Saturday, 21 November 2015

Kerr-Newman metric

The Kerr–Newman metric is a solution of the Einstein–Maxwell equations in general relativity that describes the spacetime geometry in the region surrounding a charged, rotating mass.
This solution has not been especially useful for describing astrophysical phenomena, because observed astronomical objects do not possess an appreciable net electric charge. The solution has instead been of primarily theoretical and mathematical interest. (It is assumed that the cosmological constant equals zero which is near enough to the truth.)
Scholarpedia has an outstanding, in depth article about Kerr-Newman metric: http://www.scholarpedia.org/article/Kerr-Newman_metric
Top image: Conceptual photograph of a rotating (angular momentum per unit mass a = 0.8) black hole that is not electrically charged. This is a realistic black hole, such as is surely present in some X-ray binaries and in many galactic nuclei. The curvature, K, of the black hole is shown as a function of distance from the singularity ("radius") and polar angle ("theta"). The most remarkable new feature is the presence of negative curvature.
Bottom image: Conceptual photograph of a general black hole. This particular plot is for a value of a = 0.8 (angular momentum per unit mass) and for electric charge Q = 0.8. Real black holes in the universe are unlikely to be electrically charged.
_M R S S Shourie

The Standard Model and the Future Of Particle Physics

The Standard Model of particle physics is the most beautiful and complete theory we have so far describing the electromagnetic, the nuclear weak and the nuclear strong interactions. The matter particles interact by exchanging other particles associated with these interactions. The basic grains of matter are fermions and the force carriers are bosons. The names of these two classes refer to their spin. Fermions have half-integer values of spin whereas bosons have integer values as shown in the diagram below. 
However, we know that there are several problems with the Standard Model and it's not the final ultimate theory. The problems are called "The Hierarchy Problem". Why there is a wide range in mass for the elementary particles. In the table shown, we see the electron is about 200 times lighter than the muon and 3500 times lighter than the tau. Same thing for the quarks: the top quark is 75 000 times heavier than the up quark. Other problem is the huge difference in the strength of fundamental forces, plus, the Standard Model doesn't describe gravity which seems to be very very weak compared to the other three interactions. The hierarchy problem is also related to the Higgs boson mass In the equations, the Higgs boson has a basic mass to which theorists add a correction for each particle that interact with it. The heavier the particle, the larger the correction. The top quark being the heaviest particle, it adds such a large correction to the theoretical Higgs boson mass that theorists wonder how the measured Higgs boson mass can be as small as it was found. What's more, why there are so many particles describing nature, we would like to have much simpler chart of elementary particles where we do not consider these elementary particles as elementary, like Superstring theory suggests, each particle contains a one dimensional string of energy vibrating in many modes in extradimensions and for each mode we obtain a specific particle. Finally, the Standard Model doesn't describe Dark Matter.Dark matter does not emit any light but manifests itself through its gravitational effects.
One of the most promising extensions of the Standard Model is Supersymmetry which I'm working on. In the Standard Model the vacuum is not stable. Vacuum could be stabilized by Supersymmetry. The three fundamental interactions are unified by supersymmetry. But the philosophical aspect of the theory is not satisfying, the theory predicts more particles (super-partners) and in the Next-to-The-Minimal-Supersymmetric-Standard-Model which I'm working on, there must be 7 different Higgs bosons.
The unification of gravity with the other three fundamental interactions could not be achieved if there is no Supersummetry because the most promising theories of quantum gravity are supergravity and superstring theories. There are some theorists who believe that we don't need to unify gravity because it's just a geometrical property of spacetime. But this point of view is excluded because there are cases in the universe where we need both General Relativity and Quantum Mechanics like the Black holes, because the Strength of gravity is so high thus we need General Relativity, and the matter is condensed is a very very small region of spacetime thus we need Quantum Mechanics. So we need to discover the gravitational waves and a Boson with spin 2 called Graviton. But unfortunately this is out of reach now because we need first to discover Supersymmetry.
The discovery of the Higgs Boson in 2012 was a great achievement, but as usual in science, new answers bring with them a new set of new questions.
The next run of the LHC at CERN will start in April 2015, and we will for sure either discover supersymmetry and the door will be open to the next unification, or we will discover other phenomena that our minds and mathematics couldn't find and it's cooler and more exciting because it will drive particle physics to a whole new area and physicists will face new challenges and will be forced to changed radically their views and models of the extensions of the Standard Model of Particle Physics.
-Amine Benaichouche
_M R S S Shourie

