An interesting feature of gravitons in string theory is that, as closed strings without endpoints, they would not be bound to branes and could move freely between them. If we live on a brane (as hypothesized by some theorists) this “leakage” of gravitons from the brane into higher-dimensional space could explain why gravitation is such a weak force, and gravitons from other branes adjacent to our own could provide a potential explanation for dark matter.

— Wikipedia on Graviton

2010.08.19 Thursday ACHK

However, experiments to detect gravitational waves, which may be viewed as coherent states of many gravitons, are already underway (e.g. LIGO and VIRGO). Although these experiments cannot detect individual gravitons, they might provide information about certain properties of the graviton.

— Wikipedia on Graviton

2010.08.17 Tuesday ACHK

It is not unusual to find books that erroneously describe Cavendish’s work as a measurement either of the gravitational constant (G) or the Earth’s mass, and this mistake has been pointed out by several authors. In reality, Cavendish’s stated goal was to measure the Earth’s density, and his result was later used to calculate G. The first time that this constant was used was in 1873, almost 100 years after the Cavendish experiment. Cavendish’s results also can be used to calculate the Earth’s mass.

— Wikipedia on Henry Cavendish

2010.08.16 Monday ACHK

Additionally, it can be shown that any massless spin-2 field would be indistinguishable from gravitation, because a massless spin-2 field must couple to the stress-energy tensor in the same way that the gravitational field does.

— Wikipedia on Graviton

2010.08.15 Sunday ACHK

The ultraviolet catastrophe, also called the Rayleigh-Jeans catastrophe, was a prediction of late 19th century/early 20th century classical physics that an ideal black body at thermal equilibrium will emit radiation with infinite power.

Solution

Einstein pointed out that the difficulty could be avoided by making use of a hypothesis put forward five years earlier by Max Planck. Planck postulated that electromagnetic energy did not follow the classical description, but could only oscillate or be emitted in discrete packets of energy proportional to the frequency, as given by Planck’s law. This has the effect of reducing the number of possible modes with a given energy at high frequencies in the cavity described above, and thus the average energy at those frequencies by application of the equipartition theorem.

Historical inaccuracies

Many popular histories of physics, as well as a number of physics textbooks, present an incorrect version of the history of the ultraviolet catastrophe. In this version, the “catastrophe” was first noticed by Planck, who developed his formula in response. In fact Planck never concerned himself with this aspect of the problem, because he did not believe that the equipartition theorem was fundamental – his motivation for introducing “quanta” was entirely different. That Planck’s proposal happened to provide a solution for it was realized much later, as stated above.

Though this has been known by historians for many decades, the historically incorrect version persists, in part because Planck’s actual motivations for the proposal of the quantum are complicated and difficult to summarize to a modern audience.

— Wikipedia on Ultraviolet catastrophe

2010.08.14 Saturday ACHK

Uncertainty principle and observer effect

The uncertainty principle is often stated this way:

The measurement of position necessarily disturbs a particle’s momentum, and vice versa.

This makes the uncertainty principle a kind of observer effect.

This explanation is not incorrect, and was used by both Heisenberg and Bohr. But they were working within the philosophical framework of logical positivism. In this way of looking at the world, the true nature of a physical system, inasmuch as it exists, is defined by the answers to the best-possible measurements which can be made in principle. To state this differently, if a certain property of a system cannot be measured beyond a certain level of accuracy (in principle), then this limitation is a limitation of the system and not the limitation of the devices used to make this measurements. So when they made arguments about unavoidable disturbances in any conceivable measurement, it was obvious to them that this uncertainty was a property of the system, not of the devices.

Today, logical positivism has become unfashionable in many cases, so the explanation of the uncertainty principle in terms of observer effect can be misleading.

— Wikipedia on Uncertainty principle

2010.08.12 Thursday ACHK

I think biology without mathematics is like physics before Newton: you could observe a star’s position yesterday and today, but you could not predict where it would be tomorrow. Biology without mathematics is phenomenological – we are merely collecting data, but we cannot make useful predictions or obtain a quantitative understanding. Biomathematics is still in its infancy, but has already and will make important contributions to biology (Hodgkin-Huxley etc.).

— Franziska Michor: math of cancer

— Lubos Motl

2010.08.11 Wednesday ACHK

The generators of symmetries are nothing else than the observables that are conserved if these symmetries are respected.

— Why and how energy is not conserved in cosmology

— Lubos Motl

2010.08.10 Tuesday ACHK

Connection (mathematics), a way of specifying a derivative of a geometrical object along a vector field on a manifold.

* Levi-Civita connection, used in differential geometry and general relativity; differentiates a vector field along another vector field

— Wikipedia on Connection

2010.08.07 Saturday ACHK

Cosmological horizon

The cosmological horizon, (also known as the particle horizon) is the maximum distance from which particles could have traveled to the observer in the age of the universe. It represents the boundary between the observable and the unobservable regions of the universe. The existence, properties, and significance of a cosmological horizon depend on the particular cosmological model being discussed.

