Special Relativity Study Materials

Light cone (Image Credit: Wikimedia Commons)

Introduction:

One of the greatest triumphs of Maxwell's electromagnetic theory (c. 1864) was the explanation of light as an electromagnetic wave. But a question arises; Waves in what? In conformity with the mechanistic view of nature then prevailing, it seemed imperative to postulate the existence of a medium—the ether—which would serve as a carrier for these waves. This led to the most urgent physical problem of the time: the detection of the earth's motion through the ether.

One of the many experiments were devised for this purpose. Michelson and Morley (1887), looked for a directional variation in the velocity of light on Earth. Fizeau (1860), Mascart (1872), and later Lord Rayleigh (1902), looked for an expected effect of the earth's motion on the refractive index of certain dielectrics. And Trouton and Noble (1903) tried to detect an expected tendency of a charged plate capacitor to face the 'ether drift'. All of them failed. The facile explanation that the earth might drag the ether along with it only led to other difficulties with the observed aberration of starlight, and could not resolve the problem. 

Bored? Cut the Knot!

Bored? Not anymore... this site includes a comprehensive look at mathematical proofs, concepts. There are tons of interactive games and activities. It contains a plethora of useful information (in both popular and obscure math facts and methods). This site is for everyone -- whether you are advanced or beginner.

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Herpetology: Study Materials on Amphibians and Reptiles

Panther Chameleon (Furcifer pardalis), endemic to Madagascar.
Image courtesy link

-by Aaron S. Johnson

Introduction:

Herpetology is the zoological study of amphibians (frogs, toads, salamanders, newts, caecilians [legless amphibians]) and reptiles (turtles/tortoises, snakes, lizards, amphisbaenians [non-snake, legless squamate clade], crocodilians, tuataras).  A herpetologist is an expert in amphibian and reptile behavior, diet, ecology, taxonomy, physiology, anatomy, evolution, health, conservation, and husbandry.

Amphibians have been around for over 370 million years (m.y.) and reptiles for 310-320 m.y.  Amphibians are the descendants of a fishlike ancestor, whereas reptiles descended from a common amphibianlike ancestor.  Together, reptiles and amphibians are collectively known as "herps" and are the common ancestors of birds and mammals.  

Herps may be ectotherms, but they are voracious eaters of everything humans consider as "pests" and carriers of disease, e.g. insects, arachnids, slugs, rodents.  Needless to say, world ecological systems would collapse without them.  With the decline of amphibians and reptiles due to herbicides, pesticides, pet trade, destruction of the environment, climate change, invasive species, and pathogenic microbes, the importance of these creatures have grown ever more apparent.  Accordingly, modern herpetologists should have expertise in microbiology, chemistry, climatology, conservation, and even business administration, communications, and sociology in order to professionally problem solve as difficult issues arise. 

Space Aliens on Distant Planets—They've Got Your Attention?!

As we come across many milestones in science, another quiet one has recently snuck in too. As of February this year, we have officially exceeded a thousand extra-solar planets & counting. This inevitably begs the question of life. And an inquiry into life on other planets often brings with it many fallacies (many-times perpetrated by science dweebs themselves), as much as by little green UFO enthusiasts. Many of these fallacies stem directly from an anthromorphocentric view and an inability to ever escape from it, when forming scientific queries. While/Whether the scientists working on these projects might choose to simplify their language (if they're even aware of it) in order to popularize their understanding, they do a great disservice to understanding the subject & approach for generations by stymieing the pursuit of science. 

Study Materials on Classical Electrodynamics

Introduction:

Mechanics tells us how a system will behave when subjected to a given force. There are four forces in nature known (presently) to us. If we arrange them in order of decreasing strength, they would be:

1. Strong nuclear force
2. Electromagnetic force
3. Weak nuclear force, and
4. Gravitational force

We have often thought about questions, like: Where is friction? Where is the "normal" force that keeps us from falling through the floor? Where are the chemical forces that bind molecules together? Where is the force of impact between two billiard balls? The answer is that all these forces are electromagnetic.

Detection at t=0: looking at the beginning of time

Detection at t=0: looking at the very beginning of time, we saw the echoes of the Bang imprinted across the sky.

We’ve all heard the big news yesterday. Scientists spotted the gravitational ripples that left marks in the distribution of energy, which is strong evidence for inflation, but how did they do it?