Just for Fun-1


Advanced Geometry/Quantum Psychology - Higher Dimensional Communications/Connections - Equilibrium
This is a forth dimension, inside of a third dimension, on a second dimensional surface; however, the middle sphere can be broken down to seventh dimension. Basically, what this is, is a planet existing in the fourth dimension, surrounded by the third dimension, in a second dimensional reality. So you see, even the fourth dimension and the third dimension can exist in the second dimension. If you think about the holographic universe theory, then you understand that you could be a second dimensional being, existing in a third, fourth, etc. dimensional reality, simultaneously; while still living in a holographic reality, existing in the third, fourth, fifth, etc. dimension.
So basically, you could be communicating with a second dimensional being (human), that's also living in a third, fourth, etc. existence, simultaneously. All the way up to the seventh dimension and beyond, can be represented on a second dimensional surface. We could exist in all dimensions, while existing in the second dimension. How do you think you're talking to higher dimensional beings in telepathy, aka pineal to pineal communication, or higher self communication? In a nutshell, we can exist and communicate in multiple dimensions. Could be second dimensional beings, having a third dimensional experience, communicating in multiple dimensions?

P.S. This is just for fun, a perception of multidimensional geometry and quantum psychology, we are connected. The important issue at hand is the equilibrium, balancing these communications, with self. 
_SHOURIE M R S S

Mathematical Aspects of String Theory

Here is a really good talk by Prof. Cumrun Vafa of Harvard University on Mathematical aspects of String Theory which he gave quite recently at IMPA, Brazil. As you can guess from the title, the talk is about string theory to a bunch of mathematicians, who may or may not be familiar with it. He starts off with how mathematics and physics are closely related fields and gradually moves onto topics such as duality, mirror symmetry, Calabi-Yau manifolds, etc. What I really liked in this talk was when Prof. Vafa talks about the T-duality on tori, and links it to the Fourier-Mukai transform that mathematicians. He says that the mirror symmetry may be derived as an application of the toroidal T-duality on fibers at each point of the base. And there's more to the talk. Enjoy! smile emoticon
Link to the talk: https://www.youtube.com/watch?v=yreUdrIbt2Q

_Shourie M R S S

Short biography on the "Einstein Family"

