Thursday, July 19, 2012

The Importance of the Higgs Boson


The Higgs boson is the smallest detectable wave in the Higgs field. Interacting with the Higgs field causes  articles to acquire inertial mass; without the Higgs field, no particle would have inertial mass. Some particles don't feel the Higgs field at all (photons) and so are massless; some feel it very lightly (neutrinos) and have little mass; ordinary particles feel it strongly.
In physics the current best understanding of the forces (excluding gravity) is called the Standard Model. The one remaining elementary particle in the Standard Model that hasn't been experimentally detected is - the Higgs boson.
The Standard Model describes these forces:
Electromagnetism (attraction/repulsion due to electric charge)
Weak force (causes radioactive decay)
Strong force (holds quarks together to form protons,neutrons)
Electromagnetism is the unification of electricity and magnetism, which were originally thought to be two different forces.
The next steps in physics would be:
Electroweak unification - electromagnetism and weak force unified into the "electroweak" force. The Higgs field explains why these two forces normally appear to be different. The discovery of the Higgs boson could be considered final verification for electroweak unification.
Grand unified theory - electroweak and strong force unified into the "grand" force.
Theory of everything - grand force and gravity unified. This is the ultimate purpose behind areas of research such as string theory.

Tuesday, July 17, 2012

Coursera: Quantum Mechanics and Quantum Computation

Quantum Mechanics and Quantum Computation

About the Course

Quantum computation is a remarkable subject, and is based on one of the great computational discoveries that computers based on quantum mechanics are exponentially powerful. This course aims to make this cutting-edge material broadly accessible to undergraduate students, including computer science majors who do not have any prior exposure to quantum mechanics. The course will introduce qubits (or quantum bits) and quantum gates, the basic building blocks of quantum computers. It will cover the fundamentals of quantum algorithms, including the quantum fourier transform, period finding, and Shor's iconic quantum algorithm for factoring integers efficiently. The course will also explore the prospects for quantum algorithms for NP-complete problems and basic quantum cryptography.

The course will not assume any prior background in quantum mechanics. Instead, it will use the language of qubits and quantum gates to introduce the basic axioms of quantum mechanics. This treatment of quantum mechanics has the advantage of both being conceptually simple and of highlighting the paradoxes at the heart of quantum mechanics. The most important pre-requisite for the course is a good understanding of basic linear algebra, including vectors, matrices, inner products, eigenvectors and eigenvalues, etc.

About the Instructor(s)

Umesh Vazirani is the Strauch Distinguished Professor of Electrical Engineering and Computer Science at University of California, Berkeley, and is the director of the Berkeley Quantum Information and Computation Center. Prof. Vazirani has done foundational work on the computational foundations of randomness, algorithms and novel models of computation. His 1993 paper with Ethan Bernstein helped launch the field of quantum complexity theory. He is the author of two books "An introduction to computational learning theory" with Michael Kearns and "Algorithms" with Sanjoy Dasgupta and Christos Papadimitriou.

Thursday, July 5, 2012

sim-udacity: A Github Repository for Udacity Statistics Simulations

I've created a GitHub repository for some fun simulations and other code to illustrate ideas and applications. I  believe it's helpful for many people to use simulations to better understand what's going on when learning statistics. Why are things done the way they are? Well, let's simulate the random process and find out!

These are currently in Python but I'll be adding R versions. I'll be adding simulations that illustrate particular ideas in probability and statistics, or that are just fun. Some of the most interesting and useful, I believe, will be related to hypothesis testing.

The initial repository has a basic Monty Hall simulation and two roulette simulations that sample from either a uniform or exponential distribution. I tend to use NumPy quite a bit.