage for the culminating vision I have of our solar system. Looking at the solar system in the processes I outline are important point of seeing the gravitational aspects of the universe as we have come to know it.

I had never considered what the actual surface of Mercury would look like, other then what I had thought it to be, when told as a child. A molten surface.

Using the laser altimeter, MESSENGER will verify the presence of a liquid outer core in Mercury by measuring the planet's libration. Libration is the slow 88-day wobble of the planet around its rotational axis.

Seeing Mercury the way it is below provides for some thought about Mercury facing toward the Sun. It's surface looking at the picture below, I was wondering if facing directly in opposition to the Sun would showing brighter spots as we look to the right of this image.

This also raised an interesting question on my mind about how the uniformity of the surface could retain it's moon like look while undergoing the passage of "increased heat" as it faced the sun at anyone time through it's rotation.

Question 4 : What is the structure of Mercury's core?


Credit: NASA/Johns Hopkins University Applied Physics Laboratory/Carnegie Institution of Washington

More recently, Earth-based radar observations of Mercury have also determined that at least a portion of the large metal core is still liquid to this day! Having at least a partially molten core means that a very small but detectable variation in the spin-rate of Mercury has a larger amplitude because of decoupling between the solid mantle and liquid core. Knowing that the core has not completely solidified, even as Mercury has cooled over billions of years since its formation, places important constraints on the thermal history, evolution, and core composition of the planet.

Credit: NASA/Johns Hopkins University Applied Physics Laboratory/Carnegie Institution of Washington

This MESSENGER image was taken from a distance of about 18,000 kilometers (11,000 miles) from the surface of Mercury, at 20:03 UTC, about 58 minutes after the closest approach point of the flyby. The region shown is about 500 kilometers (300 miles) across, and craters as small as 1 kilometer (0.6 mile) can be seen in this image.

The Gravity Field



Clementine color ratio composite image of Aristarchus Crater on the Moon. This 42 km diameter crater is located on the corner of the Aristarchus plateau, at 24 N, 47 W. Ejecta from the plateau is visible as the blue material at the upper left (northwest), while material excavated from the Oceanus Procellarum area is the reddish color to the lower right (southeast). The colors in this image can be used to ascertain compositional properties of the materials making up the deep strata of these two regions. (Clementine, USGS slide 11)

This is always of interest to be because it is an accumulation of the synthesis of views we gain as we come to understand not only the views of on the Window of the universe, as we look at the Sun under information obtain in the neutrino laboratory's and information modelling of how we can now look at the sun with this new view.

But the truth is, the Earth's topography is highly variable with mountains, valleys, plains, and deep ocean trenches. As a consequence of this variable topography, the density of Earth's surface varies. These fluctuations in density cause slight variations in the gravity field, which, remarkably, GRACE can detect from space.

Well, by adding the label of Grace and Grace satellite systems, it is important to me that not only is gravity considered in context of the exploration of space in terms of Lagrangian, but of viewing how we map the earth and the views we obtain of that new gravity model of earth. This application then becomes of interest as we understand how we see the gravity model of Mercury and how the geological structure of Mercury will be reflected in that gravity model.

The Culminating Vision

Fig. 1. Story line showing the principle of least action sandwiched between relativity and quantum mechanics See A call to action

See:

The Periodic Table of the Moon's Strata

Time-Variable Gravity Measurements

Andrew Wiles and Fermat

LTool

A "freeway" through the solar system resembling a vast array of virtual winding tunnels and conduits around the Sun and planets, as envisioned by an engineer at NASA's Jet Propulsion Laboratory (JPL), Pasadena, Calif., can slash the amount of fuel needed for future space missions. Called the Interplanetary Superhighway, the system was conceived by Martin Lo, whose software was used to help design the flight path for NASA's Genesis mission, which is currently using this "freeway in space" on its mission to collect solar wind particles for return to Earth. Most missions are designed to take advantage of the way gravity pulls on a spacecraft when it swings by a body such as a planet or moon. Lo's concept takes advantage of another factor, the Sun's pull on the planets or a planet's pull on its nearby moons. Forces from many directions nearly cancel each other out, leaving paths through the gravity fields in which spacecraft can travel.

