Composite particles (such as hadrons, nuclei, and atoms) can be bosons or fermions depending on their constituents. More precisely, because of the relation between spin and statistics, a particle containing an odd number of fermions is itself a fermion: it will have half-integer spin.

Fermionic or bosonic behavior of a composite particle (or system) is only seen at large (compared to size of the system) distance. At proximity, where spatial structure begins to be important, a composite particle (or system) behaves according to its constituent makeup.

— Wikipedia on Fermion

2011.02.07 Monday ACHK

怎樣區分粒子

有兩種方法可以用來區分粒子。第一種方法倚靠粒子內在物理性質的不同，像質量，電荷，或自旋。假若粒子的性質有任何的不同，我們可以藉著測量那不同的性質來區分粒子。可是，根據許多實驗結果，同一種類的粒子都具有完全相同的物理性質。例如，宇宙裏所有的電子都擁有同樣的電荷。這就是為什麼我們經常提到電子的電荷，而不是哪一個電子的電荷。

第二種區分法跟蹤每一個粒子的軌道。只要我們能夠無限精確地測量出每一個粒子的位置，就不會搞不清楚哪一個粒子在哪裡。這個方法有一個問題，那就是它與量子力學的基本原理相矛盾。根據量子理論，在位置測量期間，粒子並不會保持明確的位置。粒子的位置是由波函數來決定。而波函數只能給予粒子在每一個位置的機率。隨著時間演變，幾個粒子的波函數會擴散蔓延，互相重疊。一但重疊事件發生，我們就無法區分在重疊區域的兩個粒子。這樣，粒子就越來越不可區分了。

— 維基百科

2011.02.03 Thursday ACHK 

In mathematics (specifically in differential geometry and topology) a manifold is a mathematical space that on a small enough scale resembles the Euclidean space of a specific dimension, called the dimension of the manifold. Thus, a line and a circle are one-dimensional manifolds, a plane and sphere (the surface of a ball) are two-dimensional manifolds, and so on into high-dimensional space.

— Wikipedia on Manifold

2011.02.02 Wednesday ACHK

Gauge theory 2

Gauge symmetries can be viewed as analogues of the equivalence principle of general relativity in which each point in spacetime is allowed a choice of local reference (coordinate) frame. Both symmetries reflect a redundancy in the description of a system.

— Wikipedia on Gauge theory

2011.01.31 Monday ACHK

In geometry, the notion of a connection makes precise the idea of transporting data along a curve or family of curves in a parallel and consistent manner. There are a variety of kinds of connections in modern geometry, depending on what sort of data one wants to transport. For instance, an affine connection, the most elementary type of connection, gives a means for transporting tangent vectors to a manifold from one point to another along a curve. An affine connection is typically given in the form of a covariant derivative, which gives a means for taking directional derivatives of vector fields: the infinitesimal transport of a vector field in a given direction.

Connections are of central importance in modern geometry in large part because they allow a comparison between the local geometry at one point and the local geometry at another point. Differential geometry embraces several variations on the connection theme, which fall into two major groups: the infinitesimal and the local theory.

— Wikipedia on Connection (mathematics)

2011.01.30 Sunday ACHK

In physics, a gauge theory is a type of field theory in which the Lagrangian is invariant under a continuous group of local transformations.

The term gauge refers to redundant degrees of freedom in the Lagrangian. The transformations between possible gauges, called gauge transformations, form a Lie group which is referred to as the symmetry group or the gauge group of the theory. Associated with any Lie group is the Lie algebra of group generators. For each group generator there necessarily arises a corresponding vector field called the gauge field. Gauge fields are included in the Lagrangian to ensure its invariance under the local group transformations (called gauge invariance). When such a theory is quantized, the quanta of the gauge fields are called gauge bosons. If the symmetry group is non-commutative, the gauge theory is referred to as non-abelian, the usual example being the Yang–Mills theory.

— Wikipedia on Gauge theory

2011.01.29 Saturday ACHK

String theory 7

A separate and older criticism of string theory is that it is background-dependent — string theory describes perturbative expansions about fixed spacetime backgrounds. Although the theory has some background-independence — topology change is an established process in string theory, and the exchange of gravitons is equivalent to a change in the background — mathematical calculations in the theory rely on preselecting a background as a starting point.