Polarization means the electric vector of the photon oscillates in a specific direction. B-mode polarization is a pattern in the CMB radiation that can be broken into two components. One, a curl-free, gradient-only component, the E-mode, was first seen in 2002 by the Degree Angular Scale Interferometer (DASI). The second component is gradient-free, curl only, and is known as the B-mode. Cosmologists predict two types of B-modes, the first generated during cosmic inflation, and the second generated by gravitational lensing later, due to light encountering matter on its way. Gravitational waves squeeze space as they travel, and this squeezing produces a distinct pattern in the cosmic microwave background. GWs have a handedness or chirality, much like light waves, and can have left- and right-handed polarizations which makes them very recognizable.

Happy Birthday Einstein

Today we commemorate the birthday of one of the most well renowned physicist of the 20th century. He is none other than Albert Einstein. who developed the general theory of relativity, one of the two pillars of modern physics (alongside quantum mechanics). Even though he is known for his mass–energy equivalence formula E = mc^2, which has been dubbed "the world's most famous equation", he received the 1921 Nobel Prize in Physics "for his services to theoretical physics, and especially for his discovery of the law of the photoelectric effect", which was pivotal in establishing quantum theory.

Near the beginning of his career, Einstein thought that Newtonian mechanics was no longer enough to reconcile the laws of classical mechanics with the laws of the electromagnetic field. This led to the development of his special theory of relativity.
He realized, however, that the principle of relativity could also be extended to gravitational fields, and with his subsequent theory of gravitation in 1916, he published a paper on the general theory of relativity. He continued to deal with problems of statistical mechanics and quantum theory, which led to his explanations of particle theory and the motion of molecules. He also investigated the thermal properties of light which laid the foundation of the photon theory of light. In 1917, Einstein applied the general theory of relativity to model the structure of the universe as a whole.

Study Materials on Evolutionary Biology

This Great Tree of Life diagram is based primarily on the evolutionary relationships so wonderfully related in Dr. Richard Dawkins' The Ancestor's Tale. The smallest branches are purely illustrative; they are intended to suggest the effect of mass extinctions on diversity, and, on a few of the branches, changes in diversity through time. The diagram mainly tries to illustrate a great lesson of evolution; that we are related not only to every living thing, but also to every thing that has ever lived. 

Sponges Could Have Lived in Oceans Before the Origin of Animals

- by Aaron S. Johnson

Just how much oxygen did animals inhabiting the oceans 635-542 million years ago (mya) need to live?  Lower than one may expect.  Present atmospheric levels could drop as low as 0.5% to 4% and animals, such as the modern day breadcrumb sponge (Halichondria panicea), would have been quite alright, according to researcher Daniel Mills, PhD at the Nordic Center for Earth Evolution at the University of Southern Denmark (1, 2, 3).  His laboratory research has demonstrated that the breadcrumb sponge can survive under these conditions, and therefore, would have been capable of living in the low-oxygenated waters that predated animal life (1). 

The question then becomes, why didn’t animal life evolve sooner?  Generally, the accepted hypothesis is that animal lifestyles couldn’t be supported until ocean oxygen levels dramatically increased.  That increase occurred 635-542 mya, and the first evidence of the animal fossil record lends support to the hypothesis (1). 

Nevertheless, Mills proposes that the complexity of an animal’s biological machinery was purely difficult to develop, and so even if the required minimum oxygen level were available, animal evolution took time to keep pace (3).  Therefore, if surplus oxygen wasn’t wholly the evolutionary catalyst, other mechanisms, such as other ecological and developmental processes, may have promoted the origin of the most primitive animal life (1).  That’s still to be determined.

Quantum Mechanics Study Materials

Image Courtesy : http://bit.ly/1nxAvAM

Introduction:

Our description of the physical world is dynamic in nature and undergoes frequent change. At any given time, we summarize our knowledge of natural phenomena by means of certain laws. These laws adequately describe the phenomenon studied up to that time, to an accuracy then attainable. As time passes, we enlarge the domain of observation and improve the accuracy of measurement. As we do so, we constantly check to see if the laws continue to be valid. Those laws who do remain valid gain in stature, and those who do not are abandoned in favor of new ones that do. 

In this changing picture, the laws of classical mechanics formulated by Galileo, Newton, and later by Euler, Lagrange, Hamilton, Jacobi, and others, remained unaltered for almost three centuries. The expanding domain of classical physics met its first obstacles around the beginning of 20th century. The obstruction came on two fronts: at large velocities and small (atomic) scales. The problem of large velocities was successfully solved by Einstein, who gave us relativistic mechanics, while Bohr, Heisenberg, Schrödinger, Dirac, Born, et al.—solved the problems of small-scale physics. Quantum mechanics brings with it not only improved numerical predictions for the microscopic world, but also conceptual changes that rock the very foundations of classical thought. With that being said, we present to all of you the necessary lecture notes, lecture videos, etc., found in the WWW domain to study/learn quantum mechanics. 