"The difference between Stupidity and Genius is that Genius has its limits".
-Albert Einstein
Short biography on the "Einstein Family"
Albert Einstein was, and still is, consider the most brilliant mind of the 20th century. Albert Einstein was born in Germany on March 14, 1879. He was a Theoretical Physicist, Genius, Thinker, Creator and a Noble Prize winner. He was married to Maric Einstein in January 1903 and had 3 children named Lieserl Einstein, Hans Albert Einstein and Eduard Einstein. Albert and Maric Einstein were divorced on February 14, 1919, after being apart for 5 years.
Albert Einstein married Elsa Löwenthal on June 2, 1919, and it's said they had an ongoing relationship since 1912. Elsa Einstein was later diagnosed with heart and kidney problems in 1935. Elsa would later die in December 1936 from her health problems. Einstein would follow her in death 19 years later, on April 18, 1955 at age 76. Einstein died of heart failure at 12:55 a.m. in Princeton, New Jersey. Thomas Harvey would perform the autopsy at Princeton Hospital.
Albert Einstein’s Top 17 Major Achievements
1.) Albert Einstein demonstrated in 1905, that space and time are not absolute, but instead, that the speed of light is absolute. By making just a simple replacement in a fundamental assumption he quickly, easily and beautifully derived the transformation equations that Lorentz had painfully derived earlier. Because the replacement was so fundamental, it meant a complete reinterpretation of all of physics up to that point.
2.) He also figured out the equivalence of mass and energy, the famous formula E=mc^2, in 1905.
3.) Albert Einstein, after Max Planck's timid suggestion, argued that light should be seriously considered as a collection of particles by everyone, challenging the “Wave Theory of Light”. His particle argument that explained the photoelectric effect won him a Nobel Prize in 1921 and this accomplishment opened a whole new world of study known as Quantum Physics. It is amusing to note that Einstein received a Nobel prize for a work of his that is much less famously associated with him than Relativity, because the Nobel prize is meant to reward "correctness, not fame". It is ironic that Einstein's argument in the photoelectric effect is less watertight than Relativity (Nature's way of laughing in the face of the Nobel committee) because a wave theory of light with quantum electrons would have explained the photoelectric effect too. Nonetheless, to be clear, light is quantised.
4.) His research concerning the “Brownian Motion of Particles” would create an equation by twisting both the ideas of “Kinetic Theory” and “Classical Hydrodynamics” together. His equation would demonstrate that the mean free path of such particles as a function of time.
5.) He also showed how you could calculate “Avogadro’s Number” and the size of molecules.
6.) He was the founder of quantum mechanics, because he was the first to urge everyone to take the subject seriously, and also produced a whole lot of important results with almost no experimental input other than the stuff he knew from college. Some of these results are so amazing that they deserve a special mention later.
7.) In 1915, Albert Einstein would publish his paper on “General Relativity”, which took over where “Special Relativity” failed to do. The publication of his second paper “General Relativity” would end up starting a rising controversy.
8.) He would later demonstrate that his “General Relativity” could model the behavior of the universe itself, and Albert had his paper published in 1917. General Relativity created some of the weirdest and most important results in modern Astronomy.
9.) Modelling the evolution of the universe itself is cosmology. Creating this new field of science, along with others like de Sitter, Friedmann and so on, an understanding of the universe was finally possible to be explored.
10.) He transformed our understanding of nature on every scale, from the smallest to the cosmos as a whole, between 1905 and 1925.
11.) Working with semi-classical reasoning, Einstein predicted the existence of lasers, with extremely little mathematics, that turned out to be exactly correct even after quantum effects are included.
12.) As another example of his stunning ability to revolutionize fields of physics, Einstein derived an understanding of the thermal characteristics of ALL solids, with a bit of mathematics, and because the mathematics was difficult, just one excited quantum state. Like a true master, he worked out the extremely difficult part of making a new way of calculating something, and then left the simple improvement of the model to other people, leading to an entire string of discoveries for other people to get. Also, this exercise proved that unlike the rumors, Einstein was really good with applied mathematics.
13.) Albert Einstein received a short paper in 1924 from a Indian Physicist named Satyendra Nath Bose, requesting Einstein’s help with publication. The paper Satyendra proposed to Einstein would describe light as a gas of photons. Einstein later proposed that you could use the same statistics and it could be applied to atoms. The “Bose-Einstein Statistics” now describes the construction of indistinguishable particles known as bosons.
14.) Bose-Einstein statistics, under low temperature conditions, would mathematically lose particles. Einstein quickly showed that those "lost" particles were actually just acting as one gigantic particle, the Bose-Einstein Condensate, which is what superfluid Helium is.
15.) General Relativity solved the anomalous precision of Mercury's orbit. Einstein's derivation was mathematically sophisticated, such that in one approximation step, he worked out the value he was looking for.
16.) Seized upon the beauty that was Kaluza-Klein theory (adding extra dimensions, curled up, to General Relativity predicts physical phenomena. The first of which is that classical Electromagnetism gets turned into gravity), Einstein worked out that these extra dimensions are unstable and was rumored to have derived all the way to Yang-Mills equations (that govern the nucleus). This is the very well-known vision of the Grand Unified Theory, although Einstein both championed and killed it, because the proof of instability was very crucial.
17.) To challenge physics to improve upon quantum mechanics, he designed the EPR paradox.
Although Einstein had many successes, the scientific community does not worship him as a deity. As a founder of quantum mechanics, it was a shame that he was completely wrong in the debate with Niels Bohr about the "God playing dice" issue. The EPR paradox that was meant to challenge quantum physics ended up being an experimental evidence that classical theories will never be able to explain our universe. The latter half of his life, spent upon the Grand Unified Theories of the General Relativity form, was a drastic waste because the rest of the world was busy making all kinds of incredible quantum mechanics discoveries that he would have been very much welcome to help.
_M R S S Shourie

Matter and Anti-matter........Not only charge

Til now, there is no difference between matter and anti-matter except the electric charge. The results confirm the prediction of the Standard Model of Particle Physics with high precision. But we are not sure if they behave in the same way in the existence of the Gravitational field.
The ALICE experiment at the Large Hadron Collider (LHC) at CERN has made a precise measurement of the difference between ratios of the mass and electric charge of light nuclei and antinuclei. The result, published today in Nature Physics, confirms a fundamental symmetry of nature to an unprecedented precision for light nuclei. The measurements are based on the ALICE experiment's abilities to track and identify particles produced in high-energy heavy-ion collisions at the LHC.
The measurement by ALICE comparing the mass-to-charge ratios in deuterons/antideuterons and in helium-3/antihelium-3 confirms the fundamental symmetry known as CPT in these light nuclei. This symmetry of nature implies that all of the laws of physics are the same under the simultaneous reversal of charges (charge conjugation C), reflection of spatial coordinates (parity transformation P) and time inversion (T). The new result, which comes exactly 50 years after the discovery of the antideuteron at CERN and in the US, improves on existing measurements by a factor of 10-100.