— Wikipedia on String theory

2011.01.28 Friday ACHK

Contact with experiment

The mathematics of string theory may lead to new insights on quantum chromodynamics, a gauge theory which is the fundamental theory of the strong nuclear force. To this end, it is hoped that a gravitational theory dual to quantum chromodynamics will be found.

This means that the discovery of a new gauge group with a small quantum of charge and only heavy charged particles would falsify string theory. Since this argument is very general — relying only on black-hole evaporation and the holographic principle, it has been suggested that this prediction would be true of any consistent holographic theory of quantum gravity, although the phrase “consistent holographic theory of quantum gravity” might very well be synonymous with “String Theory”.

It is notable that all the gross features of the Standard model can be embedded within String theory, so that the standard model is not in the swampland. This includes features such as non-abelian gauge groups and chiral fermions which are hard to incorporate in non-string theories of quantum gravity.

— Wikipedia on String theory

2011.01.26 Wednesday ACHK

Physics Today, created in 1948, is the membership journal of the American Institute of Physics. It is provided to 130,000 members of twelve physics societies, including the American Physical Society. Over the last 60 years many famous physicists have written for the magazine, including Albert Einstein, Niels Bohr, and Richard Feynman.

Although its content is scientifically rigorous and up to date, it is not a true scholarly journal in the sense of being a primary vehicle for communicating new results. Rather, it is more of a hybrid magazine that informs readers about important developments in the form of overview articles written by experts, shorter review articles written internally by staff, and also discusses the latest issues and events of importance to the science community such as science politics.

The physics community’s main vessel for new results is the Physical Review suite of scientific journals published by the American Physical Society and Applied Physics Letters published by the American Institute of Physics.

— Wikipedia on Physics Today

2011.01.25 Tuesday ACHK

Gauge-gravity duality

Gauge-gravity duality is a conjectured duality between a quantum theory of gravity in certain cases and gauge theory in a lower number of dimensions. This means that each predicted phenomenon and quantity in one theory has an analogue in the other theory, with a “dictionary” translating from one theory to the other.

Description of the duality

In certain cases the gauge theory on the D-branes is decoupled from the gravity living in the bulk; thus open strings attached to the D-branes are not interacting with closed strings. Such a situation is termed a decoupling limit. In those cases, the D-branes have two independent alternative descriptions.

As discussed above, from the point of view of closed strings, the D-branes are gravitational sources, and thus we have a gravitational theory on spacetime with some background fields.

From the point of view of open strings, the physics of the D-branes is described by the appropriate gauge theory.

Therefore in such cases it is often conjectured that the gravitational theory on spacetime with the appropriate background fields is dual (i.e. physically equivalent) to the gauge theory on the boundary of this spacetime (since the subspace filled by the D-branes is the boundary of this spacetime).

So far, this duality has not been proven in any cases, so there is also disagreement among string theorists regarding how strong the duality applies to various models.

— Wikipedia on String theory

2011.01.24 Monday ACHK

But the theory also describes universes like ours, with four observable spacetime dimensions, as well as universes with up to 10 flat space dimensions, and also cases where the position in some of the dimensions is not described by a real number, but by a completely different type of mathematical quantity. So the notion of spacetime dimension is not fixed in string theory: it is best thought of as different in different circumstances.

This can be better understood by noting that a photon included in a consistent theory (technically, a particle carrying a force related to an unbroken gauge symmetry) must be massless.

— Wikipedia on String theory

2011.01.23 Sunday ACHK

Investigating how a string theory may include fermions in its spectrum led to the invention of supersymmetry, a mathematical relation between bosons and fermions.

T-duality relates the large and small distance scales between string theories, whereas S-duality relates strong and weak coupling strengths between string theories. U-duality links T-duality and S-duality.

— Wikipedia on String theory

2011.01.22 Saturday ACHK

Nomenclature

There are two issues to be dealt with here:

    * When Witten named M-theory, he did not specify what the “M” stood for, presumably because he did not feel he had the right to name a theory which he had not been able to fully describe. According to Witten himself, “‘M’ can stand for either ‘magic’, ‘mystery’, or ‘matrix’, according to taste.” According to the BBC/TLC documentary Parallel Universes, the M stands for “membrane”. Other suggestions by people such as Michio Kaku, Michael Duff and Neil Turok in that documentary are “mother” (as in “mother of all theories”), and “master” theory.