Classical Mechanics Study Materials

Introduction: 

Classical Mechanics is a subdomain of Classical physics. Classical mechanics is the study of the motion of the bodies (including the special case in which bodies remain at rest) in accordance with the general principles first enunciated by Sir Isaac Newton. Classical mechanics was the first branch of physics to be discovered, and is the foundation upon which all other branches of physics are built. Moreover, classical mechanics has many important applications in other areas of science, such as Astronomy (e.g., celestial mechanics), Chemistry (e.g., the dynamics of molecular collisions), Geology (e.g., the propagation of seismic waves, generated by earthquakes, through the Earth's crust), and Engineering (e.g., the equilibrium and stability of structures).

Classical mechanics is also of great significance outside the realm of science. After all, the sequence of events leading to the discovery of classical mechanics— starting with the ground-breaking work of Copernicus, continuing with the researches of Galileo, Kepler, and Descartes, and culminating in the monumental achievements of Newton—involved the complete overthrow of the Aristotelian picture of the Universe, which had previously prevailed for more than a millennium, and its replacement by a recognizably modern picture in which humankind no longer played a privileged role.

With that being said, we present you the necessary lecture notes and videos, found in the WWW domain to study/learn classical mechanics. 

A Short Break-Down of Maxwell's Equations

Maxwell's equations are used describe electricity and magnetism. The first two tell us about electric and magnetic effects, but the last two are the most important because they unite electricity and magnetism; hence, “electromagnetism". Their initial state are integrals in the form of differential equations in which you NEED to actually learn about how those animals are derived into standard form because they might not make any sense to you now. However, we can peek into what these equations mean. Differential equations break down into functions. They are basically relations where big functions spit out smaller functions and yield general solutions, and with a little more work, particular solutions. These relations basically state that moving charges generate magnetic fields and changing magnetic fields create changing electric fields.

A Dynamical Theory of the Electromagnetic Field is the third of James Clerk Maxwell's papers regarding electromagnetism, published in 1865. It is the paper in which the original set of four Maxwell's equations first appeared. The concept of displacement current, which he had introduced in his 1861 paper On Physical Lines of Force, was utilized for the first time, to derive the electromagnetic wave equation. But now for the details…

A Course on AdS/CFT (2013)

This is a PhD level course, designed for second year PhD students in Theoretical High Energy Physics (HEP-TH) area and assumes a background knowledge of Quantum Field Theory at the level of Peskin-Schroder book and General Relativity. It would be great if the audience are already familiar with basics of CFT’s and black hole physics.

Link to course

                                               Topics to be discussed in the course

1. AdS/CFT, a historical view on its stringy perspective.
2. AdS/CFT, formal statement, establishing the duality.
3. AdS/CFT, a tool for strongly coupled QFTs.
4. AdS/CFT, a tool for studying quantum gravity, discussing in brief  the general picture AdS/CFT has to offer for quantum gravity, quantum spacetime and quantum aspects of black holes.

LaTeX test

$\[\mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ \frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\ \frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0 \end{vmatrix} \]$

  \[P(E) = {n \choose k} p^k (1-p)^{n-k}\]

With Don Lincoln on SUSY and a career in big science

- Mar 1st, 2014 by Alma Ionescu

Don Lincoln is now a senior physicist at Fermi National Accelerator Laboratory and splits his research time studying data from the Fermilab Tevatron and from the CERN Large Hadron Collider, located outside Geneva Switzerland. 

He is co-author of over 500 scientific publications that range over subjects from microscopic black holes and extra dimensions to the elusive Higgs boson.  His two most noteworthy scientific accomplishments include being part of the teams that discovered the top quark and what is likely to be the Higgs boson.

When Dr. Lincoln isn’t exploring the energy frontier, he enjoys communicating the excitement of his cutting edge research with the public. He is a popular writer because of his ability to explain fundamental particle physics in a deeply meaningful way and because of his fine sense of humor. So far he published two books which have been translated into Polish, Russian, German and Chinese. “Understanding the Universe: From Quarks to the Cosmos” and “The Quantum Frontier: The Large Hadron Collider” explain particle physics for the public. His third book (Alien Universe: Extraterrestrials in our Minds and in the Cosmos) combines astrobiology and popular reports of alien visitation to weave together a complete tale of the possibility of life from other planets.