Welcome Back/Uncrumpling the Blog

 By: Unknown    11:53 AM     No comments

Let me explain... Like many other undergraduates, the authors of this blog suffer from both inexperience and intense workloads. This was never more true than in the past two years, when we both created and proceeded to actively neglect this blog. Having experienced the phenomenon of failure induced by inactivity, or as they say in baseball, "a strikeout looking," I can say that I do not like the taste it leaves in the mouth.  Now...

[hep-th] Unification of Inflation and Dark Energy from Spontaneous Breaking of Scale Invariance

 By: Unknown    1:11 PM     No comments

Unification of Inflation and Dark Energy This paper proposes a method using two independent non-Riemannian volume forms (integrand of a volume integral) to derive an effective potential for the scalar matter field that is capable of describing both the early universe expansion and dark energy in our universe today. In other words, they are able to derive an effective potential that produces accurate energy densities during...

Numerical Relativity: Black Holes and Gravity - Part 3

 By: Unknown    6:47 PM  Christoffel symbols, deviation equation, Eddington-Finkelstein coordinates, general relativity, gravitational physics, metric, Minkowsky metric, Schwarzschild coordinates, spacetime, special relativity, tensors   No comments

Spacetime The definition of spacetime comes from special relativity. It tells us that different inertial frames have different notions of time. Let's take three Cartesian coordinates (x, y, z). By moving these axes parallel to themselves from some origin, we create new values of x, y, and z. In addition, by moving these coordinates we are creating a notion of time, which is different in each of these inertial frames. This...

Derivation of the Newtonian Deviation Equation

 By: Unknown    6:47 PM  deviation equation, gravitational potential, gravity, Newtonian, spacetime, tensors   No comments

In this derivation, I will use "A General Relativity Workbook" by Thomas A. Moore as a reference. Below are some basic equations that will help guide us towards the derivation. $$\textbf{F}_{grav} = m \textbf{g} = - \left( \frac{GmM}{r^2} \right) \textbf{e}_r = -m \boldsymbol{\nabla} \Phi (\textbf{x})$$ where $\textbf{e}_r$ is the unit vector pointing from the first particle to the other and $\Phi (\textbf{x})$ is the gravitational...

Derivation of the Equation of Geodesic Deviation

 By: Unknown    6:47 PM  Christoffel symbols, deviation equation, Einstein, general relativity, geodesic, gravitational physics, gravity, Riemann curvature, tensors   No comments

Because this derivation is often given as homework in classes that teach relativity, I will not show step-by-step derivations. Instead, I will only show the steps that books tend to give. If you are confident in your use of tensor notation, you shouldn't have a problem filling in the steps. However, it can get extremely messy when it calls for a change in indices. I will again reference "A General Relativity Workbook" by Thomas...

Review and application of group theory to molecular systems biology [part 1]

 By: Unknown    11:05 AM  algebra, biology, biophysics, group theory, translation   No comments

Edward A Rietman, Robert L Karp, and Jack A Tuszynski; Theor Biol Med Model. 2011; 8: 21. Link. ----- My opinion: I love it when physicists stick mathematics where it doesn't belong. This paper is a bit old I know (Elwin wanted recent papers), but I really wanted to read it, and I figured I'd summarize it too while I'm at it for this blog. I'm going to break this up into a few pieces since I want to explain concepts as we go...

Numerical Relativity: Black Holes and Gravity - Part 2

 By: Unknown    9:55 PM  astrophysics, black holes, Einstein, general relativity, gravitational collapse, gravitational physics, gravitational waves, radiation, spacetime   No comments

Einstein's Theory of General Relativity You have probably heard about Einstein's Theory of Relativity. His work on special relativity was published in 1905. This introduced a new framework in physics. He showed that the laws of physics are the same in all non-accelerating reference frame and that the speed of light is constant. This revolutionized different branches of physics and led to his 1915 Theory of General Relativity,...