Cynics have noted that the M might be an upside down “W”, standing for Witten. Others have suggested that for now, the “M” in M-theory should stand for Missing or Murky.

2011.01.21 Friday ACHK

M-theory 4

The original formulation of M-theory was in terms of a (relatively) low-energy effective field theory, called 11-dimensional Super gravity. Though this formulation provided a key link to the low-energy limits of string theories, it was recognized that a full high-energy formulation (or “UV-completion”) of M-theory was needed.

Analogy with water

For an analogy, the Super gravity description is like treating water as a continuous, incompressible fluid. This is effective for describing long-distance effects such as waves and currents, but inadequate to understand short-distance/high-energy phenomena such as evaporation, for which a description of the underlying molecules is needed. What, then, are the underlying degrees of freedom of M-theory?

BFSS model

Banks, Fischler, Shenker and Susskind (BFSS) conjectured that Matrix theory could provide the answer. They demonstrated that a theory of 9 very large matrices, evolving in time, could reproduce the Super gravity description at low energy, but take over for it as it breaks down at high energy. While the Super gravity description assumes a continuous space-time, Matrix theory predicts that, at short distances, non-commutative geometry takes over, somewhat similar to the way the continuum of water breaks down at short distances in favor of the graininess of molecules.

— Wikipedia on M-theory

2011.01.20 Thursday ACHK

In mathematics, particularly in complex analysis, a Riemann surface, first studied by and named after Bernhard Riemann, is a one-dimensional complex manifold. Riemann surfaces can be thought of as “deformed versions” of the complex plane: locally near every point they look like patches of the complex plane, but the global topology can be quite different. For example, they can look like a sphere or a torus or a couple of sheets glued together.

The main point of Riemann surfaces is that holomorphic functions may be defined between them. Riemann surfaces are nowadays considered the natural setting for studying the global behavior of these functions, especially multi-valued functions such as the square root and other algebraic functions, or the logarithm.

— Wikipedia on Riemann surface

2011.01.19 Wednesday ACHK

In physics, a heterotic string is a peculiar mixture (or hybrid) of the bosonic string and the superstring (the adjective heterotic comes from the Greek word heterosis, hybrid vigour). In string theory, the left-moving and the right-moving excitations almost do not talk to each other, and it is possible to construct a string theory whose left-moving (counter-clockwise) excitations “think” that they live on a bosonic string propagating in D = 26 dimensions, while the right-moving (clock-wise) excitations “think” that they belong to a superstring in D = 10 dimensions.

Every heterotic string must be a closed string, not an open string; it is not possible to define any boundary conditions that would relate the left-moving and the right-moving excitations because they have a different character.

— Wikipedia on Heterotic string

2011.01.18 Tuesday ACHK

In physics, the first superstring revolution is a period of important discoveries in string theory roughly between 1984 and 1986. It was realised that string theory was capable of describing all elementary particles as well as the interactions between them. Hundreds of physicists started to work on string theory as the most promising idea to unify physical theories. The revolution was started by a discovery of anomaly cancellation in type I string theory via the Green-Schwarz mechanism in 1984. Several other ground-breaking discoveries, such as the heterotic string, were made in 1985. It was also realised in 1985 that to obtain N = 1 supersymmetry, the six small extra dimensions need to be compactified on a Calabi-Yau manifold.

— Wikipedia on First superstring revolution

2011.01.17 Monday ACHK

Fuzzballs are theorized by some superstring theory scientists to be the true quantum description of black holes. The theory resolves two intractable problems that classic black holes pose for modern physics:

   1. The information paradox wherein the quantum information bound in in-falling matter and energy entirely disappears into a singularity; that is, the black hole would undergo zero physical change in its composition regardless of the nature of what fell into it.

   2. The singularity at the heart of the black hole, where conventional black hole theory says there is infinite spacetime curvature due to an infinitely intense gravitational field from a region of zero volume. Modern physics breaks down when such parameters are infinite and zero.

Fuzzball theory replaces the singularity at the heart of a black hole by positing that the entire region within the black hole’s event horizon is actually a ball of strings, which are advanced as the ultimate building blocks of matter and energy. Strings are thought to be bundles of energy vibrating in complex ways in both the three physical dimensions of space as well as in compact directions — extra dimensions interwoven in the quantum foam (also known as spacetime foam).

— Wikipedia on Fuzzball (string theory)

2011.01.16 Sunday ACHK