Boltzmann's Brain

There is a new article by Dennis Overbye in the New York Times called, Big Brain Theory: Have Cosmologists Lost Theirs?

It could be the weirdest and most embarrassing prediction in the history of cosmology, if not science.

If true, it would mean that you yourself reading this article are more likely to be some momentary fluctuation in a field of matter and energy out in space than a person with a real past born through billions of years of evolution in an orderly star-spangled cosmos. Your memories and the world you think you see around you are illusions.

Source: Sean Carroll, California Institute of Technology

Alway part of the process is to find within my own site information that I had collected to help me understand where Ludwig Boltzmann comes into the picture in the above article.

Now of course I go over to Cosmic Variance's version of Boltzmann's Universe where the article above is referred too.

I look at the discussion that is taking place and try and put the exchange and points raised in mind so that I can understand as best I can "the jest" of the problem and the jest of what people are saying.

This isn't an attempt to rewrite the article, but to open the door to a better understanding of what is being portrayed.

Sean:lylebot, this is basically the point of the post — if the universe is a fluctuation around thermal equilibrium, then no matter what you condition on concerning our present state (including literally everything we know about it), it is overwhelmingly likely that it is a random fluctuation from a higher-entropy past. Even if we have memories apparently to the contrary!

The Universe and Irreversibility

Now it is quite loosely put together in my head that I went searching to try and understand the context in which the universe was placed in accordance to the state of equilibrium.

In equilibrium, the entropy of the system cannot increase (because it is already at a maximum) and it cannot decrease (because that would violate the second law of thermodynamics). The only changes allowed are those in which the entropy remains constant.

See: What is the entropy of the universe?

HENRI POINCARE : Mathematics and Science-Last Essays

Jules Henri Poincare (1854-1912)

The scientist does not study nature because it is useful. He studies it because he delights in it, and he delights in it because it is beautiful.

HENRI POINCARE Mathematics and Science:Last Essays

Since we are assuming at this juncture the point of view of the mathematician, we must give to this concept all the precision that it requires, even if it becomes necessary to use mathematical language. We should then say that the body of laws is equivalent to a system of differential equations which link the speed of variations of the different elements of the universe to the present values of these elements.

Such a system involves, as we know, an infinite number of solutions, But if we take the initial values of all the elements, that is,their values at the instant t =(which would correspond in ordinary language to the "present"), the solution is completely determined, so that we can calculate the values of all the elements at any period
whatever, whether we suppose />0, which corresponds to the "future," or whether we suppose t<0, which corresponds to the "past." What is important to remember is that the manner of inferring the past from the present does not differ from that of inferring the future from the present.

Free for all: Dream Come True

As a lay person involved and very interested in the research that in going on in science, anything that speaks to the "openness of science" which will allow me to get information that is not third hand, is a wonderful thing for me.

Even among supportive publishers, there is a fear that the transition to open access could be rough, and might even put them out of business.

Yes indeed, it could change the landscape on magazines, or, it could involve a greater research department to science editing, that will bring a science editors work to a level the public can understand. This is a wonderful aspect of the openness of the internet that I have been after and have sought for a long time.

I have followed blogs who have held this virtue for the publics benefit in helping the public with this responsibility of awareness.

Illustration by Sandbox Studio

Forget about paying for journal subscriptions. If a new proposal takes hold, particle physics journals would get their funding from labs, libraries, and agencies that sponsor research, and readers could peruse them for free.

Sponsoring Consortium for Open Access Publishing in Particle Physics(SCOAP3)

The Open Access (OA) tenets of granting unrestricted access to the results of publicly-funded research are in contrast with current models of scientific publishing, where access is restricted to journal customers. At the same time, subscription costs increase and add considerable strain on libraries, forced to cancel an increasing number of journals subscriptions. This situation is particularly acute in fields like High-Energy Physics (HEP), where pre-prints describing scientific results are timely available online. There is a growing concern within the academic community that the future of high-quality journals, and the peer-review system they administer, is at risk.