The particle horizon differs from the event horizon in that the particle horizon represents the largest comoving distance from which light could have reached the observer by a specific time, while the event horizon is the largest comoving distance from which light emitted now can ever reach the observer.

— Wikipedia on Observable universe

2010.08.06 Friday ACHK

In theoretical physics, general covariance (also known as diffeomorphism covariance or general invariance) is the invariance of the form of physical laws under arbitrary differentiable coordinate transformations. The essential idea is that coordinates do not exist a priori in nature, but are only artifices used in describing nature, and hence should play no role in the formulation of fundamental physical laws.

— Wikipedia on General covariance

2010.08.05 Thursday ACHK

In mathematics, an automorphism is an isomorphism from a mathematical object to itself. It is, in some sense, a symmetry of the object, and a way of mapping the object to itself while preserving all of its structure. The set of all automorphisms of an object forms a group, called the automorphism group. It is, loosely speaking, the symmetry group of the object.

— Wikipedia on Automorphism

2010.08.04 Wednesday ACHK

LQG is one of a family of theories called canonical quantum gravity. The LQG theory also includes matter and forces, but does not address the problem of the unification of all physical forces the way some other quantum gravity theories such as string theory do.

— Wikipedia on Loop quantum gravity

2010.08.03 Tuesday ACHK

A detailed study of these excitations may well lead to interesting dynamics that includes not only gravity but also a select family of non-gravitational fields. It may also serve as a bridge between loop quantum gravity and string theory. For, string theory has two a priori elements: unexcited strings which carry no quantum numbers and a background space-time. Loop quantum gravity suggests that both could arise from the quantum state of geometry, peaked at Minkowski (or, de Sitter) space. The polymer-like quantum threads which must be woven to create the classical ground state geometries could be interpreted as unexcited strings. Excitations of these strings, in turn, may provide interesting matter couplings for loop quantum gravity.

— Gravity and the Quantum

— Abhay Ashtekar

2010.08.01 Sunday ACHK

Both photons and material particles such as electrons create analogous interference patterns when passing through a double-slit experiment. For photons, this corresponds to the interference of a Maxwell light wave whereas, for material particles, this corresponds to the interference of the Schrodinger wave equation. Although this similarity might suggest that Maxwell’s equations are simply Schrodinger’s equation for photons, most physicists do not agree. For one thing, they are mathematically different; most obviously, Schrodinger’s one equation solves for a complex field, whereas Maxwell’s four equations solve for real fields. More generally, the normal concept of a Schrodinger probability wave function cannot be applied to photons. Being massless, they cannot be localized without being destroyed; technically, photons cannot have a position eigenstate , and, thus, the normal Heisenberg uncertainty principle does not pertain to photons. A few substitute wave functions have been suggested for the photon, but they have not come into general use. Instead, physicists generally accept the second-quantized theory of photons described below, quantum electrodynamics, in which photons are quantized excitations of electromagnetic modes.

— Wikipedia on Photon

2010.07.29 Thursday ACHK

Is Loop quantum gravity the M-theory that the Superstring theorists are looking for?

— Me@2010.07.27

2010.07.28 Wednesday (c) All rights reserved by ACHK

Type IIA and Type IIB

The Type IIA string theory and the Type IIB string theory were known to be connected by T-duality; this essentially meant that the IIA string theory description of a circle of radius R is exactly the same as the IIB description of a circle of radius 1/R, where distances are measured in units of the Planck length.

— Wikipedia on M-theory

2010.07.24 Saturday ACHK

In physics, M(atrix) theory (also known as BFSS-Matrix theory) is a fundamental formulation of M-theory as a Random matrix model. It is written in terms of interacting D0-branes (zero-dimensional Dirichlet branes) in infinite momentum frame. It was proposed by Banks, Fischler, Shenker, and Susskind in 1996. See also the discussion in M-theory.

Matrix String Theory

Matrix string theory is a set of equations that describe superstring theory in a non-perturbative framework. Matrix string theory is related to M(atrix) theory in the same sense that superstring theory is related to M-theory. Type IIA string theory can be shown to be equivalent to a maximally supersymmetric two-dimensional gauge theory, the gauge group of which is U(N) for a large value of N. This Matrix string theory was first proposed by Lubos Motl in 1997 and later independently in a more complete paper by Robbert Dijkgraaf, Erik Verlinde, and Herman Verlinde. Another matrix string theory equivalent to Type IIB string theory was constructed in 1996 by Ishibashi, Kawai, Kitazawa and Tsuchiya. This version is known as the IKKT matrix model.

— Wikipedia on Matrix string theory

2010.07.23 Friday ACHK