The photon does not carry electric charge with it, while the gluons do carry the “color charge”.

— HyperPhysics

2011.05.21 Saturday ACHK

In 1942, Paul Dirac wrote a paper: “The Physical Interpretation of Quantum Mechanics” where he introduced the concept of negative energies and negative probabilities:

    “Negative energies and probabilities should not be considered as nonsense. They are well-defined concepts mathematically, like a negative of money.”

Negative probabilities have later been suggested to solve several problems and paradoxes. Half-coins provide simple examples for negative probabilities. These strange coins were introduced in 2005 by Gabor J. Szekely. Half-coins have infinitely many sides numbered with 0,1,2,… and the positive even numbers are taken with negative probabilities. Two half-coins make a complete coin in the sense that if we flip two half-coins then the sum of the outcomes is 0 or 1 with probability 1/2 as if we simply flipped a fair coin.

— Wikipedia on Negative probability

2011.05.19 Thursday ACHK

Twistors are closely related to spinors, objects that may be understood as “square roots of vectors”. I like to say that twistors may similarly be interpreted as “square roots of spacetime points”.

Witten enters the scene

In 2003, Edward Witten published his papers on the twistor treatment of the maximally supersymmetric Yang-Mills theory in four dimensions. For the first time, geometry in the twistor space was used to calculate scattering amplitudes – quantities knowing about some real dynamics and interactions in physics.

— Lubos Motl

2011.05.11 Wednesday ACHK

c is the exchange rate between space and time.

— 2011.05.11

2011.05.15 Sunday (c) All rights reserved by ACHK

The success of the electroweak sector of the standard model teaches us that what we perceive as empty space is in reality a cosmic superconductor – not, of course, for electromagnetic fields and currents, but for the currents that couple to W and Z bosons.

— Anticipating a New Golden Age

— Frank Wilczek

2011.05.10 Tuesday ACHK

“Emptiness is everywhere and it can be calculated, which gives us a great opportunity. I know how to control the universe. So tell me, why should I run for a million?” he told the Russian newspaper Komsomolskaya Pravda.

— Math genius Grigori Perelman explains why he turned down $1 million prize

— By Nadine Bells | Good News – Wed, 4 May, 2011

2011.05.06 Friday ACHK

de Sitter Space distinguished from spacetime in general relativity

Fundamentally, the key concept behind the idea of de Sitter space is that it involves a variation on the spacetime of general relativity in which spacetime is itself slightly curved even in the absence of matter or energy.

An inherent curvature of spacetime even in the absence of matter or energy is another way of thinking about the idea of the cosmological constant in general relativity. An inherent curvature of spacetime and the cosmological constant are also equivalent to the idea that a vacuum (i.e. empty space without any matter or energy in it) has a fundamental energy of its own.

de Sitter space can also be thought of as a general relativity like spacetime in which empty space itself has some energy, which causes this spacetime (i.e. the universe) to expand at an ever greater rate.

— Wikipedia on Anti de Sitter space

2011.05.04 Wednesday ACHK

The importance of gauge theories for physics stems from the tremendous success of the mathematical formalism in providing a unified framework to describe the quantum field theories of electromagnetism, the weak force and the strong force. This theory, known as the Standard Model, accurately describes experimental predictions regarding three of the four fundamental forces of nature, and is a gauge theory with the gauge group SU(3) × SU(2) × U(1). Modern theories like string theory, as well as some formulations of general relativity, are, in one way or another, gauge theories.
 
— Wikipedia on Gauge theory

2011.04.18 Monday ACHK

In mathematics and physics, a soliton is a self-reinforcing solitary wave (a wave packet or pulse) that maintains its shape while it travels at constant speed. Solitons are caused by a cancellation of nonlinear and dispersive effects in the medium.

Dispersion and non-linearity can interact to produce permanent and localized wave forms. Consider a pulse of light traveling in glass. This pulse can be thought of as consisting of light of several different frequencies. Since glass shows dispersion, these different frequencies will travel at different speeds and the shape of the pulse will therefore change over time. However, there is also the non-linear Kerr effect: the refractive index of a material at a given frequency depends on the light’s amplitude or strength. If the pulse has just the right shape, the Kerr effect will exactly cancel the dispersion effect, and the pulse’s shape won’t change over time: a soliton.

— Wikipedia on Soliton

2011.04.17 Sunday ACHK