To address this situation for HEP and, as an experiment, Science at large, a new model for OA publishing has emerged: SCOAP3 (Sponsoring Consortium for Open Access Publishing in Particle Physics). In this model, HEP funding agencies and libraries, which today purchase journal subscriptions to implicitly support the peer-review service, federate to explicitly cover its cost, while publishers make the electronic versions of their journals free to read. Authors are not directly charged to publish their articles OA.

SCOAP3 will, for the first time, link quality and price, stimulating competition and enabling considerable medium- and long-term savings. Today, most publishers quote a price in the range of 1’000–2’000 Euros per published article. On this basis, we estimate that the annual budget for the transition of HEP publishing to OA would amount to a maximum of 10 Million Euros/year, sensibly lower than the estimated global expenditure in subscription to HEP journals.

Each SCOAP3 partner will finance its contribution by canceling journal subscriptions. Each country will contribute according to its share of HEP publishing. The transition to OA will be facilitated by the fact that the large majority of HEP articles are published in just six peer-reviewed journals. Of course, the SCOAP3 model is open to any, present or future, high-quality HEP journal, aiming for a dynamic market with healthy competition and a broader choice.

HEP funding agencies and libraries are currently signing Expressions of Interest for the financial backing of the consortium. A tendering procedure will then take place. Provided that SCOAP3 funding partners are ready to engage in long-term commitments, many publishers are expected to be ready to enter into negotiations.

The example of SCOAP3 could be rapidly followed by other fields, directly related to HEP, such as nuclear physics or astro-particle physics, or similarly compact and organized with a reasonable number of journals.

Higgs Mass and Current Issues

For example, theory says that Higgs particles are matter particles, but in most respects the Higgs behaves more like a new force than like a particle. How can this be? In truth, the Higgs is neither matter nor force; the Higgs is just different.

A least-square fit to a number of precisely known data in electroweak physics using the Standard Model as theoretical framework and the Higgs mass as a free parameter yields an expectation value for the Higgs mass around the minimum of the parabola. [Source: Precision Electroweak Measurements and Constraints on the Standard Model by the LEP Collaborations and the LEP Electroweak Working Group, arXiv: 0712.0929v2, Figure 5.]

See Backreaction for explanation. The Higgs Mass

It is an exercise for me coming across different informations on the Higg's for a better understanding of the way things are to happen in reality. I hope to provide for extra links to help one understand the potential realizations that come across as I learn to understand this field better.

I appreciate the clarity given to the writing here that allows this deeper understanding of what is taking place by the different commentors, commenting to Back reactions blog post entry.

At 9:07 AM, January 05, 2008, Anonymous a quantum diaries survivor said...

Hi Stefan,

I wish to pay a tribute to your nice post here and answer the question you pose about the counter-intuitive trend of discovery reach at the LHC versus Higgs mass (for a given integrated luminosity), waiting for Michael's posts on the Higgs.

The problem is that as the Higgs mass changes, the mixture of possible final states it decays into changes dramatically. So, while at 160 GeV the Higgs is best sought in its decay to a pair of real W bosons (which weigh 80 GeV each), and in that case backgrounds are small because the signature is very distinctive, at 115 GeV the Higgs mostly decays to a pair of b-quark jets. Seeing a bump in the jet-jet mass distribution is utterly out of the question because in that case backgrounds are HUGE. So one has to rely on very rare decays such as H->gamma gamma - which still is plagued by large backgrounds.

The Higgs search is not one, but ten different analyses, depending on the unknown parameter M_h. Each analysis has its own problems. The higher the Higgs mass, the smaller the number of produced events; but as M_h changes, the signature varies from invisible to highly distinctive. Above 180 GeV, a Higgs can be seen with no trouble in the ZZ final state, when four muons are a gold-plated signature. It is not by chance that CMS was originally conceived as a compact muon solenoid: muons are all you need, at high mass, for the Higgs.

Cheers,
T.

You can find many more explanations here to help any layman in their understanding as T is always quite help in that direction. Also check out his label of "higgs search" at the top of his page.



See:

The Higg's Boson and Memory?

Alice and the Cosmic Ballet, Now Meet Higgins